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AEDC-TR-77-107 ARCHIVE coPY DO Nor LOAN

DOMINANCE OF RADIATED AERODYNAMIC NOISE

ON BOUNDARY-LAYER TRANSITION

IN SUPERSONIC-HYPERSONIC WIND TUNNELS

Theory and Application

SamUel R. Pate ARO, Inc., a SVerdrup Oorporation Company

t !

VON KARMAN GAS DYNAMICS FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER

AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389

March 1978

Final Report for Period September 1975 - March 1977

Approved for public, relmse; distribution unlimited. I

Pmpe~, of 0, 9. Air Force AEDC LIBRARY ,

F,~0500-77-,C,0003

Prepared for

ARNOLD ENGINEE~NG DEVELOPMENT CENTER/DOTR ARNOLD AIR FORCE STATION, TENNESSEE 37389

NOTICES

When U. S. Government drawings, specifications, or other data are used for any purpose other than a defmitely related Government procurement operation, the Government thereby incun no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.

Qualified users may obtain copies of this report from the Defense Documentation Center.

References to named commerical products in this report are not to be considered in any sense as an indorsement of the product by the United States Air Force or the Government.

This report has been reviewed by the Information Office (OI) and is releasable to the National Technical Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations.

APPROVAL STATEMENT

This report has been reviewed and approved.

Project Manager, Research Division Directorate of Test Engineering

Approved for publication:

FOR THE COMMANDER

MARION L. LASTER Director of Test Engineering Deputy for Operations

UNCLASSIFIED R E P O R T D O C U M E N T A T I O N P A G E

I REPORT NUMBER [2 GOVT ACCESSION NO

AEDC-TR-77-107

4 T ITLE ( ~ d SublJtJ~ DOMINANCE OF RADIATED AERODYNAMIC NOISE ON BOUNDARY-LAYER TRANSITION IN SUPERSONIC-; HYPERSONIC WIND TUNNELS T h e o r y and A p p l i c a t i o n 7 AUTHOR(s)

Samuel R. Pate - ARO, Inc.

9 PERFORMING ORGANIZATION NAME AND ADDRESS A r n o l d E n g i n e e r i n g D e v e l o p m e n t Center/DOTR A i r F o r c e S y s t e m s Command A r n o l d A i r F o r c e S t a t i o n , T e n n e s s e e 37389

I I CONTROLLING OFFICE NAME AND ADDRESS

A r n o l d E n g i n e e r i n g D e v e l o p m e n t Cen te r /DOS A r n o l d A i r F o r c e S t a t i o n T e n n e s s e e 37389 14 MONITORING AGENCY NAME B ADDRESS(J! dlHefenf from Comtrot|inG Ofhee)

t6 DISTRIBUTION STATEMENT (ol ~hll Report)

READ INSTRUCTIONS BEFORE COMPLETING FORM

3. RECIPIENT'S CATALOG NUMBER

S TYPE OF REPORT & PERIOD COVERED

F i n a l R e p o r t - S e p t e m b e r

1975 - March 1977 S PERFORMING ORG. REPORT NUMBER

S CONTRACT OR GRANT NUMBER(s.)

10. PROGRAM ELEMENT. PROJECT, TASK AREA A WORK UNIT NUMBERS

Prog ram E l e m e n t 65807F

12. REPORT DATE March 1978

13. NUMBER OF PAGES 412

IS. SECURITY CLASS. (o! th i l ~po t~

UNCLASSIFIED

IS° DECL ASSI FICATION ; DOWNGRADING SCHEDULE

N/A

A p p r o v e d f o r p u b l i c r e l e a s e ; d i s t r i b u t i o n u n l i m i t e d .

17 DISTRIBUTION STATEMENT (o.* !he abstract em!ered Im Block 20, i f dl(leren! Irom~.Repott)

, , S U P P L E M E N T A R Y N O T ~ S ~ I " / " - - - ~

A v a i l a b l e i n DDC

,9 KEY WORDS !Co., . . . . ~ . . . . . . . . . ~. i t . . . . ;a~w . ,~ J~...,-y by bfoc~. . . . . > b o u n d a r y - l a y e r % t r a n s i t i o n / c o n i c a l boay aerody~,~mlu . l u l m ~ e - ~ f l a t p l a t e s s u p e r s o n i c f l o w b o u n d a r y l a y e r h y p e r s o n i c f l o w r e s e a r c h management t h e o r y c o r r e l a t i o n t e c h n i q u e s

R e y n o l d s number Mach number c o m p u t e r p r o g r a m

20 ABSTRACT (Continue ~ reverme a,de I ! neceeee~ ~ d Idenl l~ ~ block numbeQ An e x p e r i m e n t a l i n v e s t i g a t i o n was c o n d u c t e d t o d e t e r m i n e t h e

e f f e c t s o f r a d i a t e d a e r o d y n a m i c - n o i s e on b o u n d a r y - l a y e r t r a n s i t i o n i n s u p e r s o n i c - h y p e r s o n i c w i n d t u n n e l s . I t i s c o n c l u s i v e l y shown t h a t t h e a e r o d y n a m i c n o i s e ( p r e s s u r e f l u c t u a t i o n s a s s o c i a t e d w i t h s o u n d w a v e s ) , w h i c h r a d i a t e f r o m t h e t u n n e l w a l l , t u r b u l e n t boundar~ l a y e r , w i l l d o m i n a t e t h e t r a n s i t i o n p r o c e s s on s h a r p f l a t p l a c e s and s h a r p s l e n d e r c o n e s a t z e r o i n c i d e n c e . T r a n s i t i o n d a t a m e a s u r e (

FORM 1473 EDITION OF ! NOV 68 IS OBSOLETE D D , JAN 7,

UNCLASSIFIED

UNCLASSIFIED

20. ABSTRACT ( C o n t i n u e d )

in supersonic tunnels (M~ ~ 3) varying in test section heights from I to 16 ft have demonstrated a significant and monatonic increase in transition Reynolds numbers with increasing tunnel size. It has also been shown that the measured root-mean-square pressure fluctuations in the tunnel test section decrease with increasing tunnel size. A unique set of "shroud" experiments enabled the wall boundary layer to be directly controlled (either laminar or turbulent) and allowed transition Reynolds numbers to be correlated with the root-mean-square of the pressure fluctuations. Correlations of transition Reynolds numbers as a function of the radiated noise parameters [tunnel wall C F and 5" values and tunnel test section circumference (c)] have been developed. These correlations were based on sharp-flat-plate transition Reynolds number data from 13 wind tunnels having test section heights ranging from 7.9 in. to 16 ft, for Mach numbers from 3 to 8, and a unit Reynolds number per inch range from 0.1 x 106 to 1.9 x 106, and sharp-slender-cone transition Reynolds number data from 17 wind tunnels varying in size from 9 to 54 In. for a Mach number range from 3 to 14 and a unit Reynolds number range from 0.I x 106 to 2.75 x 106. A FORTRAN IV computer code has been developed using the aerodynamlc-noise- transition correlations. This code wlll accurately predict transition locations on sharp flat plates and sharp slender cones in all sizes of conventional supersonic-hypersonic wind tunnels for the Mach number range 3 ~ .~ ~ 15. The effect of aerodynamic noise on transition Reynolds numbers must be considered when supersonic- hypersonic wind tunnel data are used to (a) develop transition correlations, (b) evaluate theoretical stability-transition math models, and (c) analyze transition-sensitive aerodynamic data. The radiated aerodynamic-noise transition dominance theory as presented in this research provides an explanation for the unit Reynolds number effect in conventional supersonic-hypersonic wind tunnels. If a true Mach number effect exists, it is doubtful that it can be determined from data obtained in conventional supersonic-hypersonic wind tunnels because of the adverse effect of radiated noise. It has been shown that the ratio of cone transition Reynolds numbers t( flat-plate values does not have a constant value of three, as often assumed. The ratio will vary from a value of near three at M~ ffi 3 to near one at ~ = 8. The exact value is unit Reynolds number and tunnel size dependent. The aerodynamic-noise-,transition emp2rlcal equations developed in this research correctly predict this trend. The boundary-layer trip correlation developed by van Driest and Blumer has been shown to be valid for different sizes of wind tunnels and not dependent on the free-stream radiated noise levels. The trip correlation developed by Potter and Whitfleld remains valid if the effect of tunnel size on the smooth body transition location is taken into account. Wind tunnel transition Reynolds numbers have also been shown to be significantly higher than ballistic range values.

AFSC A t l l oM AFR "renn

UNCLASSIFIED

AEDC-TR-77-107

PREFACE

The research reported herein was conducted by the Arnold Engineering

Development Center (AEDC), Air Force Systems Command (AFSC), under Program

Element 65807F. The results were obtained by ARO, Inc., AEDC Division (a

Sverdrup Corporation Company), operating contractor for AEDC, AFSC, Arnold

Air Force Station, Tennessee, under ARO Projects Numbers VT5717 and VT8049.

The manuscript was submitted for publication on October 21, 1977.

This report was in i t ia l l y published as a doctoral dissertation at

The University of Tennessee, Knoxville, Tennessee, in March 1977.

I m ~ o ~

~ l l l q D B J i p J ~ I ~ m m 8 ~

I

AE DC-TR-77-107

CONTENTS

CHAPTER

I .

I I .

I l l .

IV.

V.

PAGE

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 17 Background Information . . . . . . . . . . . . . . . . . 17 Wind Tunnel Free-Stream Disturbances . . . . . . . . . 24 Objective and Approach . . . . . . . . . . . . . . . . . 32

METHODS COMMONLY USED FOR PREDICTING BOUNDARY-LAYER TRANSITION . . . . . . . . . . . . . . . . . . . . . . . . 34

Introduction . . . . . . . . . . . . . . . . . . . . . . 34 Linear S tab i l i t y Theory . . . . . . . . . . . . . . . . . 35 Kinetic Energy of Turbulence . . . . . . . . . . . . . . 37 Correlations Based on Physical Concepts . . . . . . . . . 41 Data Correlations . . . . . . . . . . . . . . . . . . . 48

Tripped flows . . . . . . . . . . . . . . . . . . . . . 48 Smooth body flows . . . . . . . . . . . . . . . . . . . 52 Summary . . . . . . . . . . . . . . . . . . . . . . . . 57

RADIATED AERODYNAMIC NOISE IN SUPERSONIC WIND TUNNELS. 59 Introduction . . . . . . . . . . . . . . . . . . . . . . 59 Origins of Disturbance Modes . . . . . . . . . . . . . . 60 Experimental Confirmation . . . . . . . . . . . . . . . 64

EXPERIMENTAL APPARATUS . . . . . . . . . . . . . . . . . . 88 Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . 88

AEDC-VKF Supersonic Tunnel A . . . . . . . . . . . . . 88 AEDC-VKF Hypersonic Tunnel B . . . . . . . . . . . . . 91 AEDC-VKF Supersonic Tunnel D . . . . . . . . . . . . . 91 AEDC-VKF Hypersonic Tunnel E . . . . . . . . . . . . . 94 AEDC-VKF Hypervelocity Tunnel F (Hotshot) . . . . . . . 94 AEDC-PWT Supersonic Tunnel 16S . . . . . . . . . . . . 97

Transition Models . . . . . . . . . . . . . . . . . . . . 97 AEDC-VKFhollow-cylindermodel (Tunnels A, D, and E) . 99 AEDC-PWT hollow-cylinder model (Tunnel 16S) . . . . . . 102 AEDC-VKF f la t -p la te model (Tunnel F) . . . . . . . . . 108 AEDC-VKF sharp-cone model (Tunnels A and D) . . . . . . 111 AEDC-VKF sharp-cone model (Tunnel F) . . . . . . . . . 116

EXPERIMENTAL TECHNIQUE~ AND BASIC TRANSITION DATA . . . . . 118 Basic Transition Data . . . . . . . . . . . . . . . . . . 118

Pitot probe data . . . . . . . . . . . . . . . . . . . 126 Heat-transfer data . . . . . . . . . . . . . . . . . . 127

Application of a Surface Microphone . . . . . . . . . . . 127 Dynamic pressure instrumentation . . . . . . . . . . . 127 Recording and analyzing equipment . . . . . . . . . . . 129 Calibration procedure . . . . . . . . . . . . . . . . . 133 Transition detection . . . . . . . . . . . . . . . . . 133 Induced errors . . . . . . . . . . . . . . . . . . . . 141 Summary . . . . . . . . . . . . . . . . . . . . . . . . 143

AE DC-TR-77-107

CHAPTER

VI.

PAGE

SUPPORTING STUDIES . . . . . . . . . . . . . . . . . . . . 144 Effects of Small Amounts of Leading-Edge Bluntness . . . 144 Investigation of Possible Leading-Edge Bevel Angle Effects . . . . . . . . . . . . . . . . . . . . . . . . . 150 Investigation of Possible Probe Tip Size Effects . . . 152 Investigation of Possible Adverse Effects of Hollow- Cylinder Internal Flow on External Surface Transition Measurements . . . . . . . . . . . . . . . . . . . . . . 153 Methods for Detecting the Location of Transition and a Correlation of Results . . . . . . . . . . . . . . . . . 153

VII. SUMMARY OF BASIC TRANSITION REYNOLDS NUMBER DATA OBTAINED IN AEDC WIND TUNNELS ON PLANAR AND SHARP-CONE MODELS . . .

VI I I .

168

EXPERIMENTAL DEMONSTRATION OF AERODYNAMIC NOISE DOMINANCE ON BOUNDARY-LAYER TRANSITION . . . . . . . . . . . . . . . 180

Introduction . . . . . . . . . . . . . . . . . . . . . . 180 AEDC Shroud Experiments . . . . . . . . . . . . . . . . . 181

Approach . . . . . . . . . . . . . . . . . . . . . . . 181 Shroud models . . . . . . . . . . . . . . . . . . . . . 185 Free-stream stat ic pressure measurements . . . . . . . 185 Long-shroud wall boundary-layer characteristics . . . . 190 Transition results . . . . . . . . . . . . . . . . . . 194 Aerodynamic noise measurements . . . . . . . . . . . . 199

Noise Measurements in Two AEDC Supersonic Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . 207 Transition Measurements in Different Sizes of AEDC Supersonic Tunnels . . . . . . . . . . . . . . . . . . . 215 NASA Act iv i t ies . . . . . . . . . . . . . . . . . . . . . 218 European and USSR Studies . . . . . . . . . . . . . . . . 226

IX.

X.

DEVELOPMENT OF AN AERODYNAMIC-NOISE-TRANSITION CORRELATION FOR PLANAR AND SHARP-CONE MODELS . . . . . . . . . . . . . 233

XI.

EFFECTS OF TUNNEL SIZE, UNIT REYNOLDS NUMBER, AND MACH NUMBER: COMPARISONS BETWEEN THEORY AND EXPERIMENTAL

DATA . . . . . . . . . . . . . . . . . . . . . . . . . 256 Introduction . . . . . . . . . . . i . . . . . . . . . . 256 Effect of Tunnel Size . . . . . . . . . . . . . . . . . . 256 Variation of Re t with Model Position Re t Trends with-Mach Number and Unit Reynolds'Number ~Z 264260 Comparison of Tunnel and Ba l l i s t i c Range Re t Data . . . . 282

COMPARISONS OF PLANAR AND SHARP CONE TRANSITION REYNOLDS NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . .

XII. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . .

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . .

286

295

299

4

AEDC-TR-77-107

FIGURE

I - i .

I-2.

I-3.

I I - l .

I I-2.

II-3.

I I -4 .

I I -5 .

I I-6.

II-7.

I I -8 .

ILLUSTRATIONS

PAGE

Schematic I l lustrat ion of a Laminar, Transitional, and Turbulent Boundary Layer . . . . . . . . . . . . . . . . . 18

An Attempt to Picture the Capability for Analyzing and Predicting Boundary Layers and Laminar~Turbulent Transi- tion. Chart considers only steady two-dimensional and axisymmetric, attached flow for Mach numbers less than 6 [from Reference (30)] . . . . . . . . . . . . . . . . . . 22

Flow Disturbances in Supersonic and Hypersonic Tunnels • . 27

Correlation and Prediction of Incompressible Flow Transi- tion Reynolds Numbers [from Reference (68)I . . . . . . . . 38

Application of Laminar Stabi l i ty Theory to Predicting Boundary-Layer Transition . . . . . . . . . . . . . . . . . 39

Comparison between Measured and Predicted Transitional Heat Transfer with Transition Triggered from Pressure- Velocity Fluctuation [from Reference (24)] . . . . . . . . 40

Data on the Effect of Free-Stream Turbulence on Boundary- Layer Transition, Compared with Data of Other Investi- gators and Theory of van Driest and Blumer [from References (39) and (76)] . . . . . . . . . . . . . . . . . 43

Comparisons of Benek-High Method for Predicting Transi- tion with Experimental Sharp Cone Data~ M® ~ 0.4-1.3 . • 45

Three-Dimensional Boundary-Layer Velocity Profile and Cross-Flow Reynolds Number Criteria . . . . . . . . . . . . 46

Crit ical Cross-Flow Influence on the Boundary-Layer Transition Profile . . . . . . . . . . . . . . . . . . . . 47

Correlation of Transition and Cross-Flow Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . 49

II-9. Ratio of Transition Reynolds Number of Rough Plate to That of Smooth Plate and Ratio of Height of Roughness Element to Boundary-Layer Displacement Thickness at Element, Single Cylindrical (Circle and Square Symbols) and Flat-Strip Elements (Triangular Symbols) [from Reference (78)] . . . . . . . . . . . . . . . . . . . . . 51

5

A EDC-TR-77-107

FIGURE PAGE

II-10.

I I - I I .

II-12.

I I I - l .

I I I -2 .

I I I -3 .

I I I -4 .

I I I -5 .

I I I -6 .

I I I -7 .

I I I - 8 .

I I I - 9 .

I I I-10.

I I I - l l .

I I I-12.

I I I-13.

Comparison of Measured and Predicted Transition Reynolds Numbers [from Reference (63)I . . . . . . . . . . . . . .

Correlation of Sharp Cone Transition Reynolds Numbers at Supersonic-Hypersonic Conditions and Zero Angle of Attack [from Reference (81)] . . . . . . . . . . . . . . . . . .

Correlation of Space Shuttle Wind Surface Centerline Transition Reynolds Number Data [from Reference (8)] . .

Comparison of Fluctuation Diagram for Three Modes [from Reference (43)] . . . . . . . . . . . . . . . . . . . . .

Mode Diagrams . . . . . . . . . . . . . . . . . . . . . .

Pressure Fluctuation from a Supersonic Turbulent Boundary Layer [from Reference (93)] . . . . . . . . . . . . . . .

Correlation of Pressure Fluctuation Levels . . . . . . . .

Comparison of Measured and Predicted Radiated Pressure Levels [from Reference (96)I . . . . . . . . . . . . .

Spectra of Free-Stream Fluctuation at M = 4.5 with and without Turbulence Generated Sound [fro~ Reference (4)] .

Free-Stream Radiated Noise Fluctuations, Directionality, and Intensity, M® = 4.5 [from Reference (74)] . . . . . .

Energy Spectra [from Reference (74)] . . . . . . . . . .

Mode Diagrams from AEDC-VKF Tunnel D at M = 4.0 [from Reference (88) ] ® i • • R • • • • i • • • • • • • • R • • •

Variation of Flow Fluctuations with Unit Reynolds Number [from Reference (88)] . . . . . . . . . . . . . . . . . .

Variation of RMS Pressure Fluctuations (Normalized by Dynamic Pressure) with Unit Reynolds Number [from Refer- ence (88)] . . . . . . . . . . . . . . . . . . . . . . . .

Variation of RMS Pressure Fluctuations (Normalized by Wall Shearing Stress) with Unit Reynolds Number [from Reference (88)] . . . . . . . . . . . . . . . . . . . . .

Hot-Wire Signal Spectra for Wire Overheat of a~ = 0.4 [from Reference (88)] . . . . . . . . . . . . . . . . . .

54

55

58

62

66

71

73

74

77

79

80

82

83

84

86

87

FIGURE

IV-1.

IV-2.

IV-3.

IV-4.

IV-5.

IV-6.

IV-1.

IV-8.

Iv-g.

IV-lO.

IV-t1.

IV-12.

IV-13.

IV-14.

IV-15.

IV-16.

IV-17.

IV-18.

V-I.

A E DC-TR-77-107

AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel B . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel D . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel E . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel F (Hotshot) Faci l i ty (M, ~ 7 to 15) . .

AEDC-PWT Tunnel 16S Supersonic Wind Tunnel Faci l i ty (16-ft x 16-ft Test Section) . . . . . . . . . . . . . .

3.0-in.-Diam Hollow-Cylinder Transition Model (AEDC-VKF Tunnels A, D, and E) . . . . . . . . . . . . . . . . .

Hollow-Cylinder Model Installed in AEDC-VKF Tunnel E . .

AEDC-PWT 16S Transition Model Instal lat ion . . . . . . .

12-in.-Diam Hollow-Cylinder Transition Model Details - AEDC-PWT 16S . . . . . . . . . . . . . . . . . . . . . .

Sketch of AEDC-PWT 16-ft Supersonic Tunnel Test Section Area . . . . . . . . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel F Flat-Plate Transition Model . . . .

Transition Model Installed in the Tunnel F Test Section . . . . . . . . . . . . . . . . . . . . . . . .

AEDC-VKF Sharp-Cone Model Geometry . . . . . . . . . . .

Photograph of Sharp-Cone Model Components . . . . . . .

Instal lat ion of the 5-deg Cone Transition Model in the AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . . . .

Probe Details and Instal lat ion Sketch of the 5-deg Transition Cone in the AEDC-VKF Tunnel D . . . . . . .

AEDC-VKF Tunnel F 10-deg Cone Transition Model.. .

Basic Transition Data from the Hollow-Cylinder Model, AEDC-VKF Tunnel A, M = 4.0 . . . . . . . . . . . . . .

PAGE

90

92

93

95

96

98

100

103

104

105

106

109

110

112

113

114

115

117

119

AEDC-TR -77-107

FIGURE PAGE

V-2.

V-3.

V-4.

V-5.

V-6.

V-7 .

V-8.

V-9.

V-10.

V-11.

V-I2.

V-13.

V-14.

V-15.

VI-1.

Probe Pressure Data Showing the Location of Boundary- Layer Transition on the 12-in.-Diam Hollow-Cylinder Model in the AEDC-PWT 16S Tunnel for M = 2.0, 2.5, and 3.0,

m

Probe No. 1, b = 0.0012 in . , BLE = 6.5 deg . . . . . . . .

Comparison of Probe Pressure Transition Traces in the AEDC-VKF Tunnels A and D and AEDC-PWT 16S for M® = 3.0 . .

Examples of Surface Probe Transition Profi le Traces on the 5-deg Half-Angle Sharp-Cone Model . . . . . . . . . .

AEDC-VKF Tunnel F Flat-Plate Transition Data . . . . . . .

Heat-Transfer Rate Distributions on a 10-deg Half-Angle, Sharp Cone at Zero Incidence in the M® ~ 7.5 Contoured Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . .

Cut-a-Way View I l lus t ra t ing Microphone Instal lat ion . . . .

Microphone Frequency Response . . . . . . . . . . . . . . .

Ambient Pressure Effects on Microphone Frequency Response, M = 3 . . . . . . . . . . . . . . . . . . . . .

Microphone System Used in the AEDC-VKF Tunnel A Aerodynamic-Noise-Transition Study . . . . . . . . . . . .

Detection of Transition from Microphone RMS Pressure Fluctuations, M = 3.0 and 4.0 (AEDC-VKF Tunnel A) • .

GO

Microphone Results M = 3 . . . . . . . . . . . . . . . .

Variation of Acoustic Spectra with Boundary-Layer State, M = 3 . . . . . . . . . . . . . . . . . . . . . . . . . .

¢ o

Oscilloscope Record of Microphone Output (Pressure Fluc- tuation) with Laminar, Transit ional, and Turbulent Flow, M =3.0 . . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of Pressure Fluctuation Spectra for Planar and Axi symmetric Flow . . . . . . . . . . . . . . . . . . . . .

Basic Transition Reynolds Number Data from the AEDC-VKF Tunnel D for M = 3, 4, and 5 with Variable ~, eLE, and Re/in . . . . . . . . . . . . . . . . . . . . . . . . .

120

121

122

124

125

128

130

131

132

134

136

137

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140

145

8

A E DC-TR-77-107

FIGURE PAGE

VI-2.

VI-3.

VI-4.

Vl-5.

VI-6.

VI-7.

Vl-8.

VI-9.

VI-IO.

VI-11.

VI-12.

V I I - I .

VII-2.

VII -3.

AEDC-VKF Tunnel A Re t Values versus b for M® = 3, 4, and 5 . . . . . . . . . . . . . . . . . . . . . . . . .

Circumferential Transition Locations on the AEDC-PWT Tunnel 16S Hollow-Cylinder Model . . . . . . . . . . . . .

AEDC-PWT Tunnel 16S Transition Results, Re t versus b for M = 2.0, 2.5, and 3.0 . . . . . . . . . . . . . . . . . .

Absence of Effects from Bevel Angle and Probe Tip Size on Transition Location Hollow-Cylinder Model, M = 3.0 . . . .

Effectiveness of Serrated Fiber-Glass Tape Boundary-Layer Trip at M = 3.0 . . . . . . . . . . . . . . . . . . . . .

Absence of Effect of Internal Flow Quality on Hollow- Cylinder Transition Data . . . . . . . . . . . . . . . . .

Comparison of Transition Location for Various Detection Methods, M® = 5, Re/in. = 0.28 x 106, b = 0.003 in. [from Reference (37)] . . . . . . . . . . . . . . . . . . .

Typical Data Showing Location of Boundary-Layer Transition on Hollow Cylinder at M = 8 [from Reference (108)] . . . .

Reynolds Number of Transition on Hollow Cylinder at M = 5 and 8 . . . . . . . . . . . . . . . . . . . . . . . . . . .

I l lus t ra t ion of Transition Location Variation with Methods of Detection . . . . . . . . . . . . . . . . . . .

Correlations of Transition Detection Methods . . . . . . .

Basic Transition Reynolds Number Data from AEDC-VKF Tun- nels D and E, M = 3.0 and 5.0, Hollow-Cylinder M o d e l . . .

Basic Transition Reynolds Number Data from the AEDC-VKF Tunnel A for M = 3, 4, and 5 and Variable~and BLE, Hollow-Cylinde~ Model . . . . . . . . . . . . . . . . . .

Basic Transition Reynolds Number Data from the 12-in.- Diam Hollow-Cylinder Model in the AEDC-PWT Tunnel 16S for M = 2.0, 2.5, and 3.0 and ~ = 0.0015, 0.0050, and 0~0090 in . . . . . . . . . . . . . . . . . . . . . . . . .

146

147

148

151

154

155

158

160

161

163

165

169

170

171

9

A E D C -T R -77 -1 07

FIGURE

VII-4.

VII-5.

VII-6.

VII-7.

V I I I - I .

VII I-2.

VIII-3.

VIII-4.

VIII-5.

VII I-6.

VIII-7.

VIII-8.

VIII-g.

VIII-tO.

VIII-11.

VIII-12.

VIII-13.

VIII-14.

VIII-15.

PAGE

Basic Transition Reynolds Number Data from the AEDC-VKF 12-in. Tunnel D, 40-in. Tunnel A and the AEDC-PWT 16-ft Supersonic Tunnel for M® = 3.0, Hollow-Cylinder Models . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Transition Reynolds Number Data from AEDC-VKF Tunnel D, Sharp-Cone and Planar Models . . . . . . . . . . . . . . . 173

Transition Reynolds Number Data from AEDC-VKF Tunnel A, Sharp-Cone and Planar Models . . . . . . . . . . . . . . . 175

AEDC-VKF Tunnel F (Hotshot) Transition Data . . . . . . . . 177

Long Shroud Installation in the AEDC-VKF Tunnel A . . . . . 183

AEDC-VKF Tunnel A Long-and Short-Shroud Configurations . . 184

Inviscid Pressure Distribution Inside Long Shroud . . . . . 186

Free-Stream Flat-Plate Pressure Data, M = 3.0, AEDC-VKF Tunnel A Centerline . . . . . . . . . . . . . . . . . . . . 189

Long-Shroud Boundary-Layer Rake . . . . . . . . . . . . . . 191

Boundary-Layer Profiles on Inner Wall of Long Shroud . . . 192

Long-Shroud Boundary-Layer Characteristics . . . . . . . . 193

Transition Data Measured with and without Long Shroud, M = 3.0, AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . 195

Surface Pitot Probe Pressure Traces on 3.0-in.-Diam Model, Short-Shroud Configuration, M = 4 and 5 . . . . . . . . . 197

Transition Reynolds Numbers Measured with and without Long and Short Shroud, M = 4.0 and 5.0 . . . . . . . . . . . . 198

Flat-Plate Microphone Model . . . . . . . . . . . . . . . . 200

AEDC-VKF Tunnel A Microphone-Flat-Plate Instal lation . . • 201

Comparisons of Transition Reynolds Numbers and Root-Mean- Square Radiated Pressure Fluctuations at M = 3.0 . . . . . 203

Comparisons of Transition Reynolds Numbers and Root-Mean- Square Radiated Pressure Fluctuations at M = 5.0 . . . . . 206

Fourier Analysis of Selected Data Points from Figure VIII-13c . . . . . . . . . . . . . . . . . . . . . . . . . 208

I0

AEDC-TR-77-107

FIGURE

VIII-16.

VIII-17.

VIII-18.

VI I I - lg .

VIII-20.

VIII-21.

VIII-22.

VIII-23.

VIII-24.

VIII-25.

VIII-26.

VIII-27.

IX-1.

IX~2.

IX--3.

Free-Stream Pressure Fluctuation Measurements, AEDC~ VKF Tunnels A and D . . . . . . . . . . . . . . . . . .

Power Spectral Density Analysis of Microphone Output Recorded at Re/in. = 0.24 x 10B [from Reference (88)] . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of Power Spectra of Microphone Output for Various Unit Reynolds Numbers [from Reference (88)] . .

Measurements of Fluctuating Pressures under Laminar and Turbulent Boundary Layers on a Sharp Cone in Mach 6 High Reynolds Number Tunnel at NASA Langley . . . . . .

Variation of Transition Reynolds Numbers with Tunnel Size . . . . . . . . . . . . . . . . . . . . . .

Effect of Tunnel Size on Transition Reynolds Numbers at M ~ 3.0, Flat Plates and Sharp Cones . . . . . . . . .

Effect of Free-Stream Disturbances on Wedge Model Transition, M ~ 20 [from Reference (89)] . . . . . . .

Correlation of Transition Reynolds Numbers with RMS Disturbance Levels [from Reference (81)] . . . . . . . .

NASA-Langley M = 5 Quiet Tunnel Concept [from Refer- ence ( 28 ) ] . . ? . . . . . . . . . . . . . . . . . . . .

Hollow-Cylinder Transition Data [from Reference (57)] . .

Effect of Tunnel Size on Re t Data from Netherland Tun- nels [from Reference (60)] . . . . . . . . . . . . . . .

Effect of Tunnel Size on Flat-Plate Transition Reynolds Numbers - USSR Studies . . . . . . . . . . . . . . . . .

Influence of Tunnel Size on the Boundary-Layer Transi- tion Reynolds Number Correlation [from Refer~.nce ( 10 ) ] . . . . . . . . . . . . . . . . . . . . . . . . .

Tunnel Size Parameter . . . . . . . . . . . . . . . . .

In i t ia l Correlation of Transition Reynolds Numbers on Sharp Flat Plates with Aerodynamic Noise Parameters [from Reference (10)] . . . . . . . . . . . . . . . .

PAGE

209

211

212

214

216

217

220

222

225

228

230

232

237

239

240

I I

AEOC-TR-77-107

FIGURE

IX-4.

IX-5.

IX-6.

IX-7.

IX-8.

IX-9.

X-1.

X-2.

X-3.

X-4.

X-S,

X-6.

X-7.

X-8.

X-9.

X-IO.

X-11.

In i t ia l Correlations of Planar and Sharp-Cone Transi- tion Reynolds Numbers [from Reference (11)] . . . . . . .

Tunnel Size Normalizing Parameters . . . . . . . . . . .

Correlation of Transition Reynolds Numbers on Sharp Cones with Aerodynamic Noise Parameters [from Reference (ii)] . . . . . . . . . . . . . . . . . . . . . . . . . .

Transi tion Reynol ds Number Corre]ation . . . . . . . . . .

Correlation of Planar Model Transition Reynolds Numbers . . . . . . . . . . . . . . . . . . . . . . . . .

Correlation of Sharp-Cone Transition Reynolds Numbers . .

Effect of Wind Tunnel Size on Planar Model Transition Reynolds Numbers for Various Mach Numbers . . . . . . . .

Effect of Wind Tunnel Size on Sharp-Cone Transition Reynolds Numbers for Various Mach Numbers . . . . . . . .

Variation of Transition Reynolds Numbers with Tunnel Size and M = 3.0, Sharp-Leading-Edge Flat-Plate/Hollow- CylinBer Models . . . . . . . . . . . . . . . . . . . . .

Variation of Sharp-Cone Transition Reynolds Numbers with Tunnel S i z e a t M ~ 8 . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel E Transition Model Locations . . . . . . .

Effect of Model Axial Locations on Re t Data (Hollow- Cylinder Model) . . . . . . . . . . . . . . . . . . . . .

Computed Values of Re t with Varying Model (~m) Locations (Planar Models) . . . . . . . . . . . . . . . . . . . . .

Effect of Mach Number and Unit Reynolds Number on Planar Model Transition Data . . . . . . . . . . . . . . . . . .

Effect ~f Mach Number and Unit Reynolds Number on Sharp- Cone Transition Data . . . . . . . . . . . . . . . . . .

Variation of Planar Model Transition Reynolds Numbers with Tunnel Size and Mach Number . . . . . . . . . . . . .

Variation of Sharp-Cone Transition Reynolds Numbers with Tunnel Size and Mach Number . . . . . . . . . . . . . . .

PAGE

241

243

244

247

249

251

257

258

261

262

263

265

266

267

270

274

275

12

A E DC-TR-77-107

FIGURE

X-12.

X-13.

X-14.

X-15.

X-16.

XI- I .

XI-2.

A-I.

A-2.

B- I .

B-2.

B-3,

B-4.

B-5.

B-6 •

B-7.

PAGE

Transition Reynolds Numbers as a Function of Local Mach Number for Sharp Cones, M® = 8 . . . . . . . . . . . . . . 276

Comparisons of Predicted and Measured (Ret) ~ Values on Sharp Cones for Various Local Mach Number~,-M = 8 . . . . 278

Comparison of Predicted and Measured Transition Reynolds Number from Current Method (Eqs. (10) and (11) and the Fortran Computer Program, Appendix C) . . . . . . 280

Variation of Transition Reynolds Numbers with Tunnel Mach Number . . . . . . . . . . . . . . . . . . . . . . . 281

Comparison of Sharp-Cone Transition Reynolds Numbers from Wind Tunnels and an Aeroball ist ic Range . . . . . . . 283

Correlation of Axisymmetric and Planar Transition Reynolds Number Ratios . . . . . . . . . . . . . . . . . 288

Comparison of Predicted and Measured Cone Planar Transition Ratios . . . . . . . . . . . . . . . . . . . . . 290

Adiabatic, Mean Turbulent Skin-Friction Coefficients as a Function of Mach Number and Length Reynolds Number . . . . 321

Mean, Turbulent Skin-Friction Coefficient Computed Using the Method of van Driest- I I . . . . . . . . . . . . . . . . 323

AEDC-PWT Tunnel 16S Boundary-Layer Characteristics . . . 328

Boundary-Layer Rakes Used in the AEDC-PWT 16S Tunnel and the AEDC-VKF Tunnel A to measure Tunnel Wall Boundary- Layer Profiles . . . . . . . . . . . . . . . . . . . . . . 329

AEDC-VKF Tunnel A Boundary-Layer Characteristics . . . . . 330

Pi lot Pressure Profiles from AEDC-VKF Tunnel E, M = 5.0 . . . . . . . . . . . . . . . . . . . . . . . . . 333

AEDC-VKF Tunnel E Turbulent Boundary-Layer Displacement Thickness (6*) for M = 5.0 . . . . . . . . . . . . . . . . 335

Turbulent Boundary-Layer Characterist ics at M = 3.0 for AEDC Tunnels PWT-16S, VKF-A and VKF-D . . . . . . . . . . . 337

Flexib le Plate Displacement Thickness Correlat ions fo r M - 1 t o 10 . . . . . . . . . . . . . . . . . . . . . . . 339

]3

AE DC-T R-77-107

FIGURE

B-8.

C-1.

D-I.

D-2.

E-1.

E-2.

E-3.

E-4.

E-5.

E-6.

E-7.

E-8.

E-g.

E-IO.

PAGE

Correlation of Hypersonic Wind Tunnel Wall Displacement Thickness (6*) . . . . . . . . . . . . . . . . . . . . . 341

Comparisons of Approximate and Exact Cone Surface Reynolds Number Ratios . . . . . . . . . . . . . . . . . . 355

Sensit ivi ty of the Reynolds Number Ratio to Various Viscosity Laws . . . . . . . . . . . . . . . . . . . . . 375

Variation of Reynolds Number Ratio with Cone Half-Angle, Mach Number, and Temperature . . . . . . . . . . . . . . . 376

Boundary-Layer Trip Geometry . . . . . . . . . . . . . . . 379

Methods of Transition Detection, M = 3.0, AEDC-VKF Tunnel D . . . . . . . . . . . . . . . . . . . . . . . . . 382

Surface Probe Transition Profi les, M = 3.0, AEDC-VKF Tunnel A . . . . . . . . . . . . . . . . . . . . . . . . . 383

Effect of Spherical Roughness on Trans i t ion Location, M 6 = 2.89, AEDC-VKF Tunnel D . . . . . . . . . . . . . . . 384

Effect of Spherical Roughness on Trans i t ion Location, M~ = 2.89, AEDC-VKF Tunnel A . . . . . . . . . . . . . . . 385

Effect of Spherical Roughness on Transition Location, M 6 = 3.82, AEDC-VKF Tunnel D . . . . . . . . . . . . . . . 386

Variation of Transition Reynolds Numbers with Trip Reynolds Number for M 6 = 2.89 and 3.82, AEDC-VKF Tunnels D and A . . . . . . . . . . . . . . . . . . . . . . 388

Correlat ion of Tripped Results Using the Methods of Van Driest-Blumer . . . . . . . . . . . . . . . . . . . . 390

Correlation of Tripped Results Using the Method of Pot ter -Whi t f ie ld . . . . . . . . . . . . . . . . . . • • 393

Comparisons of Correlation Predictions with Experimental Resul ts . . . . . . . . . . . . . . . . . . . . . . . . . . 395

14

AE DC-TR-77-107

TABLES

TABLE

I .

2.

3.

e

5.

.

e

F-1.

F-2.

F-3 .

F-4.

F-5.

F-6.

F-7.

F-8.

AEDC Supersonic-Hypersonic Wind Tunnels . . . . . . . . . .

Methods for Measuring the Location of Transi t ion . . . . .

Methods Used for Correlating Transit ion Detection Techniques (See Figures V[-11 and V[-12) . . . . . . . . . .

European Transit ion Test Fac i l i t i es [From Reference (57~, ,

Source and Range of Data Used in the Planar Hodel Transit ion Reynolds Number Correlation (See Figure IX-8) . . . . . . . . . . . . . . . . . . . . . . . .

Source and Range of Data Used in the Sharp Cone Transi t ion Reynolds Number Correlation (See Figure IX-9) . . . . . . .

Estimated Cone-Planar Transit ion Ratios . . . . . . . . . .

AEDC-VKF Tunnel D Transit ion Reynolds Number Data, 3.0-in.-Diam Hollow Cylinder . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel E 3.0- i n.-Di am Hol l ow-Cyl inder Trans t t ton Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel A Transit ion Reynolds Number Data, 3.0-in.-Diam Hollow Cylinder . . . . . . . . . . . . . . . .

AEDC-PWT-16S Tunnel Basic Transit ion Reynolds Number Data, 12.0-in.-Diam Hollow Cylinder . . . . . . . . . . . . . . .

AEDC-VKF Tunnel D Transit ion Reynolds Number, lO-Deg Total-Angle Sharp Cone . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel A Transit ion Reynolds Number, lO-Deg Total-Angle Sharp Cone . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel A Long- and Short-Shroud Transit ion Results . . . . . . . . . . . . . . . . . . . . . . . . . .

AEDC-VKF Tunnel F Transit ion Reynolds Number Data . . . . .

PAGE

89

157

162

227

250

253

293

399

400

401

402

403

404

405

406

15

A E DC-TR -77-107

PAGE

APPENDIXES

APPENDIX A. TURBULENT BOUNDARY-LAYER SKIN FRICTION . . . . . . 315 Review of Theoretical Methods . . . . . . . . . . . . . . . . 315 Method of van Driest-I I . . . . . . . . . . . . . . . . . . . 320

APPENDIX B. TUNNEL WALL BOUNDARY-LAYER CHARACTERISTICS . . . . 324 Data Reduction Procedures . . . . . . . . . . . . . . . . . . 324 AEDC-PWT Tunnel 16S Data . . . . . . . . . . . . . . . . . . . 327 AEDC-VKF Tunnel A Data . . . . . . . . . . . . . . . . . . . . 327 AEDC-VKF Tunnel E Data . . . . . . . . . . . . . 332 Correlations of Boundary-Layer Displacement Thickness ~ 336

APPENDIX C. DEVELOPMENT OF FORTRAN IV COMPUTER PROGRAM FOR PREDICTING TRANSITION LOCATIONS USING THE AERODYNAMIC-NOISE- TRANSITION CORRELATION . . . . . . . . . . . . . . . . . . . . . 343

Method of Approach . . . . . . . . . . . . . . . . . . . . . . 343 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . 345 Computer Code Nomenclature . . . . . . . . . . . . . . . . . . 356 Computer Program Listing . . . . . . . . . . . . . . . . . . . 361 Input Data Format and Check Problems . . . . . . . . . . . . . . . 369 Flow Chart for Fortran Computer Program . . . . . . . . . . . . 372

APPENDIX D. EFFECTS OF DIFFERENT VISCOSITY LAWS ON INVISCID FLOW CONE SURFACE REYNOLDS NUMBER RATIOS . . . . . . . . . . . . 373

APPENDIX E. COMBINED EFFECTS OF AERODYNAMIC NOISE AND SURFACE ROUGHNESS ON TRANSITION . . . . . . . . . . . . . . . . . 377

Transition Models and Apparatus . . . . . . . . . . . . . . . . . 378 Transition Dependency on Tunnel Size . . . . . . . . . . . . . 380 Transition Detection and Identif ication . . . . . . . . . . . . 381 Basic Results . . . . . . . . . . . . . . . . 381 Van Driest, e t 'a l . Trip Correiation . . . . . . . . . . . . . 389 Potter and Whitfield Trip Correlation . . . . . . . . . . . . . 391

APPENDIX F. TABLULATIONS OF BASIC EXPERIMENTAL TRANSITION DATA FROM THE AEDC SUPERSONIC-HYPERSONIC WIND TUNNELS . . . . . . . . 399

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . 407

16

AE DC-TR-77-107

CHAPTER I

INTRODUCTION

I. BACKGROUND INFORMATION

The growth of a boundary layer (viscous f low region) on the sur-

face of a f l a t plate is i l l u s t r a ted in the diagram presented in Figure

I-1. I n i t i a l l y , the boundary layer is laminar and can be characterized

by an in f in i te number of viscous flow stream tubes arranged in laminated

layers. The flow quantities are defined by steady-state properties,

i .e . , random fluctuations are not present. As the axial distance in-

creases, the boundary layer becomes unstable and disturbances become am-

pl i f ied (1,2). Further downstream, the appearance of turbulent spots

(bursts) wi l l occur as reported by Emmons (3), and f ina l ly the boundary

layer wi l l become fu l l y turbulent. Turbulent boundary-layer properties

are defined as the sum of time averaged I mean flow quantities plus the

fluctuating quantity ( i .e . , p = ~ + p' , p = ~ + p-, u = ~ + u' , etc.).

The transition region is defined as the region connecting fu l ly laminar

and fu l ly turbulent flow as shown in Figure I - I . This is a very simpli-

fied explanation and the reader is referred to the report by Morkovin (4)

for an indepth discussion. White (2) also provides interesting reading

on the historical background of instabi l i ty- t ransi t ion concepts, a sum-

mary of the classical studies, and a good concise sumary on the tranSi-

tion process as generally accepted today.

1 T 1Time averaged quant i t ies ~ : - / Q dT; T ~ time.

' T O

17

I nviscid Flow Region

U° Region

AEDC-TR-77-107

I I ' I I I P (Xt) - I , _ beg 7 _ ,

,- I (Xt)end v, I ~ x I I 1 Laminar Flow I Transitional I I I I I Region I Flow Region I

Turbulent Flow Region

a. Boundary-Layer Development

t -

O = E

. m

L - -

11

r - = m

f -

L I . C.)

8 C.)

10-2

10-3

10-4 i@

Incompressible Flow

Turbulent

_.. ~ .~ Transitional

La mi nar - , ,

10 6 10 7 10 8 10 9

PoUo x Reynolds Number, Reox - Po

Figure I-1.

b. Skin-Friction Coefficient

Schematic i l lust rat ion of a laminar, transit ional, and turbulent boundary layer.

18

A E DC-TR-77-107

The importance of knowing the body station where the boundary

layer changes from a laminar to a turbulent state (boundary-layer t ransi-

tion location) is well documented and can be br ie f ly i l lust rated by a

few examples:

1. The sk in- f r ic t ion drag of a f l i gh t vehicle (subsonic to

hypersonic) increases about a factor of ten when the

boundary layer changes from laminar to turbulent, as

i l lustrated in Figure I-1. Since skin f r i c t ion can com-

prise as much as 80 to 90% of the total vehicle drag at

subsonic speeds and up to 50% of the total drag at hy-

personic speeds, then the importance of knowing the lo-

cation of transit ion is obvious.

2. Similarly, surface heat-transfer rates 2 can vary a factor

of ten between a laminar and turbulent boundary layer, and

this difference must be considered in vehicle design and

selection of thermal protection system (ablation materials)

for hypersonic vehicles.

3. Effectiveness of control surfaces can be strongly influenced

because of the sensitivity of flow separation and the result-

ing surface pressure distributions to the location of transi-

tion and the state of the boundary layer.

4. Vehicle stabi l i ty and control can be affected by the loca-

tion of transition (5,6,7).

2From Reynolds analog C h = Cf

2(Pr)2/3 [(see (1,2)]

19

AEDC~R~7-107

5. Conducting successful experiments in ground test f ac i l i t i es

(wind tunnels, ba l l i s t i c ranges, engine test f a c i l i t i e s ,

etc.) often requires knowledge of the location of t ransi t ion

on the subscale test model to ensure proper simulation of

the f l i gh t conditions and/or to ensure that t ransi t ion is

occurring at the desired or expected location on the test

ar t ic le (8,9). A knowledge of the location of transit ion

can be particularly significant when data for a particular

test model geometry are obtained in several different facili-

ties and where comparisons and/or analysis and evaluations

of transition sensitive data are made (I0,II).

The study of boundary-layer transition, particularly at high

speeds, is still very much an area of active research, as illustrated by

the wide diversity of publications appearing in the last ten years.

Recent studies into the basic mechanisms contributing to boundary-layer

instability and transition have been reported in References (4) and {12)

through (15). Experimental studies of transition Reynolds numbers at

supersonic-hypersonic Mach numbers have been reported in References {8)

through (II) and (16) through (23). Correlation and semimempirical

methods for predicting the occurrence of transition have been reported

in References (8) through (12) and (16) through {22), and theoretical

studies on predicting transition have been reported in References (13),

(15), and (24). In particular, the effects of free-stream disturbances

on boundarymlayer transition at supersonic-hypersonic Mach numbers have

received much interest in recent years, as reported in References (4),

(I0) through (14), (ig), and (24) through (29).

20

AEDC-TR-77-107

In a recent article, A. M. O. Smith (30) commented on the cur-

rent state of being able to predict, in general, the occurrence of

boundary-layer transition. Presented in Figure I-2 is Smith's qualita-

tive assessment of the percentage of time that a prediction would be

about 90 to 95% correct. Note that even today (after 90 years of transi-

tion research), the understanding of the transition process rates about

only a 15% on predictability as compared to the laminar-turbulent

boundary-layer understanding level of about B5 to go%. Figure I-2 pro-

vides some appreciation for the complexity of the transition process.

The complexity of the transition process and the many contribut-

ing factors that can be a significant influence have been discussed in

detail by Morkovin (4). Morkovin provides a critical review of high-

speed boundary-layer t rans i t ion and provides an tndepth discussion on

the many factors that can contribute to the t rans i t ion process, the de-

parture of the nonlinear t rans i t ion process from the l inear s t a b i l i t y ,

and how the many factors can in ter re la te depending on the flow condi-

t ions, body surface conditions and free-stream disturbances. Morkovin

devotes considerable space to a discussion of the adverse effects of

free-stream disturbance on the t rans i t ion process.

The American Ins t i tu te of Aeronautics and Astronautics (AIM) has

also produced a nine-hour lecture series on "High-Speed Boundary-Layer

S tab i l i t y and Transit ion" (31). These lectures were prepared by

Morkovin (4) and Mack (13) and based on the i r recent, but now well-known,

work.

In general, the boundary-layer transition process can be associ-

ated with four different types of disturbance mechanisms:

21

4~

U %-

!

• r "

to

100

75

5O

25

*Major Contributions

0 & ~

1900

"W

L ~

-~ O. "7- 0 ,IC ILl ~ , . 2 ~

~ U t o

0 - - I t . ~ "~ a. , I I ~1~ H

w " o / k t o _ J J ~.

• ~ ~ - - ,.., ..~ ~ " ~ w'r "~" U ",a , .~

U e -

))))

u l " 0 0

J =

X

U C

IU --J .

IU

, r - M .

L

Ul " I C C- O U

• " 0 4J ~ ; = = = j = t - 4.) " ~ Q . U to,m-- ¢I "~"

• , - S- E = - . , , , ' Z r,.q ¢ n

Boundary Layers Laminar and Turbulent

Boundary-Layer Transition

1925 1950 1975 2000

Year

)> m [3 c}

m

~,j

0

Figure I-2. An attempt to picture the capability for analyzing and predicting boundary laYers and laminar-turbulent transition. Chart considers only steady two-dimensional and axisymmetric, attached flow for Mach numbers less than 6 [from Reference (30)].

AEDC-TR-77-107

1. Tollmien-$chlichttnq Type Ins tab i l i ty ; In an inviscid or vts~

cous f lu id , an inf lect ion point in the velocity prof i le , can~ in

general, be suff ic ient to cause ins tab i l i ty . However, in a vis-

cous f lu id an inf lect ion point is not a necessary requirement

since viscosity can also be destabil izing for certain wave

numbers (wave frequency~wave velocity) and Reynolds numbers.

Viscous ins tab i l i t ies were successfully predicted theoretically

by Tollmien and Schlichting {I) using linear stability theory.

Experimental verification was provided by Schubauer and

Skramstad {32). Tollmlen-Schlichting instabilities are char-

acterized by small finite disturbances becoming amplified in-

to sinusoidal oscillations at some critical frequency.

2. Crossflow or D2namic Instabilit2: This type instability is

associated with three-dimensional boundary-layer flow with

the instability being the result of a component of flow

{crossflow) that is normal to the outer flow streamline and

which develops from a spanwise pressure gradient. This cross-

flow prof i le inherently has a maximum point and a basically

unstable inflection point. Crossflow instability was first

investigated by Owen and Randall {33) on subsonic swept wings

and later by Chapman {34), Pate {18), and Adams, et al. (35),

{36) at supersonic and hypersonic speeds.

3. RouBhness-Dominated Transition: This type of instability

occurs when two- or three-dimensional disturbances are gen-

erated by isolated roughness elements which produce a wake-

type turbulence. Van Driest {16,17), Potter and Whitfield

{37), Whitehead {20), and Whitfield and lannuzzi {21) have

23

AEDC~R-77-107

experimentally studied isolated spherical roughness effects

at supersonic-hypersonic Mach numbers.

4. Influence of Free-Stream Disturbance Levels ( i . e . , spectra

and intensity levels): Schubauer and Skramstad (32) showed

free-stream velocity f luctuations affected transi t ion loca-

tions in subsonic wind tunnels. Pate and Schueler (10) and

Pate (11) have shown that free-stream pressure fluctuations

(aerodynamic noise) in supersonic-hypersonic wind tunnels

can dominate the transi t ion process. Horkovin (4) discusses

the effects of free-stream disturbances in promoting transi-

t ion and Mack (13) recently used l inear s tab i l i t y theory in

conjunction with free-stream pressure f luctuations (aero-

dynamic noise) as measured by Laufer (38) to predict the on-

set of t ransi t ion.

The bulk of the transit ion data published to date has been ob-

tained in wind tunnels. Consequently, most of the experimental data

used in the development of essentially al l correlations of t ransi t ion

Reynolds numbers and for ver i f icat ion of transit ion theories have been

obtained in wind tunnels. Unfortunately, the location of transit ion on

test models can be strongly affected by wind tunnel free-stream distur-

bances. The next section provides a br ief summary of the various types

of wind tunnel disturbances.

I I . WIND TUNNEL FREE-STREAM DISTURBANCES

I t has been known for many years that disturbances present in

the free-stream of subsonic wind tunnels can have a dominating effect on

24

AEDC-TR -77- I07

the boundary-Iwer instability and transition process. The incompres-

sible stability theory developed by Tollmien and Schllchtlng in the

1920's, see Reference (I), had to wait about 20 years for experimental

confirmation by Schubauer and Skramstad (32) because of the high level

of turbulence {velocity fluctuations) present in most conventional sub-

sonic wind tunnels. The classical experiments of Schubauer and Skramstad

{conducted in the early Ig40's) not only showed that the infinitesimally

small Tollmien-Schlichting type disturbance waves could be amplified as

predicted by theory {provided the tunnel velocity fluctuations were suf-

ficiently small), but they also showed that the location of transition

was dependent on the tunnel turbulence level. The low turbulence, sub-

sonic transition Reynolds number data (Re t = 2.9 x 106) of Schubauer-

Skramstad were the maximum values obtained for many years and conse-

quently were the values used in many data correlations and data compari-

sons. Van Driest and Blumer (39) used the data of Schubauer-Skramstad

(32) in studying the effects of subsonic disturbances on the location of

transition. Recent data (1968) obtained by Spangler and Wells (40) have

shown that the subsonic transition Reynolds number could be increased to

Re t = 5.2 x 105 by reducing the background noise levels and by changing

the frequency distribution from fans, diffuser, etc. Thus i t has been

shown that the disturbance level {intensity) as well as the type of dis-

turbance are major contributing factors to the transition process at sub-

sonic speeds. Consequently, i t has been accepted that Re t data obtained

in subsonic wind tunnels can vary between faci l i t ies. Correlations that

have been developed to predict transition on subsonic, smooth wall models

25

AEDC-TR~7-107

have usually been based on data from low turbulence wind tunnels. One

well-known correlation was developed by Michel in 1951 (41).

Experiments conducted at supersonic speeds by NACA personnel (42)

in the early 1950's also showed signi f icant differences in t ransi t ion

locations measured on a 10-deg cone for similar test conditions but d i f -

ferent wind tunnels. Differences exhibited in these data were found to

decrease sharply as the Mach number increased to about 3 or 4. The d i f -

ferences in the Re t values were believed to be di rect ly related to the

free-stream turbulence levels (velocity f luctuations (u/U®) present at

low supersonic speeds.

Kovasznay in 1953 (43) theoret ical ly ident i f ied three possible

disturbance sources in wind tunnels: (a) vor t i c i t y f luctuations (turbu-

lence), (b) entrow fluctuations (or temperature spottiness), and

(c) sound waves. Morkovin discussed these three possible modes of dis-

turbance in 1957 (44) and 1959 (45) and speculated on where their origins

could originate in a supersonic wind tunnel. The vor t i c i t y and entropy

fluctuations were essentially convected along streamlines and were

traceable to conditions in the sett l ing chamber. Sound disturbances

could travel across streamlines, and they could originate in the s t i l l i n g

chamber and from the boundaries of the test section. Morkovin identi f ied

the turbulent boundary layer (shear layer) on the tunnel wall as a poten-

t ia l source for radiating a sound disturbance. Figure I-3 i l lust rates

the origins of these disturbances.

Vort ic i ty (turbulence) f luctuations were investigated at Mach

numbers from 1.7 to 4 by Laufer and Matte (46) by varying the turbu-

lence level in the s t i l l i ng chamber from 0.6 to 7¢. In the low Mach

26

A E DC-TR-77-107

T u r b u l e n t ~

. \ , ' I " ~ ....... , . I , . . ~ - - "~ ~ "~ -=======~----~ ~ ~ Test

Mach Number Range Type Disturbance Effect on Transition

Moo = 1.5 to3

Mo) = 3 to 15

20 (Cold Flow)

Mo~ > 10 Arc Tunnels Shock Tunnels MHD Tunnels

Vorticity (Turbulence)

Noise

Entropy (Temp. Spots)

Radiated Noise (p)

Entropy ~)

Radiated Noise ~)

• " Usually Dominant

- May Be Dominant

- Negligible

• - Usually Domi na nt

May Be Dominant

Figure I -3 . Flow disturbances in supersonic and hypersonic tunnels.

27

AE DC-T R-77-107

number flow, ~ < 2.5, the s t i l l i n g chamber turbulence ]eve] was found

to have a strong ef fect on sharp cone boundary-layer t rans i t ion Reynolds

numbers; however, no s ign i f i cant ef fect was noted for M® > 2.5. Similar

experiments were conducted at Mach 1.76 by Morkovin (44), and no mea-

surable sh i f t in f l a t -p la te t rans i t ion Reynolds number resulted when

the se t t l ing chamber turbulence was raised from 0.7 to 4.6%. Van

Driest and Boison (47) also showed that for M® ~ 2.5 the s t i l l i n g cham-

ber turbulence ]eve] had no s ign i f i cant ef fect on sharp cone t rans i t ion

Reynolds numbers. Therefore, i t is concluded that for H ~ 2.5 to 3

veloci ty f luctuat ions have a neg] igible ef fect on wind tunnel t rans i t ion

data.

Sources of the entropy f luctuat ions (temperature spottiness) are

traceable to the set t ] ing chamber and farther upstream. In the test sec-

t ion, the temperature f luctuat ions are related isent rop ica l ly to those

in the s t i l l i n g chamber. Effective means such as the use of mixing sec-

tions and screens in the supply passage are used to reduce temperature

f luctuat ions to small levels in supersonic tunnels and consequently the i r

influence on t rans i t ion in well-designed tunnels is thought to be ins ig-

n i f i cant . Limited studies of the effects of temperature f luctuat ions on

t rans i t ion locations have been conducted by Brinich (48) and Ross (49).

Brinich (48) changed T O from 52 to 176°F at M = 3.1 and found that the

t rans i t ion location on a f l a t plate was essent ia l ly unchanged. Transit ion

measurements were conducted by Ross (49) at M® = 4 where T O was varied

from 295 to 434°K, keeping the uni t Reynolds number constant, and he

found no appreciable change in Re t data obtained with a hol low-cyl inder

mode]. Thus, i t is concluded that in well-designed supersonic wind

28

A EDC-TR-77-107

tunnels ( i . e . , a s t i l l i ng chamber equipped with proper mixing screens),

entropy fluctuations wi l l have a negligible effect on transi t ion data.

The third type of unsteady disturbances, the radiated sound (or

pressure fluctuations) (43) generated by the turbulent boundary layer on

the walls of the test section, remain as a possible major factor af fect-

tng transit ion In supersonic and hypersonic wind tunnels for M > 2.5.

In 1952, AGARD established a series of cal ibration models with

somewhat the same general objective as the NACA (42) had tn testing a

lO-deg cone in several wind tunnels. One of the cal ibration models was

a high fineness rat io , parabolic body (AGARD Calibration l~odel A) which

had been tested extensively by the NACA to compare zero l i f t drag meas-

urements made in many di f ferent wind tunnels. Tests of the same model in

the Arnold Engineering Development Center, von Kannan Faci l i ty (AEDC-VKF)

12-tn. and 40-in. supersonic tunnels (Gas Dynamic Ntnd Tunnels, Super-

sonic (D) and (A)) revealed discrepancies tn base pressure and drag data

that could be explained by differences in transi t ion Reynolds numbers in

these tunnels (50). These tests were followed by tests of a hollow-

cylinder model to obtain transit ion locations for a range of Hach numbers

and unit Reynolds numbers. Schueler (51) showed from these tests that

transit ion Reynolds numbers obtained in the AEDC-VKF 40-in. supersonic

tunnel were s igni f icant ly larger than those from the AEDC-VKF 12-in.

supersonic tunnel. Aerodynamic noise generated in the tunnel boundary

layers was suggested as being responsible for the variations in t ransi-

t ion Reynolds numbers.

By the early 1960's, primarily as a result of Laufer's research

(38), radiated noise had been identi f ied as a signi f icant source of wtnd

29

AEDC-TR-77-107

tunnel test section free-stream disturbances at supersonic Mach numbers

(M ~> 2). However, there were no data available that demonstrated di-

rectly the effect that radiated sound (noise) disturbances might have on

supersonic-hypersonic transition data taken in wind tunnels. Conse-

quently, all of the transition experiments and resulting data correla-

tions that were developed in the lg50's and '60's in an attempt to pre-

dict the behavior of f l ight transition Reynolds numbers at supersonic

and hypersonic Mach numbers did not consider (include) the effects of

free-stream disturbances (radiated noise).

Research by Pate and Schueler (10) and Pate (11) presented the

f i r s t data showing the dominating effect of wind tunnel "aerodynamic

noise" on boundary-layer transition. This research was undertaken after

the f i r s t author (10) developed a correlation of transition Reynolds num-

bers as a function of the free-stream aerodynamic noise parameters (C F,

6*, and C). This correlation was based on existing f lat-plate and

hollow-cylinder Re t data published from eight wind tunnels covering the

Mach number range from 3 to 8 with test section heights varying from I to

4 f t . The correlation was independent of unit Reynolds number and Mach

number. To confirm the validity of the correlation and to establish that

Re t values increased monotonically with increasing tunnel (test section)

size as predicted by the correlation, an extensive experimental program

was formulated. This program provided for hollow-cylinder transition

data to be obtained in the largest supersonic tunnels in the world, with

test sections ranging from 1 to 16 f t , and the in i t ia l results were re-

ported in Reference (10). Transition experimental studies were also

30

A EDC-TR-77-107

conducted using a sharp, slender 5-deg half-angle cone model to determine

i f the correlation held for an axisymmetric configuration, and these re-

sults were reported tn Reference (11). This i n i t i a l research also in-

cluded a series of unique experiments that allowed the radiation of the

free-stream aerodynamic noise to be controlled and measured and thus pro-

vided direct confirmation of the dominance of noise on transit ion.

Since the late 1960's, considerable research has been conducted

by NASA on the effects of aerodynamic noise on transi t ion [ i . e . , see

References (26), (28), and (29)]. Currently, a new type of supersonic

(M = 5) wind tunnel, designed to eliminate the turbulent boundary layer

on the tunnel wall and thus provide a test environment free of radiated

noise disturbances, is being constructed at NASA-Langley Research Center

as reported by Beckwtth (28). Extensive studies of the effects of wind

tunnel free-stream disturbances on transit ion at transonic and low super~

sonic speeds are also being conducted at the USAF AEDC 3 fac i l i t i es (52).

Transition measurements using di f ferent sizes of wind tunnels, similar

to those conducted by Pate (10,11), have also been carried out in the

USSR (53) and (54) and in several European countries (55 through 60).

All of these studies have supported the findings of Pate and Schueler

(10,11) and have provided additional and independent ver i f icat ion that

the noise that radiates from a turbulent boundary on the wall of a

supersonic-hypersonic wind tunnel can dominate the transit ion process on

smooth wall planar and sharp cone models at zero angle of attack.

3Arnold Engineering Development Center (AEDC), Air Force Systems Command (AFSC), Arnold Air Force Station, Tennessee.

31

A E DC-TR -77-107

Wind tunnel disturbances, particularly turbulence (~/U®) and ra-

diated aerodynamic noise (p/q=), primarily influence boundary-layer

transition. However, free-stream disturbances can also affect aerody-

namic data such as buffet onset and stabi l i ty of wind tunnel models as

recently discussed by Michel (61).

I I I . OBJECTIVE AND APPROACH

The objective of the present research is to extend the study of

the effects of radiated aerodynamic noise on the location of boundary-

layer transition on test models in supersonic-hypersonic wind tunnels.

Hollow-cylinder (planar model) and sharp-cone geometries were

selected as the transition models because they represent two basic con-

figurations used in the design of supersonic-hypersonic vehicles. These

configurations also allow leading-edge bluntness effects, surface rough-

ness, and surface pressure gradients to be eliminated as variables, and

at zero angle of attack the flow f ield is two-dimensional in nature.

Also, a considerable amount of transition data from various wind tunnels

on these configurations already existed. These configurations are also

used as wind tunnel calibration models.

To present as complete a picture as possible, the in i t ia l inves-

tigations that identified aerodynamic noise as a major disturbance source

are reviewed. The author's previous work showing that radiated noise

dominates the transition process in supersonic-hypersonic wind tunnels is

discussed in detail. New transition data obtained by the author on a

f la t plate at M® = 8 and (Re/ft)® ~ 15 x 106 and a lO-deg half-angle sharp

cone at M= ~ 7.5 (Re/ft)® ~ 30 x 106 are presented. Additionally, recent

32

AE DC-TR-77-107

research of aerodynamic noise effects on t rans i t ion conducted in the

USSR, the European countries, and by the NASA are reviewed and evaluated.

The aerodynamic-noise-transition correlations developed by the

author for sharp-leading-edge f l a t plate and sharp slender cones are re-

examined in l i gh t of this new data. A FORTRAN computer program has been

developed which allows the location of t rans i t ion on sharp-leading-edge

planar models ( f l a t plates and hollow cyl inders) and sharp slender cones

to be accurately predicted in a l l size wind tunnels for 3 ~ 15.

The variat ions of t ransi t ion Reynolds numbers with tunnel size,

unit Reynolds number, and Mach number are discussed in deta i l . Extensive

comparisons are made between the experimental data and results from the

FORTRAN computer program.

A detailed evaluation and comparison of planar and sharp cone

t rans i t ion Reynolds numbers over the Mach number range from 3 to 10 is

also made.

The possible ef fect of aerodynamic noise on the effectiveness of

spherical boundary-layer t r ips was investigated and these results are

presented.

The fol lowing supporting studies were also conducted and are in-

cluded: (a) a review of methods current ly used to predict t rans i t ion

locations, (b) correlations of t ransi t ion locations determined using

various detection methods, and (c) the influence of various v iscosi ty

laws on the calculat ion of Reynolds number.

33

AE DC-TR-77-107

CHAPTER I I

METHODS COMMONLY USED FOR PREDICTING BOUNDARY-LAYER TRANSITION

I. INTRODUCTION

Methods that have been used for predicting boundary-layer transi-

tion can be grouped into four general classifications:

I. Linear stability theory

2. Kinetic energy of turbulence approach

3. Semi-empirical methods and correlations based on physical

ideas

4. Data correlations based on observed trends in experimental

data.

Linear stability theory and the kinetic energy of turbulence ap-

proach offers perhaps the best possibility of eventually modeling and

predicting the onset of the boundary-layer transition, even though to

date they have not yet been very successful. However, these methods will

probably not be widely used {at least not for many years) by the design

engineer, wind tunnel experimentalists, or the aeronautical engineer in-

volved in trying to predict the occurrence of transition on his aircraft

or missile of interest. The linear stability and kinetic energy theories

are very sophisticated, both in the concepts involved and the numerical

and analytical mathematics required. Years of experience are required

in developing and using the complicated computer programs. Vehicle con-

figurations, particularly in the preliminary design stage, often change

faster than the theory can be modified and/or the geometry is too compli-

cated to be modeled.

34

AEDC-TR-77-107

Because of the absence of a readily available, easily used, and

successful theoretical transition model, researchers, from necessity,

have pursued the traditional path of attempting to develop data correla-

tions that allow reasonable estimates to be made. These correlations

have been and s t i l l are the basis on which most transition locations on

aircraft and missiles are estimated and wind tunnel test programs are

planned.

Reviews of smooth body transition prediction methods have been

given by Gazley (62), Deem et al. (53), Morkovin (4), Granville (64),

Kistler (65), Shamroth and McDonald (24), Tetervain (66), Hairstrom (67),

Smith and Bamberoni (68), Reshotko (69), and Harmer and Schmitt (70).

White (2) also gives a good review of many of the older well-known

methods and some of the more recent methods. Of course, the interested

person will want to read the sections on stability and transition by

Schlichting (I).

Since i t is not the purpose of this paper to present a critical

review of the many published papers and methods, only a few of the more

well-known techniques will be presented to illustrate types of methods,

the correlation parameters used, and some of the typical results obtained.

I I . LINEAR STABILITY THEORY

The s tab i l i t y of f lu id flow was f i r s t considered by Raleigh for

incompressible, inviscid flows (1,2). He found that an inflection point

in the velocity profile was a necessary requirement for instabilities to

occur. Prandtl extended linear stability theory to include the destabi-

lizing effects of the fluid viscosity (1,2). A detailed theory of

35

AEDC-TR-77-107

s tab i l i t y for incompressible, viscous flows was developed by Tollmien and

Schlichting (1). The confirmation of the existence of the Tollmien-

Schlichting type waves was provided by the classical experiments of

Schubauer and Skramstad (32). Extension of the l inear s tab i l i t y theory

to compressible flows was accomplished by Lees and t in (71). Experi-

mental ver i f icat ion of this theory was provided by Laufer and Vrebalovich

(72). Mach (13,73) extended l inear s tab i l i t y theory to higher Mach num-

bets, ident i f ied and studied the presence of higher modes 4 of distur-

bance, and showed that the destabil izing effects of viscosity begin to

decrease above M ~ 3. Kendall (14,74) provided experimental ver i f ica-

t ion for many of Mack's theoretical predictions. One part icular ly sig-

n i f icant finding of the Mack-Kendall research at JPL was the prediction

and experimental confimation that free-stream aerodynamic noise d is tur-

bance, regardless of frequency, are amplified by the laminar-boundary

layer and this amplif ication begins at the leading edge of a f l a t plate

and continues downstream unti l t ransi t ion occurs. Mack-Kendall showed

that a laminar boundary layer at M = 3 to 4 can amplify the free-stream

disturbance by an order of magnitude (73,74). The fact that a11 free-

stream disturbances are amplified and can be an order of magnitude higher

in the laminar-boundary layer than in the free stream is discussed later

with regard to surface microphone measurements.

The use of l inear s tab i l i t y theory to predict the onset of

boundary-layer transit ion as opposed to jus t predicting the onset of am-

p l i f i ca t ion of small disturbance waves has been studied by Smith (68),

4The Tollmien-Schlichting type were defined as the primary mode.

36

AEOC~R-77-107

Jaffe, Okamura, and Smith (15), Mack (13), and Reshotko (12). This ap-

proach is based on the observation by Michel (41) that the location of

transition occurred at a constant value (~ e g) of the amplification of

the Tollmien-Schlichting type sinusoidal disturbances. Presented in Fig-

ures II-1 and II-2 are results computed by Smith (68), Jaffe, Okamura,

and Smith (15), and Mack (13), respectively, and comparisons are made

with experimental data.

The theoretical results presented in Figures II-1 and II-2 have

limited application because of the following reasons. The theory of

Smith, et al. (15) and (68) is applicable only to incompressible, low

turbulence flows. The Subsonic data presented in Figures II-2 were ob-

tained in very low turbulence wind tunnels where the free-stream distur-

bance levels were negligible. Mack (13) made the assumptions that:

(a) the in i t ia l disturbance amplitude (Ao), at a reference Mach number

(M = 1.3), varied as the square of the Mach number ratio, (b) the dis-

turbances in the boundary layer are proportional in amplitude to the

free-stream radiated sound, and (c) the disturbance spectrum in the

boundary layer is f la t with respect to frequency and independent of axial

location.

I l l . KINETIC ENERGY OF TURBULENCE

More recently, kinetic energy of turbulence model equations, as

investigated by Shramroth and McDonald (24) have been used to investigate

transit ion as shown in Figure I I -3. This method considers a part icular

type of free-stream disturbance which is introduced into the laminar

boundary layer and follows the disturbance unti l t ransit ion occurs. One

37

lO 4 m O

Oo

m

m

m

m

lo3 _ ¢ D

e v ,

m

D

102 105

Figure I I - 1 .

o Flat Plates; Body of t See Table 1 Revolution; Airfoils )" Reference (68)

Michel's Line (41) [(Res) t - 2.9 (Ret ,0" 4]

O

Smith and Gamberoni (68) (Amplification Ratio -- e 9)

Ree)t_ P6 U6 8t P6

Ret-- P6 u~ x t

I I I I I I ~ i I I i i i 106 107 108

Re t, Measured

Correlation and prediction of incompressible flow transition Reynolds numbers [from Reference (68)].

0 :4 -n

,,,4

o ,~j

t~

" 0

u l

v

~0 Q

X

Data Represent Incompressible Flow over Flat Plates, Airfoils, and Bodies of Revolution as Specified in Ref. 15.

Calculated at Amplification Ratio = e I0

100 80 60 40

20

10 8 6 4

• Experimental Data (Flat Plate, = O), T w = TAw

- - Calculated

9

/ 8 /

/ 7

// ~~ 6 Ao = Ar (". /1"3) 2

S whelM > i . 3 4

/ 3 /C , 0

1 2 4 6 810 20 40 60 100 0 1 2 3 4 S 6 7 8

Re t x 10 -6 M®

a. Overall Correlation of Transit ion Data [from Reference (15)]

Figure I I - 2 .

b. Theoretical Calculations of Effect of Mach Number on Transition for Two A/A r and Two Assumptions About Initial Disturbance Amplitude [from Reference (13)]

Application of laminar stability theory to predicting boundary-layer transition.

m 0

~a

o

A EDC-TR-77-107

r ~

l - - q3

. O E

Z

" O

O e -

03 e ~

e - o

e -

m I - -

a .

10 7

~. Tw/T 0 = (l 6

} KET Theory

Tw/T o = O. 4

% %

106 I0 -2 2 5 I0 - I

Free- Stream Pressure Fluctuation, pip6

Effect of Free-Stream Fluctuating Pressure on Boundary-Layer Transition Location on Sharp Cones at M e = 5 [from Reference (24)]

2

Figure II-3.

E

Z t - O

10-3 ~o~ Turbulent

, Energy Loss = 1~ / / r - ~ \

~ T Theory

r).... Laminar Theory

10-4 106 2 5 1~ 2

Reynolds Num~r, Re x

b, Heat-Transfer Dis t r ibut ions

Comparison between measured and predicted t rans i t iona l heat transfer with transition triggered from pressure- velocity fluctuation [from Reference (24)].

40

AE DC-TR-77-107

objection to this approach, at least by the proponents of l inear sta-

b i l i t y theory, is the absence of a c r i t i ca l frequency in the theory and

only a requirement that the free-stream disturbance amplitude (or energy)

be specified.

This technique has been used with some success in predicting the

occurrence of transit ion and of relaminarization of turbulent boundary

layers subjected to strong favorable pressure gradients.

Of part icular significance to the present research is the fact

that pressure fluctuations (aerodynamic noise) as presented in this

thes is are considered by Shamroth and McDonald (24) as the primary source

of the free-stream disturbances which they incorporate into their kinetic

energy of turbulence formulation. Shamroth and McDonald (24) reported

that only a small amount (~1%) of acoustic energy absorption is required

to tr igger transit ion. Presented in Figure I I -3 are computed results of

Shamroth and McDonald (24) compared with experimental heat-transfer data.

I t is important to note that the acoustic energy loss (absorbed) must

be specified. Therefore, for the data presented in Figure. I I -3 i t is not

known a pr ior i which disturbance level should be used to predict the lo-

cation of transition.

IV. CORRELATIONS BASED ON PHYSICAL CONCEPTS

Several examples of this type prediction technique wi l l be

br ie f ly discussed:

1. Michel (41) was successful in correlating low turbulence

wind tunnel transit ion Reynolds number data obtained on

smooth surface wings having varying pressure gradients in

41

AEDC-TR~7-107

subsonic incompressible flow. Michel used the momentum

thickness Reynolds number (Re B) as the correlat ing parameter.

His correlat ion is shown in Figure I I - 1 , Granvil le (64) using

Michel's hypothesis that the t rans i t ion Reynolds number (Ret)

was related to a momentum thickness Reynolds number (Re e) i

[ just as there is a minimum cr i t ical Reynolds number (Recr)

s tabi l i ty theory] successfully correlated low speed flows us-

ing the parameter (Re t - Recr) with Re B. (Below Recr, al l

small disturbances are damped).

2. van Driest, et al. (39) used Liepman's hypothesis (75) that

transition wi l l occur at a cr i t ical Reynolds number (Recr)

that is equal to the ratio of the turbulent shear stress

{Reynolds stress) p ~ a n d the viscous stress ~ du/dy, i .e . ,

Recr = p~'~-~/[~(du/dy)]. By evaluating the Reynolds stress

using Prandtl 's mixing length hypothesis and using the

Pohlhausen veloci ty p ro f i l e to determine du/dy, van Driest

developed a semi-empirical equation for t rans i t ion Reynolds

number in incompressible flow that accounts for the ef fect of

free-stream turbulence through the ef fect of the pressure

f luctuat ion on the pressure gradient and consequently the

veloci ty p ro f i l e through the Pohlhausen shape factor. Pre-

sented in Figure I I -4 are some of the classical subsonic data

plotted versus free-stream vo r t i c i t y disturbance (or veloci ty

f luc tuat ion) . Included in Figure I I -4 is van Driest 's semi-

empirical equation with the constants adjusted to match the

older data. Note that the more recent data of Spangler and

42

AEDC-TR-77-107

pxiO 6

4

G

sym [ ]

%7

0

0

Spangler, Wells Boltz, Kenyon, and Allen Dryden Schubauer and Skramstad Hail and Hislop

3

(Ret)

1

0 1 0

Theory of Van Driest and Blumer (39)

1690 = I + 19. 6(Ret) I/2 (~/U 0 )2 i (Rp~)i/2

Theory of Van Driest and Blumer As Modified by Wells (76)

2220 = 1 + 38.2(Rex) 1/2 ~AJ6) 2 (Rex) I/2

°oO~o

|

1 ~'/U 6 x 100

, t ~ 2 3

Figure II-4. Data on the effect of free-stream turbulence on boundary- layer transition, compared with data of other investigators and theory of van Driest and Blumer [from References (39) and (76)].

43

AEDC~R-77-107

Wells (40) are much higher than the older Schubauer-Skramstad

data (32). Wells (76) developed a new expression using the

new data, and this equation is also shown in Figure I I -4.

3. Benek and High (77) followed the approach used by van Driest

et al. and successfully developed a semi-empirical expres-

sion for compressible transonic and low supersonic flow that

successfully predicts transit ion on sharp slender cones.

Typical results are shown in Figure I I -5 .

4. The laminar boundary-layer prof i le in a three~dimensional

viscous flow such as a swept wing or cylinder wi l l have a

twisted prof i le that can be resolved into tangential (u) and

normal (w) velocity components as i l lust rated in Figure I I -6 .

Owen and Randall (33) found that the instantaneous jump of

transit ion from the t ra i l ing edge to near the leading edge of

subsonic swept wings could be correlated with a c r i t i ca l

crossflow Reynolds number. This phenomenon is i l lust rated in

Figure I I -7. This c r i t i ca l crossflow Reynolds number is a

function of the maximum crossflow velocity (normal component)

and a thickness defined as nine-tenths the boundary-layer

thickness as shown in Figure I I -6 . This type of t ransi t ion

process can be related physically to the ins tab i l i t y of the

boundary layer as a result of the inf lect ion point in the

crossflow prof i le.

The crossflow concept was investigated i n i t i a l l y at subsonic

speeds by 0wen and Randall (33) and at supersonic conditions by Chapman

(34) using swept cylinders and by Pate (18) using supersonic swept wings.

44

A E D C - T R - 7 7 - 1 0 7

® 0 . 6

-. 0.5 , I J X

~ O.4 0

"G 0.3

L. I-.-

o 0.2 e--

t , -

l l J

1.0 , , / 0.9 AEDC 4T 0.8 M®: 0 . 3 - 1.3 -- t / / 0,7 --(Re/f t )® [] 1.5 - 4.3 x 10 6 -

- - z [] Model Length I I 8 "

/ ~ L i n e of Perfect Agreement

0.1 /

0.1 0.2 0.3 0.4 0.50.6 0.8 1,0

Beginning of Transition, Xt/z Predicted

a. Comparison of Predicted and Measured Transition Locations [from Reference (77)]

I I I I

(Re/ft)® x 10 -6

o 2.0 - - - -

o 3,0 - -~

6.O I

= o 5.0 0 ,-4

"~ ~ 4.0 c

I .

~- C ~- ~ 3.0 0 .Q

E

C "~. ~ t - . . ~

q . .

"6 2.0 C >~

1.5

Dnset cb.

Predic d Onset

Solid Symbols - Walls Taped

0.4 0,50.6 0.8 1.0 1,5 2.0 3.0 4.0

Acoustic Level, aCp, percent

b. T rans i t i on Reynolds Number as a Funct ion o f Acoust ic Level in the AEDC-PWT 16T. Comparison wi th P red ic t i on [from Reference (77) ]

Figure I I - 5 . Comparison; o f Benek-High method f o r p red i c t i ng t r a n s i t i o n wi th experimental sharp cone data, M ~ 0 .4 -1 .3 .

45

AEDC-TR-77-107

Local Crossflow Reynolds Number

X = (pe) (Wmax) (0. 9)(6)

Pe

100

Crossflow-Domi hated Transition Criteria

X < 100.* Laminar Boundary Layer < 3¢ < 200.* Vortex Formation and Transitional = = Boundary Layer

X > 200-* Turbulent Boundary Layer

Y

Twisted Prof i le-~ Plane Normal to the Outer Flow / Stream Line, i.e., the Crossfiow Plane

Plane Tangential to Crossflow Component, w Outer Flow Streamline [. Profile Injection Point

Tangential ~ Wmax Component, u - - ~ ~ ,,- z

Body Surface

X

Figure I I -6. Three-dimensional boundary-layer velocity pr,ofile and cross-flow Reynolds number cr i ter ia .

46

A E DC-TR -77-107

x t

Region # I

Wing Profile Region #2 . / F Usual Transition Trend

" ~ . 1 ' xt~'Relin.) n ' l

I n __.<l _

X max -- Critical = 175

Region # 1

(Re/in.) W

Figure II-7. Critical cross-flow influence on the boundary-layer transition profile.

4'7

A EDC-TR-77-107

More recently, Adams (35) extended this concept to supersonic sharp cones

at incidence. Adams, et al. (36) explained high heating rates on the

NASA space shuttle at incidence using the crossflow concept.

This technique is classified as semi-empirical since i t requires

a theoretical solution of the three-dimensional laminar boundary, and

transition is then predicted to occur when the crossflow Reynolds (x)

number reaches a value of %150 to 175 as f i r s t reported by Owen and

Randall. This empirical constant appears to hold for subsonic and super-

sonic flow regimes and for all types of geometries as shown by the cor-

relation presented in Figure II-8.

V. DATA CORRELATIONS

By far the largest effort to provide methods for predicting

boundary-layer transition has been devoted to conducting experimental

studies and attempting to develop useful correlations based on the ob-

served trends and variations in transition with certain parameters and

vari abl es.

1.

2.

These correlat ions can be divided into two general areas:

Tripped flows

Smooth body flows.

Tripped Flows

Since surface roughness is present, more or less, on a l l vehicles,

its effect on the location of transition has received much attention at

both subsonic and supersonic speeds. Also the necessity for simulating

fully developed turbulent flow on wind tunnel models has prompted many

trip-effectiveness studies, If one knows the local flow conditions,

48

4:=

;<max Computed at Experi mentally

sym BI

O

A

Source Reference (33) Reference (34) Reference (18)

Configuration Subsonic Swept Wings Yawed Cyli nders Supersonic Swept Wing

Method of Detecting X t

Flow Visualization Heat- Transfer Surface Pitot Probe

Determi ned Transition • Reference (36) Space Shuttle (M m = 8) Heat Transfer Location (a = 30 and 50 deg)

Flow Visualization o Reference (35) Sharp Cone (Moo = 7. 4) (a = 5 deg) 300~ .~ Turbulent Flow

z I1~ . . . . . - ~ - Xmax = 175

~'~ 100 I ~ ~ t Laminar Flow

o 0 2 4 6 8 10

Free-Stream Mach Number, Moo

Figure II-8. Correlation of transition and cross-flow Reynolds number.

m O

~g

o

A E DC-TR-77-107

trip geometry, and certain boundary-layer properties (i.e., 6, ~*) at

the trip location, then, in general, reasonable estimates of the location

of transition can be made using existing methods. Results from three of

these methods are briefly discussed to illustrate the correlation param-

eters used.

At subsonic speeds, Dryden (78) successfully correlated the ef-

fectiveness of two-dimensional elements {wires) and cylindrical roughness

elements in promoting early boundary-layer transition. This correlation

is shown in Figure ll-g.

Van Driest et al. ~16,17,79) conducted a systematic experimental

and analytical program and successfully correlated the location of the

"effective" transition location for spherical roughness heights, and the

effects of roughness in conjunction with wall cooling and Mach number

{0 < M® < 4) on flat plates, sharp cones, and hemispherical blunt bodies.

The trip correlation developed by Potter and Whitfield (37) for

flat plates and sharp cones is, to this author's knowledge, the most

comprehensive of any published to date and incorporates the effects of

trip size, wall cooling, and local Mach number (0 < M~ < I0). This cor-

relation also predicts the trip size required to move transition from

its smooth body location to the trip location or any point in between.

A portion of the research presented in this dissertation is di-

rected toward determining if the radiated noise disturbance present in

the free stream of supersonic wind tunnels and the resulting large varia-

tion in smooth body transition on flat plates and cones with tunnel size

invalidates the correlations of van Driest and Potter-Whitfield. These

results are presented in Appendix E.

50

A E D C - T R - 7 7 - 1 0 7

k = Roughness Height

6 ~( [] Boundary-Layer Displacement Thickness at x k Location

Ret -- Tripped Transition Reynolds Number

Reo = Smooth Body Transition Reynolds Number

Ret

Reo

1.0

0.8

0.6

O.4

0.2

0

&

O~OQ

[]0

A A

8

O

A

I ! I I i

0.2 0.4 0.6 0.8 1.o k/6

• Tani o Tani [] Scherbarth ,, Sti.iper

Figure I I-9. Ratio of transition Reynolds number of rough plate to that of smooth plate and ratio of height of roughness element to boundary-layer displacement thickness at element, single cylindrical (circle and square symbols) and f la t - strip elements (triangular symbols) [from Reference (78)].

51

AEDC~R-77-107

Other extensive experimental studies using di f ferent trip geom-

etries at hypersonic conditions have been performed and reported in

Reference (20).

The problem of roughness effects on transit ion is always a cur-

rent problem 5 as i l lust rated by recent wind tunnel tests conducted to

establish the effect ive roughness of the thermal insulating t i les on the

space shuttle orbi ter (80).

Smooth Body Flows

In correlations of transition Reynolds numbers on smooth wall,

two-dimensional models {flat plates or hollow cylinders) at supersonic

speeds the effects of Hach number, leading-edge bluntness, wall cooling,

unit Reynolds number, and leading-edge sweep have been considered. The

studies by Deem et al. (63) were perhaps the most extensive in scope of

these types of correlations.

Deem et al. (63) consideredall five of the above parameters and

variables, and their research included both extensive experimental and

analytical efforts. Their objective was to place in the hands of the

design and test engineer a tool in the form of an analytical expression

that would give reasonable prediction of the location of transition on a

flat plate at zero incidence and at supersonic-hypersonic Hach numbers.

5Aircraft companies have very tight fabrication tolerances for rivet heads, joints, etc. on aircraft to ensure maximum lengths of laminar flow is maintained.

52

A E DC-TR-77-107

Their correlation did not include the effects of free-stream dis-

turbance 6 and consequently often provides only qualitative predictions.

Nevertheless, there is s t i l l considerable interest in these types of cor-

relations as evidenced by the report by Hopkins and J i l l i e (22) and

Hairstrom (67). In References (22) and (67) the analytical expressions

developed by Deem et al. have been presented in graphical form for

rapidly estimating the transition location for f lat-plate wind tunnel

models with supersonic leading edges at zero angle of attack. Deem et al.

also compared the estimated Re t for each data point used in developing

their correlation, and the result is shown in Figure II-lO. The standard

deviation was 33%.

Beckwith and Bertram (81) developed supersonic-hypersonic transi-

tion correlations using boundary-layer parameters such as Res, and local

flow conditions M e and h e and the wall parameter h w. Their correlations

were developed using a digital computer to define functional relation-

ships and corresponding coefficients that produced the smallest standard

deviation (6x). An example of one correlation developed for wind tunnel

data is presented in Figure II-11. Correlations for bal l ist ic range and

free-f l ight data were also developed and published in Reference (81).

)(,,)'] = r aij MJ e Cl)

6In conventional supersonic wind tunnels, the transition location is dominated by aerodynamic noise and can vary as much as a factor of three between small {l-ft) and large (16-ft) wind tunnels as discussed in Chapters Vll through Xl.

53

AE DC-T R-77-107

I,..

E

108

lo 7

p.,.

lO6

See Table 4 for Identification of Symbols, Reference (63)

8 f 7

~ e e ®

G

®

:#

ID A

13

Ik 291 Data Points Overall Standard Deviation, o = 33%

1051 , I , , , , I , , , i , , , , I

10 6 107 Rt calculated

l i i I

Figure II-lO. Comparison of measured and predicted transition Reynolds numbers [from Reference (63)].

54

AEDC-TR-77-107

N

v , . . , . .

Cene~a, Eq. r2: r. ~0 aij e/t he) i=O j j

For Wind Tunnel Data:

F2= 1.6002+ O. 14207 Me+ O. 27641 - ( hw ~ - O. 032828 M e ( .w he / \ he )

- o. ~888 • o. ® ~ Me (, -Lw/~ he/ 5,000

I, O,gG

100

10

O

Wind Tunnel Data ~x = -+0. 150

(D

x t - Xtmea n 0 o Xtmean

= / , . ~ 1 0 ° x - 1) 2

=0.41, o=+0.15 = 0. 29, o = -0. 15

I I 2 3 4

F2

Figure II-11. Cor re la t i on o f sharp cone t r a n s i t i o n Reynolds numbers a t supersonic-hypersonic cond i t ions and zero angle o f a t tack [ f rom Reference (81 ) ] .

55

AE DC-TR-77-107

For wind tunnel sharp-cone transition data, Beckwith and Bertram

determined the F 2 parameter to be

F2 = 1.6002 +0.14207 Me+ 0.27641(h'~e-e 1

- 0.032828 M e ~ee " 0.042888 \Fee / (2)

+ 0.0054027 Me\he /

The location of transition can be determined using the F 2 param-

eter in conjunction with Eq. (3) as determined from Figure II-11.

loglo

where A and B are constants.

and

-R6*,t I =

From Reference (81) for sharp cones

n = 0.225

A = 0.11168

B = 0.94935

(3)

Re6,,t = Reynolds number based on the boundary-layer displacement

thickness at the transition location, x t .

R D = Reynolds number based on model base diameter.

From Figure II-11 and Eqs. ( I ) , (2), and (3), i t is seen that the

transition correlation becomes quite complicated. The results presented

in Figure II-4 and the additional correlations presented in Reference (81)

are the most comprehensive published to date and represent several years

of effort by researchers at the NASA Langley Research Center. The

56

A E DC-TR-77.107

standard deviation for wind tunnel sharp-cone transition data is between

29% and 41% as illustrated in Figure II-II. These correlations can only

be judged to be fair in their ability to provide reasonable predictions

of transition Reynolds numbers.

Recently, Kipp and Masek {82) and Fehnnan and Masek {8) attempted

to correlate high Rach number transition Reynolds numbers measured on the

windward centerline of the NASA orbiter at angle of attack using Re e, Me,

and the local unit Reynolds number (Ree/ft) as the correlating parameters.

The correlation from Reference (8) is shown in Figure II-12, and the

scatter in the correlation of the data is seen to be quite large.

Sumary

In concluding this section, it seems that past history indicates

that the transition correlations and prediction methods for smooth bodies

that are based on physical concepts seems to withstand the test of time

and give more acceptable results than correlations based on observing

trends and variations in experimental data.

57

A EDC-TR-77-107

a, de 9 Comment • 40 Smooth Body Transition from

Shuttle Model Tested in r AEDC-VKF Tunnel F at Moo -- 10

30 E [Reference (g)] I - Shuttle Shapes /,1

25 I,z- Data from Three Facilities, / IZ Three Configurations / / I /--Least Squares

20~- [Reference(8)]-~//-- y F i t o,, [Reference (8)]

0 , , , I I I I I J I I I I I 0 10 20 30 40 50 60 70

Local Angle of Attack, deg

Figure II-12. Correlation of space shuttle wind surface centerline transition Reynolds number data [from Reference (8)].

58

AE DC-TR-77-107

CHAPTER I I I

RADIATED AERODYNAMIC NOISE IN SUPERSONIC WIND TUNNELS

I. INTRODUCTION

In Chapter I , the various types of test section free-stream dis-

turbances present in wind tunnels were discussed. The origins of these

disturbances (both steady and unsteady) were identi f ied along with their

relative intensity and their effect, or probable effect, on boundary-

layer transit ion.

This chapter is devoted exclusively to discussing the dominant

source of disturbance present in well-designed supersonic wind tunnels,

i .e. , radiated aerodynamic noise from the tunnel wall turbulent boundary

layer. The major literature references dealing with wind tunnel gen-

erated aerodynamic noise are reviewed and the significant contributions

from these publications are discussed. The mechanism that generates the

aerodynamic noise, the intensity and spectra of these unsteady isen-

tropic pressure waves, and the wind tunnel parameters that affect the

radiated pressure rms value (Prms) are identified. Emphasis is placed

primarily on presenting and discussing experimental pressure fluctuating

intensity and spectra data obtained in the tunnel free-stream using the

hot-wire anemometer. The theory (83,84,85) is not presented here; how-

ever, analytical expressions as required in discussing the experimental

data are presented. Extensive discussions of the application of the

technique to measure aerodynamic noise has been presented in detail in

References (38) and (85) thrnugh (91).

59

A E O C-TR-77-107

I I . ORIGINS OF DISTURBANCE MODES

Kovasznay (43) identified three major types of disturbance fields

in compressible flow wind tunnels: (a) vorticity (velocity fluctuations),

{b) entropy f luctuat ions {temperature spott iness), and (c) sound (pres-

sure f luctuat ions). Start ing with the Navier-Stokes equation for a f l a t

plate {three momentum equations) plus the energy equation, the cont inui ty

equation, and the perfect gas equation of state, Kovasznay introduced the

small perturbation concept, i . e . , p = p + P' , T = T + T' , p = ~ + p ' ,

into the equations of motion. Dropping higher order terms, he obtained

a set of l inear , part ia l d i f fe rent ia l equations. By taking the curl of

the momentum equation, Kovasznay obtained a separate, second order par-

t i a l differential equation for vorticity (= = curl V) that was un~

coupled from pressure and entropy and which was similar to the classical

heat equation. By combining the continuity equation and the divergence

of the momentum equation, he then obtained an uncoupled second order par-

tial differential equation for pressure. This equation was similar to

the wave equation, and consequently Kovasznay defined the pressure that

obeyed this equation as a sound wave. Using further manipulation, he

developed a second order, partial differential equation for entropy that

was also similar to the classical heat conduction equation but uncoupled

from pressure and vorticity. Since the resulting equations were linear,

then the different modes did not interact {uncoupled); however, if

strong gradients exist such as a shock wave then small perturbation

theory no longer is valid, the resulting equations are nonlinear, and

there is a coupling between the three modes.

60

AEDC-TR -77-107

Kovasznay (43) then showed that the hot-wire anemometer could be

operated in a supersonic flow and the three disturbance modes (vo r t i c i t y ,

entropy, and sound) could be represented by the rms output of a hot wire

operated at d i f ferent temperatures. Figure I I I -1 i l lust rates the char-

acterist ics exhibited by these three modes.

Kovasznay conducted hot-wire experiments and showed that al l

three disturbances could be present in wind tunnels. The presence of

entropy fluctuations (temperature spottiness) was confirmed from st i l l ing

chamber measurements and free-stream measurements using various types of

st i l l ing chamber arrangements and tunnel air heating apparatus. Free-

stream hot-wire data produced a mode diagram similar to Figure I I I - l c .

A fluctuating pressure field (sound waves) was generated using a weak

shock emanating from the leading edge of a sharp f la t plate. The mode

diagram of a hot wire placed in an oscillating flow field generated by a

weak wave produced a mode diagram similar to Figure I I I - la . Thus J

Kovasznay developed the analytical models and produced some experimental

data at M® = 1.7 to support his three-mode theory.

In 1955, Laufer and Marte (46) presented results of a systematic

investigation of factors affecting the location of transition on adiabatic

cones and f la t plates at M between 1.5 to 4.5. They investigated var-

ious methods for detecting transition and predicting the effects of the

st i l l ing chamber turbulence level, surface roughness, Mach number, and

unit Reynolds number on transition. Following the earlier work of

Kovasznay (43) Laufer and Marte showed that even though significant

levels of st i l l ing chamber turbulence could be present, above about

M = 2.5 the effects on cone transition Reynolds numbers were negligible

6]

AE DC-TR o77-107

a. Sound (from Stationery Source)

b. Turbulence (vorticity Mode)

~J (hA,! I ~

J - - c { (M).- ,-

1 1+ Y) AA 2

Sensitivity Ratio, Ae/mlAeT

Figure I I I - l .

c. Temperature Spottiness (Entropy Mode) Comparison of fluctuation diagram for three modes [from Reference (43)].

62

AEDC-TR-77-107

(as discussed in Chapter I I ) . They also speculated that the pressure

disturbance turbulence f ie ld generated by the tunnel wall turbulent

boundary might influence transi t ion. They commented on operating the

JPL supersonic tunnel with a laminar and turbulent boundary layer on the

tunnel walls to check this possib i l i ty , but the tunnel could not be op-

erated at a low enough pressure to produce the laminar flow condition.

As an alternate approach, they tr ied shielding a hollow-cylinder t ransi-

t ion model from the radiated noise by using a larger protective hollow-

cylinder shield model. The idea was to isolate the transit ion model

from the turbulence f ie ld emanating from the tunnel walls. However, dis-

turbances generated by the larger outer shield model impinged on the

inner transi t ion model and caused the transit ion point to move forward;

thus the experiments were invalidated. However, Laufer and Marte were

the f i r s t to focus attention d i rect ly on radiated aerodynamic noise as a

possible source of significance disturbances in supersonic wind tunnels.

They further speculated that the effects of tunnel pressure level ( i . e . ,

unit Reynolds number) on transit ion Reynolds numbers might be explained

as an effect caused by acoustic disturbances.

Horkovin in 1957 (44) discussed the possible sources of free-

stream disturbance in supersonic wind tunnels. Following Kovasznay (43)

he discussed the sources that could produce free-stream turbulence:

(1) vor t i c i t y f luctuations, (2) entropy f luctuations, and (3) sound waves.

He further classif ied sound waves as; (1) radiation from the wall turbu~

lent boundary layer, (2) shimmering Hach waves from wall roughness or

waviness, {3) wall vibrations, and (4) d i f f ract ion and scattering of

otherwise steady pressure gradients. Horkovin further stated that any

63

A EDC-TR -77-107

of the three principle modes or any of the four specific sound sources

could promote early transition i f the disturbance levels were high

enough. In conclusion, Morkovin stated that transition studies must be

conducted with care, all experimental transition data evaluated with

care, and all inferences drawn with caution.

Morkovin in 1959 (45) commented further on wind tunnel distur-

bances. He discussed ways to effectively reduce vorticity fluctuations

and entropy fluctuations by proper st i l l ing chamber design. However,

he stated that the sound from the turbulent boundary layer would proba-

bly be the major disturbance. Morkovin stated that this type of dis-

turbance was very d i f f icu l t to measure or to predict theoretically.

Furthermore he stated that seemingly l i t t l e could be done to appreciably

reduce its intensity level.

I I I . EXPERIMENTAL CONFIRMATION

Laufer (38) reported in 1959 on an investigation using a hot

wire to study free-stream disturbances in supersonic wind tunnels. The

experiments were conducted in connection with boundary-layer stability

experiments and the knowledge that Tollmien-Schlichting oscillations

could not be detected i f free-stream disturbance levels were high (32).

Starting with the basic hot-wire equation

e" = Ae T T~/T T - Ae m m'/~ (4)

the time averaged, mean-square of the measured voltage fluctuation (e 2)

can be written as

( ; ) 2 _ ; 2

(AeT)2 AeT 2 T - m T T + r2 (m.)2 (4a)

64

AE DC-TR-77-107

where

Ae m (m')(T~) - Rm T =

Ae T and Ae m are sensit ivity coefficients that are determined by mean flow

conditions and the mean temperature of the hot wire (38).

The values of (T~)2 = ~ 2 (I) 2 (T T) , ~..., = and RmT can be calcu-

when (e') 2 is measured for three different values of r ( i . e . , three d i f -

ferent mean wire temperatures. Typical results measured by Laufer are

presented in Figure I I I -2 .

Laufer pointed out the start l ing fact that fluctuations at the

high Mach numbers were 50 times greater than fluctuations measured in a

low turbulence subsonic wind tunnel. Laufer also found that the correla-

tion coefficient (RmT) had a value of - I (within measurement accuracy)

for al l conditions. This means that the mess flow and total temperature

fluctuations are perfectly anticorrelated. Laufer then pointed out that

no further information could be obtained directly from the hot-wire mea-

surements; however, he showed analytically that i f i t were assumed that

the fluctuations were pure vort ic i ty (velocity fluctuations) then i t

could be shown that RmT = +I; but RmT = +i contradicts the experimental

data. Consequently, vort ic i ty as the cause was eliminated. Laufer then

assumed pure entropy fluctuations (temperature fluctuations) to exist and

he obtained the correct slope. However, the computed value of r at

e/Ae T = 0 was not consistent with the measurements. As shown by Kovasznay

(43) at e/Ae T = 0 then r = -~. For M® = 2.2, one has (43) r = -~ =

- (1 + Y " I M2)-I = -0.508 and for M = 5, r = -a = -0.167. From in- 2 ®

spection of Figure I I I -2 , one sees that the experimental data does not

65

AE DC-TR-77-107

24 x 10 -3

2o !" ~ Fairing of E x p . / I

0 - - 0 0.4 0.8 1.2 1.6 2.0 2.4 Aem/Ae T

a. Mode Diagrams for Free-Stream Radiated Noise Fluctuations [from Reference (38)]

10-3[ = ] 16x ~ M~--2.8

12~ Free Stream Plus//" I = ~- Mach W a v e ~ I

4

O0 0.2 0.4 0.6 0.8 1.0 Aem/AeT

b. Mode Diagram for a Fluctuating Mach Wave Superimposed on Free-Stream Fluctuations [from Reference (38)]

Figure I I I -2. Mode diagrams.

66

A E D C-TR -77 -107

agree with these values. Thus, Laufer ruled out entropy fluctuations as

the cause of the measured hot-wire f luctuations. Laufer also argued on

physical grounds that vor t i c i t y and entropy could be ruled out. Since no

temperature fluctuations had been measured in the s t i l l i n g chamber and

since temperature fluctuations are convected along streamlines, then i f

they are negligible in the s t i l l i n g chamber they wi l l be negligible in

the test section. He also argued that the large contraction rat io in the

JPL tunnel (40 at H = 1.6 and 1,500 at H = 5) diminished the s t i l l i n g

chamber velocity fluctuations to such a low value that they could not be

the source of the disturbance. Following Kovasznay (43) Laufer then

postulated that the only other simple f luctuating f ie ld would be a pure

sound f ie ld in which the isentropic relationships between the f luctuating

quantities hold. Inserting the small disturbance isentropic relationships

£ = y p ' _ ~ T" m_~'=u__:_'+!p_:. T~ ~(M)(y 1) FP- '+M2F]L J into the hot-wire equation (Eq. 4), Laufer (38) showed that the following

root-mean-square voltage equation could be obtained when the condition

Rm T = -1 was applied.

e =(M)(y - 1) M 2 u ~ Aem AeT ~ yF YP

where

(1 X._~. ) / + - - M 2\-1 ~ ~ = and_P__= p _ 1 T y F W y - 1T

Equation (4b) is a l inear equation and is consistent with the hot-wire

data presented in Figure I I I -2a. The f luctuating pressure (~/p--) and ve-

loc i ty (~/~-) ratios can be determined from Eq. (4b) by solving two equa-

tions for two unknowns (p/~and ~/-u-)and by realizing the f i r s t term is

67

AEDC-TR-77-107

the ordinate intercept and the coefficient of Aem/Ae T is the slope of the

faired data presented in Figure III-2a.

Laufer, therefore, concluded that the measured free-stream dis-

turbance was a fluctuating isentropic pressure field that emanated from

Laufer also presented other evidence the tunnel wall turbulent boundary.

to confirm his hypothesis.

i. A flat-plate shield that protected the hot wire from one

tunnel wall caused a 25% drop in the mean-square voltage

output.

2. He showed analytically, as did Kovasznay (43), that a fluc-

tuating Mach wave {weak shock) would produce a straight line

on the mode diagram and pass through the origin as illustrated

in Figure III-i, page 46. By placing tape on the tunnel wall

at exactly the right location, he showed that at r = 0 the

measured value of e/Ae T equaled the no shock data and was a

linear line but had a steeper slope. Thus he ruled out

shimmering Mach waves as a possible source.

3. He also produced free-flight Schlieren photographs showing a

sound field emanating from the turbulent boundary layer on a

model.

Based on the results from his very thorough experimental investi-

gation and supporting analytical analysis, Laufer concluded that the

source of free-stream disturbances was the sound field {aerodynamic

noise) emanating from the tunnel wall turbulent boundary layer. Laufer

pointed out, however, that direct measurements of the sound field were

68

AEDC-TR-77-107

not yet available. Laufer further cautioned that stability and transi-

tion studies in supersonic wind tunnels would be handicapped by the

presence of the sound field.

Vrebalovich (92) commented on Morkovin's paper on free-stream

disturbances (45) and stated that hot-wire measurements made in the test

section of the JPL tunnels showed that when the wall boundary-layer was

turbulent, the free-stream mass-flow fluctuations not only increased

with Hach number but were higher at the lower unit Reynolds number.

Vrebalovich further stated that experiments (early 1960's) in the JPL

12-in. supersonic tunnel with either laminar, transitional, or fully tur-

bulent boundary-layer flow on the tunnel wall produced the following re-

sults: (a) free-stream pressure fluctuation levels were smallest when

the boundary layer was laminar and (b) tripping the boundary layer intro-

duced less fluctuations in the free stream than when transition from

laminar to turbulent flow occurred naturally between the nozzle throat

and test section. These experiments in which the only change was in the

nature of the tunnel wall boundary layer showed that a dominant source of

free-stream disturbances at the higher Mach numbers was the aerodynamic

sound radiated from the wall boundary layers.

During continuing studies conducted in the JPL wind tunnels,

aerodynamic noise radiated by supersonic turbulent boundary layers was

reported in January 1961 (93). In Reference (93) i t was pointed out that

previous JPL studies (38) had shown that: (a) the amplitude of pressure

fluctuations increased with Mach number, (b) the intensity was uniform

in the flow field, and (c) the pressure field manifested a certain di-

rectionality. Reference (93) presented results of investigations de-

signed to establish i f a correlation between the measured free-stream

69

A E DC-TR-77-107

pressure f luctuation and certain boundary-layer characteristics could be

found. Figure I I I -3 presents the results of this e f fo r t . Figure I l l - 3

is of part icular interest since i t was developed following the argument

of Liepmann that pressure fluctuations are produced by displacement-

thickness f luctuations.

The correiation shown in Figure I [ [ - 3 is of special interest to

the present study since in Chapter IX an aerodynamic noise transit ion

Raynolds number correlation wi l l be developed and the displacement thick-

ness (6") appears as one of the correlating parameters.

Phi l l ips (94) proposed a theory to describe the generation of

sound by turbulence at high ~ch numbers. Laufer (86) in commenting on

Phi l l ips ' theory, noted that i t is based on the premise that the sound-

. generating mechanism consists of a moving, spacially random, virtuaZly

wavy wall formed by an eddy pattern that is convected supersonically with

respect to the free-stream and is consistent with the principal features

of the sound f ie ld found in experiments. Using this view, Laufer de-

rived an expression for the pressure f luctuation intensity which is

shown to be a function of the mean sk in- f r ic t ion coeff ic ient , the wall

boundary-layer thickness, lengths which scale with the boundary-layer

thickness, convection speed, angle of the radiated disturbance, and

free-stream Mach number. This theory was found to be in partial agree-

ment with experimental data at Mach numbers from 1.5 to 3.5 and con-

siderably below experimental data at Hach 5.

From Reference (86)

p =._y._ u L_ . r U U c M

V T

(5)

70

A E DC-T R-77-107

O. 016

O. 014

O. 012

O. 010

~"/~ o.oo8

0.006

0.004

O. 002

0 0

Figure I I I - 3 .

Sym Am • 5.0 o 4.5 o 4.0 zx 3.5 o 3.0 v 2.2 Y

Y f

J 0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

8~,in.

Pressure f luc tuat ion from a supersonic turbulent boundary layer [from Reference (93)].

7]

AEDC-TR-77-107

where

Uc U 2 ~ = U - ~ 0.5; T = CF/2U ; T = time constant; U c convection veloci ty

CSa)

1 cos e = [ , 1 - ~-~. Uc ] (5b)

An important point to note from Eq. (5) is that the mean boundaw-

l ~ e r characterist ics Cf and 6 and certain lengths appear as parameters

in the free-stream pressure f luctuat ion equation. This fact is relevant

to the analysis presented in Chapter IX.

Kis t ler and Chen (95) reported on pressure f luctuat ions that

were made under a turbulent boundary layer on the sidewalls of the JPL

18- ~ 20-in. supersonic wind tunnel at M® = 1.3 to 5.0. ~ o findings

of particular importance weR:

1. The normalized pressure fluctuation (P/Tw) on the surface of

a f la t plate was found to cor~late with Re6*, and

2. The tunnel wall root-~an-square (~) of the pressure fluc-

tuation was found to be proportional to the tunnel wall tur-

bulent skin fr ict ion as shown in Figure I I I -4.

Laufer (87) discussed the radiation f ield generated ~ a super-

sonic turbulent boundaw layer at Mach numbers from 1.5 to 5 and com-

pared the hot-wire results with those obtained by Kistler and Chen (93)

using microphones positioned in the tunnel wall. In each of these tests,

the wall and free-stream pressure fluctuations were found to scale with

the mean wall shear for all Mach numbers as shown in Figure I I I -5 , which

was taken from ~ferences (87)and (96). In addition, i t was noted that

72

A E DC-TR-77-107

6

5

4

3 ~ 3

2

"~ Measured on Sidewall of JPL Wind Tunnel Tw Local Wall Shear

0

- 0 °

Data from Reference 95

0

0

0

m

[ I I [ [ O0 I 2 3 4 5

NtG0

Figure I I I -4. Correlation of pressure fluctuation levels.

73

A E D C - T R - 7 7 - 1 0 7

... 6

4 ~3

, . J

L_

, , , 2 I=.

O -

(1o

sym []

O

Wall Pressure Fluctuation (Kistler and Chen, 1963) [ Reference (95)]

Radiated Pressure (Laufer 1964) [Reference (87)] Theoretical Prediction (Mach Wave Strength)

(FFOWCS Williams and Niaidanik, 1965) [Reference (96)]

[]

[]

0 @0

C] []

,,@

I~ r C

[] r'l []

II

0 1 2 3 4 5

Free-Stream Mach Number, Mo)

1.2~

0.8 > L_

O.l ~.® a .

i m

0 ~

Figure I I I -5 . Comparison of measured and predicted radiated pressure levels [from Reference (96)].

74

A E DC-TR-77-107

the intensity of the radiated pressure fluctuations was an order of

magnitude less than the pressure fluctuations on the wall. By operating

the JPL 18- x 20-in. supersonic tunnel at low pressures, the boundary

layer was maintained laminar on al l four walls. Then by tripping the

boundary layer on one wall, Laufer showed that the intensity of the

radiated pressure fluctuations was proportional to the size of the test

section. For example, radiation from one wall was approximately equal

to one-fourth the radiation measured from four walls. Also the measured

values were constant across the test section, once the hot wire was one

to two boundary-layer thicknesses away from the wall.

Williams reported in 1965 (96) that the sound f ie ld in super-

sonic flows would be dominated by eddy Mach waves. He stated that the

efficiency of radiation increases with Mach number as a result of the

turbulent "eddies" moving supersonically with respect to the mean flow

and creating Mach waves. Also the waves were highly directional and had

their fronts aligned near the Mach angle as pointed out by Phil l ips (94).

Williams commented that Phil l ips in 1960 (94) was the f i r s t to

make a thorough theoretical attack on the supersonic shear-radiated wave

problem. Williams (96) developed an analytical equation, Eq. (6), for

estimating the Mach wave radiation from a supersonic turbulent shear

layer based on a description of the pressure fluctuation in the boundary

layer. Basic in his derivation was the assumption that turbulent pres-

sures scale with the boundary-layer thickness.

i p_ _- _Pw 5c I (M 2 - I) ~ dM

~w ~w 242 I Mm ( i + 0.2 M 2 } 2 (6)

7S

A E DCoTR-77-107

¢ = 0 . 2

y = 1 . 4

M = Mach number

T w = Wall local shear

m=O

The results from Eq. (6) as computed by Williams using the meas-

ured wall Pw of Kistler are shown in Figure I I I -5. Excellent agreement

between the computed values of Williams and the free-stream measurements

of Laufer are seen to exist.

I t should be remembered that the data of Kistler can be used

since they were obtained on the wall of the same tunnel (the JPL 18- by

20-in. tunnel) as were Laufer's free-stream data.

Kendall (74) continued the outstanding work begun by Laufer at

JPL and in 1970 published additional experimental hot-wire data on wind

tunnel free-stream disturbances. Before beginning his f lat-plate

boundary-layer stabi l i ty- t ransi t ion studies [which were directed toward

providing experimental confirmation of Mack's s tab i l i ty theory (73)],

Kendall demonstrated that the fluctuations picked up by the hot wire lo-

cated in the laminar boundary layer on the f la t plate were the result of

forcing by the tunnel free-stream sound f ie ld which emanated from the

tunnel wall boundary. Data taken by Kendall and published by Morkovin (4)

are shown in Figure I I I -6. These data represent free-stream hot-wire

measurements obtained when the JPL tunnel wall boundary layer was laminar

and then turbulent. By operating the JPL tunnel at low pressures, a

laminar boundary layer could be maintained on a11 four walls. Then by

tripping the flow on one wall and then rotating the f la t plate, Kendall

showed the hot-wire response was greatest when facing the turbulent wall,

?6

A E D C - T R - 7 7 - 1 0 7

m

e -

L .

L .

L . m ~ J ~ L .

0

0

A

A

0 0

0 0

Laminar Sidewalls

A A

&

A

O 0 0 0

0

0

I

Kendall's Data from JPL Wind Tunnel

Turbulent Sidewalls

0 0

0

0

t l

o

A

A

J ~1 I

10 10 2 1@ 10 4 Frequency

0

0

0

m

o

Figure I I I -6. Spectra of free-stream fluctuation at M. = 4.5 with and without turbulence generated sound [from Reference (4)].

??

-2"I

A E DC-TR-77-107

as shown in Figure I I I-7. The data shown in Figures I I I -6 and I I I -7 re-

move any doubts as to the intensity of the radiated aerodynamic noise.

Kendall (94) also found that the free-stream pressure fluctua-

tions were amplified one to two orders of magnitude by the laminar

boundary layer on a f la t plate as shown in Figure I I I -8. This amplifica-

tion has significance when comparing surface microphone (~) and free-

stream hot-wire (~) measurements as wil l be discussed in Chapter V.

In 1969, Wagner, Maddalon, Weinstein, and Henderson (89) re-

ported on the f i rs t of a long series of investigations conducted at

NASA/LRC 7 on the influence of free-stream disturbances on boundary-layer

transition at hypersonic speeds. Using an approach similar to Laufer's

(38), they found that the mode diagrams were linear with a positive

slope for all pressure levels investigated in the M = 20, 22-in.-diam

helium tunnel. They found that when the tunnel flow was laminar, the

free-stream fluctuations were lowest and when the nozzle flow was transi-

tional, they were highest. Analysis of the mode diagrams led to the con-

clusion that the disturbance was radiated noise as described by Laufer

(38).

Fischer and Wagner (90) reported on hot-wire measurements con-

ducted in the NASA-LRC 22-in.-diam and 60-in.-diam helium tunnels at

M = 20 and 18, respectively. Using the mode diagram method of analysis,

they found the free-stream fluctuation disturbances to be consistent

with the radiated noise hypothesis.

7National Aeronautics and Space Administration (NASA) Langley Research Center (LRC), Hampton, Virginia.

78

A EDC-TR-77-107

~ unnel Wall

(Hotwire Probe- 7

--Laminar

Turbulent--

7 2 I nte ns ity

-180 0 180 B, deg

Figure I I I -7 . Free-stream radiated noise fluctuations, direct ional i ty, and intensity, M® = 4.5 [from Reference (74)].

79

A E DC-TR -77-107

M m = 4.5

Flow

Tunnel Wall \ \ \ \ \ \ \ \ \ \ \ \ \ \ k\__~ ~ \ \ \ \ \ , \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ~ \ \ \ \ \

- - = - - \ ~.~,, ~, "1~ ~ ~ ~ -~ . ~, \ -'~----Turbulent Boundary

? ' - - (~) /

Laminary Boundary Layer - /

Layer

~--------~Hotwire i _Probe

Flat Plate Model

lo 4

lo3

~2

lO 2

101

lO o 0 10 20 30 40 50 60 70

Frequency, kHz

Figure II I-8. Energy spectra [from Reference (74)].

80

A E D C-TR -77-I 07

Further measurements by Stainback and Wagner (91) showed that a

pitot probe instrumented with a flush-mounted pressure transducer could

be used to measure the free-stream pressure fluctuations in hypersonic

wind tunnels.

Donaldson and Wallace (88) in 1971 reported on hot-wire

anemometry measurements made in the AEDC-VKF 12-in. supersonic wind tun-

nel to determine the level of flow fluctuations in the test section free

stream. They also obtained supplementary acoustic measurements made us-

ing a microphone mounted flush with the surface of a f la t plate. The

flat-plate model was the one designed and used by Pate (10). The mode

diagram for several free-stream unit Reynolds numbers are shown in Fig-

ure I I I-9. Donaldson and Wallace analyzed the hot-wire data using the

mode diagram concept of Kovasznay (43) and the data reduction technique

of Morkovin (84) following the assumption used by Laufer (38). Their re-

sults supported the hypothesis of Laufer that the disturbance was a fluc-

tuating pressure field (aerodynamic noise) that radiated from the tunnel

wall boundary layer. Using the mode diagrams shown in Figure I I I -g,

along with the assumption that the fluctuating field was a pure sound

field, then the hot-wire rms voltage equation [Eq. (4b), page 57] was

used to estimate the fluctuating quantities of pressure, mass flow

density, temperature, velocity, and total temperature. Results of these

calculations as taken from Reference (88) are shown in Figure III- lO.

The rms pressure fluctuation data measured by Donaldson and Wallace are

presented in Figure III-11 and compared with Laufer's data (38). Note

that both sets of data have been divided by four to correspond to the

radiation from one wall only. By normalizing p with the wall shear

8]

O0 b~

% X

&- <~

2. 4 I I I I [ I I I

L Re/in. x 10 -6 2.0 0.05

1.6

1.2

0.8

0.4

0. 24

0 i , I I I I I 1 I 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

AemlAe T

> m o o

-n

0 ,,4

Figure I I I -9 . Mode diagrams from AEDC-VKF Tunnel D at M® = 4.0 [from Reference (88)].

A E D C - T R - 7 7 - 1 0 7

O. 014

O. 012

O. 010

o = :,= 0.008

0.006 ,-r

0.004

O. 002

Figure III-10.

m

m

0 1@

Notes: 1. Bars indicate data spread possible with alternate fairings of mode diagram for each unit Reynolds number.

2. Absence of bars indicates data spread is within symbol.

I I I I I I I 1 [ I I I I I I I

_ ~1~ ~.. . "'~ _

_ , ~

T / T

Tol~o "B= = =:,B.----~ I I I I I I III I I I I I III

10 5 10 6 Unit Reynolds Number, Re/in.

Variation of flow fluctuations with unit Reynolds number [from Reference (88)I.

83

A E D C - T R - 7 7 - 1 0 7

8 . 0

"~ 6.0- e,,,,,4

X

B

z = - 4.0 -

m

2.0 lo 4

.Figure III-11.

Note Bars indicate data spread possible with alternate fairings of mode diagrams for each unit Reynolds number.

! I I I I I I I I I I $ I I I I I

Single-Wall Configurations

_ 0 , ~ Laufer [(38), ~:~. ~ _ . JPL]

Tu nnet D VKF

[ I I I I I I I I I I I m

Unit Reynolds Number, Re/in.

I I I t

1P

Variation of RMS pressure fluctuations (normalized by dynamic pressure) with unit Reynolds number [from Reference (88)].

84

AEDC-TR-77-107

stress as done by Laufer and computing T w from T w = ~ p=U~ Cf where Cf

was determined from the method of van Driest, then the dependence of p

on the unit Reynolds number is almost completely removed as shown in Fig-

ure I I I -12. The power spectral density for the three unit Reynolds

numbers are shown in Figure I I I -13 as taken from Reference (88) where

the experimental boundary-layer thickness (6) obtained from Reference (97)

was used to normalize the data.

Recently, hypersonic free-stream disturbance measurements have

been reported by Demetriades (98). Donaldson (99) provided information

on equipment and techniques used in the hot-wire experiments conducted

at M= = 6 and 8 (99).

From the now classical experimental work of Laufer (38,86) and

the follow-on work of Kendall (14,74), Wagner, et al. (89) and Donaldson

and Wallace (88) and the theoretical work of Kovasznay (43), Phi l l ips (94),

and Williams (96), i t is def in i te ly concluded that the dominant source of

free-stream disturbance in a well-designed supersonic-hypersonic wind

tunnel wi l l be the pressure f luctuating f ie ld (radiated noise) emanating

from the tunnel wall turbulent boundary layer.

85

A E D C - T R - 7 7 o 1 0 7

3

0.8

0.6

0 . 4 -

0.2 lo 4

Not~ Bars indicate data spread possible with alternate fairi rigs of mode diagrams for each unit Reynolds number.

I I I I m I I l l I I I I I I i l

_ Four-Wall ¢ - - - - - 0 " Configurations Laufer [ (38).

w

- Figure 12]

Tunnel D VKF

i , I m f I I I I n I I

Unit Reynolds Number, Re/in.

I I I l l

Figure III-12. Variation of RMS pressure fluctuations {normalized by wall shearing stress) with unit Reynolds number [from Reference(88)].

86

A E DCoTR-77-107

Reli n.

- -o . 05 x zo 6

Ir 0.24x106 " "

I A

I A N

=I= v

=£ A

B

I0-I

10-2

o.12xz~

Note: Bars (Typical of the Three Re/in. ) Indicate Estimated Uncertainty of +1 db on Power Spectral Density Analysis for Re/in. = O. 12 x 10 o

I0 -31 ' ' I I0 -2 10 -I 1 10

fBlum, Hz sec

Figure I l l -13. Hot-wire signal spectra for wire overheat of a~ = 0.4 [from Reference (88)].

8?

AEDC-TR-77-107

CHAPTER IV

EXPERIMENTAL APPARATUS

I . WIND TUNNELS

The primary boundary-layer t rans i t ion data and pressure f luctua-

t ion data used in support of the present research e f fo r t were obtained

in the wind tunnels located at the Arnold Engineering Development Center,

AEDC, AFSC. This section describes the wind tunnel f a c i l i t i e s , experi-

mental apparatus, instrumentation and the f l a t -p l a te , hol low-cyl inder,

and sharp-cone t rans i t ion models used to supply these basic data. The

f a c i l i t i e s in which the author conducted t rans i t ion experiments (~), in-

cluded f ive wind tunnels located in the yon K~rm~n Fac i l i t y (VKF) and

one in the Propulsion Wind Tunnel Fac i l i t y (PWT), as l is ted in Table 1.

Br ief descriptions of these wind tunnel f a c i l i t i e s are presented in the

following sections.

AEDC-VKF Supersonic Tunnel A

Tunnel A 8 (Figure IV- l ) is a continuous, c losed-c i rcui t , variable-

density wind tunnel with an automatically driven, f lex ib le-p la te- type

nozzle and a 40- by 40-in. test section. The tunnel can be operated at

Mach numbers from 1.5 to 6.0 at maximum stagnation pressures from 29 to

200 psia, respectively, and stagnation temperatures up to 300°F (R== 6).

Minimum operating pressures range from about one-tenth to one-twentieth

8AEDC-VKF Tunnels A, B, and C are equipped with a model in ject ion system which allows removal of the model from the test section while the tunnel remains in operation.

88

AE DC-T R-77-107

Table 1. AEDC supersonic-hypersonic wind tunnels.

Tunnel Test Section Type H

AEDC-VKF Tunnel A AEDC-VKF Tunnel B AEDC-VKF Tunnel D AEDC-VKF Tunnel E AEDC-VKF Tunnel F AEDC-VKF Tunnel F AEDC-VKF Tunnel F AEDC-PWT 16S

*40 tn. x 40 in. Supersonic 1.5 to 6.0 "50-in. D i a m Hypersonic 6, 8 "12 in. x 12 in. Supersonic 1.5 to 5.0 "12 in. x 12 in. Hypersonic 5 to 8 "25-in. D i a m I(ypersonic 7.5 "40-in. D i a m Hypersonic I0, 12

* '54- in . D i a m Hypersonic 10, 14 16 f t x 16 f t Supersonic 1.6 to 4.0

*Contoured Nozzles

**Conical Nozzles

ITunnels used by the author in d i rect support of the present research.

89

A E DC-T R -77-107

318 -- io3.

Screen Design Screen

No. Wire Diam Mesh No. Porosity, %

I Cheese Cloth and/or Felt Filter 2~4 . . . . . . . . . . . . Removed . . . . . . . . . . . . 3 0.023 in. 10 59

5-12 0.008 30 58 Sti l l ing Chamber

Screen Section 12 ,---End of Flexible 3 L._ \ Plate / - F l e x i b l e ~ a t e Test Section

Sta. P-A

;ta. 7 45

:6.3o 369 464.5

Screen No. Diam All Dimensions in Inches

1 1o2.8 2 121

3-12 148

a. Assembly

Nozzle and Test Section (40 in. by 40 in . )

Figure IV-1. AEDC-VKF Tunnel A.

b.

90

A E DC-TR-77-107

of the maximum pressures. A description of the tunnel and ai r f low ca l i -

bration information can be found in Reference (I00). Additional informa-

t ion on the tunnel wall boundary-layer characteristics can be found in

Appendix B.

AEDC-VKF H},personic Tunnel B

Tunnel B (Figure IV-2) has a 50-in.-diam test section and two

interchangeable axisymmetric contoured nozzles to provide Mach numbers

of 6 and 8. The tunnel can be operated continuously over a range of

pressure levels from 20 to 300 psia at M = 6, and 50 to go0 psia at

M = 8, with air supplied by the AEDC-VKFmain compressor plant. Stagna-

tion temperatures suff icient to avoid air liquefaction in the test sec-

tion (up to 1,350°R) are obtained through the use of a natural-gas-fired

combustion heater. The entire tunnel (throat, nozzle, test section, and

diffuser) is cooled by integral, external water jackets. A description

of the tunnel and in i t i a l calibration can be found in Reference (101).

Information on the tunnel wall boundary-layer characteristics is pre-

sented in Appendix B.

AEDC-VKF Supersonic Tunnel D

Tunnel D is an intermittent, variable density wind tunnel with a

manually adjusted, flexible-plate-type nozzle and a 12- by 12-in. test

section. The tunnel can be operated at Mach numbers from 1.5 to 5.0 at

stagnation pressures from about 5 to 60 psia and at average stagnation

temperatures of about 70°F. A description of the tunnel and airflow

calibration information can be found in Reference (97). An i l lus t ra t ion

showing the pertinent Tunnel D geometry is presented in Figure IV-3.

91

A E D C - T R - 7 7 - 1 0 7

Screen Pi, Wire Oi~m. pcr~ril p o r l ~ | e M | I 1(6 m. 41 3-10 0,0ms (6

M-IIM 0,Gi~ /9 l i l icki~l Scrm~

~ n ~Wm

~ - - thrOW

I T T

x H d'J

Tink ~15"lnce

a. Tunnel Assembly

Nozzle ' • " i

Tank [ntrinc.e [ ~

Or In~Ncllon ~I md

b. Tunnel Test Section (50-in. Diam)

Figure IV-2. AEDC-VKF Tunnel B.

92

A E D C - T R - 7 7 - 1 0 7

High Pressure Air Storage

7,550 f t 3 Max Pressure • 4,000 asia Max Temperature - 150°F

½ Vacuum Sphere V = 200,000 f t 3

Sti l l ing Chamber-~ Nozzle Plates & Jacks / - I n s e r t Plate Window C~trel ~ Safety \ ~ " /.. rSafety Devices

0 3 5 Feet

a. Assembly

Screens Mesh Wire Diara Porosity, %

| -4 20 0.017 in. 43.5 Baffle Pla teq S 30 O.OOGS in. 65

i

. S i n |1'3',4 ~

(~ i;l 1 i ' l ; ' i I i

b. Stilling Chamber Screen Geometry

. + _ _ , + . . . ~ . ++ , , ~ +n

. . . .

c. Nozzle and Test Section (12 in. by 12 in.)

Figure IV-3. AEDC-VKF Tunnel D.

93

A E DC-TR-77-107

AEDC-VKF Hypersonic Tunnel E

Tunnel E g (Figure IV-4) is an intermittent, variable-density

wind tunnel having a contoured throat block and a flexible-plate-type

nozzle with a 12- by 12-in. test section. The tunnel operates at Mach

numbers from 5 to 8 at maximum stagnation pressures from 400 to 1,600

psia, respectively, and stagnation temperatures up to 1,400°R (102).

Minimum stagnation pressures for normal operation are one quarter of the

maximum at each Mach number.

For the present investigation at Mach number 5, the maximum stag-

nation pressures were approximately 400 psia and 6gO°R, respectively. A

minimum operating pressure of 50 psia was obtained by removing a second

throat-block located in the diffuser section which had been used to pro-

vide improved operating conditions at M® = 8.

AEDC-VKF Hypervelocity Tunnel F (Hotshot)

The Hypervelocity Wind Tunnel (F) is an impulsively arc-driven

wind tunnel of the hotshot type and provides a Mach number range from 7.5

to ~i5 over a Reynolds number per foot range from 0.05 x 106 to 50 x 106 .

The fac i l i t y is equipped with three axisymmetric contoured nozzles

(M = 8, d = 25 in. ; M = 12, d = 40 in. ; and M® = 16, d = 48 in.) which

connect to a 54-in.-diam test section as shown in Figure IV-5. Nitrogen

is the test gas used for aerodynamic testing. Air is used for combustion

tests. The test gas is confined in either a 1.0-, 2.5-, or a 4.0-f t 3

gThe Tunnel E f lex ib le plate nozzle was removed from service in 1969 and replaced by a t4= = 8, axisymmetric contoured nozzle having a 13.25-in.-diam test section and equipped with a magnetic model suspen- sion system.

94

m F L r~ 1 2 7

Screen Section (I0.0 in. ID)

St i l l ing Chamber Baffle Geometry

t#i

High Pressure Air Storage V = 7,550 f t ~ Maximum Pressure = 4,000 psia Maximum Temperature = 150OF

Screen No. Wire Diam Porosity, %

I 0.105 41 2-7 0.006 67

2A-7A 0.063 76 % (Backing Screens)

(Distance from Throat to ~ . ~ s t Section Centerline)

By-Pass ~ " ~ - - 7 4 i n . ~ r----" ~ ~ T Centerline of Model Rotation i Air Supply fr~n ~ ,J ~ ,, i

High Pressure m w • IH < " • II I/jacks. \ ,Model Support __J_~eservolr ~, i i ' i ~ ', i / Through Heater. ~ ~ " - ' ~ . . . . . ~ - ~

'. I ... i / I ' ~ / - . 4,500-kw Electric Heater-- ~ <~-~. ""~-~--~--.~- ~ I f ~ Io vacuum

Instrumentation Ring-.-/\ _ ~ o Ac<ua<or-~_L iL 0,:,>

Screen ~ . . . . . . . . . . . . Section 0 1 2 3 4 5 6

Feet

Figure IV-4. AEDC-VKF Tunnel E

m

,wi

o

• i:i~ii: ~ H H

~!!i!ii!iiii~ii!i!iii!ii!i!i if! il ,,i:/̧

~c~, ~

i;ii!i~i!iiiiiiii::: i !ii;!i:.:i~ ¸ i i

'i'~'i'i i ~ i~!iii,~i~,~ i ii~

m 0

0

Figure IV-5. AEDC-VKF Tunnel F (Hotshot)

Nozzle

Sta Sta 3T5 /- 4-deg Half-Angle 33 , _ ~ . ~ i c a l Nozzle

~ ~ ~ ~ L m mmeter - ~ In. M® - 8 Contoured Nozzle

sta Wi ndow ~.

~ e t e r - 40 in. MOO " 12 Contoured Nozzle

~ e t e r -48 M m - ]6 Contoured Nozzle

Facility (X® ~ 7 to 15).

In.

AE DC-TR-77-107

arc chamber where i t is heated and compressed by an electric arc dis-

charge. The increase in pressure results in a diaphragm rupture with

the subsequent flow expansion through the nozzle. Test times are typ-

ically from 50 to 200 msec. Because of the relatively short test times,

the model wall (and tunnel wall) temperature remains essentially invari-

ant from the in i t ia l value of approximately 300°K; thus Tw/T o ~ O.I to

0.3. Additional details, test capabilities, and flow calibrations re-

sults can be found in References (103) through (lOS).

AEDC -PWT Supersonic Tunnel 16S

Tunnel 16S (Figure IV-6) is a closed-circuit, variable-density

wind tunnel with an automatically controlled, flexible-plate-type nozzle.

Current test capabilities include a Mach number range from 1.65 to 4.5

at stagnation pressures from approximately 0.7 to 11 psia. For these

tests, the stagnation temperature was held constant at approximately

200°F. The test section is 16 f t square by 40 f t long, and the transi-

tion model was located in the f i r s t I0 f t of the test section. Addi-

tional information on the tunnel may be found in Reference (106) and in

Appendix B.

I I . TRANSITION MODELS

Flat-plate, hollow-cylinder, and slender-cone models were

selected as the basic transition models for this research. These con-

figurations were selected for the following reasons:

1. Planar and sharp-cone geometries are basic configurations

used in many supersonic-hypersonic designs.

97

A E DC-TR -77-107

16- by 16-ff Test Section

A E D C : 5 6 - 7 4 2

Figure IV-6. AEDC-PWT Tunnel 16S Supersonic Wind Tunnel Fac i l i t y (16-f t x 16-ft test section).

98

AEDC-TR-77-107

2. Leading-edge bluntness effects could be systematically

eliminated as a variable.

3. Surface Mach number (and pressure) gradients are absent and

therefore do not enter as variables.

4. These configurations produce two-dimensional flow fields at

zero angle of attack.

5. There are no spanwise or axial pressure gradients, flow ex-

pansion or compression fields, or surface areas with flow

separation.

6. Surface roughness can be eliminated as a variable.

7. Fairly large amounts of transition data already exist on

these configurations.

8. Sharp-cone and f lat-plate models are often used as standard

wind tunnel calibration geometries.

The models used in this research and which provided transition data from

the AEDC wind tunnels are described in this section.

AEDC-VKF Hollow-C@linder Model (Tunnels A, D, and E)

The basic transit ion model was a 3.0-in.-diam by 32-in.-long

hollow cylinder having a surface f inish of 15 microinches (~in.) as shown

in Figure IV-7. This transit ion model was used in the AEDC-VKF Tunnels

A, D, and E. The same basic model was used in the previous investiga-

tions of Potter and Whitfield (37) and Schueler (51). Four new inter-

changeable nose sections having leading-edge, internal bevel angles of 6

and 12 deg and leading-edge bluntnesses (b) of 0.0013, 0.0021, 0.0030,

and 0.0036 in. were designed and fabricated for use in the present

99

' - 32. 0---

(-~---A--- 3

_ . ~ =: 18 2.0 ,-- -(Probe Travel) \

X_ Interchangeable Nose Section

/ - Hol low- Cyli nder Model Con nected to P robe -, Drive Mechanism Located

/ __ -{ Outside T u n n e l - ~ .

,

= Su Remotely Moveable ' Strut

Model Details

%]5p Finish Fiber Glass Resin Skin--A \ 0 092

" ~ ~, % ~, \ I / / / / / / / / / / / / / / / / / / / / / / / / / / I O ~_

L0.15

b, in. BLE, deg O. 0021 O. 0036 O. 0013 O. 0023 O. 0030

6 6

12 12 12

BLE, ~ - Stainless Steel Core

Stainless Steel Nose Section

View A

*Original Nose Used in References (37) and (511 (Maximum Deviation of +0. 0001 in. around Leadi ncj-Edge C i rcu reference)

~_-.+_ -...mo. 032 re..- Probe "A" Tip Detail

oo,

-0.037-1 Probe "B" Tip Detail

All Dimensions in Inches

m O c)

30

,Q

O

Figure IV-7. 3.0-in.-diam hollow-cylinder transition model (AEDC-VKF Tunnels A, D, and E).

AEDC-TR-77-107

research. A remotely controlled, e lec t r ica l ly driven, surface p i to t

probe provided a continuous trace of the probe pressure on an X-Y p lot ter

from which the location of transit ion was determined. Details of the

3.0-in.-diam hollow-cylinder transit ion model are given in Figure IV-7.

Several techniques were investigated to determine the best method

for determining the bluntness of sharp-leading-edge f l a t plates and In-

cluded: (a) wax impressions that were sliced into thin str ips and then

examined with a comparator, (b) direct measurement with a micrometer,

(c) impressions made using a rubber compound, and (d) impressions made in

sharpened lead sheet. Method (d) eventually proved to be the method

most often used because of i ts s impl ic i ty and ab i l i t y to produce repeat-

able impressions. Methods (a) and (b) produced unacceptable results.

The model leading-edge nose bluntness quoted in this report was

determined from impressions (depth equal to approximately two to four

times the bluntness value made in thin (sharpened) soft lead sheet and

from rubber molds made from General Electric Company RVT 60®sil icone rub-

bet compound. Both methods were nondestructive to the model leading edge.

Profi les of the lead impressions and the rubber slices (approximately

O.04-in. in width) cut from the rubber mold were then read on a lO0-power

comparator to determine the leading-edge bluntness. Several lead impres-

sions and several cuts from each of the rubber molds were averaged to ob-

tain the bluntness value at each of several circumferential stations

around each of the leading-edge sections. The maximum difference bet~veen

average bluntness values obtained using lead impressions and rubber molds

was ±0.0002 in. Measurements with the lead impressions were repeatable

to within ±0.0002 in. and measurements with the rubber molds were

101

AEDC-TR-77-107

repeatable to within ±0.0001 in. The circumferential variation in blunt-

ness around the model leading edge was typically ±0.0001 in.

It should be noted that the 3.0-in.-diam hollow-cylinder model,

surface probe, and all related apparatus used in Tunnels A, D, and E

were identical. A photograph of the hollow-cylinder model installed in

Tunnel E for testing at M = 5 is shown in Figure IV-8.

AEDC-PWT Hollow-C~1inder Model (Tunnel 16S)

A photograph of the hol low-cyl inder model insta l led in the AEDC-

PWT 16-f t test section is shown in Figure IV-9. A sketch of the model is

presented in Figure IV-IO. The posit ion of the hol low-cyl inder t rans i t ion

model and the locations of the two wall boundary-layer rakes re la t ive to

the test section and the tunnel throat are shown in Figure IV-11. This

t rans i t ion model was designed 10 spec i f i ca l l y for th is research program and

consisted of a 12-in.-diam by 115-in.-long steel hollow cyl inder having an

external surface f in ish of 15 ~in. The location of t rans i t ion was deter-

mined from pressure data obtained from four equally spaced, external sur-

face p i to t probes (0.016- by 0.032-in. t ip geometry) as shown in Figure IV-IO.

IOA major factor to be considered in the desiqn of a hollow- cyl inder t rans i t ion model is the assurance that the internal flow remains supersonic. The length (z) to internal diameter (d) ra t io (z/d) for the AEDC-PWTmodel was z/d = 9.6. To ensure that the internal flow remained supersonic for M.~ 2.5, the shock wave generated by the leading-edge internal bevel angle was evaluated considering the shock waves and expansion f ie lds generated inside the cyl inder. The method of A. H. Shapiro (177) was also used as a guide in the design of the AEDC-PWT hollow cyl inder. This method accounts for f r i c t i on losses which can drive supersonic flow to the sonic condit ion.

102

0

Figure IV-8. Hol 1 ow-cyl i nder model installed in AEDC-VKF Tunnel E. m t ) (3

~0

o

Q 4~ ~S upport Strut :

Ip--12'n i°"°w CY"nOer MoOe' - -

ii , i iiiiiii i ~,:vO ....... ~ ....... i l i& ̧ii~,ii,)~i i ~i~!~,~

.....

ii [

x

~;i~i #i[ ~ ~i

m 0 c} q -n

-4

o . , j

Figure IV-9. AEDC-PWT 16S transition model installation.

c~

Probe Locations 1

)

Downstream View

Probe Location b, in. b, In.

1 O. 0012 2 0.00]8 ( 0.0015 3 o.o~3 l 4 0.0009

I O.OO44 I 2 0.00~ 0.0050 3 0.0054 4 0.0l~3

Collar i~smbly 1 0.0014 ) _~_b ~ ) . 004 Wall (Sup~rtedf~ Cylinder 2 0.0081 ( ~ 0090 ~1122~i ~ ) l - P Surface by Teflon* Slide ) O. ~ ( u" ; ~ . ~ " ~ ~ 0 . ~ m Blocks 8 Places-----~ I 4 0.0098 ) oLE ~ ~ oe9 View C

\ ...471r~-'~1~ View B Surface Probe

Flow I - -A~- - - -~ ~ " ell#triacl~ing CableS-Nylon Sii/! Ring ITyp.i Tunnel tt , , , _ , ) mr . . . . l , . . . . . . . . . . . . . . . . . . . . . . . ~ - -

~de lJ ~ ~Tmns(~c~ luli~-Coated/~, r - i .. " " l

Reference PressurePllot / _l~.ai]on-_-'" S p r i n g ~ I I ~ I u I L Probe for Oifferentlal Transducer/ ,~.- 4 , ~ , I I I i---Tension ancl'rRelriction (O.OQ)O. D. TYP-4 Places) - - - - - j I t C a ) l e t) Calibrated

Interchangeable Nose I_ intlimedlate $1¢t,o n Sup~rt S t r u t ~ I ~u','$=i'"" Section (Tool Steel - \ l l 'ool Steel - LS-li F4.50 ~r" 1 -~" 15-p Flnlsh~ \ Flnlshi F liiiln Cylinder ..-16. 3 deL_.,,.v..... ..................... t. . . . . . . . . . . . . . . I . / 5

~---~2 I _ . L ~ ~ . 1 \ BOdy (Centrifugal ~ ~ ................................. J ~ / ~ r • I T , , . w Castllloylteel- L 70.00 t " l

Pressure ~ Tunnel Floor I I I I

Figure IV-lO. 12-in.-diam hollow-cylinder transition model details - AEDC-PgT 16S.

> I11

o

:ll

o

AE DC-TR -77-107

Test Cart ---x Nozzle --k \

Sta. 0 Test Section 116 ft by 16 ft)

a. Plan View.

Tunnel Ceiling --~ (774 to Tunnel Throat)

/~exible Plate -,,-/

Airflow~ Tunnel ~ ----.~

• _ / M°del £E

~- ' ~ ~m : 792 in.

Tunnel Floor

Nozzle Test Section [14-Probe Boundary-Layer , /Rake Cryp-Ceiling and

12.0 i uFlexible Plate)

-,--64. 5--~ 1 /-12-in.-diam Hollow-Cylinder

192 ~ n s i t i o n M o d e l /

Sta. 0 Sta. 12. 0


Figure IV-11. b. Test Section

Sketch of AEDC-PWT 16-ft supersonic section area.

tunnel test

106

AE DC-TR-77-107

Details of the hollow-cylinder model, model support, and probe

drive mechanism are shown in Figure IV-IO. Small variations in the

model leading-edge thickness existed, and these bluntness values are

tabulated in the table included in Figure IV-IO as a function of the

model circumferential location. The leading-edge bluntness was deter-

mined by making bluntness impressions (impressions depth approximately

two to four times bluntness value) in thin (sharpened) soft lead sheet

and viewing the prof i le on a lO0-power comparator. The individual blunt-

ness values (b) l isted in Figure IV-IO for each model leading-edge loca-

tion are the average of several impressions. Additional coments con-

cerning the accuracy of this method were given in the previous section.

Three interchangeable, leading-edge, nose sections with an in-

ternal bevel angle of 6.5 deg and average leading-edge bluntness (b) of

0.0015, 0.0050, and 0.0090 in. were tested. The maximum bluntness devia-

tion around the leading edge was approximately ±0.0005 in.

In order to maintain absolutely smooth jo in ts , each leading-edge

section was hand polished after each attachment. This produced a jo in t

that had no measurable (or detectable) discontinuity.

A sl iding col lar arrangement which was separated from the model

surface by eight Teflon®inserts supported the four p i to t probes and

housed four d i f ferent ia l pressure transducers. An actuating apparatus

consisting of a coil spring and a hydraulic cylinder (used for compress-

tng the spring) provided the means for automatically positioning the

p i tot probes along the surface. Probe pressure data were recorded at

small intervals of probe travel at discrete model axial locations.

107

AEDC~R-77-107

Profiles of the boundary layer on the tunnel straight wall and

f lexible plate at the model location were measured with two 14-probe

rakes to determine the characteristics of the wall turbulent boundary

layer. The experimental boundary-layer characteristics obtained on the

tunnel walls can be found in Appendix B.

AEDC-VKF Flat-Plate Model (Tunnel F)

The f lat-plate model used in Tunnel F is shown in Figure IV-12.

The model was 18 in. long and 12 in. wide and had a leading-edge bevel

angle of 30 deg and a leading-edge radius of 0.00025 in. (total blunt-

ness b = 0.005 in . ) . The model was equipped with side plates to minimize

edge effects resulting from outflow from beneath the model.

The model upper surface (transition surface) was instrumented

with 45 flush-mounted heat-transfer gages and nine pressure ports. The

surface pressures were measured with on-board fast-response transducers

(103). The pressure orif ices were positioned 2.0-in. of f centerline to

eliminate any possible roughness effects 11 on the transition location.

The surface thermocouples were sanded absolutely flush with the model

surface using emery paper. A discussion of this type of heat-transfer

gage is given in References (103) and (107). The model surface f inish

was 10 ~in. as measured with a profilometer. The model leading edge was

located at ~m = 381 as shown in Figure IV-13.

l lEffects of pressure orifices promoting premature transition has been reported in Reference (9).

108

A E D C - T R - 7 7 - 1 0 7

__•b-- 0. 00050 in. Sym

•

x

30 de9 Leading Edge Geometry

18.00

- !

-,A 1~o.50(zyp) " ~ ,I i ' l l . . . . . . . ~ ~

, ~ o o o e om o * • e o o o o e o o e t e o e e m o ~ e o o e e m * K

J-~%. • • • ° ]'o • I

L C~ .---6.t"- C~\\-I--I'-~-~--'- . . . . _ ,__: , 2. C~ (T~)

Heat Tra nsfer Gages Pressure Orifices

f m

I M-sur'r F 12. 00 Surface---

Measuring 0~----1~00 ~Surface-~-- .

Flow - 2.50

B --3.00 ow Half Angle--30deg All Dimensions in Inches

Figure IV-12. AEDC-VKF Tunnel F f lat-plate transition model.

109

C~

4-deg Conical

Contoured Nozzles (Calibratod~ Mm- 16 r~

M m = 12 Mco--- 8 r/

Flow s

Cone Model

Model Pitch Sector

> m C~

~O

0

Sta Sta Sta Sta 365 375 390 O5 Nozzle Exit Test Section Schlieren Window

Figure IV-13. Transition model installed in the Tunnel F test section.

AEDC-TR-77-107

AEDC-VKF Sharp-Cone Model (Tunnels A and D)

The cone mode] used in the AEDC-VKF Supersonic Tunne]s A and D

(Figures IV-14 and IV-15) was a lO-deg tota]-ang]e, r ight c i rcular ,

stainless-steel cone equipped with a tool steel nose section. The mode]

had a surface f inish of approximately 10 gin. and a t ip b]untness (b) be-

tween 0.005 and 0.006 in. The Tunnel D model consisted of the nose and

center section as shown in Figures IV-14 and IV-15. The Tunnel A model

was obtained by adding an af t section as shown in Figure IV-15. In order

to maintain a near-perfect jo in t between the sections, the model surface

was refinished after attaching each model section. A photograph of the

model installed in Tunnel A is shown in Figure IV-16a. Sketches i l l us -

trating the position of the models in Tunnels A and D are presented in

Figures IV-16 and IV-17.

A remotely controlled, e lectr ical ly driven, surface pi tot probe

as shown in Figures IV-16 and IV-11 provided a continuous trace of the

probe pressure on an X-Y plotter from which the location of transition

was determined. Details of the surface probe design are given in Fig-

ure IV-17b. I t should be noted that a spring apparatus (Figure IV-17)

was used to keep the probe t ip in contact with the cone surface.

Schlieren and shadowgraph photographic systems were used as a

secondary method for detecting the location of transition in Tunnels D

and A, respectively.

A ~-in.-diam. flush-mounted surface microphone having a frequency

response from 0 to 30 kHz and a dynamic response from 70 to 180 db was

also used to measure the model surface pressure fluctuations in the lam.

inar, transit ional, and turbulent flow regimes and to determine the

111

t~

/F'Nose Section (Tool Steel) ~ Stainless Steel / N o s e Bluntness (b) < 0 . 0 0 6 l n ~ (17. 4 P.H. Heat Treated) /

--t ,-+, _ I_ 24.47 -, ..I, E - 49.05 ' - 1

. . ~ . ~ - - r _ _ ~ . . _ _ . . . ~

T Nose Bluntness

Sym X

I

O

All Dimensions in Inches Tunnel D Model Configuration ~ • 24. 47 in. Tunnel A Model Configuration ~ -- 49. 05 in. Model Surface Finish 5 to 10 Microinches

Model I nstrumentation

Type Pressure Orifice, (0. 020-in. -diam) Thermecouple Microphone

Quantity 4

Surface Location x. in.

15. 59, 37. 26 (90 deg Apart) 16. 08, 37. 76

45.51

0. 0 6 0 0 . ~ . ~ r

Probe A (Used in Tunnels D and A)

0.065 0.020

Probe B (Used in Tunnel A Only)

PROBE DETAI LS

> m o (->

",,,I .% O

F~gure IV-14. AEDC-VKF sharp-cone model geometry.

A E DC-TR-77-107

Figure IV-15. Photograph of sharp-cone model components.

113

AE DC-TR-77-I 07

~m "213. 6 in.

a. Model Installation Photograph

S Flexlble Plate PinA

= 213.6~ 3 1 . a ~ ~ .Tunnel C,. I - '_- ' ] ' _1 , I / . . . . . ~ ~ , ~ 1-6-50


Figure IV-16.

b. Model Installation Sketch

Installation of the 5-deg cone transition model in the AEDC-VKF Tunnel A.

114

AE DC-TR-77-107

Tunnel Center of Rotation

/

Flexible Plate ~ Tunnel Ceiling

View C-C

+ p- - - lz , z87 5: :2. z~-- - - t ._ 4 ~o ~PI': 5 ®,., m~ 574 ;IriT~o Tunnel I ' _ /-- Probe Drive Mechanism

Tunnel Floor


a. ~del Installation Sketch

(1004 0.007 Probe "B" np Dimensions

View A-A

Cone Surface

,•jJ• 5. 00 deg

Sp r i ng - -~ ,

Surface Pitot Probe

~25

~ ~ 2 5

Figure IV-17. b. Details of Surface Probe

Probe details and installation sketch of the 5-deg transition cone in the AEDC-VKF Tunnel D.

115

A E DC-T R-7 7-107

location of transition. A description of the microphone instal lat ion is

given in the next chapter.

AEDC-VKF Sharp-Cone Model (Tunnel F)

The lO-deg half-angle sharp-cone model used in AEDC-VKF Tunnel F

is shown in Figure IV-18. The cone was 17.01 in. in length (base diam-

eter = 6.0 in.) and was instrumented to measure heat-transfer rates at

34 locations and surface pressures at 25 locations. Surface static pres-

sures were measured using on-board transducers, and surface thermocouple

data were used to compute the heat-transfer rates. The heat-transfer

gages were f i led and sanded (using emery paper) flush with the model sur-

face as discussed in Reference (103). The model surface finish was

15 ~in. and the nose bluntness was less than 0.005 in. Figure IV-13,

page 94, shows the position of the cone models in the Tunnel F test sec-

tion.

I16

, .4

sym o Heat Transfer Gage Locations

• x Pressure Orifice Locations

/ - Sharp (b < 0.010 in.) ~ T

/ - _~ ~.L~--. - - < ' - - " - ~ - L J_ o . o . o .

" " ~ Xt - E;O0 In

_1_ - I :- 17. O1 in. -,

Figure IV-18. AEDC-VKF Tunnel F lO-deg cone transition model. ]> m C~ t') .h

" , , I

0 -,,I

AEDC-TR-77-107

CHAPTER V

EXPERIMENTAL TECHNIQUES AND BASIC TRANSITION DATA

I. BASIC TRANSITION DATA

Many techniques have been used and reported in the l i terature on

ways to determine the location of boundary-layer t ransi t ion on the sur-

face of wind tunnel models. The basic methods used in thts research

were the surface probe method for M® ~ 6 and measurement of surfact heat-

transfer rates for ~ ~ 6. Some data were obtained using optical tech-

niques (schlieren and shadowgraph) and a surface microphone for M ~ 6.

Further discussion on these methods and other techniques and a correla-

t ion of the location of t ransi t ion as determined by the di f ferent tech-

niques are presented in Chapter VI.

The location of t ransi t ion used in this report is defined as the

peak in the p i tot pressure prof i le as indicated in Figures V-1 through

V-4 or the peak in the heat-transfer rate as shown in Figures V-5 and V-6.

These methods of t ransi t ion detection are generally accepted as being

near the end of the transi t ion process (region) and have been established

as some of the more repeatable and rel iable methods of selecting a par-

t icu lar and f i n i t e location for t ransi t ion. The locatton of the peak in

the surface heat-transfer-rat~ value for M ~ 8 is approximately equal to

the location of the peak in the surface probe pressure (pp) value as

shown in Chapter VI.

The surface p i tot probe is par t icu lar ly well suited for detecting

transit ion at subsonic and supersonic speeds, whereas heat-transfer-rate

data provide the better method at hypersonic ~ch numbers.

118

A E D C - T R - 7 7 - 1 0 7

tl.

Probe A

b - 0.0021 In. Xt" 8.41n. _ 8- 6deg Re/in. - 0.46 x 10 ° ~,~:~.. Ret. 3.85 x 106 . , ~ ' ~ . , ~ / - - X t " 9.1 in. _

~'. I % % / R e / i n . - 0.405x lIP

" l " "

'h "°°" " % "

~%,o • • , I - , % . ° , , ,

• ,, / _ • ,% - - - ~ , : ~ / / ~ ~ ' ~ . ~ . ,~.

...~.~..3.~,,o~--? _,/_.i~1 ~ ~ x, ]-ze. in. , / ~ . ~ - . , ~ r ~ - . , ~ .

T ~ ~ . ' / i.~" / x , - 14.6in.

0.2 psla 20- Probe DIrectlon

I I I I I I I I J ~ i 1 ~ j I I I I I ! 2 3 4 5 6 7 8 Q 10 I1 12 13 14 15 16 17 18 19

X, in.

a. Surface Pitot Probe Pressure Traces

6 x ~

, r m

4 B

m

3 ~

Ret

2 D

I 0.1

Peak PD Value Indicated in FigureV-la

, I , I , I , I , I = I J 0.2 O.) 0.4 0.5 0.6 0.6 t .0x 106

Re/re.

b. T r a n s i t i o n R e y n o l d s Numbers

F i g u r e V - 1 . B a s i c t r a n s i t i o n d a t a f r o m t h e h o l l o w - c y l i n d e r m o d e l , AEDC-VKF T u n n e l A , M = 4 . 0 .

119

A E D C - T R - 7 7 - 1 0 7

FIo_~w n ' r P p Boundary Layer -~ ~ . _ t . Solid Symbols are Repeat Points

2.] in.

F o0. sur,.. . . . .

/ I I I I I I 1 I I I I I I I I I I I I I I I I

Me) = 3.0

/ \ Re/in, x 10 .6 J f T ~ ' ~ ~

Probe No. M m - 2.50

0. 002 ] Scale

3

Pp - ~ , . . _ Rein. x l,'° X F

I I I I I | I I q r ' = " r I L I - - I I I I I I I I I I I I

0 10 20 30 40 50 x, in.

Moo = 2.0

Figure V-2. Probe pressure data showing the l oca t i on o f boundary- layer t r a n s i t i o n on the 12 - in . -d iam h o l l o w - c y l i n d e r model in the AEDC-PWT 16S Tunnel f o r M= = 2 .0 , 2 .5 , and 3 .0 , probe No. 1,

= 0.0012 i n . , eLE = 6.5 deg.

120

0.O4 Scale

0 elin. x 10 - 6 O. 39 O. 20

Pp@o

0

0.58 0.31 0.20

I Transition Location (x)) Deft ned by Peak in pplPo

AEDC-VKF Tunnel D

b = l1 0036 in. ) 3-in. -diam Model OLE 6 deg J Hollow Cylinder (Probe No. 2)

AEDC-PWT- 16S Tun nel

~~j x/xt j / ~ ~ AEDC-VKF Tunnel A b = O. 0050 in.~ 12-i n.-diam Model - - b - 0-~-00~ in. ~-in.-diam Model6LE = 6.5 deg }HollowCylinder (~F = 6 deg ~Hollow Cylinder --- ~ _ Re/in. x 10 -6

'

O. 010 ~ " ^ " -" -" " - " " ~ - ' ~ - ~ t O. 0 5 2

! ! I I

' ' ' ' ' ' ' ' ' 50 10 20 X, in.

Figure V-3. Comparison of probe pressure t rans i t ion traces in the AEDC-VKF Tunnels A and D and AEDC-PWT 16S for M [] 3.0.

¢o

3, m 0 c)

-n

o ,,4

A E O C - T R - 7 7 - 1 0 7

Relative Scale 0.1 '

Pp. Meo • 3.0 M 5 • 2. 89

I I

. 1 1 g' I D a ) ' ; ~ I - . I~ i~ r l~ v 1(16

I I I I I

,] ;9, (Re/in.)8 "0.134 x 106

[ in. ) 6 • O. 198

I I I I J

Re" l s c a l e / I o.:

Pp

po

Moo - 4 . 0 I ~ - x t - 10,5, (Rel in . ) 6 - 0 . 5 4 o x 106

M 6 • 3. 82 I ~ ~ (Re/in.)6 "O. 269 x 106

/ ~ ~ x t .zT.o. / (Re/in')6 • O. ]95 X 106

I I I I I I I I I I I I

Relative~ Scale i

0.1 J

Pp

p;

Moo -5.03 M 6 - 4. 74

lo 6

5 .o.4o7 x zo 6

I, (Re/in.)6 "o. 244 x 106

I I I I i i i I i I I I

O 8 16 24 32 40 48 x, in.

Figure V-4.

a. AEDC-VKF Tunnel A

Examples of surface probe transition profile traces on the 5-deg half-angle sharp-cone model.

122

J

A E D C - T R - 7 7 - 1 0 7

M®.3.o / , " ~ ~ xt'l~1 Relative , , . z , x , o . , . ~ , j Scale (Re/in.)6 0..1

, , , o.~,41 ~ ~ , ,

m

Relative Scale 0.1

MOo • 4.0 M 6 -3.82

I I

x t -8.4 IRe/in. )6 x I0 "6 • O. 61

x t . 13.1

x t - 19.1

O. ]52

I I I - ' ~ 1 I I n *

Relative---~ Scale | 0.1 __.JI[

Pp

-4.55 ,,~/-x t • 11.7 Moo / , \ M 6-4.32 ] \ ;,..-x t-14.5

(Relin.)6 x 10_6.0.385 / / ( I ' . ~ x t . 16.6

~~/ i o. l~ j /Lxt -~, u n I I I I I I I I I

4 8 12 16 20 .24 x, in.

b. AEDC-VKF Tunnel D

Figure V-4. (Continued)

123

AE DC-TR-77-107

O. 200

O. 100

O. 080

O. 060

O. 040

o O. 020 ,l~"

O. 010

O. 008

0.006

0.004

O. 002

Sym Run Time, msec Mm Re/in. x l0 -6

o 5307 76 = 8. 0 = 1. 07 * o 5307 86 = 8. 0 = O. 8)

A 5307 140 = 8. 0 ~- 0. 54 - ~1o Is the.Stagnation Heat Transfer Rate Measured

on a 1.04n. -diam Hemisphere Probe

~max - ~ o a

- o OO --A Or] _ u \ oooo , , , ,

o°ooF

- - - - - - *Theory, Provided by J. C. Adams Using Method Described in [Reference 109]

Turbulent

Laminar

0 i i i [ i i i i i i

4 8 12 16 20 X, in.

Figure V-5. AEDC-VKF Tunnel F flat-plate transition data.

124

AE DC-T R-77-107

~ : 17.01 t n . - ~

Flow

180 o

9 0 0 4 0 2 7 0 0

¢ = 0

a. Model Geometry

ST = ~/p®U®(H o - H w)

4 x 10 -3 m End of Transition, 3 ~ (Xt)en d rTheory, 2 L Turbulent ~ /Reference (109)

ST 1.0 ' ~ t , 7 ~'~" i=~ l :~ - - ' '~ -

0.6 - ~ ~ M® (Re/in.)® x 10 -6

0.4

0,2

0 -" 7.5 _== 4.2 - Beginning of ~ = 7.5 =0,88 - Transition

I I I I I I I I I 0 0.2 0,4 0.6 0,8 1.0

x/~.

Oa= 0

Figure V-6. b. Surface Heating Rates

Heat-transfer rate distributions on a lO-deg half-angle, sharp cone at zero incidence in the M® ~ 7.5 contoured nozzle.

125

A E DC-TR-77-107

Pitot Probe Data

Examples of the basic transition data obtained using the surface

pitot probe on the hollow-cylinder models at supersonic Mach numbers in

the AEDC-VKF Tunnel A are shown in Figure V-I. Note that the peak pitot

pressure is well defined, and this was typical of all the probe data.

The beginning of transition (defined as the minimum pp value) is usually

less well defined as observed from Figures V-I through V-4. Also plotted

in Figure V-I are the (Ret)en d values determined from the probe peak

value. The trend of Re t with the unit Reynolds number is a well-docu-

mented variation. The unit Reynolds number effect has been extensively

studied by Potter and Whitfield (37,108) and by Potter (23,27).

Pitot traces obtained on the hollow-cylinder model in the AEDC-

PWT Tunnel 16S at M® = 2.0, 2.5, and 3.0 are shown in Figure V-2.

A comparison of the surface probe profile data obtained in the

AEDC-VKF Tunnels A and D and the AEDC-PWT Tunnel 16S is presented in Fig-

ure V-3 to illustrate the consistency and quality of the probe data ob-

tained. I t should be noted that the location of transition moved aft as

the tunnel size increased. This behavior is the direct result of free-

stream radiated noise disturbance and will be explained in Chapters VIII

and IX.

Examples of the surface probe data obtained on the 5-deg half-

angle cone at several Mach numbers in the AEDC-VKF Tunnels A and D are

shown in Figure V-4. Again the consistency and good quality of the data

and the distinctive location of the peak Pp/P~ v value are exhibited.

126

AEDC~R-77-1 07

Heat-Transfer Data

Typical heat-transfer-rate distributions obtained in the AEDC-

VKF Tunnel F on the flat-plate model at M ~ 8 and the lO-deg angle

sharp cone at M ~ 7.5 are presented in Figures V-5 and V-6, respectively.

The peak values of the q/qo ratio are indicated. Theoretical 12 laminar

and turbulent heating rates are included as reference values and for

comparative purposes. The well-defined minimum-maximum values in the

distribution should be noted. The surface heat-transfer distribution

is an excellent method for defining the beginning and the end of transi-

tion region.

I I . APPLICATION OF A SURFACE MICROPHONE

Dynamic Pressure Instrumentation

The transducer used to measure the cone surface pressure f luctua-

t ions was a Bruel and Kjar, Model No. 4136, ~-in.-diam condenser micro-

phone mounted as i l l us t ra ted in Figure V-7. The microphone cartr idge,

when connected to Bruel and Kjar types UA0122 f l ex ib le adapter and 2615

cathode fol lower, and powered by a Bruel and Kjar type 2801 power supply,

has an atmospheric pressure frequency response of 30 Hz to 70 kHz and a

dynamic pressure range of 70 to 180 db, referenced pressure = 0.0002

microbars.

Since the a i r mass inside the cartr idge is used to provide

c r i t i c a l damping for a f l a t frequency response at one atmosphere of pres-

sure, the microphone has a resonant peak in i ts frequency response curve

12These theoretical values were supplied by Dr. J. C. Adams, J r . , AEDC-VKF and were obtained using the method reported in Reference (109).

127

25-in. B & K Microphone ;artridge Type 4136)

k L . I ~ I . . . . I--JL---- I ' I r . . p )

m

c}

0 , , j

oo

(Typ) " - - " ' - ~ ~ - - Adapter Connected to Cathode Follower (Type 2615) with Flexible Cable

Figure V-7. Cut-a-way view illustrating microphone installation.

A E DC-TR-77-107

when operated at ambient pressures lower than one atmosphere. Figure V-8

shows the change in sens i t i v i t y versus frequency at a pressure of 300 n~n

Hg. This curve was obtained using Brue] and Kjar type 4142 ca l ib ra t ion

apparatus. A Fourier analysis of tunnel data (Figure v-g) shows the ef -

fect of the microphone's resonance when operated at a low pressure and

exposed to wideband f luc tuat ing pressures. The output signals centered

about the resonant frequency w i l l cause errors in the nns values of the

f luc tuat ing pressure. To reduce these errors , frequencies above 25 kHz

were f i l t e r e d out of selected tunnel data with a f i l t e r having a 12 db

per octave r o l l o f f .

Recording and Analyztn 9 Equipment

The output of the microphone was fed through a Spencer-Kennedy

Laboratories, Inc. ~de l 302 var iable e lect ron ic low pass f i l t e r to a

Bruel and Kjar type 2409 voltmeter. The ms values of pressure f luc tua-

t ions were read d i r ec t l y on- l ine from the voltmeter, and the time varying

pressure f luc tuat ions , using the vol tmeter 's ampl i f ie r as a preampl i f ie r ,

were recorded on an Ampex Nodel FR1300 analog tape recorder for post- test

data analysis and fo r ve r i f i ca t i on of the on- l ine ms values. The data

were recorded simultaneously on a d i rec t and an FN channel having f re -

quency responses of 300 Hz to 300 kHz and 30 to 20 kHz, respect ively.

For analysis, loops were made from the data tapes and the re-

corded signals were played back into a Technical Products Model TP-625

spectrum analyzer. Power spectra] density analyses were made from the

recorded data using a lO-Hz bandwidth f i l t e r and covering a frequency

range from 10 Hz to 20 kHz. Figure V-IO shows a ca l ib ra t ion curve and

129

12

I 0 -

8 -

6 -

-6 -

- 8 -

-10 -

-12 -

-14 100

" 4

" 2

o 0 03

: : ' -2 ( I ) ,v -4

0 ~ 0

Ambient Pressure, 300 mm Hg I

I I I I I I i l l

5OO I, 000

I I 1 I I I I I I

5,000 10, 000 Frequency, Hz

I I I I I I I 1 ' 50,000 100, 000

7> m 0 o

~o

o

Figure V-8. Microphone frequency response.

( / ) q

0

I n m

E <C

Data Analyzed Using lO0-Hz Bandwidth

Predicted Resonance Frequency from Microphone Calibration (Model No. 4136) Pm = O. 34 psia

0

Figure V-9.

10 20 30 40 48 Frequency, kHz

Ambient pressure effects on microphone frequency response, M = 3.

) , m

0 o

',11

, , , , , I

o ,,,,,i

AEDC-TR-77-1 07

1.0

0.8

0.6 0

0 .

"5 0.4 o

0.2

0 0

jar / Type 4136 Microphone

- / through ,~r Spencer-Kennedy Laboratories, Inc.

/ Model 302 Filter

~" I I I I 0.0~ 0.10 0.15 0.20

Input Pressure, psi

a. Microphone Transfer Characteristics

I MICROPHONE Br;;el and Kjar Type 4136 Cartridge Type UA0122 Flexible Adapter Type 2615 Cathode Follower Type 2801 Power Supply

FILTER Spencer - Kennedy Laboratories, Inc.

Model 302

RMS VOLTMETER Brliel and Kjur

Type 2409

SPECTRUM ANALYZER Technical Products

Model TP-625 A

RECORDER/REPRODUCER AMPEX FR 1300

b. Dynamic Pressure Recording and Analyzing System Figure V-IO. Microphone system used in the AEDC-VKF Tunnel A

aerodynamic-noise-transition study.

132

A E DC-TR -77-107

the block diagram for the dynamic pressure recording and analyzing

system.

Calibrat ion Procedure

The voltage versus pressure characterist ics of the microphone

were obtained by applying known pressure levels to the microphone and

recording the voltage output from the f i l t e r . This cal ibrates the f i l t e r

and microphone as a single uni t . Known pressure levels were generated

using an osc i l l a to r , a power ampl i f ie r , a horn dr iver , and a standard

microphone. Using a frequency of 250 Hz, the pressure levels were set

with the standard microphone and then transferred to the working micro-

phone. The resul t ing cal ibrat ion curve is shown in Figure V-IO. Since

the sens i t i v i t y of a microphone is usually l i s ted in decibels, appro-

pr iate scale factors were used to convert the sound pressure levels to

psi.

Transit ion Detection

Presented in Figure V- l l are the surface pressure f luctuat ions

(~/q=) measured with the Z-in. microphone on the surface of the lO-deg

sharp-cone model at stat ion 45.5 in. (see Figure IV-14, page 112). These

data were measured in the AEDC-VKF Tunnel A at Mach numbers 3 and 4. The

data show a low p/q= value exist ing when the boundary layer was laminar

over the ent i re model surface followed by a very sharp peak and then

rapid decay with increasing Po or (Re/in.) a, as t rans i t ion moved fon~ard

and the sensor was exposed to f u l l y developed turbulent flow. The f i n i t e

p/q= levels that existed when the flow was laminar is the d i rect resul t

of the noise level that radiates from the tunnel walls turbulent bound-

ary as discussed in Chapter I I I .

133

AE DC-T R-77-107

qm

Relative Scale Frequency Range, 0 to 25 kHz

3 0 I I I I I I l l I I I I I I 1 1 1

- B - - "--'Pmax,~,_, " 4.91 x 106 - " = t ' 6

- Transitional i0

- Local Flow - . j " ~ L o c a l Turbulent Flow

~ C z~ Repeat / - ~ Po,n.

1 I I I I I l l l l I I I I I l l l

o.= ==o.o6 o.]lRe/ro. L 0.4 =6¢sl.o 2xlO6 I I I I I I I I I I 2 3 5 ]0 ]520 30 40.50 lO0

Po, psla

a. M = 3 .0 0o

%

Relative Scale I I I I I I I I I I I I I I I I 1

lO0 : A - - ~ l R e t ) 6 • 3. 68 x 106

I ~ , Transitional I ~

Local FIOw-~ 0 ~ , ulent Flow

,0 °

(X)microphone - 49.51 in. ' ~ B

~P I I I I I I I I I I I I I i l l l

0.02 6.04 0,05 O.l 0.2 0.4 0,60.81.0 IRe/in. 16

I I I I I I I 1 I I 4 6 8 IO 20 30 dO 60 60100

Po, psia

zx~¢

J 2O0

Figure V-I1.

b. R = 4 . 0 oo

Detection of t rans i t ion from microphone ms pressure f luc - tuations, Moo = 3.0 and 4.0 (AEDC-VKF Tunnel A).

134

AEOC-TR-77-107

Data as presented in Figure V- l l in terms of ms alone can be

misleading, as has sometimes occurred in the l i t e ra tu re , when one is not

aware of the l imi ta t ions imposed by the microphone or data-recording sys-

tem frequency range. The absolute values of the f luctuat ing pressure

p ro f i le expressed as p are presented in Figure V-12a for M= = 3. These

data c lear ly indicate the re lat ion of the absolute levels of the pres-

sure f luctuat ion when the flow was laminar, t rans i t iona l , or turbulent.

Four selected data points, designated points A, B, C, and D, have been

analyzed, and the i r spectral d is t r ibut ions are shown in Figure V-t2b. As

discussed in the preceding section, a 25-kHz f i l t e r was insta l led to

eliminate the microphone resonance effects at frequencies above 25 kHz.

The spectral d is t r ibut ions presented in Figure V-12b show that a s i g n i f i -

cant amount of the overall rms data in Figures V- l l and V-12a were not

recorded for test points C and D. Based on the results of References

(110) and (111), i t can be estimated that frequencies up to approximately

200 to 300 kHz are present in the cone turbulent flow. Consequently, the

turbulent p data for (Re/in.) a ~ 0.15 x 106) presented in Figures V- l l

and V-12a are s ign i f i can t l y lower than a true total overall rms would in-

dicate.

Figure V-13 presents a replot of the spectral data in Figure

V-12b to more c lear ly show certain pert inent features. The spectra of

the laminar flow pro f i le (A) Which is related to the tunnel radiated

aerodynamic noise levels) are more c lear ly i l l us t ra ted . Also evident is

the concentration of energy present in the t rans i t ion pro f i le (B) at the

lower frequencies of ( f < 1000). The exact source of the low frequencies

associated with the t rans i t ion process is not completely understood, but

1:35

A E D C - T R - 7 7 - 1 0 7

° m

, , ,q

Relative Scale 3 -

I -

0

(Ret) 0 = 4.91 x 10 6 ~ Repeat Data Points

Transitional FI~ D

i: J o . . . . . .

I

I , ~ T u r b u l e n t Flc~v

A~" ~ L a m i n ~ r Flow I I I 1 I

0.1 0.2 0.5 0.6 0.Tx 10 "6 0.3 0.4 (Reli n. )8

a. RMS Pressure Fluctuations (~)

Relative scale 1000-

1.2

"~= 1.0

0.8

0.6

~ 0.4 g.

0.2

0 0

~ B Data Analyzed Using ]O-Hz Bandwidth

r Data FI uctuation ~ T / Bandwidth T (Re/in. 161 10 -6

\ " ~ c ~ o~ - " ~ " ~ - " ~ ~ - - - - ~ T r a n s i t i o n al Flow ~ 0.11 Laminar FI,ow~, A

i ' i I i i i i o .o81 2 4 6 8 10 12 14 16 18 20

Frequency, kHz

b. Spectral Distribution

Figure V-12. Microphone Results, M = 3 .

136

A E DC-TR-77.107

Relative Scale 1000

100

10 B

A h

"~ 1.0

0.100 0

D.

Data Analyzed Using 10-Hz Bandwidth

Microphone Location at x - 45.51 In.

I Turbulent Flow, xt~ 9 in. (Re/in.)6 x lO "6

Turbulent Flow, xt~ 22 in. ..................... 0.25

o.n

LTrans]tional Flow, x t = 45 in.

I ~ L a m i n a r Flow, x t > 49 in. o. ozo I - "

0.001

0 2 4 6 8 I0 12 14 16 18 20 22 24 Frequency, kHz

Figure V-13. Variation of acoustic spectra with boundary-layer state, H = 3.

137

AE DC-TR-77-107

they are tentatively believed to be aerodynamic and not structurally

generated. Figure V-14 presents photographs of the oscilloscope record

showing the time-dependent microphone pressure fluctuation output for

the selected data points A, B, C, and D plus a fully laminar point

= 0.054 x 106 . (Re/ in.)6

The sharp peak in the ms pro f i les or p/q® pro f i les indicates

that the microphone is an excel lent ind icator of t rans i t i on . This con.

clusion is also consistent with recent ly published data obtained with a

th in f i lm (112). The peak in the p/q® data is more pronounced than the

p i t o t probe trace data as seen by comparing Figures V-11, page 118, and

V-4, page 106. The peak point in the ms pressure f luc tuat ion was se-

lected to define the point of t rans i t ion . This de f i n i t i on is consistent

with the peak probe pressure obtained using the traversing surface probe.

I t should now be clear to the reader that the t rans i t i on process occurs

over a f i n i t e length rather than instantaneously at a speci f ic locat ion.

Transi t ion Reynolds numbers for M = 3 and 4, as defined by the peak l o -

cations in the ms pressure f luc tuat ion p ro f i l e and the surface probe

pressure trace, w i l l be discussed in Chapter VII and compared with re-

sul ts from other methods. These data w i l l show that the locat ion of

t rans i t ion as determined by a surface microphone is consistent with p i t o t

and shadowgraph data and is an excel lent ind icator of t rans i t i on at super.

sonic speeds.

Presented in Figure V-15 are the spectra data obtained when the

boundary layer on the cone surface was f u l l y turbulent . The power

spectra density is correlated with the 5trouhal number ~6*/u 6. Several

138

' AEDC-TR-77-107

Output, psi

0.188

Output, psi =

O. 0188

Output, psia

O. 188-

O.

a. Laminar Flow, b. (Re/in.)(~ - 0.054 x 106, ~t > 49 in.

Output, psia

0.0188 -

_

Laminar Flow, (Re/in.)6 "O. 054 x 106, x t > 49 in.

C. Approximate Beginning of Transition (Profile A) (Re/in.)6-0.081 x106, xt > 49 in.

d. Approximate Beginning of Transition (Profile A) (Relin.) 6 - 0.081 x 106, xt> 49 in.

0.188 Output, psia

0

e. Peak Transitional Flow (Profile B) (Re/in.)6" O. 11 x 106, x t = 45 in.

O. 188 Output, psia

0

f. Turbulent Flow (Profile C) (Relin.) 6 - 0.25 x 106, x t = 22 in.

O. 188 Output, psia

0

g.

0 o12 Time, sec

Fully Developed Turbulent Flow (Profile D) (Re/in.) 6 - 0.64x 106, x t = 9 in.

Figure V-14. Oscilloscope record of microphone output tuation) with laminar, transitional, and M =3.0.

(pressure fluc- turbulent flow,

139

A E D C - T R - 7 7 - 1 0 7

sym 2. 52

o 2.52

• 2. 89

Xef f , i n . 6", in. 6, in.

~t + 2. 0 0. 179 --

~t +6"5 0.194 --

40. 5 O. 14 O. 43

10-4 -

(Re/in.)6 x 10 -6

0.78

O. 78

0.64

Ref. 111

111

Present Study

Flat Plate

Flat Plate

Cone

10-5

0

i '~ 10 -6 I~

10-7

4

Xef f = Length of Turbulent Flow

Jt [] Distance from Tunnel Throat to Microphone Location [ Reference 1111

6" and 6 for Present Study Estimated Using [Reference 114]

10 -8 i I I I I I i I I

lO "2 10 "1 1.0 10

e 6"

U6

Figure V-15. Comparison o f pressure f l u c t u a t i o n spectra f o r p lanar and axisymmetric flow.

140

A E OC-T R-77-107

other sets of data are included in Figure V-15, and there is good agree-

ment exhibited between the cone data and the previously published data.

The ab i l i t y of the flush-mounted microphone to measure the in-

tensity and spectra of the fluctuating pressure associated with the

transition process and to detect the location of transition at super-

sonic speeds is clearly i l lustrated in Figures V-11 through V-15. These

results indicate the u t i l i t y of the microphone to provide valuable in-

formation on the transition process at supersonic Mach numbers. Addi-

tional information relating to these experiments can be found in Refer-

ence (113).

I t is of interest to note that the present data (113) were used

as a guide in evaluating transition data obtained on the X-15 aircraf t as

reported in 1971 (115).

Induced Errors

Microphone resonance was shown in a previous section to be a

source of possible error at high frequencies and subatmospheric mean

pressures. Errors in overall rms values and spectra distributions as a

result of microphone size and microphone flushness wi l l be discussed in

this section.

Errors associated with transducer size and surface flushness

should always be considered. Unfortunately, the available information

for supersonic flows is rather scarce. As a part of the present investi-

gation, the ~-in.-diam surface microphone as installed in the f lat-plate

model (Figure V-7) was displaced upward about ±0.010 in. above the model

surface to establish i f surface flushness was a cr i t ica l factor. This

141

A E DC-TR-77-107

was done at H = 3 for laminar flow over the microphone with no s ign i f i -

cant change occurring in the on-line rms reading.

A recent publication by Hanley (116) showed that i f the micro-

phone protusion (y) ratioed to the boundary-layer thickness (6) is

greater than about y/6 ~ ±0.002 for M® = 2.5 then the effect on the f luc-

tuating pressure coeff ic ient (Cprln s = p/q.) and the power spectral den-

s i ty d ist r ibut ion wi l l be s igni f icant. The microphone data presented in

Figures V-11 through V-15 were obtained with the microphone diaphragm

extruding about 0.009 in. above the cone model surface as shown in Fig-

ure V-7. From Figure V-15, one sees that the computed value of the tur -

bulent boundary-layer thickness was 6 = 0.43 in. for H~ = 2.89 and

(Re/in.)6 = 0.64 x 106 . Thus one has y/~ = 0.009/0.43 = 0.021. The re-

sults from Reference (116) indicate that the data presented in Figures

V-11 through V-15 may be s igni f icant ly higher than those which would have

been obtained with a perfectly flush microphone.

However, note that the various data presented in Figure V-15

show reasonable agreement. I t is of interest to point out that a 0.001

extension would have given for the present tests y/8 = 0.001/0.43 =

0.0023. Also, note that a model length of 45 in. (Figure IV-14, page

l l2) was required to produce 6 = 0.43 in. Hanley ( l l6) used 1/8-in.-diam

microphones with boundary layers up to 4-in. thick (Tunnel Wall NASA Ames

9- f t x 7- f t supersonic wind tunnel). Hanley alwo reported that a micro-

phone submerged below the surface (y/6 ~ -0.012) had negligible effects

on the measured data. Also he showed that increasing the Rach number

s igni f icant ly decreased the effects of microphone extrusion.

142

AE DC-TR-77 -107

The a b i l i t y of a microphone to measure high-frequency turbulence

is l imi ted by the size of the microphone. That is , a microphone cannot

measure wavelengths smaller than the microphone diameter. Considerable

error w i l l resul t i f mR/U® • =/2 [see White (117)]. For the present

data, one has ~ < nU6/2R ~ [=(2000)/(2)(0.25)/(2)12] ~ 300,000 rad/sec.

Since a l l frequencies above 25 kHz were f i l t e red out, the transducer

diameter did not introduce a s ign i f i cant error.

Fellows (118) also investigated the ef fect of microphone extru- %

sion on the overall rms value (Prms/q,) measured in the t rans i t ion re-

gion. She found that the Prms value was very sensit ive to a protruding

microphone (y ~ 0.0078 in . ) and a recessed microphone had negl ig ib le ef-

fects as compared to an exactly f lush microphone. However, i t is s i g n i f i -

cant to note that Fellows also found that the location of t rans i t ion as

determined by a microphone was not s ign i f i can t l y affected by the degree

of flushness.

Sugary

In sumary, it is concluded that the surface microphone can be

used successfully on supersonic wind tunnel models to measure the loca-

tion of transition. However, microphone flushness is a critical factor,

and the microphone should be intentionally recessed a very slight amount

when quantitative overall rms and spectral data are to be measured.

143

A EDC-TR-77-107

CHAPTER VI

SUPPORTING STUDIES

I. EFFECTS OF SMALL AMOUNTS OF LEADING-EDGE BLUNTNESS

Results reported by Brinich (48,119) and Potter and Whitfield

(37,108) and Deem et al. (63) have established that small amounts of

leading-edge bluntness on two-dimensional planar models {hollow cylinders

and flat plates) have a strong effect on the location of transition in

the Mach number range M® = 3 to 8. Consequently, in order to eliminate

as many variables as possible in the present research, it was necessary

to establish an effective zero bluntness for the data to be used in eval~

uating the effects of aerodynamic noise on transition. This was accom~

plished by obtaining transition data at several leading-edge thickness

values and then extrapolating the transition data to zero bluntness.

The basic transition Reynolds number data obtained in the AEDC-

VKF Tunnels A and D and the AEDC-PWT Tunnel 16S for several bluntness

ratios are presented in Figures VI-I through Vl-4 as a function of the

leading-edge bluntness. The strong effect of small amounts of bluntness

is obvious. To be noted is the good agreement in Figure Vl-I between the

present data and the previously published Tunnel D data obtained by

Potter and Whitfield {37). Good agreement also existed between the pres-

ent data and previous Tunnel A data published by Schueler (51) as shown

in Figure Vl-2.

There was a slight variation in leading-edge bluntness that

existed around the circumference of the AEDC-PWT hollow-cylinder model

144

AE DC-T R-7 7-107

_L

8LE, de@ Source

• 6 Ref. 37 o 6 Present Investigation o 12 Present Investigation Q 12 Present Investigation

Flagged Symbols Represent Extrapolated Data; Double Flagged Data Estimated from Fig. 27. Ref. 37

8X1~5 [ , I , I • f , i , r • i • i , r , I '

7 Re/in. x lO "~

4

Re t 3 ~ 0.4 0.3

0.2

~ ' 0 . 1

J l l l a l l l l l l l l i i l i l !

,%-~.o 7xzo 6

6 5 4

3 R~ 2

l

M m - 4.0

6xlO 6 5

,o,! I

O 1 2 3 4 5 6 7 8 g lO x 10 -3

E in.

#A m • 3.0

Figure VI-I . Basic transition Reynolds number data from the AEDC-VKF Tunnel D for M® = 3, 4, and 5 with variable IF, BLE, and Re/i n.

145

A E D C - T R - 7 7 - 1 0 7

0LE. deg Source

• 6 _L o 6 T ~ o 6

b - ~ - E A 12 0 12

10 x 10 6 Leading-Edge Geometry 'q 12 / 1 I I I I I I I I I I & I I I I I I ~ [

IT Re/in. x lO "u -. -I

7~- j a r ~ . - : ; . . _ _ 4 -~ U, IWP ~ ,tomb ~

°3 -:1 Re t 4

2

1.5 M m - 5.0

. . . . _.,

5

2 ~

M m - 4.0

zx lo 6

2 ~ 0 1 2 3 4 5 6 7 8 9x 10 "3

6, in.

Ref. 51

Present Investigation

M(I ) - 3.0

Figure VI-2. AEDC-VKF Tunnel A Re t values versus ~ for M = 3, 4, and 5.

146

A E D C - T R - 7 7 - 1 0 7

a .

O.Ol Scale

0

Probe No. )

4 ~ 2 x t

4

! I

iO 20 ~0 40 48 x. in.

O. 0012 ]

! i

Surface Probe Pressure Trace, M = 3, Re = 0.069 x 106/in.

3.0 x lO 5

2.8

2.6 Re t

2.4

22

2.0 0

Re/in. x 10 -6 I~ - 0.9015 In, O. 104

0 ,-, u - - - 0.087

o" ~ 0 . 0 ~ Q P robe ~ 1 2 3

No. 0 Data From FI~ a

I I I I lO 1.5 20 2.5x IO "3

b. in.

b. Circumferential Transition Reynolds Number Distribution, M® = 3.0

4.0x 106

3.8

36

3.4 Re t

32

t 0

28

25

• 0.0(]50 Re/in. x 10 "6

~ O. IlO

Probe l 2 4 ) NO.

o ~ o ' ' - " 0'068

0

I I I I 0 4 5 5 0 5.5 5.Ox lO "3

b. in.

C .

Figure V I - 3 .

C i rcumferen t ia l T r a n s i t i o n Reynolds Number D i s t r i b u t i o n , H = 2.5

Ci rcumferen t ia l t r a n s i t i o n loca t ions on the AEDC-PWT Tunnel 16S h o l l o w - c y l i n d e r model.

147

AE DC-TR-77-107

_L

-~b, in.--VOLE= 6.5 deg

6 x ]0 6 5

4

Re t 3

2

1.5 0

6 x 10 6 5

4

Re t 3

2

l 2 3 4 5 6 7 8 9 lOx 10 "3 b, in.

-3.o

Re/in. x 10 -6

1 . 5 ~ 0 1 2 3 4 5 6 7 8 9 10 x 10 -3

6. rn. 6 x lO 6 Moo - 2. s

5

4

Re t 3

2 0 1 2 3 4 5 6 7 8 9 10x 10 "3

b, in. Moo = 2.0

Figure VI-4. AEDC-PWT Tunnel 16S transition resul ts, Re t versus ~ for M = 2.0, 2.5, and 3.0.

GO

148

AEDC-TR-77-107

(see Figure IV-lO, page 105) that was suf f ic ien t to influence the location

of t rans i t ion. Figure VI-3a shows the p i to t pressure traces obtained

with the sharpest nose section insta l led (b = 0.0015 i n . ) . Measurements

from the four surface probes c lear ly show variat ions in the x t values.

Figures VI-3b and VI-3c show a systematic var iat ion of Re t with the local

leading-edge bluntness value (b), and the slope is in general agreement

with the slope of the data presented in Figures VI-1 and VI-2. This in-

dicates that the small var iat ion in Re t that existed between the four

p i to t probes is traceable to variations in the model leading-edge blunt-

ness rather than to individual probe effects or from any tunnel flow

angular i ty. The internal l i p pressures measured on the AEDC-PWT model

indicated that a free-stream flow angle less than appreximately ±0.1 deg

existed, and this is in general agreement with Reference (106). The

AEDC-PWT t rans i t ion data presented in Figure VI-4 represent the average

value of Re t detemined from the four independent p i to t probes. The

average leading-edge bluntness (b) is the average of the four bluntness

values that existed at the leading-edge upstream of each individual probe.

The t rans i t ion Reynolds numbers for each probe location are tabulated in

Appendix F, page 381. Agreement between the four sets of Re t values for

a given test condition was good and in general agreement with the leading-

edge thickness var iat ion of approximately ±0.0005 in. around the leading-

edge circumference. The standard deviation of Re t determined using each

individual probe Re t value and the mean Re t curves presented in Figure

VI-4 for b = 0.0015, 0.0050, and 0.0090 in. was Re t = ±0.011 x 106 .

Al l of the planar t ransi t ion data using the aerodynamic noise

t rans i t ion correlat ion developed in Section IX are for zero bluntness

149

AEDC-TR-77-107

(b = O) and were obtained by extrapolating to zero bluntness as shown in

Figures VI-1 through VI-4.

Cones are not nearly so sensitive to small amounts of t r ip blunt-

ness as are planar models as reported by Brinich (120), Stainback (121),

and Fischer (122). For t ip bluntness values less than about 0.010 in. ,

cones can be considered to be effectively sharp.

I I . INVESTIGATION OF POSSIBLE LEADING-EDGE BEVEL ANGLE EFFECTS

Brinich (48) reported that the effect of leading-edge bevel

(BLE = 5 and 30 deg) on boundary-layer transition was negligible at

M = 3. However, Potter and Whitfield (37) correlated three sets of

M = 3 transition data using the bevel angle as a parameter. Unfortu-

nately, the three sets of data were from three different wind tunnels.

Later experiments by Whitfield and Potter (108) at a Mach number of eight

showed no bevel angle effect. Therefore, in order to use transition data

in this research from various sources, i t was fe l t necessary to determine

conclusively i f the leading-edge bevel angle has an influence on transi-

tion at supersonic speeds. The data presented in Figure VI-5 (see also

Figure VI-1, page 145) from the AEDC-VKF Tunnel D for bevel angles of 6

and 12 deg clearly show no bevel angle effect at M = 3. Similar results

were also obtained at M® = 5 in Tunnel A (see Figure VI-2, page 146).

Therefore, i t was concluded that there is no leading-edge bevel-angle ef-

fect on transition Reynolds numbers from sharp-leading edge models at

supersonic and hypersonic speeds.

150

AEDC-TR-77-107

b ~ - ~ I18

eLE Leading-Edge Geometry

0. 007- F- 0. 015 0. 029-z 0.015 | 1-0.004

I ~ O . O 5 2 I~ B --I 0.045

All Dimensions in Inches Probe Tip Details

Sym b, in. eLE, deg Remarks

o 0. 0021 6 Probe A d O. 0021 6 Probe B

O. 0023 12 Probe A 6x 106

5 4

Re t 3

2

I 0.1 0.2 0.3 0.4 0.60.81.01.5xi06

(Re/i n. )m

Figure VI-5. Absence of effects from bevel angle and probe t i p size on t rans i t ion location hol low-cyl inder mode], R = 3.0.

151

AEDC-TR-77-107

I I I . INVESTIGATION OF POSSIBLE PROBE TIP SIZE EFFECTS

The possible effect of the probe t ip size on the location of

transition was investigated using two probes with different t ip geom-

etry as shown in Figure VI-5. The data presented in Figure VI~5 estab-

lish that there was no adverse effect from the probe t ip geometry. In

addition to size effects, there is the possibility of pressure lag in

continuously moving probes having small t ip openings. This possible ad-

verse effect was checked at all Mach numbers and tunnel pressure levels

by comparing the forward and rearward traverse of the probe as shown in

Figure V-l, page 103. The data presented in Figure V-1 are typical of

the hollow-cylinder and sharp-cone pitch traces obtained in the AEDC-VKF

Tunnels A and D. I f a small difference happened to exist (i.e , AX t <

0.25 in.) in any particular sequence, then the two values were averaged.

Fellows (118) reported that at M® = 1.8 and 3.0, the transition

Reynolds numbers measured on the surface of a 7.13-deg total-angle sharp

cone using a surface pitot probe were adversely affected i f the probe t ip

size was significantly larger than 0.027-in. in height. These results

give confirmation to the conclusions reached in t ip effect studies con-

ducted in the present research. For probe t ip sizes of O.02g-in. in

height and O.015-in. in height, no difference in Re t values was measured

at M® = 3 on the hollow-cylinder model as shown in Figure VI-5.

I t is of interest to point out that Fellows (118) suspected a

probe tip effect only after the probe Re t data disagreed significantly

from Re t values determined on a subsequent experiment using a surface

152

A E DC-TR-77-107

microphone. These findings emphasize the necessity for always using two

independent methods for measuring the transition location.

IV. INVESTIGATION OF POSSIBLE ADVERSE EFFECTS OF HOLLOW-CYLINDER

INTERNAL FLOW ON EXTERNAL SURFACE TRANSITION MEASUREMENTS

A brief experiment was conducted at M [] 3.0 to determine i f the

state of the boundary layer on the inside of the hollow-cylinder model

could adversely affect the transition location on the outside surface.

There was the possibi l i ty that the pressure fluctuations associated with

the turbulent boundary layer on the inside wall of the model might gen-

erate a mechanical vibration disturbance within the model wall which would

adversely affect the transition location on the outside surface.

A boundary-layer t r ip consisting of serrated glass tape was used

to t r ip the flow inside the hollow cylinder. The effectiveness of this

type of t r ip was established by f i r s t placing the t r ip on the outside

surface and recording the location of transition downstream of the t r ip .

These results are presented in Figure Vl-6 and show that the t r ip was ef-

fective above a unit Reynolds number of about 0.2 x 10 6 per inch.

Transition data obtained on the outside surface with and without

the t r ip placed on the inside surface are shown in Figure IV-7. As evi-

dent from these data, the state of either the laminar or turbulent bound-

ary layer did not affect the transition location on the outside surface.

V. METHODS FOR DETECTING THE LOCATION OF TRANSITION

AND A CORRELATION OF RESULTS

The primary methods used to determine the location of t rans i t ion

in this research were the surface p i to t probe for M ~ 6 and surface

153

AEDC-TR-77-107

-,------2.0 In.-~- b" 0.0036 --,= I-,,- ~ I/8 in. &

. . . . . . . ~. A ( . . . . .

View A

x t, in.

If nt::ch a ngeable

20

18

16

14

]Z

I0

i 0 ~ - - - ,

0

\

l ~ n r r = f a r l I:;hnr ~l=cc

I 0. 7 x 106

f 3. O-in. -diam Hollow-Cylinder Transition Model

~. - Serrated Fiber Glass \~ Tape Trip ~ Model Geometry

o Trip on Outside Surface ~ k ~ No Trip

o Tripon Inside Surface

/-Transition Location ~ th Trip on Outside Surface

Trip~tx=,l/8in. , ~ o ~ . . ~ . . ~ ¢ . ~ . . . . , _ _ ~ , I ,

0. l 0.2 0.3 0.4 0.5 0.6

Re/i n.

Figure VI-6. Ef fec t iveness o f ser ra ted f i b e r - g l a s s tape boundary- layer trip at M= = 3.0.

154

A E D C - T R - 7 7 - 1 0 7

X t on External ~ '~S urface ----.._1 nternal Boundary FIow---~ / ~

I ~ . . _ - . . . . . . - - ~ - ~ - ~

M=-3 Leadi ng~dge"" ~ . . / " ) I ~nterknawlave_, ~

6 x 10 6

s_.m 0

5 4 3

~2

Internal Boundary Layer Laminar (x g 6 in. ) Internal Boundary Layer Turbulent (See Figure V I-6)

m

m

g

, , I , I , I I i I l

0.1 1 I

0.2 0.3 0.4 0.6 0.81.0 1.5X106 (Re/i n. )oo

Figure Vl-7. Absence of effect of internal flow quality on hollow- cylinder transition data.

155

AEDC-TR-77-107

heat-transfer rates for M® g 6. However, many other methods are com-

monly used and, unfortunately, the d i f fe rent methods do not provide a

consistent location of t rans i t ion. For example, there is a s ign i f i cant

difference in the location of t rans i t ion defined by the minimum value of

a surface p i to t probe and the maximum value (see Figure V~I, page 119).

Either location can be used to define the ]ocation. The same is true for

heat-transfer rate d is t r ibut ions (see Figure V-5, page 124). The t rans i -

t ion location determined by a schlieren photograph usually l ies in the

middle of the t rans i t ion region. In general, no one method is applicable

to a l l types of flow conditions and body geometries. Table 2 provides a

summary of the techniques that have been used=

Transit ion data obtained from many d i f fe rent sources w i l l be used

in the aerodynamic noise t rans i t ion correlat ion developed in Chapter IX.

Since d i f fe rent methods were often used to measure the location of t rans i -

t ion in the various sources, i t was necessary to establish a correlat ion

between the d i f fe rent methods used. This correlat ion then allowed a l l

the data to be adjusted to the location corresponding to one common tech-

nique. The maximum value of the surface p i to t probe trace was the method

to which a l l data presented in this study have been adjusted.

Potter and Whit f ie ld conducted extensive experimental studies at

M= = 3 to 5 (37) and M= = 8 (108) using several d i f fe rent techniques to

measure the location of t rans i t ion and define the t rans i t ion region.

Their work is the cornerstone in allowing some sort of systematic corre-

la t ion between the various methods to be developed.

Presented in Figure VI-8 are comparisons of the basic data pub-

]ished in Reference (37) using f ive d i f fe rent techniques (schl ieren,

156

AE DC-TR-77-107

Table 2. Methods for measuring the location of transition.

131.

142.

Boundary-layer profile and edge measurements. References (37), (45), (62), (98), and (108). Surface pitot probe. References (lO), (11), (18), (19), (32), (37), (44), through (60), (63), (108), (113), and (llS).

3. Surface skin-friction measurements. Reference (123).

4. Hot-wire and hot-film probing. Reference (3), (26), (37), (45), (74), and (112).

5. Surface temperature distribution. References (17), (26), (37), (39), (46), (47), (79), (89)through (91, (98), and (108).

136. Surface heat-transfer-rate distributions (gages, paints, phosphorous). References (6), (7), (9), (21), (26), (28), (29), (36), (98), (103), (107), (122), (124), (126), (127).

137. Sublimation and oil-flow patterns. References (17), (18), (33), (35), and (63).

138. Schlieren and shadowgraph photographs. References (10), (11), (23), (27), (37), (46), (79), and (98).

139. Surface microphones (acoustic-pressure fluctuations). References (11), (76), (113), (115), and (118).

10. Static pressure distribution. References (46) and (123).

13Methods used by the author.

14All data used in this report correspond to the end of transition as defined as the maximum value in the surface pitot probe trace (see Figures V-1 through V-4, pages 119through 123).

157

A E DC-TR -77-107

Data Compiled from [ Reference (37)] ~a Twmax Twconst.

e~ax I PPma x i 0.4- Averae, III " ~ . Turbulent 0. 3 - Schlieren Growth

Limit of . , , . ! I L I ~ • -~ 0.2-Laminar6 ) r P ~ ~ _ +

0.1 La ina Gr --

O0 4 8 12 16 X, in.

a. Thickness Profile

i o.n " - -

2 I i u n o I ~ I , I

4 8 12 16 x, in.

b. Hot-Wire Trace

~, 0.90 gS~ ~g~, ,~ 0.88

O. 86 I 4 8 12 16

X, in.

c. Surface Temperature Distribution

P

&¢i

PPmax y:, O. 02 in.

~°Tin/ i T " ~ ' 5 " ~ I l I I I

4 8 12 16 x, in.

d=

Figure Vl-8.

Surface Pitot Probe Pressure Distribution

Comparison of transition location for various detection methods, M= = 5, Re/in. = 0.28 x 106, b = 0.003 in. [from Reference (37)].

158

AEDC-TR-77-107

boundary-layer profile thickness, hot-wire, surface temperature, sur~

face pitot probe) at M= = 5 on a hollow-cylinder model. The beginning

of transition can be defined at the locations given by: (a) l imit of

laminar 6 ~ x ½, (b) minimum hot-wire output, or (c} minimum pitot pres-

sure (ppmin). Likewise, the end of transition can be defined using:

(a) turbulent growth 6 ~ x 4/5, (b) maximum hot-wire output, or (c) maxi-

mum probe pressure (ppmax). Figures VI-Sb, c, and d show the individual

data traces (variations) and Figure VI-8a provides a direct comparison

of the different location. I t is obvious that a considerable and sig-

nificant difference in the transition location can exist depending on the

technique and method of definition. Figure vI-g is a similar type of

plot for M = 8 as determined by Whitfield and Potter CI08)L Presented

in Figure VI-IO is a comparison of the different techniques as a function

of unit Reynolds number. Fortunately, the locations relative to each

other appear to remain constant for a given Mach number over a wide unit

Reynolds number (or range of tunnel pressure levels). Similar compari-

sons between the surface pitot probe, schlieren, and sublimation tech-

niques at M = 2.5 to 5.0 have been published by Pate (18).

Table 3 provides a l isting of transition data taken from eight

different sources plus the present investigation, that have been used to

develop a correlation of methods of detection. These data are presented

in Figure VI-11 for Mach numbers 2.5 to 8.0. The variation in the data

at a given Mach number for a given technique and reference include the

variation with unit Reynolds number. Although there are many data in-

cluded in Figure VI-11, the data when normalized by (Ret)ppma x and

159

0.03

PP o.o2 Po

O. O1

0.80

Xw O. 75

0. 70

0. 65 I I I I

1 b. St r face Temperature Distribution

Transition Region .~

0. O24

6 0 . O22 X

0. 020

O. 018 10

Figure v l - g .

AEDC-TR -77-107

I I I I

a. P i t o t Pressure Trace

Tw _TwTw = 0.76 -0.83 Taw T O Taw 0.908

20 30 40 X, in.

50 60

c. Boundary-Layer Growth

Typical data showing location of boundary-layer transition on hollow cylinder at M® = 8 [from Reference {I08)].

160

A E D C - T R - 7 7 - 1 0 7

Figure VI-ZO.

4

" 3

z 2

ev, to 6

sym o Maximum '~ 2 z~ Maximum pp o Schlieren 0 Limit of Laminar 6

Maximum T w

VKF Tunnel D [from Reference (371]

5 I i I l l I I I

5 6

1 1 1 1 ,

8 10 5 2 3 4 5 6 8 106

Unit Reynolds Number, Ucolvoo per inch

M = 5, b = 0.003 in . a.

Sym Basis of Location

0 6. ~ x 1/2 End of Laminar Flow

6 ~ x 4/5 Beginning of Turbulent Flow

'q T w = Maximum

~7 T w = Constant at Turbulent Level

o PPmax

10

4 3

2

1 0.2

_ VKF Tunnel B

, , I , I , , , I I I I I

0.4 0.6 1 2 4 UQo/Veo x 10 "5 in. - 1

m

b. M = 8, b = 0.0006 in .

Reynolds number o f t r a n s i t i o n on hol low cy l inder at M = 5 and 8.

161

A E DC-TR-77-107

Table 3. Methods used (see Figures

for correlating transition detection techniques VI-11 and VI-12).

i

Symbol

! r]M

I

III

I

X

Reference

(18)

(123)

(37) (108)

(63)

(37)

(126)

P resent Study P rese nt Study

(3"/) (108)

(63)

(18)

Present Study

(118)

Model Configuration

Sharp Swept Wing

Sharp Flat Plate Sharp Hollow Cylinder Sharp Flat Plate Sharp Hollow Cylinder Sharp Flat Plate Sharp Hollow Cylinder

S harp Cone

Sharp Hollow Cylinder S harp Flat Plate Sharp Swept Wing

S harp Cone

S harp Cone

Method X L Detection

Minimum Pp Value

Minimum Shear Stress (Tmi n)

End of Laminar Growth Rate (6 ,,. x 112)

Minimum pp Value

Minimum pp Value

Minimum Surface Heat Transfer (Clmi n )

Minimum pp

Minimum pp

Average Schlieren

Sublimation

Sublimation

Surface Microphone Maximum (Prms) rms P ressu re Fluctuation Surface Microphone Maximum (Prms) rms Pressure Fluctuation

(112) Sharp Flat Hot Film Maximum rms Voltage (Vrms I Plate

(37) Sharp Hollow Maximum Surface Temperature ('l'wmax) and 77/'7/'/7, (108) Cylinder Maximum Hot Wire Output (~)

]~ Present Sharp Cone Average Schlieren Study

(37) Sharp Hollow Constant Maximum Surface Temperature (Twconst) (108) Cylinder and Beginning of Turbulent Growth Rate (6 ~ x 4/5)

m (63) Flat Plate Pp Inflection Point

(123) Flat P la te Maximum Surface Static Pressure

I Indicates Data Spread Over Reported Re/in. Range

162

AEDC-TR-77-107

"'f / z.3 i E - ~" End of Transition Region

1.2

Z.l.OZ t ~,\xxxx~'~x% ~ ÷ x

~'1 ~ 0"81 " i I ' ~ ~ ~ T ~ i ="--'-'£"M~dle°fTransltl°nRegl°n

,~" °"r~ II 7 i I ~ o .61-~___~ - ~I o . ~ ~ ili/e ,

0, 4 gi nni ng of Transition Region 0.3

0.2 0. I

0

See Table 3 for Symbol Identification

I t I I ] I i) 4 5 6 7 8

M 6

Figure VI-11. I l lustrat ion of transition location variation with methods of detection.

163

AEDC-TR-77-107

grouped according to similar techniques form systematic patterns~ as

shown in Figure VI-12. The correlations and recommended lines of adjust-

ment shown in Figure VI-12 can be used to adjust transition data from

various techniques to an equivalent (Po)max location. The justif ication

for doing this should be obvious, i .e. , a 20-percent error is better

than a 50-percent error.

Several assumptions were made in developing and applying the re-

sults shown in Figure VI-12. First, note that in Figure VI-12 for M® = 8,

the maximum wall temperature Re t value normalized by the probe peak pres-

sure (Ret)ppma x value is equal to one. I t is assumed they are also equal

for M® > 8. Second, i t is assumed that the location of transition given

by (Tw)ma x and (q)max are equal. This assumption is supported by (Tw)ma x

and (q)max data published in Reference (98) and which was obtained on a

sharp cone at M = 8. Thus for M > 8, i t is assumed that the location

of transition given by (q)max equals the value determined from (PP)max"

Third, most of the data presented in Figure VI-12 are from planar models

with small amounts of leading-edge bluntness (b < 0.01 in.) and sharp

slender cones at zero angle of attack. I t is assumed that the relative

ratios are not strongly dependent on small amounts of bluntness. This

assumption is supported by the data presented in Reference (37).

There are several significant features to note in Figure VI-12.

The beginning of transition is about one-half the end of transition loca-

tion. I t is interesting to note that this is in agreement with the re-

sults presented by Masaki and Yahura (125) which was based on a correla-

tion of transition data taken from several sets of sharp cone and f la t

plate data. The data from sharp slender cones also seem to have the same

164

A EDC-TR-77-107

1.4

1.3

1.2

Data Presented in This Figure Represents 14 Methods of Detection, 3 Different Geometries (Sharp Flat Plates, Sharp Slender Cones, Sharp Swept Wings) and 11 Different Sources as Defined in Table 3

/---End of Transition Region as Determined by:. Constant l:,w; P o Inflection Point; Maxi~J m

t Growth (x)

l- / - - Middle of Transition Region as Determined by: l. l J / Surface Microphone (PRMS)max I . O ~

0.9

_>< 0. 8 I ~ - ' £ Z Z ~ ¢ ~ ~ /---Middle of Transition Region as I Determined T w. I ~ ~ ~ b~ Maximum

_ Sublimation, Maximum Hot Wire (~2) 0.7

.

0.5 ~ ~ ~

O. 4 Beginning of Transition Region as Determined I~. _ Minimum ppValue; Minumum Surface Shear, T rain;

End of Laminar Growth (x)112; Minimum Surface - Heat Transfer Rate, ilmin

0.3

0.2

0.1

O

Recommended Lines for Adjusting to (PP)max Values I I I I I I

3 4 5x 6 7 B Local Mach Number. M 6

Figure VI-12. Correlations of transition detection methods.

165

AEDC-TR-77-107

correlation as the planar models ( f l a t plates, hollow cyl inder). Optical

techniques give a location of transit ion at about the middle of the tran-

s i t ion region.

The data presented in Figure V1-12 show that f la t -p la te transi-

t ion locations determined at (Tw)ma x and from schlieren photographs

should be the same in the range 2.5 ~ M® ~ 3.5. Transition results ob-

tained by van Driest and Boison (47) using a magnified schlieren concept

and surface temperature measurements also show that schlieren x t data

are essentially equal to (Tw)ma x locations on a sharp cone for M® [] 1.8,

2.7, and 3.7.

Transition data published by Mateer (127) on a 5-deg half-angle

cone at M® = 7.4 has shown that thermographic paint and thermocouples

give the same results. Similar results have been shown by Matthews et al.

(124) on a space shuttle configuration.

Based on the author's experience, the surface pitot probe is the

easiest and most dependable method for determining the location of transi-

tion for 0 < M ~ 6 and surface heat-transfer ratio is recommended for

M > 6.15 When conducting transition studies at least two methods should

always be used. Optical methods (schlieren, shadowgraph) often provide

a satisfactory second technique.

Unless indicated otherwise all the boundary-layer transition

Reynolds numbers presented in this thesis correspond to the location de-

termined by the peak in a surface pitot probe pressure trace (ppmax).

15Surface skin-friction measurements, detailed hot-wire data~ and surface temperature or surface heat rates probably provide data best suited to support theoretical studies. Unfortunately, these methods are also the most d i f f i cu l t to apply.

166

AEDC-TR-77-107

Trans i t ion loca t ions obtained from references wherein other methods of

detection were used have been adjusted in accordance with Figure VI-12,

e,g., see data on pages 250 and 253.

167

A E DC-TR-77-107

CHAPTER VII

SUMMARY OF BASIC TRANSITION REYNOLDS NUMBER DATA OBTAINED

IN AEDC WIND TUNNELS ON PLANAR AND SHARP-CONE MODELS

The basic planar (hollow-cylinder and f lat-plate) and sharp-cone

transition Reynolds number data obtained at AEDC in support of this re-

search are presented in Figures VIIml through VII-1. Tabulated data are

also provided in Appendix F, page 381.

To maintain as nearly identical free-stream flow disturbances as

possible, the cone model was positioned in Tunnels A and D very near the

hollow-cylinder locations (see Figures IV-16, page 98, and IV-17, page

99)~

Tunnel A

(am)cone = 215 in.

(am)hollow = 231 in. cylinder

Tunnel D

(~m)cone = 44 in.

(~m)hollow = 48.5 in. cylinder

The experiments were also conducted at equivalent free-stream Mach num-

ber and unit Reynolds number values.

The hollow-cylinder data measured in the AEDC-VKF Tunnels A, D,

and E and AEDC-PWT Tunnel 16S using a surface probe are presented in Fig-

ures VII-I through VII-4. Figure VII-4 presents a composite plot of

al l the hollow-cylinder transition Reynolds number data obtained at

M = 3 in the AEDC-VKF Tunnels A and D and the AEDC-PWT Tunnel 16S. The

difference in the Re t data from these three wind tunnels is the result of

radiated aerodynamic noise effects as discussed in Chapters VIII and IX.

168

A E DC-TR -77-107

10 x 10 6

8 7 6

5

4

,IT' ,.,. 3

2

m

m

m

m

B

m

u

m

m

m

m

' I ' I ' I ' I ' I ' I ' I I i

j - / o -

o/ / / _- i

~m = 59. 8 in.

= O. 0023 in. Hollow Cyl inder Model

, I , I , I , I , I , I , I 1 2.0x I06 b. 1 0.2 0.3 0.4 0.6 0.81.0 Re/in. a. AEDC-VKF Tunnel E, M = 5.0

8 x 1 0 6 ' I ' I ' I ' I ' l ' I ' I ' 7 - Sym b , i n .

6 - _ _ 0 Extrapolated (see Fig V1-1, Page 129) - - 5 - o 0.0021 -_ 4 -- [] O. 0023 3t-21 ~ A 0.0036 " ~ l-i

~ , ~ ~ / / ~ m = 48.5 in. _~

0.1 0.2 0.3 0.1 0.6 0 .81 .0 2.0x106 Reli n.

b. AEDC-VKF Tunnel D, M = 3.0

Figure VI I - I . Basic transit ion Reynolds number data from AEDC-VKF Tunnels D and E, M = 3.0 and 5.0, hollow-cylinder model. ®

169

A E DC-T R-77-107

3_

Leading-Edge Geometry

Sx ]o 6 7 6

5

4 Re t

2

1.5

I

Flagged Symbols Represent Data OMained with Duplicate Set of Rul,'~r Bolt Heads on Top Plate (See Appendix B, Page 3011.

m l u u u u ~ M l l J ' ~ 1 I I ]

b, in.-1 _ - - o O. 0013

- o O, 0023 = O. 0030

O. OO36

- " " " - - Extrapolated (See Figure V I-2, " Page L~ l - A

M m - 3.0

b, in. 81. E , deg ].2

6 12 12

6

a. M®=3

lmo In, - - z~T"-

Figure VI I-2.

8 x 106 7 6 5

Re t 4

' ' ' I ' ' l ' l i ' l ' " l ' q ' ' q " i ' l i I ' I I I I

z . ~ , ~ O. 0036

oozz

. - .

polaled (See Figure Vl-2, " Page L30m

i I l i I I l l i . J i l l l l l I I I 11111 , | I , I I J-]

M m -- 4.0

b. M ® = 4

10 x 106

8

6

Re t

_ . . . . , . . . . , .... ,,,,,,,.,,.,,... , , , , ~,l illl , . - ~ 0 . 0036

t " 0 . 0 0 2 1

4

3 Exh'apotated (See Figure V I-2. Page 130~

i i I I , i i ! l , u ! ! ! , , . ' , h , , l l i , , , I I 11

O. 0.2 0.3 0.4 0.6 0.8 1.0x10 6 Re/In.

c . H= = 5

B a s i c t r a n s i t i o n Reyno lds number d a t a f rom t h e AEDC-VKF Tunnel A f o r H = 3 , 4 , and 5 and V a r i a b l e b a n d eLE, ho l l o w - c y ] i nde~ mode l .

170

b. in.T'e = 6. 5 deg Jm = 792 in.

,...I

]096 ~., ] O x - i , I , i , , ' I

8 7 6 Moo = 2.0 5 b, in.

0.0015 Re t 4 " ' ~ ~ ° 0

3 _ -Extrapolated ~ (See Figure V I-4,

2 Page I32)

~ . I I l l I I I I , • , l. 04 0.06 0.080.10 0.]5 0.20 0.3 0.04

Re/in. x ]0 "6

,'IMoo, '=2.5 ' --co'=3.0 i

i I , I I I I I I

0.06 0.10 0.15 0.2 0.04 0.06 O. lO 0.]5 0.20

Re/in. x lO -6 Re/in. x lO -6

Figure VII-3. Basic t rans i t ion Reynolds number data from the 12-in.-diam hol low-cyl inder model in the AEDC-PWT Tunnel 16S for X = 2.0, 2.5, and 3.0 and b = 0.0015, 0.0050, and 0.0090 in.

go > m 0 t~

-n

o

A E D C - T R - 7 7 - 1 0 7

Hollow-Cylinder Leading-Edge Geometry

AEDC-PWT

b-, in. erE, - - - 0 6.5 - - - 0 - - o O. 0015 / o O. 0013 6 D 0.0050 ~ ~ 0.0021 6 0 O. 0090 o O. 0023 12

O 0. 0030 12 P' O. 0C86 6

lOxlu~ _ i l l i i , I I ] i i i i I i i i , i l l

R -t r- AEDC-VKF 40-in.--~

6 ~ Tunnel A

5F- AEDC-PWT 16-ft ~ 4 i_ Supersonic Tunnel ~ " ' ~ j - I

l - AEDC-VKF 12-in. A~,~F~ ~ . . - , " I

F ] 1

Ret.

0.04 0.06 0.080.1

AEDC-VKF

b, in. BLE, de9 Tunnel /'m, in. 16S 792 A 231 D 48.5

0.2 0.3 0.4 0.6 0.8 1.0x 106 Re/in.

Figure VII-4. Basic transition Reynolds number data from the AEDC-VKF 12-in. Tunnel D, 40-in. Tunnel A and the AEDC-PWT 16-ft Supersonic Tunnel for M = 3.0, hollow-cylinder models.

172

A E DC-TR-77-107

J Sym Configuration

_.o.o~ 5-de9 Cone 5-de9 Cone 5-deg Cone Hollow Cylinder

5xlO 6

4

3

(Ret) 8

2

Surface Ray

Top Bottom Bottom Bottom

I I I

Source

M 8 = 2.~9 8 c = 5 deg

m

Method d Detection

Schlieren Schlieren

Surface Probe (Pmax) Surface Probe (Pmax)

Present Study Present Study Presenl Study

Reference 37 and Present Study

I m . in_____~.

' I ' I ' J,, ' I ' I |

4 , , .o

.Q Figure V I-I, Page 129

. ~ - M 6 [] 3.0

j O t - j

I 1 ~ , 1 I I , I , I , I 1 O.Ol 0.1 0.2 0.3 0.4 O.7xlO 6

(Relin) b

a. M = 3.0

5xlO 6

4

3

(Ret) 6

1 I I ' 1 ~ ' I ' I ' 1 '01

M~ = 3.34 ~ o z~

0 A IS

X ~.~.~,f,i f'~''--~

I I , ~ " , l , I , I , I ~ i

Planar, b = 0 Reference 37 M 6 = 3.5

1

0.07 O.l 0.2 0.3 0.4 0.7x106

(Re/in.)6

Figure VI 1-5.

b. M= = 3.48

Trans i t ion Reynolds number data from AEDC-VKF Tunnel D, sharp-cone and planar models.

173

A E D C - T R - 7 7 - 1 0 7

6xlO 6

(Ret) 6

1 0. 07

(Ret) 6

. I I I ' I ' I ' I ' I ' I

M 6 = 3.82

0 c = 5 d ~ : ~ : p ~

I"I" I .I °

I - '~L- Planar, b = 0 / . . ~ . i " Figure V I-1, Page 129

, I I , I , ,M5,=,4"0, , , J

0.1 0.2 0.3 0.4 0.5 0.7xtG 6

(Re/in.)6

C. M = 4.0

6xlO 6 i ~i

5 M 8 = 4. 32 Oc =5 deg _ ~ J D ' E ~ O 0

3

2

' 1 ' 1 ' I ~ i ' =

1 . 1 " ~ ' Planar, b -- 0 . I " Reference 37

M 6 = 4. 55

L I t I m I I I , [ , I ~ l ] 0.07 O.l 0.2 0.3 0.4 0.5 0.7xlO 6

(Re/in.)6

d. H= = 4.55

Figure V I I -5 . (Continued).

174

A E D C - T R - 7 7 - 1 0 7

Sym Configuration

zx 5-deg Cone o 5-deg Cone [] 5-deg Cone

_ . B Hollow Cylinder x 5-deg Cone

S urface Ray

Top Bottom Bottom Side Top

Method of Detection

Shadowgraph Shadowgraph Surface Probe(Pmax) Surface Probe(Pnla x) Microphone(~'ma xl

Source

Present Study Present Study Present Study Present Study Present Study

!, m , in.

215 215 215 231 21.5

lOxlO 6

8

6

(Ret) 6 4

3

21

O. 06

M 6 = 2.89, 9 c =5 .deg I I I l , . ' I ' I ' I ' I ' 1 I I I

Dew Poim -2 5-~ . - -9 5 - Temperature, OF . . " / 5. 5 / " -

1 4 . ~

teO,:a,r,n, " b-O (No Condensation Effects).. M 6 = 3.0

I I I I " r ' ~ l = I , I J i l l I I I

0.1 0.2 0.3 0.4 0.6 0.8 l.Ox10 6

(Re/in.) 6

a. M = 3.0

(Ret) 6

7xi06 M 6 =3.82, e c=Sdeg

1 I 1 I ' I ' I ' I ' I ' I I I I

~ . ~ ~ .

,-- Planar, b - 0 Figure V I l-2 M 6 =4.0

l l l l , I , r , J . J , l , i l l

0.06 0. I 0.2 0.3 0.4 0.6 0 .8 l.Ox106

(Re/in.)6

b. M = 4 . 0

Figure VII-6. Transition Reynolds number data from AEDC-VKF Tunnel A, sharp-cone and planar models.

175

A E D C - T R - 7 7 - 1 0 7

(Ret) 6

(Ret) e

lOxlO 6

10x10 6

2 / I !1 0.06 0.08 O. 1

4

3

! I [ ! ' ' ' l ' I ~ I w I I I [

M 6 - 4. 29

Planar. b - 0 • . FigureVIt-2 (Data Crosspl~J.~..-

M 6 • 4. 52 ~ . / "

! l I I , I , I , I I I I

0.2 0.3 0.4 0.6 0.8 l.Ox]O 6

(Re/in.)6

c. H = 4 .52 o ~

] ' I ' I ' I I I r _ I I I I ' I '

MS== 4. 74

A / Planar, b • 0 / o

" Figure V 11-2 ~ - M6 • 5 .o -> , , . -

I I I I • I , I . I , I . I I I I

0.06 0.080.1 0.2 0.3 0.4 0.6 0.8 l.OxlO 6

(Relin.) 6

d. M [] 5 .03 o o

(Ret) 6

M 6 = 5.5, 0 c = 5 deg, (T O - 719°R)

10xt06 i , , I ' r , , ' i ' 1 ' , i , ,

6 I I I I , ! , I . I . I . I I I I

0.06 0.080.1 0.2 0.3 0.4 0.6 0.8 1.OxlO 6

(Re/in.)6

e. H -- 5.94 QO

F i g u r e V I I - 6 . ( C o n t i n u e d ) .

176

AEDC-TR-77-107

30 x 106

20

Sym Ntm Tunnel Nozzle Geometry Reference o = 8.0 VKF-F 40-in.-diamContoured Present Investigation o = 7.5 VKF-F 25-in.-diamContoured Present lnvestigation O =14.2 VKF-F 54-in.-diamConical 21

' I ' I f I I I , I I I , i I I ' I ' I '

15 Sharp Cone Sharp Flat ~ < ~ de9 z ) , " Plate

, , / - (b -- 0. 00(]5 in.)

0c= zo deg 6 5

m

i

i

o--0 4

3

I

m

i

m

2 , I , I , I , l a l I I l l ~ I , I e l l

O.l 0.2 0.3 0.4 0.50.6 0.81.0 2.0 3.0 4.05.0x106 (Re/i n. )m

Figure VII-7. AEDC-VKF Tunnel F (Hotshot) transition data.

177

r

AEDC-TR-77-107

The sharp-cone data obtained in Tunnels A and D are presented in

Figures VII-5 and VII-6. The locat ion of t r a n s i t i o n was determined us-

ing the surface probe, schlieren photographs, and a flush-mounted sur-

face microphone. The data presented in Figures VII-1 through VII-7

appear quite normal in that they exhib i t the usual increase in (Ret) 6

with increasing (Re/in.)6 and increases in Re t with increasing small

amounts of bluntness (Figures VII-2 and VI I -3) . Although the microphone

results were l imited to two data points (Figure VI I -6) , the peak in the

pressure f luctuat ion pro f i le provided (Ret) 6 values consistent with the

surface probe and photographic values.

One of the known (but sometimes forgotten) variables that can

af fect the t rans i t ion location is the dewpoint (temperature at which

water condensation occurs) as discussed in Reference (46). In Tunnel D,

the dewpoint was sufficiently low (<O°F) at all Mach numbers not to af-

fect the x t locations. Also, in Tunnel A, the dewpoint was sufficiently

low 16 at all Mach numbers except for the lower unit Reynolds numbers

(subatmospheric pressure levels) at M = 3, as il lustrated in Figure

VII-6a. Therefore, a recommended (Ret) 6 trend as indicated by the

dashed line has been included in Figure VII-6a for M = 3.

The location of transition as determined from schlieren and

shadowgraph photographs was selected at the body station where the

boundary layer had developed into what appeared visually to be ful ly

turbulent flow. This location of transition provided (Ret) 6 values, in

16The relatively high dewpoint existing in the M= = 3 data re- flects fac i l i ty limitations existing on that particular date and does not necessarily represent standard test conditions.

178

A E DC-TR-77-107

genera], about 10 to 20 percent lower than (Ret) 6 results obtained from

the surface probe peak pressure locations. Any burst, r ipple, or rope

[see References (14) and (128)] effects that were observable upstream of

the fu l l y developed turbulent location were ignored in the selection of

x t . The transi t ion values presented represent an average of x t value

determined from approximately four d i f ferent photographs.

Flat-plate transit ion Reynolds number data obtained in the AEDC-

VKF Tunnel F at M= ~ 8 are presented in Figure VII-7. Sharp-cone data

obtained at M= ~ 7.5 and 14.2 are also included in Figure VII-7. I t

should be noted that the transit ion Reynolds number continued to in-

crease with increasing unit Reynolds number for al l Rach numbers and unit

Reynolds numbers investigated. To the author's knowledge, the transi t ion

data obtained in Tunnel F at M= = 8 and 7.5 are at the highest unit Reyn-

olds number reported to date from hypersonic wind tunnels.

179

AE DC-TR-77-107

CHAPTER VIII

EXPERIMENTAL DEMONSTRATION OF AERODYNAMIC NOISE DOMINANCE

ON BOUNDARY-LAYER TRANSITION

I. INTRODUCTION

Primarily as a result of the research by Laufer (38), i t has

been established, as discussed in Chapter I l l , that the only significant

source of free-stream disturbance in a well-designed supersonic wind

tunnel is the aerodynamic noise that radiates from the tunnel wall tur-

bulent boundary layer. Although these early experiments investigated

the intensity and spectra of the free-stream aerodynamic noise distur-

bance, there were no experiments conducted that showed what effect radi-

ated noise would have on transition locations on test models. Laufer and

Marte (46) attempted one such experiment but the effort was unsuccessful,

as discussed in Chapter I I I . The present research produced the f i r s t

experimental data that showed conclusively the dominating effect that

aerodynamic noise has on the location of transition on f la t plates and

cone model tested in supersonic-hypersonic wind tunnels.

There have been subsequent aerodynamic-noise-transition experi-

ments conducted by NASA and in several European countries including

Russia. Results from all of these studies have supported the conclusions

published in the present research and have provided additional confirma-

tion of the dominance of aerodynamic noise on transition. This chapter

includes results from the present study and results from other experi-

mental studies that have been published in recent years.

180

AEDC-TR-77-107

I I . AEDC SHROUD EXPERIMENTS

Approach

To determine if radiated noise significantly affected the loca-

tion of transition, it was necessary to create a test environment where

a transition model could be exposed to various levels of aerodynamic

noise intensity. One obvious approach would be to try to keep the

boundary layer on the tunnel walls laminar. This approach is possible

[see References {14), (74), and {92)] but at the very low tunnel pres-

sure level (or unit Reynolds number), low enough to obtain laminar flow

on the tunnel walls, transition will not occur on a test model. A

second approach could be to try and shield a test model from the tunnel-

wall-generated aerodynamic noise. Previous experiments using two con-

centric hollow cylinders with the outer cylinder serving as a shield to

protect the small hollow cylinder from the tunnel radiated aerodynamic

noise were reported in Reference {46). The idea was to measure the

transition point on the inside of the small shroud using a pitot probe

and, thereby, provide some measure of the effect that a radiated pres-

sure field had on transition. Unfortunately, the presence of the outer

cylinder introduced disturbances in the flow, and the results were in m

conclusive.

Based on the negative results of the experiments reported in

Reference (46), a somewhat different approach was used in the present

research. Results of these studies are reported in this section. The

experimental apparatus employed to demonstrate the effects of radiated

aerodynamic noise generated by a turbulent boundary layer consisted of

181

AE DC-TR-77-107

a iZ-in.-diam shroud model placed concentrically around the 3.0-in.-

diam hollow-cylinder transition model (Figure IV-7, page lO0). This de-

sign was selected because it allowed a controlled boundary-layer environ-

ment to be maintained on the shroud inner wall upstream of the transition

model. The specific design {shown in Figure VIII-I) resulted from a de-

tailed engineering study that evaluated: {a) shroud lip shock locations,

{b) optimum position of the transition model and microphone model inside

the shroud, {c) aerodynamic choking inside the shroud from model block-

age, {d) tunnel choking, (e) shroud lip bluntness effect on the shroud

inner wall boundary-layer transition location, {f) utilization of the

hardware at M = 3, 4, and 5, {g) aerodynamic loads, and {h) the ability

to control and provide laminar, transitional, and turbulent flow as de-

sired on the shroud inner wall. The 12.0-diam shroud model, as shown in

Figures VIII-1 and VIII-2, was the result of this study. The shroud

also provided some protection from the noise radiating from the turbu-

lent boundary layer on the wall of the 40-in. Tunnel A. The basic pro-

cedure was to measure the location of transition on the 3.0-in.-diam

model and pressure fluctuations on a microphone f lat-plate model as the

boundary layer on the shroud inner wall upstream of the transition model

changed from laminar to turbulent.

From the earl ier experiments of Laufer (38,86,87) and Morkovin

(44,45), i t was anticipated that when the shroud wall boundary layer

changed from laminar through transitional to fu l l y turbulent, then the

radiated aerodynamic noise would increase and adversely influence the

location of transition on the internal 3.0-in.-diam transition model.

182

Long Shroud Model in Mco -- 3 Position

-Iollow-Cylinder Support Strut

oo

J

Figure V I I I - I . Long shroud installation in the AEDC-VKF Tunnel A.

m

c} q

o

oo 4=,

--"Tunnel SideWall

B-B

Tunnel q.

~ 2 3 1 to Throat _1.~ Tunnel Station "0" Tunnel

- i i i / Short Shroud / / l.~-,I Long Shroud / (Fixed Position)-,/ / SUODOrt S t ru ts~ /

42

i 11.42

~ol!o,- Cylinder_

............ ~ 9-21" 1 . ,,'"

ng Shrou-d-- ! ~- ---~-----~ ~: ~ !-~ ~[--~---~ L_ \___~I __~ . . . . . . . . . . . i . . . . . . .

~----Moo - 3 P o s i t i o n ~ - -L--50. 8 - - -

• 4 Position 22. 5 " 1

32. 0 M_ - 5 Position-.J -L w 38.5 ~ ~-

r 20.0

F-- b = 0.0075 + 0.0015 around Leading- Edge Circumference

T ~ I0 deg

1 Tunnel

~l / -50-p in. " _ ~ S u r f a c e Finish

tun ,

• 0-in. -diam Hollow-

Cylinder Transition Model

View A (Long and Short Shroud)

View B-B


m o ¢-}

",4

o ~J

Figure VIII-2. AEDC-VKF Tunnel A long- and short-shroud configurations.

A EDC-TR-77-107

Shroud Models

Long and short shrouds (Figure VIII-E) were used to shield the

3.0-in.-diam hollow-cylinder transition model and a f lat-plate micro-

phone model. The 1E-in.-diam shroud model instal lat ion in the AEDC-VKF

Tunnel A is shown in Figure VI I I - I . The short shroud (Figure VIII-E)

was maintained at a fixed position, and the long shroud was repositioned

axial ly to prevent shroud leading-edge shock interference in the region

of transition measurements on the transition and microphone models, as

shown in Figures VIII-1 and VIII-3. The state of the boundary layer

(laminar or turbulent) on the shroud inner wall was controlled by vary-

ing the tunnel pressure level and/or by using a boundary-layer t r ip .

The steel shroud had an external, leading-edge bevel angle of 10 deg and

a leadlng-edge bluntness value of approximately 0.007 in. with an in-

ternal surface finish of 50 ~in. The shroud design was such that the

weak shock waves emanating from the shroud leading edge did not impinge

on the test area of the 3.0-in.-diam transition model, as i l lustrated in

Figure VIII-3.

Free-Stream Static Pressure Measurements

Static pressures were measured on the surface of the 3.0-in.-diam

hollow-cylinder transition model and the f lat-plate microphone model dur-

ing al l experiments. The purpose of these measurements was two-fold:

I. to ensure that the internal flow inside the shroud was super-

sonic as required; that the l ip shock location was in the

desired location; and there were no other shock waves or

compression or expansion fields impinging on the models, and

185

oo o~

| d

F l-I: 11.42

] . 4

1.3

Ps ].2

Pm ]. ]

].0

I t

50.8

Lip Shock J

M6 = 2-95 [

0.9 I I I O 4 8 12

I I

M 0 - 2 . 9 0 I o" I

I

I I I I

16 20 24 28

x, in.

. J

-I ,Sharp Leading-Edge 8- x 5-in. Flat Plate .~ise Model

I i I

I I I I I i I I i

I

I - -3 . O-in. -diam Hollow- i--~-Cvli nder Transition ]_IL M'odel

Shroud Model

Shock Location as Determined from Pitot ProbeTrace (x~ ]P.P in.)

~ Theoretical Two-Dimensional Pressure Distribution for a I-deg Initial Turning Angle at the Shroud Lip

I 0 [] Shroud Pressures I d ) - i~ Hollow Cylinder Pressures

(~ " - - Shroud Removed 13" Rat Plate Pressures

I I I I I I

32 36 40 44 48 52


m 13 t~

-n

0

Figure V I I I - 3 .

a. M = 3 .0 , Re/ in . = 0.30 x 106 OD

Inviscid pressure distribution inside long shroud.

~o

Ps

Pc)

i / e O f L o n g Shroud Model

I - - - - --- ... .....-]---- ~ - ~ Noise Model J - - -~ . . . . . . . . .- . . . . ~ ' ~ r Transition Model I = ' - ~ ~.---" " " E 11 .='~ I Lip S h o c k - ~ ~ . . . - > < . ~ . I I= ~ ! = ', J I _ ~ ' ~ . - - - " " ---- . . . . I , , n ' i ' I . . . - - " " " " " - -LL" I - - - ' - ' - - J I I I . . . . - - ~ " , - - .... ~! I I .

; , 0 7 ' ' ' ! - - v I I ! '

M 6 - 4.89

1.4

1.3

1.2

1.0

0.9 I 4

M 6 - 4. 78

I I I I I I I I I t

[ ~ I

I I I I

( /

I I I !

t r -Two- Dimensional ~ f Theo retical P ressu re,

Rise for a 1-deg Flow Angle

o ' - , - -Sh roud Removed

I I I I I I I I I I I I

8 12 16 20 24 28 32 36 40 44 48 52

x, in.

b. M = 5.0, Re/in. = 0.48 x 106

Figure VI I I -3 . (Continued).

m o o

.11

o , , , I

AE DC-TR-77-107

2. to ensure that the free-stream flow f ield in the AEDC-VKF

Tunnels A, D, and E were free from shock waves, compression

or expansion waves, and the static pressures were in agree-

ment with the tunnel calibration data.

Flow inside the shroud remained supersonic at all times as con-

firmed by static pressures measured inside the shroud at all test condi-

tions. Figure VIII-3 presents the static pressure data measured inside

the long shroud for M = 3 and 5 as determined from static pressure

orifices located on the shroud inner surface near the shroud leading

edge, from orifices on the 3.0-in.-diam hollow-cylinder transition model,

and from orifices on the f lat-plate microphone model. These data con-

firm that the shroud internal flow was supersonic at all times. A fa i r l y

good theoretical estimate of the static pressure distribution inside the

shroud was obtained assuming that a 1-deg, two-dimensional shroud l ip

shock existed.

Presented in Figure VIII-4 are the static pressure data measured

on the f la t plate at M = 3 and a large range of unit Reynolds numbers.

For comparative purposes, the Tunnel A centerline calibration data 17 are

also included in Figure VIII-4, and good agreement is seen to exist.

These types of data were obtained at all test conditions using the f l a t -

plate model and/or the 3.0-in.-diam hollow-cylinder model to establish

that uniform flow existed over the model at all test conditions. Addi-

tional free-stream measurements (shroud removed) are also included in

Figure VIII-3.

17The bar I shown in Figure VIII-4 indicates the spread of the experimental data.

188

AE DC-TR-77-107

~- 8.00 ~ - - 3 . 5 o - - - - - - , .

Pressure 7 , 0 - - ~ Lead FilIMm

Orifice ( T y p ) ~ B&K 1/4 in. , Microphone (~) . ~ i ~ 3 I o _--I..--_~_- I . ~ ~ - ~ ~ _ , . ~ Macn LI nes

[

25 deg

1 5. 00

I All Dimensions in Inches

1.04

8 ._~ 1.02

1.00

O. 98 0

I Tunnel A Calibrated Centerline Mach Number (Determined from Pitot Rake)

o Flat Plate Static ) Present Press u re l I nvestigation (Shroud Removed)

l i T - " ~ j 0. I 0.2 0.4 0.5

- 2 . 9 6

- 2. 97

- 2 . 9 8 8

- 2 .99 =E

- 3. O0

0.3 Re/in.

0 . 6 x 106

Figure VIII-4. Free-stream f lat-plate pressure data, M Tunnel A centerline.

= 3.O, AEDC-VKF

189

A E DC-TR-77 -107

Long-Shroud Wall Boundary-Layer Characteristics

A p i tot rake having f i f teen probes (Figure VIII-5) was used to

determine the long shroud inner-wall boundary-layer characterist ics.

From these data, the condition of the boundary layer, whether turbulent

or laminar, along with other boundary-layer characteristics was del~r-

mined.

The local boundary-layer velocity (u) was determined using the

p i tot probe total pressure and the shroud stat ic pressure. The stat ic

pressure (measured shroud stat ic) and total temperature was assumed to

remain constant through the boundary layer. The local flow velocity (UL)

outside the shroud boundary layer was calculated using T o with the meas-

ured shroud stat ic and the p i tot pressure from the outermost probe on

the rake which was outside the shroud boundary layer.

The shroud inner-wall boundary-layer displacement (~*) and mo-

mentum thicknesses (B) were evaluated using the following equations:

6" = f _ u - dy (7a) O

O = f pu 1 - u - dy (7b) o PLUL

Detailed data reduction equations are presented in Appendix B.

Typical velocity profiles, momentum thickness profiles, and displacement

thickness profiles are presented in Figure VIII-6. These data were inte-

grated graphically (using a planimeter) to produce the values of o and ~*

presented in Figure VIII-7.

At M = 3.0 and 5.0, the boundary layer (no trip) was ful ly tur-

bulent at the rake location for Re/in. ~ 0.2 x 10 6 , as shown in

190

AE DC-TR-77-107

Probe No__j_. 15 1.940 14 1,690 13 1,525 12 1.330 11 1.100 10 0.970 9 0.815 8 0.700 7 0.630 6 0,525 5 0,390 4 0,310 3 0,160 2 0,070 1 0.037

Note: y Is Distance to Centerline of Probe Tube Size: 0.0310.D. x 0.023 I.D.

4 2

200

>15 =14 a13 Radius = 5,625 =12

~Io \

~7 ~5

4 - - 0.20

-.p- -'1 TVD.

]- 2.5 _1

Dimensions in Inches

Figure VII I -5. Long-shroud boundary-layer rake.

191

A E D C - T R - 7 7 - 1 0 7

1.2 , I , I , 1 , I , 0.12 1 , I ' I ,

1.0 ~ ~ 0.10 O. 8 0.08

u O. 6 Re/in. x 10 .6 d._.ee 0.06 \ % ,-Transitional UL o 0.39 dY

0.4 z~ 0.15 0.04 ooo 0. 2 0.1)2 Turbulent

0 0 I I I I , I , I , 0 0 , I , I , I ~ . ~ . . . ~ : : a ~ . 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.6

9 " Y "(y)212R

a. M® = 3 . 0 , w i t h T r i p on Shroud

0.12 0.128~ i , i , i , ~ , i , I I - ~ r ' F ~ % _ o,o o~oll A \

o. o.| \ \ u o . ~o.oo t ~,\ UL 0.04 0.04l. \ ~ - i ~ L a m i n a r

" - ' Turbulent 0. 02 0. 02 ~ \ x ~

0 / = I , I , ' ~ 1 J I , 00 0.1 0.2 0.3 0.4 0.5 u 0.1 0.2 0.3 0.4 0.5 0.6

- y - (y)212R

b. Moo = 3 . 0 , No T r i p on Shroud

1 . 0 ~ O.O8~i.,.~O. lO]_,,.,,,. , , , , , ,

0.8

u o. 6 IJ _.,~,,,_.~,_u _ idle 0.06

l o.~ o.o~ r , o , . ~ o . , , , . , . , , o . , . - u - " .

o o.~ o .~ o . , o . , o . , o .~ o o.~ o .~ o . , o . , o . , o .~ o . ,

- y - (y1212R

Velocity Profiles Momentum Thickness Profiles

c. M = 5 . 0 , No Trip on Shroud CO

Figure VIII-6. Boundary-layer profiles on inner wall of long shroud.

192

~ J

M m R e m a r k s -----Theoretical 0 Estimate o 3 No Trip Crx=n • 3 With Trip e " ~ ; C F from Reference 135

O. 03 ~ Boundary-Layer Trip • ~,L f-Lonq Shroud

0.02 ~r 25.8~ "-~r.~r Rake

6; in. O. ]5 Moo • 3 Rake Position

F- r -4Ls O. lO .'I O. 08 Moo - 5 Rake Position

0.04 0.06 0.08 O.IO 0.15 0.2 0.3 0 .50 .?x 106 Re/in. c. Rake Locations

a. Displacement Thickness

o

8, in. 0.020

0.01 0.060.1110.10 0.15 0.2 0.3 0 .50 .Txl~ Re/in.

b. Momentum Thickness

x t Estimated Using Figure V II- 2

"14 x ~ " Z ~ _ x , , _.J Rake

L a m ~ u r ~ l e n t ~ , , , ~ ' : . . . . .,, . . . . . ~ ..

uounoary-Layer urowm

d. Sketch of Boundary-Layer Growth

All ~menstionsin Inch~

Figure VIIIm7. Long-shroud boundary-layer characteristics.

m

.h - n

4a , , j

0 ,,,,I

AE DC-T R-77-107

Figures Vl I I -6a and b. For M = 3.0 and Re/in. = 0.05 x 106 , the bound-

ary layer was laminar at the rake for the no- t r ip condit ion. When an

equivalent length concept (Xeq .) was used as outl ined in Figure VI I I -7d,

the experimentally no- t r ip , momentum thickness (e) data were in good

agreement with the theoretical calculat ions, as shown in Figure VII I -7b.

With the t r i p ins ta l led, the boundary layer became f u l l y turbulent at

the rake location for Re/in. ~ 0.12 x 106 . This resul t is as expected

since the serrated f iber-glass tape had been demonstrated to be an effec-

t ive t r i p at M® = 3 and Re/in. ~ 0.15 x 106 as shown in Figure VI-6,

page 138. The t r i p was inef fect ive at M® = 5.

Transit ion Results

Surface p i to t pressure traces obtained on the 3.0-in.-diam

hollow cyl inder , with and without the long shroud in posi t ion, are pre-

sented in Figure VIII-8a for N= = 3. The p i to t probe was remotely con-

t re l l ed , and a continuous p i to t pressure trace was provided by an X-Y

p lo t te r , as discussed in Chapter IV. As previously discussed, the loca-

t ion of t rans i t ion was defined as the peak in the p i to t pressure trace.

The impingement location of the long shroud l i p shock (x s) on the 3.0- in. -

diam hol low-cyl inder model was c lear ly v is ib le on the probe pressure

trace and was near the anticipated station.

The locations of turbulent flow on the shroud inner wall for two

conditions of particular interest are shown in Figure Vlll-8a. The no-

trip location was estimated using the data presented in Figure Vll-2,

page 154, and the tripped location was determined using Figure Vl-6, page

138. The probe traces presented in Figure Vlll-8b show a large forward

194

AE DC-T R-77-107

0.4 Scale

0

psia

a.

Figure VIII-8.

= 22.5in.

?~-. A-l-decjAngle I ~ . ~ ' - " " ~ . i , . .Tr i~ ' - - j , " ~ Lip Shock , ' ~ x " ~ .~,/ Location ~ ~. . . ~ , ::Radiated _,.,/'r~ t " >" " . . -. J / / tXs • ].5.5 in. :: Noise~"T-urbulent ~ " ~ ~ 1-

.~:~---J Laminar.,,....-Turbulent ~ .. ~ I -'+

L I -I //,--Long Shroud

I I

J L3.0.diam Hdl~-~llnder Transition Model <_3,n. IF'--" 21In. (Estimated)

ith Trip 0. 20x ,,,dlNo Trip IRe/in- ,u llRe/in . O. ZOx 10" - i xt

in, x_]O "6

~ 0.203 • Long Shroud, No Trip

i ~x t j / ' ~ ' ~ o n g Shroud, With Trip

o . I , I , I , I , I , I , I , I , I , I , I , I , I , l ,

I 4 5 6 7 8 g 10 11 12 13 14 15 16 17 18 19

X, in.

Surface Pitot Probe Pressure Traces for 3.0-in.-Diam Model, M = 3.0, Long

sxz@ I 0 No Shroud

A Long Shroud ~ , ~ : ~ _ [ ] Long Shroud with Tdp _"

R~ 2 % ~ -- _

[, • O, 0621 in,, 9LE • 6 deg

!


, [ , I I I I I , I , I , 0.I 0.2 0.3 0.4 0.5 0.6 0.8 l .OxlO 6

Re/In.

b. Transition Reynolds Numbers

Transition data measured with and without long shroud, M = 3.0, AEDC-VKF Tunnel A.

195

AEDC~R-77-107

movement of the locat ion of t rans i t i on on the 3.0-diam model when turbu-

len t f low occurred near the shroud leading edge ( t r ipped case). Based

on the estimated locat ion of turbulent f low on the shroud inner wa l l , i t

was ant ic ipated that for the no- t r ip long shroud case, t rans i t i on on the

3.0- in.-diammodel would be affected near Re/in. ~ 0.15 x 106 to

0.2 x 106 . This is indeed the case as seen in Figures VI I I -8a and b.

Al l of the t rans i t i on Reynolds number data obtained at M® = 3 are pre-

sented in Figure VI I I -8b. These data provide conclusive evidence that

the t rans i t i on locat ion on the 3.0- in. -d iam model is adversely affected

by the presence of a turbulent boundary on the shroud inner wal l . This

e f fect is shown in the next section to be the resu l t of radiated aero-

dynamic noise.

In addi t ion to the long shroud, a short conf igurat ion was also

tested, as shown in Figure VIII-9o The purpose of th is conf igurat ion

was to maintain laminar f low on the inner wall and attempt to shield

some of the radiated aerodynamic noise from the wal ls of the 40-in. Tun-

nel A from the 3.0- in. -d iam t rans i t i on model. However, i t was suspected

that th is short shroud conf igurat ion would not shield an appreciable

amount of rad ia t ion since the radiated pressure f luc tuat ions t ravel along

inc l ine rays s im i la r to, but somewhat steeper than, Mach waves [see Refer-

ence (86)] . Again, the leading-edge shock impingement (Xs) was c lear l y

v i s ib le on the probe pressure traces presented in Figure VI I I -9 and oc-

curred on the 3.0- in. -d iam model near the ant ic ipated locat ion.

Figure VI I I -10 presents the t rans i t i on Reynolds number resul ts

obtained without the shroud conf igurat ion and with the short and long

shroud configurat ions placed concentr ica l ly around the 3.0- in. -d iam

196

A E D C - T R - 7 7 - 1 0 7

. • . . • D - 11. ~ b = O.OOlP in. r Short Shroucl . . . . . . . . . . . . . . . . . . .

• /N BLE • ]0 deg 50P I ~ransition Model

I ~= I I4 in ' t ; s=12",xs']6" ' t (~

I I ... ~'~"~ ~ -" : " ~ Shock Wave for a I L.~ I ~ - -3 - ]-deg Angle I

. . . . . . . . . . . . . . " " ' : i

to Tunnel Tunnei Station "'O" Throat x s = 16

81.E 6deg / " "~" Moo Relin" x 10"6 / S c a l e

I , _ . . . , ~ IX t

5.0 0.29 .... "'"" . . . . . . . . . . . . . . . . . . . . 0 ! Xs = ]2 5 Scale r "~ Pp, pSlal '

q, Direction of u "Probe Travel / ~ ./P "-....._~

Mill -"

"~. Relin. x lO "° ...f ~ ~ -z)

Pp, psia

, I I z I , I , I , I , I , I , J I [ i [ , I , I

3 4 5 6 7 8 9 10 1l 12 13 14 15 16

x, in.


Figure VIII-9. Surface pi tot probe pressure traces on 3.0-in.-diam model, short-shroud configuration, M® = 4 and 5.

197

A E DC-TR-77-107

a.

1 0 6 _ 0 No Shroud 10 X • Short Shroud 8 . 0 ~ A Long Shroud (No Trip) 7.0 6.0 5.0

~t 4.0 ~ / 3.0

Wall 1 . , I , I , I ,

• • . 0 . 6 0 . 8 1 . 0

Re/in• x 10 "6

M= = 4, b = 0.0021 i n . , BLE = 6 deg

In6 • Short Shroud 10 x .v i~- 0 No Shroud

8•0~ A Long Shroud 7.0~ [] Long Shroud with 6.0~ Trip s•°1:- 4 . 0 -

Ret 32100 ~ V ~ a r y

Layer on Shroud Wall

1•0 , I , I , I i i i i , I , 0.I 0.2 0.3 0.4 0.6 0.81.0

Re/in. x 10 -6

10 x 106 / 8.01:: 0 No Shroud 7 , 0 ~ A Long Shroud 6.0 5,0 /

Re t 4.0 - 3.0 - s~"

2 • 0 -

bulent Boundary Layer on Shroud Wall

1.0 i I , I i l l , , I , I , I 0.1 0.2 0.3 0.4 0•60.81.0

Re/in• x 10 -6

b. M® = 5, b = 0.0021 i n . , OLE = 6 Deg

C . M = 5, b = 0.0013 i n . , OLE = 12 Deg

Figure VIII-IO. Transition Reynolds numbers measured with and without long and short shroud, M® = 4.0 and 5.0.

198

AE DC-TR-77-107

hol low-cyl inder model for M= = 4 and 5. These data were taken with and

without the boundary-layer t r i p on the long shroud inner surface at

H= = 5. The t r i p was not e f fect ive at M= = 5, which was not unexpected.

The t rans i t ion Reynolds number decreased at M = 4 and 5 as the shroud

inner wall boundary layer became turbulent.

These resul ts are discussed in more detai l in the next section.

Al l of the t rans i t ion resul ts obtained in th is invest igat ion are tabu-

lated in Appendix F, page 399.

Aerodynamic Noise Measurements

A f la t -p la te model (Figure VlII-11)instrumented with a surface

microphone was used to measure the free-stream aerodynamic noise levels

inside the long shroud as the boundary layer on the shroud inner wall

was changed from laminar to turbulent. The f l a t - p l a te microphone model

was also positioned inside the long shroud, as shown in Figure VI I I -12.

The microphone model was an 8- by 5 - i n . , sharp-leading-edge f l a t - p l a t e

instrumented with two ~-in.-diam microphones and two s ta t i c o r i f i c e s , as

shown in Figure VI I I -11. One microphone was mounted f lush with the

model surface and the other mounted in te rna l l y to record model v ibra-

t ions. The microphone model locations inside the long shroud were s imi lar

to the 3.0- in.-diam t rans i t ion model locations and were repositioned

with changes in free-stream Mach number to prevent the shroud leading-

edge generated shock wave from impinging on the model surface, as shown

in Figure V I I I - 3 , pages 186 and 187.

The rms pressure f luctuat ions were read d i rec t l y from two on- l ine

rms voltmeters during test operation. The microphone output was also

199

c~ C~

F I

5.00

Tunnel ~.

I =..C

i I

• - - 1.50 Typ. ~'t Static Pressure Orifice (]~jp.)

1.25 Typ. I" --~ ! II ~ ) I 1 ~

_ _ , _ ,, ,, - - -

o _ _ ~ )

. . . . ,I C Car.. z ~ e ( Microphone

Model - ~ ~

Lead Fill - ~

S U rface N~::;oii:iret .-~.~-~] P'~°iMseeaS u re Radiated

7777;

Internal Microphone to / - Determine Effects of

/ Model and Sting Vibrations /-Ventilated

/ Protectipg Grid

;>

-L-4,-.C L.__ .8 00 ._.~- 0.0015

l-- •

I /-" Microphone View A 6LE " 6 deg All Dimensions in Inches A, Nylonlnsert "~ I / ~1.19 f l , - p i n . Finlsh ~ / / / / / / / / / / / / / / / / / / / / / ] f Microphone Cable / Support Sting ~-L 00-~ ~ n s u l a t o r ~ J./c j _ IF" ~

I t ' -"T- Tunne,

View B-B ~ ' ' ~ - - - 1 J

~> m o

:4 ~J

0 .,,I

Figure V I I I - 1 1 . F l a t - p l a t e microphone model.

l ,J O

Tunnel A Station "0"

TU nnel A~---25" 8 ~ ~ - Flat ~e] ~ _

Mm : 3 Position fLong Shroud . ~ ~ - F l a t Plate

Tu n nel A ~_~ ~.- ~_---.-----4~._~--i--i- I

M m = 5 Position All Dimensions in Inches

Figure VIII-12. AEDC-VKF Tunnel A microphone-flat-plate installation.

m

O

"11

O ~d

AE DC-TR-77-107

recorded on an Ampex ® data tape system and later checked for verif ica-

tion of the on-line rms values. Microphone interference from model vi-

bration was minimized by providing a nylon insert around the surface

microphone, using insulator strips on the mounting plate, and f i l l i n g

the microphone cable cavity with cotton. Model vibrations as determined

from the internally mounted microphone were found to be negligible. See

Chapter V for additional details on data-recording procedures. The

microphone model was also tested in the free-stream of the AEDC-VKF Tun-

nels A and D.

Pressure fluctuations data measured on the f lat-plate model with

and without the long shroud in position are presented in Figure VlIl-13.

Significant results to be concluded from this figure are:

1. The no shroud data exhibited a monatomic decrease in the

p/q= data with increasing unit Reynolds number. Note that

the Re t data (taken from Figure VIII-8b) show just the op-

posite trend, i .e . , an increase in Re t values with increas-

ing unit Reynolds number.

2. For Re/in. ~ 0.05 x 106 , the boundary-layer flow on the

shroud inner wall was definitely laminar past the f lat-plate

model location. This was established from the boundary-layer

rake data obtained at position x = 25.8 in. , as shown in Fig-

ure VIII-7, page 177. At Re/in. ~ 0.05 x 106 the p/q® data

shown in Figure VIII-13 have a lower value than the no-

shroud condition. This means that the long shroud shielded

the f lat-plate model from the tunnel wall radiated pressures.

202

A E DC-TR -7 7-I 07

b.

Flow Long Shroud - - ~ " /

Bot.n:la,y- f Layer Trip / g Noise Model Locahon ~ Radiated '~clse -7 - .~ . . . . . "/].

/ St - " , o i . . . . . /Relin. x ] 0 - 6 / L..~__.~._j . . . . . .

- - o - | i >0 2 , 7 O.?,/"~Lamir, ar O. 05 .~ 'u rbu len t ;,o,, ,,a;eJ

3. O- i f " - d ram Hollow-Cylinder Transltm'l Model

I xt < 3 m. x t -" 21 in. No Trip With Trip ,Estimatedl (Measured La'nmar at Rakel

No Trip

a. Boundary-Layer Development Inside Long Shroud

6x]P 5

4

3 Re t

_ Shroud R e m o v o d - ~ . b - 0 0021 in.

"BEE = 6 deg ~ , . . , D ' ~ L o n g Shroud. _ _ ~ _,,/ Trip Removed

2 " ~ ' ~ - - - ~ ' ~ / / "

with Trip - - - J ~

]. I I I I I I l l I l i t l . t I i I , I ! l I I t RO4 0 0 6 0 0 8 0 . 1 0 (115 0 2 0.3 0 4 0.6 0 8

Re;ir. Ox lo 6

Transition Reynolds Numbers on the 3.0-in.-Diam Hollow- Cylinder Model

O.l~

O. Ol

EOOB

O. 006 q.~ 0.005

0. 0O4

O. OOB

0.0(9

O. OOI

/ , .,-Long Shroud

t ~ L o n g Sh , moved

- 0. 0015 in. BTn,6, . . i , , n ~ deq , , , i , , , , , ,

0.04 0.06 0.080.10 0.2

Re/in.

o • Shroud Removed

,,,. A Shroud in Position, No Trip n • Shroud in Position, with

Boundary-~yer Trip at Shroud Leading Edge

Open Symbols - Nov. 1966 Solid Symbols - Dec. 1966 (Dec. data adjusted by factor of 1.27)

Fourier Analysis of Data Points '~,., ~, , . L~ are Presented in Figure VIII-15.

0 3 0.4 0.6 0.8 l .Ox10 6

c. Root-Mean-Square Radiated Pressure Fluctuations

Figure VIII-13. Comparisons of transition Reynolds numbers and root- mean-square radiated pressure f l u c t u a t i o n s a t M = 3.0.

203

A E DC-TR -77-107

3. As the uni t Reynolds number was increased, the t rans i t ion

on the shroud inner wall moved forward and t r a n s i t i o n oc-

curred at the rake station {x = 25.8 in.) at approximately

Re/in. ~ 0.I0 x 106 (see Figure Vlll-7, page 193). Radiated

pressure waves strike the microphone model when Re/in. ~ 0.15

x 106. The p/q= data presented in Figure Vlll-18c confirm

this expected result. As transition moved closer to the

shroud leading edge and the flow became fully turbulent, the

p/q= data increased to a maximum value that is approximately

three times higher than the no-shroud data.

4. With the boundary-layer trip placed on the shroud inner wall,

it was expected that the boundary layer would be fully tur-

bulent for x > 3 in. and Re/in. ~ 0.2 x 106 {see Figure

Vl-6, page 138). Also the trip was shown to be ineffective

for Re/in. ~ 0.I x 106 . The p/q= data {obtained with long

shroud and with the trip) presented in Figure Vlll-13c show

that the pressure fluctuations reached a maximum value at

Re/in. ) 0.15 x 106 and remained essentially constant for

0.15 < Re/in. < 0.6 x 106. This trend is in agreement with

the expected behavior of the tripped boundary layer on the

shroud inner wall. %

5. The pressure fluctuation data {p/q=) presented in Figure

Vlll-13c are essentially a reverse image of the hollow-cylinder

transition data presented in Figure Vlll-13b. For example,

the Re t data increased with decreasing noise {p/q=) levels,

or vice versa. Also the points of intersection present in

204

A E DC-T R-77-107

the Re t data are in close agreement with the p/q. points of

intersect ion. Furthermore, the minimum Re t value corre-

sponds to the peak p/q® value.

6. Confirmation of the data presented in Figure VI I I - I3c was

obtained by conducting a second complete set of measurements

as indicated in the f igure.

Presented in Figure VIII-14 are the pressure f luctuat ion data

and Re t data measured at M= = 5 with and without the long shroud in posi-

The H = 5 data exhib i t characterist ics s imi lar to the H = 3 re- tion.

sul ts:

1. For the no-shroud condition, Re t increases monotonically

with decreasing p/q® values.

2. The p/q® values are initially low, which would be character-

istic of laminar i'Iow on the shroud wall. The p/q® data

then increase with increasing Re/in. until the flow becomes

fully turbulent on the shroud inner wall for the Re/in. ~ O.I

x 106 (see Figure Vlll-7, page 193). %

3. The Re t data are a reverse image of the p/q® data and exhibit

similar points of intersectlon.

4. It is of interest to note that the ~ = 5 transition Reynolds

number results shown in Figure Vlll-14b exhibited the char-

acteristic decrease in Re t with a decrease in leading-edge

bluntness (b) even when exposed to the intensified field of

radiated noise.

205

AE DCoT R-7 7-1 07

BoJndary- Layer Trip Location

Flow

Long Shroud I . , ] / - ~.o, se ",,todei

Radiated I ~ - - - ~ I

Re,,n.x,o'6 ~ ~ _ o _ _ ~ 1 _ , _ _ _ _ _ ' L~,~i~ar - . , 0 4 / I 0 . , to O.~_.~S'T:rbJl~-- ~ l ':3.0-,n.-d'a~ Ho,o,',-

. . . . . . . . . . . . . . " - ' - / Cyhnder Transition f f t M~el

=- x t :,teasured TJrbL.lert Profile at Rake.

(Estimated x t Location. No Trip) Without Tripl

a. Boundary-Layer Development Inside Long Shroud IO x tO 6 I I [ ; I I i I ' I ' I ' I ' I I I I . . ]

8 o • ShroLcl Req'oved ~- . ] 7 " & Long Shroud, Trip Removed ° ' i n -1

6 0 Lone Shroud With Trip ...:~0.~2] "~

. . I 4 ShroUd Removed ~ -~

. , . . /

Long Shroud

l l 1 I I t I t I i I z I , I I I I

04 0.060080.10 0.2 0.3 0.4 0.6 0.8 l .Ox]O 6 Relin.

b.

_L %0

Transition Reynolds Numbers on the 3.0-in.-Diam Hollow-Cylinder Model

O. 03 I ' I I I I I i I I ' i ' I ' I I I

O. 02 ',,

00 l

0,008 ~ o ~ /-Shroud O. (}06 ~ r l o v e d

O. 005 b - O. OOl5 in. 0 004 8LE = 6 deg

O. 003

0 , 0 0 2 I , I I l I I I I i I i I . I . I I

0.04 0.06 0.08 0.10 0.2 0.3 0.4 0.6 0.8 1.0x 106 Re/in.

c. Root-Mean-Square Radiated Pressure Fluctuations

Figure VIII-14. Comparisons of transition Reynolds numbers and root- mean-square radiated pressure fluctuations at M = 5.0.

206

A E DC-TR-77-107

The long shroud data presented in Figures VIII-13 and VIII-14

show that the boundary layer on a model can be dominated by the presence

of aerodynamic noise in the free stream.

Presented in Figure VIII-15 are the Fourier analysis of the

three data points identif ied in Figure VIII-13c as (T) , (~) , and (~).

The spectra data follow the same qualitative trend as exhibited by the

overall rms (p/q®) data presented in Figure VlIl-13c. The pressure f luc-

tuations at low frequencies were quite large. Two spikes appeared in

al l three sets of data at approximately 7 kHz and 14 kHz. These were

probably mechanically induced vibrational effects.

I I . NOISE MEASUREMENTS IN TWO AEDC SUPERSONIC WIND TUNNELS

Pressure fluctuation data measured on the f la t plate positioned

in the free stream of the AEDC-VKF Tunnels D and A are presented in Fig-

ure VIII-16. The present data obtained at M = 3 and 4 are compared

with data taken at M® = 4 by Donaldson and Wallace (BS) using the same

model. There are several points to note in this figure:

I. At Re/in. = 0.025 x 106 , the Tunnel D p/q® values were very

low. This corresponds to a laminar boundary layer on the

tunnel wall as determined from boundary-layer data published

in Reference (97).

2. At Re/in. ~ 0.05 x 106 , the wall boundary layer was est i-

mated to be transitional and the measured high peak is in

agreement with the findings of Vrebalovich (92), Laufer (38),

and Wagner, et al. (89).

207

AE DC-TR-77-107

See

Figure VIII-136

® ® ®

No Shroud Long Shroud, No Trip Long Shroud, With Trip

Relative Scale

N

~- 0.1

0.02

I\

M= = 3.0 ~ ' ~ Re/in. = 0.15 x 106 @~

0 10 20 30

Frequency, kHz

Figure VIII-15. Fourier analysis of selected data points from Figure VIII-13c.

208

A E D C - T R - 7 7 - 1 0 7

4.8 .- 112!o Tunnel D . ~-~~~;i~"

Downstream View a. Tunnel

T u n ~ u n n e l Wal~l Boundary I Boundary ~

Layer I Layer Probably Transitional

Laminar Ref. 97

0.03

O. 02

qm

O. 01

O. 001

m

B

m

0.003 O. O1

Tunnel D Station "0"

I 4.0"I }~- ) / Side View

D Instal lat ion

Tunnel Wall Turbulent

i

i~, Moo / - Tunnel D / ~,,4 ~. . = _ /

t eference88 / T FlatPlate / _ i .Loc~".L o~ 3 o....9..C -^ (Microphone)----// ~ " ' d o o u ~)

IA ~ 3 / Flat Plate / /

/ Present _ / / Investigation

m

- /~Tunnel O - / H o t Wire

/ / ~ ~ / Mm=4, / ~ [ R e f e r e n c e 88] I I I I I I I I I I I I I I I I I

0.1 l.Ox tO 6 Reli n.

Tunnel ~.

-Present Investigation Flat Plate (Microphone) Tunnel D

Microphone Data

sym , - - . , ~ , o ~ RMS Data - - - - Recorded

0-80 kHz RMS Data Recorded 0-40 kHz

Figure VIII-16. b. Pressure Fluctuations

Free-stream pressure f luctuation measurements, AEDC-VKF Tunnels A and D.

209

A E DC-T R-77-107

3. The microphone p/q= measurements in Tunnel D were s i g n i f i -

cantly higher than the free-stream hot-wire data. These re-

sults are as expected, i f the findings of Kendall (74) are

considered. Using a hot wire, Kendall found that the free-

stream disturbance (~) was amplif ied by the laminar boundary

layer on a f l a t plate by as much as a factor of one to two

orders of magnitude, as previously shown in Figure I I I - 8 ,

page 64. The data presented in Figure VIII-16 are consis-

tent with the results of Kendall.

The most s ign i f i cant resul t obtained from Figure VIII-16 is that

the Tunnel D ~/q= data are s ign i f i can t l y higher than the Tunnel A data.

Referring back to Figure VII-4, page 172, i t is noted that the Tunnel D

Re t data are s ign i f i can t l y lower than the Tunnel A data. These results

are in agreement with the aerodynamic noise theory, i . e . , the higher the

noise in tens i ty , the lower the t rans i t ion Reynolds number.

Power spectral density plots as measured in Tunnel D by Donaldson

and Wallace (88) are shown in Figures VIII-17 and VIII-18. The peak at

45 kHz evident in Figure VIII-17 is the microphone resonance frequency.

Donaldson and Wallace concluded that the other peaks must be mechanically

introduced by the microphone or mounting system since no such peaks ap-

peared in the free-stream hot-wire data.

Recent data published by Beckwith (28) supports the assumption

that a microphone mounted on the surface of a model w i l l measure s i g n i f i -

cantly higher pressure f luctuat ion in tensi t ies than a hot-~ire or f lush-

mounted microphone-pitot tube positioned in the free stream at certain

210

A E D C - T R - 7 7 - 1 0 7

1 0 = 3 i | I I I I i I I I I I l I I I i I I I I '

Microphone Resona nce --,,,,,,

10-4 _

Data from AEDC-VKF Tunnel I) _ Moo 4.0 10 -5

a lO -6

10 -7

10-8

I 10-9 , i l l i i i i i i i i i i i i i i i i i

i@ 1@ Frequency, f, Hz

Figure V I l l - l / . Power spectral density analysis of microphone output recorded at Re/in. = 0.24 x 10 o [from Reference (88)].

211

A E DC-TR-77-107

N

I0-4 i I I I I I I I 1

Ii I= '( I0_5 b Tunnel Wall Moo 4.0 I " |

I • Tu ~ . J . I , I

10 -7 I m

c ¢ D

,, ' 10-8

~. 10-9 o

I1.

I I I I I I

Data from AEDC-VKF Tu nnel D

Re/in. x 10-

Transitional

O. 2'

O. I;

0.0!

. . i ' q~ Laminar |

o,o J

10 -12 0. 025

z~ 1o4 Frequency, f, Hz

Figure VIII-18. Comparison of power spectra of microphone output for various unit Reynolds numbers [from Reference (88)].

212

AEDC-TR-77-107

supersonic-hypersonic ~ch numbers. Presented in Figure VIII-19 are

Beckwith's data taken from Reference (28). There are two signif icant

factors to note:

I. Pressure-fluctuating ms levels measured on the surface of a

model may not be strongly dependent on the model boundary

layer provided the mode] boundary layer is fully turbulent

or fully laminar, as shown in Figure VIII-Iga. This conclu-

sion was also reached by ~ugherty (52) for low supersonic

and transonic test conditions.

2. The mode] microphones measured a significantly higher pres-

sure fluctuation intensity, Figure VIII-Igb. This result

supports statement three above. Beckwith also concluded that

the amplification of the free-stream radiated noise by the

laminar boundary layer as reported by Mack (73) and Kendall

(74) might be the reason.

A recent paper by Bergstrom (59) compared wind tunnel free-stream

disturbance measurements from several sources and commented on the large

scatter in the data. The data used for the comparison included free-

stream hot-wire and model surface microphone data. Bergstrom noted that

the model surface microphone data were significantly higher than the hot-

wire data and concluded that additional studies need to be directed

toward resolving this apparent discrepancy. It is proposed that a sig-

nificant part of the differences in the data are the result of the free-

stream radiated noise disturbance being amplified by the model laminar

boundary layer and producing the higher microphone ms levels.

213

AE DC-TR-77-107

Tra nsducer . . . . i " ~ e = 5 Diam in. 4 t n . - ~ / _ _ . _ . ~ on 118 M,., = 6-- - " ~ _-~'~1._ 20ur10.3 in.

'~' Laminar- . . . . , kTra nsitionq' ---~ .-4 °"°- A 0.05 ~/," " , / 1 , / Turbulent

Transition 0.01 i i.~._L.=.~,,t i._ , , . , , , , I

1P 10 7 10 8 Relft

a. Variation of Overall RMS Pressure with Unit Reynolds Number

Arbitrary Scale,

psi, Hz

t , • Mm -- 6

. X, tn. Cone Surface ~', 4 - - - Laminar

Ii i " , 10.3 - - Fully Turbulent } Me= 5, Relft ~ 14x 106

~ , - - - Free Stream, RQo/ft= 17 x 106

J ~.,, j . . 1 . _ . j ~ P i t o t Tu~ (1/4-in. Diem)

. . . . . . / \ / - T r a n s d u c e r Noise and Vibration

"~ / - ' - - ~X, / - F l u s h Transducers \ . / / / ' , , . . ~ . ~ on Cone (118 in. Diam)

__//__ ~_~- _ _, . . . . :, . . . . . r-#s . . . . . -.-_ . . . . . . . . , - -

0 40 80 120 160 Frequency, kHz

b. Spectra of Pressure Fluctuations with AF = 200 Hz

Figure VIII-19. Measurements of fluctuating pressures under laminar and turbulent boundary layers on a sharp cone in Mach 6 high Reynolds number tunnel at NASA Langley.

214

A E DC-T R-77-I 07

I I I . TRANSITION MEASUREMENTS IN DIFFERENT SIZES

OF AEDC SUPERSONIC TUNNELS

Results obtained in this research and presented in Figures VIll-13

and VIII-14 (the shroud experiments), pages 203 and 206, have provided

conclusive evidence that radiated noise can dominate the transition pro-

cess. The free-stream pressure fluctuation data measured in the AEDC-

VKF Tunnel A (40- by 40-in. test section) and the AEDC-VKF Tunnel D (12-

by 12-in. test section) presented in Figure VIII-16, page 193, have

shown that higher noise levels are associated with smaller tunnels.

To verify that the transition location is dependent on tunnel

size (or radiated noise levels) an extensive experimental transition pro-

gram was conducted. The location of transition was measured in five d i f -

ferent AEDC supersonic-hypersonic wind tunnels using planar ( f lat-plate

and hollow-cylinder) and sharp-cone models as described in Chapter IV.

The basic data from these studies were presented in Chapter VII.

Transition Reynolds numbers measured at M = 3.0 on hollow-

cylinder models in three AEDC wind tunnels having test sections ranging

in size from I to 16 f t are presented in Figure VIII-2Oa. Sharp-cone

transition data obtained at M = 4.0 in two different sizes of AEDC wind

tunnels are presented in Figure VIII-2Ob. The large increase in transi-

tion Reynolds numbers with increasing tunnel size is attributed to the

decrease in radiated aerodynamic noise levels as discussed in Chapter

I I I and the previous sections. The monotonic increase in transition

Reynolds numbers with increasing tunnel size is i l lustrated in Figure

VIII-21 for M = 3.0.

215

A E D C -T R -77-107

5x 1 ! i Tunnel AEDC'PWT"16S ._. (16 x 16 f t ) ~ .

140 x 40 in. ) ~ Moo - 3. 0 M 6 -3.0

AEDC-VKF-D .x~ (b - O) - 8 ~ (12 x 12 in.)! 0 J - , I , t ~ l I i l , I , ! , I , l J ! I I I I .

0.03 0.04 0.06 0.08 0.1 0.2 0.3 0.4 0.6 0.8 1.0xld s (Re/in.)m

a. Planar (Hollow Cylinder) Model

)oxzP -

-VKF - MOO- 4.0 ~.Tunnels ,~ ~ r , . - - - - ' 0 ' ' - 0 " t From Figures

( Vl I-5 and " ~ J vim-6 "

4 . i A I ~ , ~ ~" Planar

2

"-D.ta s

0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.OxlO 6 (Re/in.)6

Figure VIII-20. b. Cone Model

Variation of t ransi t ion Reynolds numbers with tunnel size.

216

b,3

" • Sym Tunnel and Test Section Size Reference q RAE (5 by 5 in. ) Bc 136

6 x 106 - ,, , o USSR-1325 (7. 9 by 7. 9 in. ) 53 u o aeg t, • AEDC VKF-D (12 by 12 in. ) Present Invest.

" - - 5 - - j [] • JPL-SWT (18 by 20 in. ) 123 _ / 5 f O $ AEDC VKF-A (40 by40 in. ) Present Invest.

5 ~ zi AEDC PWT-16S (16 by 16 ft) Present Invest. / \

"- Sharp Cones

4 ~ , Flat Plates (Ret)6 / (Hollow Cylinder) -~

3

2 ~ 0 Test Sedion [ ] "~ (Re/i

(Ret) 5 Values Correspond to Surface Probe

f-- Model Leading Edge (PP)peak Values. See Tables 4 and 5 I I I I I , I I

0 200 400 600 800

~m, in.

Figure VIII-21. Effect of tunnel size on transition Reynolds numbers at M ~ 3.0, f l a t plates and sharp cones. =

m o

-11

,=

0

AEDC~R-77-107

The data presented in Figures VIII-20 and VIII-21 show conclu-

sively that transition data obtained in supersonic tunnels is strongly

dependent on the size of the tunnel. The increase in Re t values with in-

creasing tunnel size is attributed to a decrease in the radiated noise

levels.

IV. NASA ACTIVITIES

In the late 1960's, the National Aeronautics and Space Administra-

tion (NASA) at the Langley Research Center (LRC) began a series of de-

tailed and very extensive experimental research programs to investigate

the effects of radiated pressure fluctuations on the location of bound-

ary-layer transition on wind tunnel models. These studies were confined

primarily to the hypersonic Mach number range 5 ~ M® ~ 20 and included

conventional continuous-flow and intermittent air and nitrogen tunnels

as well as their M ~ 20 helium tunnels. These research efforts have

been underway continuously since 1969 and have progressed to the point

where NASA-LRC is currently involved in defining the cr i ter ia for a

"quiet" hypersonic, M® = 5 wind tunnel that wi l l incorporate unique

mechanical and aerodynamic design features. These features wi l l enable

a laminar boundary layer to be maintained on the tunnel walls and there-

by eliminate the radiated aerodynamic noise disturbance that is now

known to dominate the transition process in conventional supersonic wind

tunnels.

Wagner, Maddalon, and Weinstein (89) reported in 1970 on one of

the most fundamental and informative of the NASA-LRC transition studies.

They used a M® = 20 helium flow tunnel (test section diameter = 20 in.)

218

AEDC-TR-77-107

to investigate radiated aerodynamic noise disturbances in the tunnel

free stream when the tunnel wall boundary changed from laminar to tur-

bulent. They used a hot wire positioned in the free stream to determine

the type and magnitude of the free-stream disturbances using the

Kovasznay-type model diagram and the analysis developed by Laufer as

discussed in Chapter I I I . Presented in Figure VIII-22 are the rms pres-

sure fluctuations measured in the test section free stream (Station 139)

of the M = 20 helium tunnel. Note that below a unit Reynolds number of

40.15 x 106, there was a sharp drop in the p/p® data, and this was the

result of a laminar boundary developing on the tunnel wall (89). Bound-

ary-layer transi t ion Reynolds numbers were measured on a sharp-leading-

edge, lO-deg inclined wedge positioned in the test section as shown in

Figure VIII-22a. Included in Figure VIII-Z2b are the measured free-

stream radiated pressure f luctuation data. Although, there were no

transit ion data obtained below (Re/in.) ~ 0.15 x 106 (transi t ion o f f the

back of the model), i t can be seen that the changes in Re t data varied

inversely with the p/q® values. The results presented in Figure VIIIm22

provide direct confirmation to the results obtained in this research and

presented previously in Figures VIII-13 and VIII-14, pages 203 and 206.

The shroud results obtained in the present investigation and

presented in the previous section (Figures VIII-13, page 203, and VIII-14,

page 206) and the NASA studies, Figure VII I-22, have produced essential ly

the same results using completely independent methods. The NASA studies

provide additional ver i f icat ion of the present research that was f i r s t

published (10) in 1968.

219

A E DC-TR-77-107

M m = 20

I0 x 10 6 - i

( re t )6 -

10. 01

~ 8

10 deg Wedge

J , i I , I , l , l , I t , I L , , [

0.1 1.0x 10 6 (Re/in.)m

a. lO-Deg Wedge Transition Reynolds Numbers

0 . 1 - m

m

f ~ p -

P~O

O. 010. Ol

b o

Figure VIII-22.

NASA Langley Helium Tunnel

Laminar Boundary Layer on

Tunnel Wall I I I 1 l i l l e

0.1 (Re/i n. )~o

I I t I

ulent Boundary ~ 1 ~ " Layer on

I I Tunnet Wall

I I | I I I I I 1

1.0x 106

Free-Stream Pressure Fluctuations

Effect of free-stream disturbances on wedge model transition, M ~ 20 [from Reference (89)].

220

AEDC-TR-77-107

Fischer and Wagner (90) extended the NASA-LRC transit ion studies

to include the study of transit ion on sharp cones and the measurement of

the free-stream radiated noise levels in two helium tunnels 18 (H® = 20,

22-in.-diam tunnel and the M = 18, 60-in.-diam tunnel). The found

transit ion Reynolds numbers varied inversely with the measured noise

levels as reported ear l ier in Reference (89). They also compared their

(Ret) 6 data with the sharp-cone Ret-nolse correlation developed by Pate

(11). These data are presented later in Chapter IX.

NASA personnel have attempted to correlate Re t data d i rect ly

with the measured p/q. values and found fa i r correlation provided the

free-stream Mach number remained constant, as i l lust rated by the data

presented in Figure VIII-23 taken from Reference (81).

Fischer (122) conducted an experimental study of boundary-layer

transit ion on a 10-deg half-angle sharp cone at M = 7. He compared his

Re t data with the f la t -p la te aerodynamic noise correlation published by

Pate and Schueler (10) and found good agreement af ter giving considera-

t ion to the fact that sharp-cone Re t data should be higher than f l a t -

plate Re t data at comparable test conditions.

Stainback (130) studied the effects of roughness and bluntness

(variable entropy) on cone transit ion in Reynolds numbers. One major

result from these studies was the finding that (Ret) 6 data were insensi-

t ive to Mach number variations obtained by changing the cone angle while

18In Appendix D, page 355, a discussion of the signi f icant effects of using inappropriate viscosity laws when computing transit ion Reynolds numbers wi l l be discussed. I t is of interest to note that similar problems have occurred in helium tunnels as discussed in Reference (129).

221

AEDC-TR -77-107

10 8

107

(Ret) 6

106

tOp

C w

Sym ~ M e deg

o 6 5 10 0. 6 Air O 6 5 10 0. 6 Air o 8 5 16 0.4 Air z~ 20 5 16 I. 0 He ~, 20 5 16 0. 6 He 0 20 ~ 16. 2 2. 87 I. 0 He 0 20 ~15. 8 2. 87 1.0 He c~ 18 - 14. 4 2. 87 1.0 He o 20 6. 8 Wedge 1.0 He I~ ~0 Flat Air

Plate

Test Tunnel Oiam Tw/T o Gas in. cm

_

I I | I I I ]

10-I i0-2 10-3

- - o r - -

Pe Ue

20 50. 80 I2 30.48 f ]8 45.72 ,) Stainback 22 55. 88 22 55. 88 22 55. 88 ] Fischer 22 55.88 t and 60 152.40 Wagner 22 55. 88

Figure VII I-23. Correlation of t ransi t ion Reynolds numbers with rms disturbance levels [from Reference (81)].

222

A E D C-TR -77-107

maintaining a constant (Re/in.)~ value. These data were discussed in

Reference (10) and i t was pointed out that the aerodynamic-noise-domi-

nance theory could explain this anomaly. Stainback (I21) published the

data as presented in Reference (10) and comented on the absence of a

var iat ion of (Ret) ~ with Mach number. Stainback mentioned the fact that

the aerodynamic noise correlat ion as published in Reference (10) offered

an explanation of this unusual resul t .

Measurements of free-stream pressure f luctuat ions using a p i to t

pressure probe instrumented with a flush-mounted transducer was invest i -

gated and reported by Stainback and Wagner (91). They also investigated

the ef fect of changing the tunnel s t i l l i n g chamber screen configurations

and found a s ign i f i cant ef fect on the Re t data measured on a 5-deg ha l f -

angle sharp cone. Also the t ransi t ion data did not correlate very well

with the rms pressure f luctuat ion levels measured with the p i to t probe

at M = 5.

As a resul t of unusual t rans i t ion data reported by Mateer and

Larson (131) in 1969 and because of considerable differences in the

(Ret) 6 data measured in the NASA Ames 3 .5- f t hypersonic tunnel and the

NASA Langley M= = 8 variable density tunnel on sharp slender cones, an

indepth review and remeasure of t rans i t ion data in these two f a c i l i t i e s

were conducted by NASA personnel (26,132).

These very exhaustive studies and reviews ( including sending re-

search engineers to Ames to make measurements and vice versa) f i n a l l y

established that, when certain tunnel modifications were made which in-

cluded heater changes at Ames and in ject ing a i r into the tunnel wall

boundary layer for cooling [instead of helium as used in Reference (131)]

223

AEDC-TR-77-107

and making changes in upstream values and tunnel settl ing chamber screen

design, then similar Re t results were obtained. Similar free-stream rms

pressure fluctuations were measured in each fac i l i t y using flush-mounted

transducers on the cone surface. However, free-stream rms pressure f luc-

tuating data measured using the pitot probe technique (132) gave results

that were about 30% different. The cone Re t data were found to corre-

late with the cone surface rms data.

The high Reynolds number "quiet" tunnel currently being investi-

gated by NASA-LRC is shown in Figure VIII-24 and described by Beckwith

in Reference (28). Some of the basic studies conducted in support of

the tunnel conceptional design have been reported by Harvey, Stainback,

Anders, and Cary (29). The proposed fac i l i t y wi l l u t i l i ze a combination

of unique mechanical and aerodynamic design features to try and maintain

a laminar boundary layer on the tunnel inter ior walls as i l lustrated in

Figure VIII-24. The objective wi l l be to maintain a laminar boundary

layer over the most of the in i t i a l conventional nozzle (29). The rod wall*

The concept of rod wall application to supersonic wind tunnel

design can be attributed to Spangenberg and Klebanoff, National Bureau of

Standards, Washington, D.C. In i t ia l work conducted at the NBS in the mid

and late 1960's demonstrated the feas ib i l i ty of using rod walls to maintain

laminar flow on supersonic tunnel walls. This technique provided a means

for eliminating "aerodynamic noise" disturbances which radiate from the

turbulent boundary layer that exists on conventional solid surface walls.

Fundamental research work is currently continuing at NBS under sponsorship

and funding by the USAF Arnold Engineering Division (AEDC), AFSC, Arnold

AFS, Tennessee.

224

A E DC-TR -77-107

Boundary- Layer Removal Slot Shield

Rapid-Expansion . . . . . . . . Subsonic Nozzle ~ wlm ~ucuon

-~S u ctio n " ~ ~'~c---~ -~- ~-/C-J~-z~.

--" ~, - .-~.: " -~- .F~-~

Test Model:./ Measurements of Transition and Sound Disturbance Field

a. Sound Shield Concept

15 in.

Rodded Sound Shield

Rapid Expansion No~

Boundary Layer Removal Slot - -

Nozzle Approach -~ .~_....,~, /

J 2in. R

5.75 in. R

12 in.

2.5 in. R

15.5 in.

Figure VIII-24. b. Nozzle Details

NASA-Langley .M= = 5 quiet tunnel Reference (28)].

concept [from

225

AEDC-TR-77o107

section shield w i l l allow the turbulent boundary layer to bypass the test

section. A pressure drop across the rod walls sound shield w i l l then

serve the two-fold purpose of maintaining a laminar f low along the in-

side of the rods and preventing any background noise from radiat ing back

into the test section. Noise cannot be transmitted across the sonic

l ine that w i l l ex is t in the rod gaps.

Successful completion of the "quiet" tunnel w i l l not only allow

t rans i t ion Reynolds numbers at high Reynolds number, hypersonic condi-

t ions (M® = 5) to be obtained in a "quiet" test environment, but w i l l

also provide for the f i r s t time a test condition that wi l l allow

microscopic studies and evaluation of eddy viscosity models, turbulent

shear stresses, etc. in hypersonic turbulent boundary layers that are

free from free-stream disturbance effects.

V. EUROPEAN AND USSR STUDIES

LaGraff (57) reported on a series of supersonic t rans i t ion

studies conducted using a hol low-cyl inder model. He stated that as a

resul t of the paper by Pate and Schueler (10) a test program was in i t ia ted

at Oxford Universi ty, England to fur ther investigate the dependence of

t rans i t ion on fac i l i ty-generated disturbances. The model was a 3 - in . -

diam hol low-cyl inder model having a leading-edge diameter of 0.0003 in.

The location of t rans i t ion was measured using a s l id ing p i to t probe ad-

jacent to the model surface. Four research groups part ic ipated in the

study as l i s ted in Table 4 taken from Reference (57). The two sets of

data that can be compared d i rec t l y are the Oxford University data for

M = 6.95 and the Aerodynamic Research Ins t i tu te of Sweden data for

226

Table 4. European t rans i t ion test f a c i l i t i e s [from Reference (57)] .

b,3

Organization

Oxford University Dept. Eng. Science (O.U.)

Imperial College Aero Dept. (I.C.)

Roils Royce Bristol Engines (R.R.) Aero Research Inst. of Sweden (F. F. A)

Facility

GunTunnel

Gun Tunnel

Gun Tunnel

Research Personnel

J.E. LaGraff D.L. Schultz

A. Hunter J.L. Stollery

E. Charlton R. Hawkins

Mach No. (Moo)

6. 95

~eynolds No./in. c 10 -~ (Reli n. )oo

4.45-8.7

Tw/To

O. 410

Working Section Diameter (in.)

Open Jet (6. 1)

Hyp. 500 B Iowdown Tunnel

Bo Lemcke

8.2

7.75

3.82 - 6.81

3.78 - 7.10

O. 378 Open Jet (7. 5)

O. 369 Open Jet (11.1)

Open Jet (19. 7) 7.15 10.5 O. 454 > m t~ ¢')

7l

O ,,,I

A E DC~R-77-107

M = 7.15. These gun tunnel data are presented in Figure VI I I -25 and

show the ef fects of tunnel size s imi lar to the f indings found in the

present research (see Figure VIII-20, page 216). The results presented

in Figure VIII-25 provide added confirmation of the increase in Re t with

increasing tunnel size.

Ross (60) conducted an experimental

supersonic blowdown wind tunnels (Netherlands):

Tunnel M® Size, m

SST 3.6 1.2 x 1.2

transition program in two

Nozzle Length, m

5.42

GSST 3.6 0.27 x 0.27 1.22

10 x 10 6

8

6

Re t 4

See Table 4 for List of Transition Tunnels

= O. 0013 in.

(Tw/To)mode I Sym Moo wall Tunnel Size

o 1.0 0.41 O.U. 6. 1-in. -diam Gun Tunnel

z~ 7. ! O. 45 F.F.A. 19. 7-in. -dia m - HYP. 500 Blowdown Tunnel

Re t = Peak in Surface Probe Pressure I I I I

2 4 6 8 10 2 x 10 6 Reli n.

Figure VIII-25. Hollow-cylinder transition data [from Reference (57)].

228

AEDC-TR-77-107

The transition model was the 3-in.-diam hollow-cylinder model

(d = 0.0003 in.) used by LaGraff {57). The transition location was de-

termined using a surface pitot probe. Ross found a large variation in

Re t with tunnel size as shown in Figure VIII-26. These results are in

agreement with the present findings and provide independent confirmation

of the strong variation of Re t data with tunnel size.

Bergstron, et al. {55) analyzed three sets of gun tunnel flat-

plate transition data {56,57,133) in addition to his transition studies

conducted at M = 7.0 in the Loughborough University of Technology gun

tunnel. Using the PatemSchueler aerodynamic noise correlation (I0) de-

veloped for conventional wind tunnels, he correlated gun tunnel Re t data

and concluded that transition data obtained in hypersonic gun tunnels

were influenced essentially by the aerodynamic noise present in the test

section. He further concluded that maw of the discrepancies in gun

tunnel transition data could be explained on this basis. The transition

data from the four gun tunnels displayed good overall correlation with

aerodynamic noise and tunnel size parameters according to the method of

Pate and Schueler {I0). For a given Mach number, Bergstrom et al. (55)

also found that transition Reynolds numbers correlated very w@ll against

the free-stream rms pressure fluctuations ratioed to free-stream static

(~rms/p®) as calculated using the method of Williams and Maidanik (96)

[Eq. (6), page 59] for a wide range of tunnel sizes,

Studies were conducted in the USSR by Struminskiy, Kharitonov,

and Chernykh (53) in the early 1970's to establish i f unit Reynolds num-

ber effects and tunnel size effects as reported in Reference (10) existed

at higher unit Reynolds numbers at M = 3 and 4. Two wind tunnels were

229

AE DC-TR-77-107

Re t

10 x 10 6 9 8 7

6

Sym

0 A

M® Tunnel

3,6 CSST

3,6 SST

Test Section Size

10,6 x 10,6 in,

47,2 x 47,2 in,

~m* in .

4 8

213

B

B

m

m

B

Hol low Cylinder

b = 0,0003 in,

I I I

2 3 4

(Re/in,)=

I I I i I

5 6 7 8 9 10 x 10 6

Figure VIII-26. Effect of tunnel size on Ret data from Netherland Tunnels [from Reference (60)].

230

AEDC-TR-77-107

used (Tunnel T-313, 0.6 by 0.6 in. and Tunnel T-325, 0.2 in. by 0.2 i n . ) .

The test model was a sharp f l a t plate having a surface f in ish of 2 )m

and posit ioned at zero angle of attack. Transi t ion locations were de-

termined using the surface p i to t probe technique. Values of Re t fo r an

e f fec t ive zero leading-edge bluntness was obtained by extrapolat ion (see

Section VI). Presented in Figure VII I -27 are the basic t rans i t i on data

from Reference (53). An attempt was made in Reference (53) to corre late

the Re t data for a given Mach number using a Reynolds number based on

the test section diameter. For the H= = 3 data, f a i r agreement was ob-

tained by corre la t ing Re t with Re ~D" In 1975 Kharitonov and Chernykh (54) extended the i r research to

include pressure f luc tuat ion measurements on the walls of Tunnels T-325

and T-313 at H= = 3 and 4. Their studies established a change in Re t

levels with a change in acoustic levels. They concluded that the change

in Re t with a change in un i t Reynolds number (Re/ in.) was the resu l t o f

the acoustic perturbations (aerodynamic noise) present in the test sec-

t ion . They reasoned that the scale of turbulence was related to the tun-

nel wall turbulent boundary-layer displacement thickness. Using a theory

proposed by Taylor (134) that related Re t to the in tens i ty (u /u) , the scale

of turbulence (6 = 6") , and a character is t ic length (L = d) , they ob-

tained a cor re la t ion of Re t = F[(u/u)(L/~) l / n ] for n = 0.25 and M= = 2.5

to 6. The scatter for f l a t - p l a t e t rans i t i on data obtained in six wind

tunnels was ±15%. They included data from AEDC-Tunnels VKF A and D and

AEDC-PWT Tunnel 16S as taken from Reference (10). They concluded that by

cor re la t ing the experimental t rans i t i on Reynolds numbers with the tunnel

wall boundary-layer character is t ics then i t was possible to explain the

nature of the un i t Reynolds number e f fec t in conventional wind tunnels.

231

AE DCoTR-77-107

Ret

0.1

- b = O. 00591 in.

- From [Reference (53)]

- Tunnel / - I , . , o . "

_ -

T325 I I I 1 1 1 1 1 1 I

0.2 0.3 0.4 0.6 0.8 1.0 2.0 (Re/i n. )m

3.0 x 106

a. M =4.0

10 x 10 6

B

6

5

4 Ret

3

I0. 1

Sym b, in. Tunnel Test Section Size o 0. 00394 "1325 7. 9 by 7. 9 in. A 0. 00197 1325 7.9 by 7. 9 in. • 0. 00394 13D 23. 6 by 23. 6 in. & 0. 00197 1313 23. 6 by 23. 6 in.

B

-[Reference (.53)]

- Extrapolated

f~ff I l

0.2 0.3 I I I I I 1 [

0.4 0.6 0.8 1.0 (Reli n. )oo

I 2.0 3.0x 10 6

Figure VIII-27.

b. M = 3.0 ¢0

Effect of tunnel size on f la t -p la te numbers - USSR studies.

transit ion Reynolds

232

CHAPTER IX

A E DC-TR-77-I 07

DEVELOPMENT OF AN AERODYNAMIC-NOISE-TRANSITION CORRELATION

FOR PLANAR AND SHARP-CONE MODELS

Theoretical and experimental studies contributing to the basic

understanding of the radiated pressure f ie ld (aerodynamic noise) gen-

erated by a turbulent boundary layer were reviewed in Chapter I I I . Re-

sults were presented which ident i f ied the tunnel wall turbulent boundary

layer mean shear and displacement thickness as major parameters in f lu -

encing the radiated pressure fluctuations (p/q=).

The experimental results obtained in this research using the

long shroud apparatus (Chapter VI I I ) demonstrated that aerodynamic noise

could have a dominating effect on the location of t ransi t ion. The shroud

experiments demonstrated, conclusively, that the radiated noise domi-

nated the transit ion process on models with simple geometry such as f l a t -

plate and slender sharp-cone models in supersonic-hypersonic wind tunnels

(M= ~ 3). The shroud experiments also showed that Re t data could be cor-

related di rect ly with rms pressure f luctuations.

Subsequent studies by NASA-LRC at M= = 20 have provided indepen-

dent confirmation of the dominance of radiated noise on transit ion and

that Re t data can be correlated with radiated noise intensi t ies, i . e . ,

p/q= data. Attempts at correlating Re t data di rect ly with measured ~/q=

data are s t i l l hampered by inconsistencies in the measured p/q= data.

Experimental scatter (nonrepeatable) in pressure f luctuation data was

i l lustrated in Figure VIII-13, page 203, of the present research. Refer-

ences (28) and (132) provide additional information on differences in

233

A E D C-TR -77-107

measured p/q= data. There are also basic differences in the absolute

levels of intensity measured using a f lat plate equipped with micro-

phones and hot-wire anemometers positioned in the free stream as dis-

cussed in Chapter VIII.

During the init ial efforts of the present research the only wind

tunnel free-stream pressure fluctuation data available before about 1970

were the data of Laufer (1950) published in Reference (38). Since tran-

sition data from many different wind tunnels existed at the beginning of

this research and essentially no pressure fluctuation data existed (ex-

cept Laufer's), an effort was made to correlate Re t data with the param-

eters that could be identified as related to the radiated aerodynamic

noise intensity, i .e., the tunnel wall shear stress, displacement thick-

ness and a characteristic length.

From Figure II I-4, page 57, one sees that

since

P/Zw = f(M) ~ constant

z" w T W

P® U 2® q®

then

Cf =

P : f(M®, Cf~, q®

From Reference (135) one knows that for turbulent flow

Then

C F ~ 1.2 Cf

-P-= f(C F, M®) (8a) qw

234

A E D C - T R - 7 7 - 1 0 7

From Figure I I I -3 , page 71,

P ~ 6* 1 ~ u (8b) P® length scale

Since

q . --

nu

P ~ M 2 ~* . q® ® ~ ,

then

Combining Eqs. (8a) and (8b), one obtains the funct ional re la t ionsh ip

Assuming

%

~-= f (S C F, 6 - ~) (8c) q ~ ' 5

Ra t = f q=

Then one has

Re t = f(M=, C F, 6* , ~) (8d)

The use of 6" as a cor re la t ing parameter in an aerodynamic-noise-

t rans i t i on corre la t ion is not only suggested by Figure I I I - 3 , page 7 i ,

but also from physical reasoning. Weak ( isent rop ic) waves can be re-

lated to a supersonic wavy wall analogy where the turbulence eddies

"globs" that create the turbulence are related to the boundary thickness

(or displacement thickness) as discussed in References (87), (93), (94),

and (96). I t is also reasoned that 6" could enter into the cor re la t ion

because of a frequency dependency related to the physical s ize, i . e . ,

scale ef fects as shown in Figure V-15, page 140, where 6* appears in the

frequency corre la t ing parameter (Strouhal number).

235

AEDC-TR-77-107

Attempts were made to correlate Re t data directly with C F, but

these efforts were unsuccessful. I f a plot of Re t versus C F were made,

i t ~muld be shown that the Mach number and tunnel size would appear as

additional parameters.

Presented in Figure IX-1 is a successful correlation of

R e t ~ * / C as a function of the tunnel wall mean skin-fr ict ion coeffi-

cient (CFI) with the tunnel size appearing as a parameter. This corre-

lation evolved from a series of t r ia l and error efforts and was f i r s t

published in Reference (10). The data included in Figure IX.l repre-

sent sharp-flat-plate and hollow-cylinder model transition data obtained

in nine wind tunnels covering a Mach number range from 3 to 8, unit

Reynolds number per inch range from 0.05 x 106 to 1.1 x 106 , and tunnel

test section sizes from 1.0 to 16 f t .

Values of the transition Reynolds number used in the correla-

tions correspond to the transition location determined from the peak in

the surface pitot probe pressure trace and are for a zero bluntness

leading-edge thickness. Transition data from other sources which were

not obtained using a pitot probe were adjusted as listed in Table 5,

page 234, as determined from Figure VI-12, page 165. The zero bluntness

Re t data were obtained by extrapolating the transition values from sharp,

but f in i te , leading-edge models (see Chapter VI) to b = O. I t is de-

sirable to correlate Re t data for b = 0 since this in effect removes any

model leading-edge geometric influences.

I t is seen from Figure IX-1 that Mach number does not appear as

a parameter. Also, the systematic variation with the tunnel size

236

--,1

1.2xlO 6

lie 1.0~--

o.9 -

0.8 ~-

o.7 -

o.6 -

o.5 --

0 . 4 -

0.3 ~-

~ 2 -

o . ] -

o - 0

CFI Determined Assuming Adiabatic Tunnel Walls

Re t Corresponds to Peak in Surface Probe Pressure

|

All Ret Values Extrapolated to b - 0

(L4 O.8

Tunnels

12-in.

40-in. and 50-in.

1.2

CF I

Ref. Present Study

37 37

VKF 169

Present Study

108

170 ]7O

]19 Present Study

16"ft

1.6 2.0 2.4x 10 "3

Figure IX-1. Influence of tunnel size on the boundary-layer correlation [from Reference (10)].

Sym M__~m o 3.0 A 4.0 a 5.0 Cf 5.0 O 6.1 q 7.1 (] 8.0 • 3.0 • 4.0 • 5.0 I 8.0 0 3.7 O 4.6 0 6.0 0 6.0

8.0 6 3.1 0 5.0 • 3.0

transition

Source AEDC-VKF-D (12- by 12-in. )

,1 AEDC-VKF-E 112- by 12-in. )

1 AEDC-VKF-A 140- by 40-in. )

AEDC-VKF-B (50-in. Diam) JPL-SWi" 118- by 20-in. )

NASA-Langley 120- by 20-in. ) AEDC-VKF-B (50-in. Diam)

NACA-Lewis (12- by 12-in. ) NASA-Lewis (12- by 12-in. ) AEDC-PWT-16S (16- by 16-ft)

Reynolds number'

m O

',,4

O ,,,,J

AEDC-TR-77-107

suggests that the data can be collapsed into a single curve i f the tun-

nel test section size is incorporated into the correlat ion as a no~a l i z -

ing parameter.

The normalizing parameter

Ret ~ / ~ / ~ e t ~ -~ )Ci=48 in"

is a function of the tunnel test section circum~rence as shown in Fig-

ure IX-2. A linear fairing of these data provides a method for collaps-

ing all of the Re t data presented in Figure IX-1 onto a single correla-

tion curve, as shown in Figure IX-3.

The empirical equation presented in Figure IX-3 for sharp flat

plateswasmodified ~ Ross(58) into asi~leanalyticalexpression. ~f in-

ing C F = (d)(ReCm)e where d = 0.0276 ~.22 and e = -0.146 - 0.011M and

= (O.0194)(M®)(¢m)(Re~m)'I/7,~ss expressed Eq.(1) in Figure IX-3 as 6*

Ret = O.44 ( mi0.028 M-O.05? (Re/miO.443÷O.O28M® (g}

Equation (8) gives reasonable results over the Mach number range

3 ~ M ~6 for adiabaticwall wind tunnel and adiabaticwall models.

A similar correlation for sharp slender cones has also been de-

veloped. The ini t ial correlation of cone ~ t data obtained using the

planarcorrelation parameters is presented in Figure IX-4. Although the

sharp-cone data correlated fairly well using the planar correlating

parameters, the correlation exhibited two systematic inconsistencies.

First, the slope of a linear fairing of the data is somewhat steeper than

238

A E D C -T R -77-107

~ From Figure IX-1

1.0 ,~

0,9 -- ~ ~

0 . . 8 - . .. - ' " ~ " "

Tunnel Size 0.2

16-ft 40-ft 20-in. 12-in. °'1!- [ [ I (C1= 48 i n ' ) ,

0 I I I I I I I I I I 0 0.2 0.4 0.6 0.8 1.0

CI C

Figure IX-2. Tunnel size parameter.

239

A E DC-TR-77-107

0. 0141 CF -2" 55 (0. 56 + 0. 44 C11C) Eq. (A)from Ref. 10, Ret =

Based on data from Nine Facilities varying in size from 1 to 16 ft, Ntach number range from 3 to 8 and (Re/ft)oo range from 0. 6 x 10 6 to 13. 2 x 10 6.

(.TI

d ÷

ur~

m

L ~ o.2 _ ~-, ,-," O. 15 -

0 . 1 -

0.08

0.06 - 0.05 '

0.4

2.ox1 i f ' I

1 .5 -

1 .0 -

0 .8 - m

0 .6 - m

0 .5 - B

0 .4 - B

0 . 3 -

I I I I ' I ' I ' I '

All Re t Data Extrapolated tob = 0

Eq. (A)

Symbol Notation is Consistent with Table 5, Page 234

m

m

m

m

m

m

m

i

m

I , I , I , I I I I I = 1 = - 0.6 0.8 1.0 2 3 4 5x10 -3

CF I

Figure IX-3. In i t ia l correlation of transition Reynolds numbers on sharp f la t plates with aerodynamic noise parameters [from Reference (10) ].

240

AEDC-TR-77-107

Planar Data Consistent with Data Presented in Figure IX-3 Sharp-Cone Data from Eleven Facilities Varying in Size from 1 to 4. 5 ft in Test Section Diameter. Mach Number Range from 3 to 14, and (Re/ft) m Range from 1.2 x 106 to 14. 4 x 10 6

Symbol Notation for Cone Data is Consistent with Table III in Reference 11.

3x10 6, ~,~,,

2xi0 6

' I ' I ' I

From Reference 11

~ - i 0t G ' I ~ 1.0 o '

°.6

• ~ O. 4 I S harp L ~ ' C°nes 7

0 . 2 -

0.1 m

0 . 0 8 -

0.06 , i , i 0.4 0.6

Planar

I I , 1 , I I 1 , I ,

0.8 1.0 2 3 4 5xlO -3

CFI

Figure IX-4. In i t ia l correlations of planar and sharp-cone transition Reynolds numbers (from Reference (11)].

241

AEOC-TR~7-107

the slopes of most of the indiv idual data sets. Second, the data from

the larger tunnels show a systematic grouping somewhat higher than the

smaller tunnels. Systematic dif ferences of th is type and magnitude were

not apparent in the cor re la t ion of the planar data. These two incon-

sistencies were el iminated by establ ishing a d i f f e ren t tunnel size

normalizing parameter for the sharp-cone data. A p lo t s im i la r to Figure

IX - l , page 221, was made fo r the sharp-cone data. The new normalizing

parameter for sharp slender cones was determined to be 0.8 + 0.2 (Cl/C)

for C1/C < 1.0 as shown in Figure IX-5.

Presented in Figure IX-6 is the cor re la t ion of the cone (Ret) 6

data using the slender-cone normalizing parameter. A s i g n i f i c a n t l y im-

proved cor re la t ion of the data was accomplished.

One factor that must be recognized in the cor re la t ion of cone

data is the absence of a one-to-one re la t ionsh ip or even a constant ra t i o

between the free-stream and cone surface un i t Reynolds number (see Appen-

dix D, page 373). I f a series of cone angles had been selected that

would have allowed a constant ra t io of cer ta in cone to free-stream

parameters - - say, the un i t Reynolds number ra t i o to have been main-

tained - - then any re la t ionsh ip that might have existed between the

strength of the cone bow shock wave and the inf luence of the radiated

noise levels on the cone laminar f low a f te r passage through the bow

shock might possibly have remained more constant. Future invest igat ion

in these areas would, of course, be desirable.

Since the cor re la t ion only included (Ret) ~ from sharp slender

cones (e c ~ 10 deg), caution should be exercised when using the corre la-

t ion to predict t rans i t i on locat ions on large angle cones with a strong

bow shock.

242

AE DC-TR-77-107

1.2

Sharp Cones

('Ret) 6 : 0.80+ 0.20 C1 C

, i

B

0

r v ,

ev ,

1.0

0.8

0.6

0.4

0.2

B

B

B

-16 ft 40 in.

O - l , , I , 0

Fi gu re

/

Flat Plates

R e t ~

/Ret 6~ /C- -48 in.

C 1 - 0.56+ 0.44

o Sharp Flat Plates (From Figures IX-1 and 2) o Sharp Cones

Sharp Flat Plates from Figure IX-1

23.6 in.

i i i ' ~ t I I I i I I I

0.5 1.0 1.5 2.0 C1 C

IX-B. Tunnel size normalizing parameters.

5.0in. i i I

2.4

243

A E DC-TR-77 -107

48. 5 CF -1" 40 (0. 8 + O. 2 CI/C) Eq. (B)from Ref. 11, (Ret) 6 -- JPlc

1 1 1

Based on Data from Eleven Facilities Varying in size from 1 to 4. 5 ft in diameter, tvlach number range from 3 to 14, and (Reoo/ft)(z) range from 1.2 x 1~ to 14. 4 x 106.

3 x 106

2.0

1.0

0;7 0.6

.4-

oo 0.5 c~

0.4

0.3

0.2

(B)

Symbol Notation Is Consistent with Table 6, Page 237

O. 15 0.4 0.6 0.8 1.0 2.0 3.0 4.05.0x10 -3

CF I

Figure IX-6. Correlation of transition Reynolds numbers on sharp cones with aerodynamic noise parameters [from Reference (11)].

244

A E DC-TR -77-107

The average turbulent skin-fr ict ion coefficient (CFI) used in

the correlations presented in Figures IX-I through IX-6 was determined

using the method of van Driest (van Driest - I) as published in Refer-

ence (135). The values of the tunnel wall turbulent boundary-layer dis-

placement thickness (6*) used in the correlations were the experi-

mentally measured data or computed values as indicated in the data pre-

sented on pages 250 and 253 and discussed in Appendix B, page 324.

Since the original aerodynamic-noise-transition correlations

were published (Figures IX-3, page 224 and IX-6, page 229, there has

been a great deal of world-wide attention devoted to studying aerody-

namic-noise-transition correlations as discussed in Chapter VII. Conse-

quently, there have been new transition data published from a number of

different wind tunnels on which data were not previously available.

New and unpublished transition data have also been obtained at

AEDC-VKF. These data have been obtained primarily in the AEDC-VKF Tun-

nel F (hotshot) hypersonic wind tunnel (see Chapter IV) on a sharp

slender cone and f la t plate for M ~ 7.5 and 8, respectively. The Tun-

nel F fac i l i t y has been undergoing a major modification program, includ-

ing the addition of a family of contoured nozzles [see Reference (103)].

Sharp slender cones and the f lat-plate models described in Chapter IV

were the standard flow calibration models. These models have provided

new transition data which allow the aerodynamic-noise-transition corre-

lations presented in Figures IX-3, page 240, and IX-6, page 244, to be

extended to higher Reynolds numbers.

The data published by NASA, the European countries, and the USSR

plus the new hypersonic tunnel data obtained by the author has prompted

245

AE DC-TR-77-107

a re-evaluation of the aerodynamic-noise-transition correlat ions pre-

sented in Figures IX-3 and IX-6. Specif ical ly:

1. the tunnel normalizing parameter w i l l be re-evaluated using

new data from very small tunnels ( test section height less

than 12 in . ) and

2. the tunnel wall sk in - f r i c t i on coef f ic ient w i l l be computed

using the method of van Dr iest - I I (see Appendix A, page 315)

including nonadiabatic wall ef fects. In References (10) and

(11) (and Figures IX-1 through IX-6), an adiabatic wall tem-

perature was assumed. This was a val id approach since most

of the t rans i t ion data were from supersonic tunnels having

essent ia l ly adiabatic wal ls. However, there can be a sig-

n i f i can t ef fect of wall temperature on C F at the higher Mach

numbers and high Reynolds numbers as discussed in Appendix A,

page 315. Also the method of van Dr ies t - I I is now generally

accepted to be better than van Driest- I as discussed in

Appendix A, page 315.

Presented in Figure IX-7 are new t rans i t ion data (53) compared

with the t rans i t ion correlat ion curves from Figure IX - l , page 237. Note

that the data from the medium size tunnel (T313) correlates as would be

expected but the data from the very small tunnel (T325) does not estab-

l i sh a new tunnel size correlat ion curve, but follows the 12-in. tunnel

data fa i r ing closely. Results from these data were included in Figure

IX-5, page 243, and i t is seen that the normalizing parameter for C1/C >

1.0 should be held at a constant value of 1.0. Data obtained on a sharp-

cone model (136) have also been evaluated, and the results are included

246

AE DC-TR-77-107

1.2x 106

1.1

1.0

0.9

0.8

0.7

t~' 0.6

0.5

0.4

0.3

0.2

O.l

Sym Reference Moo

o 53

Tunnel Size

3. 0 USSR Tunnel - T325 (7.9 by 7.9 in.) 4,0 USSRTunneI-T325 (7.9by7.9 in.) 3.0 USSRTunnel -T313(23.6 by23.6 in.) 4. 0 USSR Tunnel - T313 (23. 6 by 23. 6 in. )

Fairing of Data from Figure IX-1 (Moo - 3 to 8)

m

m

u

m

m

I

, 40 by 40 in. - and 50-in. Diam-

Tunnel Test Section Size

,12 by 12 in.

20 in.

by 23.6 in.

S6by Z6ft

7.9by 7.9 in.

m

I t l l i I l t t t l l l l I t i t I i O i 0 0.4 0.8 1.2 1.6 2.0

CFI

I f i 2.4x 10 "3

Figure IX-7. T rans i t i on Reynolds number c o r r e l a t i o n .

247

A E DC -T R -77- t 07

in Figure IX-5. These data also indicate that for Cl/C ~ 1.0, the cone

normalizing parameter should also be 1.0.

Presented in Figure IX-8 is the new correlation of planar model

transition data obtained using transition Reynolds number data from 13

wind tunnels covering the Mach number range from 3 to 8 and tunnel sizes

from 7.g-in. to 16-ft test sections. The tunnel wall turbulent skin

friction was computed using the method of van Driest I I . The value of

CFI I includes nonadiabatic tunnel wall effects. Table 5 l ists the values

of the tunnel wall temperature ratios (TwJTaw) used in these computations.

Table 5 provides additional information on test conditions, tunnel size,

method of transition measurement, amounts of adjustment in Re t values,

etc., and identifies the sources for all the data presented in Figure

IX-8. I t should be noted that the slope of the correlation shown in Fig-

ure IX-8 is identical to the init ial results presented in Figure IX-3,

page 240.

The correlation presented in Figure IX-8 is recommended for use

in estimating Re t values on sharp f lat plates in wind tunnels. Equation

(9) has been programmed in FORTRAN for digital computer application as

discussed in Appendix C, page 343:

o.o126 (CFIz) -2"s5 (Ret~)flat = (10)

plates

The new correlat ion of sharp-cone t rans i t ion Reynolds number ob-

tained from 16 supersonic-hypersonic f a c i l i t i e s is presented in Figure

IX-9. These data cover the Mach number range from 3 to 20 and tunnel

248

AEDC-TR-77-107

10 x 106 B

L Ret =

1.0 x 10 6 -

IU

¢ v

0 . 1 -

0.05 O. 0001

Figure IX-8.

O. 0125(CF)-2.55(~)

C 1 C

>I.0

~l.O

1.0

0.56 + O. 44 C~, 1

I I

Correlation

Original Correlation Curve from Figure IX-3, Page 224

b = 0 Leading Edge Geometry

Sea Table 5 for Specific Information on the Data Sources

Ret Corresponds to Adiabatic Wall Conditions Ret Based on Peak Pressure Location in Surface Probe Pressure Trace

i J ~ Jill

O. 001

CFII

of planar model

I I

transition

t I I I i I

0.01

Reynolds numbers.

249

AEDC-TR-77-107

Table 5. Source and range o f data used in the planar model transition Reynolds number correlation (see Figure IX-8).

Source Symbo~ Mao

Present Study o 3.0! I. 3, Z. 1. 2.3, 3.0,3.6

(sea Figure V-l) ~, 4 .0 3,8 a 5.0' 3.8

Present Study o" 5.0 l (Figure V I I - I ) Reference

(169)

Present Study (see Figure Vl- Z)

Reference (3i') tsee Figure VI- l e "

o 6.1 1L2,4 ~q 7.1 1.L2,4

8.0 1.1.2 • 3.0 13.21,23,

3 0,~ 6, S • 4.0 2. L 3, 3.6.8 • 5 0 1.3,2.1,3,

3.6,8 II 8.0 0.6 to 9.4

- l ' ' *,,ool---.Tr.o..,oo x lO ). in. eLE, de 9 (RUin.}oox |0 "6 Conliguratiotl Tunnel ize ' De lec l ion Adjustment I in Delerminelion lw.rfew

6,12 0. ItoO.6 tIC AEOC-VKFD i I210 ]2in. Peakpp None 145. fleaiblePiate ].0

6 0.1to0.6 ' ! q l r . 56in ) Reference 6 0.11o0.4 i I~/I

15 O, 3to 1.1 FP . . . . . . . M i n ~see 1 0.2to0 7 1 Fiour. B-,.

0 3 to05 I Appendix B

6.]2 0.15100.6 HC tAE[~VKFA J 40 - " Peakpp 231 FleaibtePlate L.0

6 0.15 to 0 6 23 l i t ' ~ i r ~ I 6,12 see fkjure B-

]r Appendix B 5.6.12.5 0.1lo0.3 HC AEOC-VKF8 SO'in {diem - Peekpp 2~ RakeProtile 0.$

le r " 244 in. I

Raterence 11231 o 3.7 <1 15 O. 11o0.4 o 4.6 <1 15 O. I to0 4

Reference (]261 0 6. 0 <2 20 0. 59. n_ 59

Reference (17Ct $ 6.0 1 20 (1 ]4. 0. 27 4" 8.0 1 ZO 02

Reference C]201 d 3.1 O.Sto &0 5 O.ltoO.5 Reference I].19) O 5. 0 1, 5,10 15 O. 15 to O. 4

Preaent Study • 3.0 L 5,5.9 5.5, 0.08 toO. l [

Present Study o 5 2.3 v 5

0.53 ~0 1.06

12 0.3to 1.3

Ratere~e (53) ~ 3 2,4 14.5 0.3to 1.~ zt 4 6 O.4to 1.5 G 3 2,4 O.4to 1.35 At 4 6 0.4to 1.5

I~ateronce (63) -r 5 2 IO 0. 2 to O. 6 x 8 0.2,0.3 .K- 10 C~2

FP FP

FP

FP FP

HC HC

HC

PLZO-in. SWT 18byZOin. Maximum'r w PLY- in SWi" ] 8 b y . i n . Maximumz" w

MASA-LanoleY 20 by 20 in. Peak pp

AEDC-VKF B 50-in. diam Peak Pn Z.EDC-VKF B 50-in. diem Peak

NACA-Lewis 12 ~ ]2 in. Maximum T w NASA-Lewis 12' by 12 in. Maximum F w

AEDC-PWT 165 16 by 16 ft. Peak pp

EC - Hollow Cylinder FP - Flat Plate

• *Adjustment ~sed on resuils from Figure V1-12, PaOe "r w - Surface Shear Stress q - Heat Transfer pp - Peek in Surfece PilOt Probe Pressure T w - Maximum Surface Teml~rature

FP AEDC -VKF F ~-in. diam Maximum (j

I~ AEOC-VKF E 12 by ~ in. Peak pp

FP USSR-T~ 1.9 by7.9 Peak pp USSR-T325 7.9 by?.9 )SSR-T3]3 23.6 by 23.6

USSR-T313 Z3.6 by ~ .5 FP AEOC-VKF A 40 by 40 Peak pp

AEDC-VKF B 50-in. diem ~EDC-VKF C 50-in. diam

I.O 0.8 eL}' 0.6

Exp. Oat& Figure 0-8

= l l ! Fl~ible P~e LO *: l l t Rake Pr~ilea

I~r • 117 in.I Reference (9)F

1.1 =9C 6 Correlation 0. ! Figure 6-7, Appendix B

None =23~ Rake Protile 0.1 None =232 I t r - 2Min.) 0.5

Exp. Data, Figure B-8

1.2 ~ ~' Correlation I. 0 1.15 47 Figure B-?,

Appendix B

None 792 Fk=ible Plate L.O Rake P r,~iles 4L r • 839 in.) see FkJure B-l. Appendix D

None ~qlI ]5" Correlation G 3 Figure B-& Appendix B

None 39.6 Flaible Plaqe 1.0 56. 8 Meas Figure

B-5. A pl~'~ix D

None 36 6 ° Correlation I,O Figure B-'/,

106 ARoendix O 106

None Z'].i Experimental L0 232 Data, see 300 Figures B-7

end B-8, Appendix B

250

A E DC-TR -77-107

10 x 10 6

, , 0

p..,

1.0

48. 5 (CFI I )-1.40(~,)

See Table 6 for Symbol I dentificatlon (Ret) 6 Corresponds to Adiabatic Wall CondlUons (Ret)6 Based on Peek Pressure Location in Surface Probe Pressure Trace

C I

C 0

>I.0 1.0

_<I.0 0.8+ 0.2~

0.1 0.0001 0. 001 0.01

CFII

Figure IX-9. Co r re la t i on ot' sharp-cone t r a n s i t i o n Reynolds numbers.

251

AEDC-TR-77-107

sizes from 5- to 54-in.-diam test sections (see Table 6). The use of

CFI I did not change the correlation. The linear fairing of the cone cor-

relation in Figure Ix-g matches the data correlation previously devel-

oped (Figure IX-6, page 244) exactly. Equation (10) represents the

analytical expression for the correlation curve:

48.5 (CFII)-1"40 (C) (Ret6)con e = ( I I )

Of particular interest is the recent transition data obtained in

the NASA-LRC 22-in.-diam helium tunnel at M ~ 21 as reported by Fischer

and Wagner (go). Included in Figure Ix-g are the Langley data from

Reference (go), and good agreement with the correlation is shown to exist.

I t should be noted that the Langley data l ie about an order of magnitude

outside the range of the original correlation. The total skin-friction

coefficient (C F) and the parameter (Ret) 6 ~-~*/C used for the Langley

data are the values reported in Reference (gO).

The sharp-cone Re t correlation shown in Figure IX-g [Eq. (11)]

has been programmed in FORTRAN IV digital computer application as dis-

cussed in Appendix C, page 326, for predicting transition Reynolds num-

bers and locations in conventional supersonic-hypersonic wind tunnels.

Tunnel wall turbulent boundary-layer displacement thickness (6*)

values used in the correlations presented in Figures IX-8 and Ix-g repre-

sent experimentally determined values or estimates using the theoretical

or empirical methods as discussed in Appendix B, page 324. See Tables 5

and 6 for additional information on how 6* was determined for specific

data sets.

252

AEDC-TR-77-107

Table 6. Source and range of data used in the sharp cone transition Reynolds number correlation (see Figure Ix-g).

' " Sea FigureVl-]2 ~Nitrogen Test Gas - Heat Transfer pp • Peak in Surface Pilot Probe Pressure T W- M~imum 5urfaceTernl~rature

Symbols cortespondi r~ Io data in FkJure IX-9

253

A E D C - T R - 7 7 - t 0 7

I t is well known that the model wall temperature (Tw/Taw) can

have a significant effect on the location of transition at supersonic

speeds (2,4,16). Consequently, all the transition data presented in

Figure IX-8 were obtained at Tw/Taw ~ 1, except the AEDC-VKF Tunnel F

data (M® ~ 8) where Tw/Taw ~ 0.3. For M ~ 6, Deem et al. (63) and

Rhudy (169) have shown that the location of transition on flat-plate

models tested in wind tunnels was not dependent on Tw/Taw. Therefore,

all the transition data included in Figure IV-8 are assumed to represent

adiabatic wall conditions.

The sharp-cone transition data obtained in the present research

were also measured at adiabatic wall conditions, Tw/Taw ~ I. However,

a large percentage of the transition data obtained from other sources

for M® ~ 6 were measured at nonadiabatic wall conditions (T w < Taw).

Table 6 provides a tabulation of the Tw/Taw value for each data set.

Based on the results of Deem et al. (63), Rhudy (169), and Kendall (14),

i t is assumed that the cone transition data are not a function of Tw/Taw

for M= ~ 6. Therefore, all the transition data included in Figure Ix-g

are assumed to represent adiabatic wall values.

The correlation presented in Figures IX-8 and IX-9 and the

digital computer program developed in Appendix C, page 326, wi l l allow"

reasonably accurate predictions of transition Reynolds numbers and tran-

sition location on adiabatic wall, sharp f la t plates and cones for

M ~ 3 and all size conventional supersonic-hypersonic wind tunnels.

The reader is reminded that the transition Reynolds number cor-

relations cannot be applied to bal l ist ic ranges, atmospheric free f l ight ,

or any test environment other than a conventional wind tunnel (M ~ 3)

254

AEDC-TR-77-107

because of the obvious restrictions imposed by the aerodynamic-noise-

dominance hypothesis and the correlating parameters C F, 6*, and C. Sim-

i lar ly, since the correlation was developed for f inite size wind tunnels,

the proper boundary conditions for free f l ight are not included. Con-

clusions relative to possible fundamental influences of Mach number and

unit Reynolds number on Re t in a disturbance-free environment cannot be

drawn from these results.

I t is fel t that the results obtained in this research conclu-

sively show that the fluctuating pressure field radiated by the tunnel

wall turbulent boundary layer dominates the transition process on sharp

f lat plates and sharp cones at zero angle of attack in conventional

supersonic and hypersonic wind tunnels (M ~ 3). I t is concluded that

the unit Reynolds number effect exhibited in supersonic-hypersonic wind

tunnels is primarily the result of the radiated aerodynamic noise. Ig

Furthermore these results show that i t will be very di f f icul t i f not im-

possible to separate out "true" Mach number and unit Reynolds number

trends ( i f they exist) from conventional wind tunnel Re t data that are

dominated by the radiated pressure field (aerodynamic noise).

lgsee Reference (23) for a detailed discussion of the unit Reyn- olds number effect in a "quiet" ballistic range environment.

255

AEDC-TR-77-107

CHAPTER X

EFFECTS OF TUNNEL SIZE, UNIT REYNOLDS NUMBER, AND MACH NUMBER:

COMPARISONS BETWEEN THEORY AND EXPERIMENTAL DATA

I. INTRODUCTION

Presented in this chapter are experimental transition Reynolds

number data obtained in wind tunnels varying in size (test section

height) from 5 in. to 16 f t , for Mach numbers from 3 to 14, and over a

unit Reynolds number range from 0.1 x 10 6 to 2.5 x 10 6 per in. Transi-

tion Reynolds number data for both sharp f la t plates (and hollow cyl in-

ders) and sharp slender cones at zero incidence are presented.

A FORTRAN IV computer program was developed to predict (Ret) 6

and x t values on zero bluntness, f lat-plate, and cone models tested in

conventional supersonic-hypersonic wind tunnels (M ~ 3). This model

uses the aerodynamic-noise-transition empirical equations [Eqs. (10) and

(11)] developed in Chapter IX. Details of the program are presented in

Appendix C. In the following sections extensive comparisons are made

between the experimental data and calculations from the math model.

I I . EFFECT OF TUNNEL SIZE

Experimental data illustrating the large variation of transition

Reynolds numbers on sharp flat plates and sharp slender cones with tun-

nel size are presented in Figures X-I and X-2, respectively, for a Mach

number range from 3 to 16. The predicted variations of {Ret) l with

256

A E DC-TR-77-107

30 x lo 6

Open Symbols Represent Computed Data. Eq. (10) and Appendix C Solid Symbols Represent Experimental Data (Relate Tunnel Size and M m to Table 5)

Represents Fairing of Computed Data ------Represents Approximate Maximum Envelope of Wind Tunnels

Re t

20

15

10 9 8 7 6 5

4

(Tw/Taw)tunnel .,1 Moo wall . . ~ ~ ~

/ \

/ _

"/7 0 ~ - (Re/in.)m: O. 20x 106

3 , /1.0 ~ A. _ A b = 0 A 1 Y , , I , l l l l , ] 1 , 1 , I I , I , I l l l l , T I , 15 20 30 T 40 50 60 80 I00 200 300 400 600 8001,000

C, in.

Figure X-1. Effect of wind tunnel size on planar model transit ion Reynolds numbers for various Mach numbers.

257

AE DC-TR-77-107

30 x 10 6

Open Symbols Represent Computed Data, Eq. (11) and Appendix C Solid Symbols Represent Experimental (Relate Tunnel Size and Moo to Table 6)

~ - Represents Fairing of Computed Data - - - - - - Represents Approximate Envelope of Wind Tunnels

25

20

15

(Rat)6 6 5

4

3

2

(Tw/Taw)tu nnel j ~ , - . ~ _ ~ MO:) _ wall _..1.~ ~>~a \ ~

12 O. 25 ~ - -

s o.5 /

3 1. 0 (Re/in.)oo = O. 20 x 106

15 20 30 40 50 60 80 I00 200 300 400 600 800 1,000 C, in.

Figure X-2. Effect of wind tunnel size on sharp-cone transit ion Reynolds numbers for various Mach numbers.

258

A EDC-TR-77-107

tunnel size and (Re/in.)= = 0.20 x 106 for a Mach number ranging from 3

to 16 are included in Figures X-1 and X-2.

The predicted values were computed for specif ic tunnel geometries

and the calculated results were then faired to clearly i l lus t ra te the

signi f icant and monatomic increase in Re t with increasing tunnel size.

Experimental data have been included for comparative purposes, and in

general, the agreement between the computed results and the experimental

data is considered good. I t should be noted that the computed data cor-

respond to the correct tunnel wall temperature rat io (Tw/Taw) tunnel

geometry and model location as indicated in Figures X-1 and X-2. Addi-

tional specif ic information can be obtained from Tables 5, page 234, and

6, page 237. I t should be noted that the planar (Ret) 6 data (Figure X-l)

is not as strongly Mach number dependent as the cone data (Figure X-2).

Included in Figures X-1 and X-2 are estimates of the available

ranges of size and Mach number offered by today's wind tunnels. In

general, the available experimental data confirm the predicted trends

over about one-half of the envelope.

Results presented in Figures X-I and X-2 show that the variation

of (Ret) ~ with tunnel size is significant for all Mach numbers (M~ 3).

This variation must be considered when comparing (Ret) ~ data or transi-

tion-sensitive aerodynamic data from different faci l i t ies, developing

new Re t correlations, verifying (Ret) ~ theories, or planning wind tunnel

test programs where the location of transition on the model could affect

the data.

259

AEDC~R-77-107

Figure X-3 shows the variation in Re t data obtained on planar

models in five M = 3 wind tunnels having test section heights varying

from 7.7 in. to 16 f t . The recent Russian data (53) have provided Re t

values at considerably higher unit Reynolds numbers than were obtained

in the present research. I t should be noted that the increase in Re t

with increasing Re/in. values appears to continue, at least up to

Re/in. % 2 x 106 . The predicted results from the computer code are in

good agreement with the experimental data and correctly predict the ef-

fects of tunnel size and unit Reynolds number.

Transition Reynolds numbers obtained in four M% 8 wind tunnels

are shown in Figure X-4. The M = 7.5 data obtained in the present re-

search are, to the author's knowledge, the highest unit Reynolds number

wind tunnel Re t data published. As was the case at M = 3, the values

of (Ret) a continue to increase with increasing (Re/in.) values and in-

creasing tunnel size. The computed values are in good agreement with

the experimental data.

I I I . VARIATION OF Re t WITH MODEL POSITION

It was shown in Figures X-1 through X-3 that a very large variation

in Re t occurred with increasing tunnel size. To gain further insight in-

to tunnel size effects, an experimental study was conducted to determine

whether a significant variation in Re t occurred with fairly large changes

in model axial locations in a specific tunnel. The 3.0-in.-diam hollow-

cylinder model was tested in the AEDC-VKF Tunnels D and E at several

axial locations as illustrated in Figure X-5 for the AEDC-VKF Tunnel E.

The transition Reynolds number data obtained over a wide range of axial

260

A E D C - T R - 7 7 - 1 0 7

Sym o

13

O

A

0 Q

5.0x 10 6

4.0

$&llem:

Re t 3.0

Reference 53

Present Study

2.0

1.0

0.8

53

i I

Computed Eq. (10) and Appendix C

Re t =

C 1

o. o,26

t >1.0

m

C <1.0

Mo) C, in. '~m, in. 3.0 31.6

35. 8 48. 0

160. 0 768. 0 94.4

0.56+ 0.44C I C

1.0

C I = 48. 0 in.

Tunnel 31. 6 USSR, 1325 22. 5 VKF Long Shroud 48. 5 VKF-D

231.0 VKF-A 792. 0 PWT-16S 94.4 USSR, 1313

- e l

, I , J , l I I , l

0.04

b = 0 Moo _L " - "

Leading Edge Geometry , m m l m I m I ' I ' I ' I m i ' l I I ' I '

, l , l , l , , , l , I , I , l

0.06 0.08 0.1 0.2 0.3 0.4 0.6 0.8 1.0 2.0

Re/in. x I0 -6

Figure X-3. Variation of transition Reynolds numbers with tunnel size and H® = 3.0, sharp-leading-edge flat-plate/hollow- cylinder models.

261

AEDC-TR-77-107

Sym Reference M m 0 c, deg

o Present Invest. =7.5 10 n 26 ~LO 5, I0, 16 A 137 8. 0 10 o 137 8. 0 6, 9

Tunnel

AEDC VKF-F (~ - in. Diam) NASA-Langley (18.3-in. Diam) AEDC VKF-E (]2 by 12 in. ) AEDC VKF-B (50-in. Diam)

f F

I0 B N A s A ~ E O ~ o

6

(R~) 6

~ C o m p u t e d , Eq. 11 and Appendix C

1 , I I I i l i I i I I 1 , I , 1 0.1 0.2 0.3 0.4 0.6 0.81.0 2.0 3.0

(Refi n. )oo

(Tw/Taw)tunnel wall

0.3 0.6 0.6 0.5

m

5. 0 x 10 6

Figure X-4. Variation of sharp-cone transition Reynolds numbers with tunnel size at M ~ 8.

262

t , ~

f, aa

Throat

74

= ~ = 39. 65 _l m L ] 32.o0 p.o0 r -I

!1

I I

Test Section

._1

~ , ~ / (Steel or Glass) I

L '~m -- .59. 8

I ~ ' - ~ _ / ~ - - = ~ I L Last Characteristic --/-" _1 F t, r -- 56.8 -I

s T2,4,6,8

I


L

Figure X-5. AEDC-VKF Tunnel E t ransi t ion model locations.

m 0 ( }

-,4

o .d

A E DC -TR-77-107

locations in Tunnels D and E for M= = 4.5 and 5.0, respectively, are

presented in Figure X-6. The data show a small, but systematic, in-

crease in Ret values as the model was moved closer to the throat section,

i .e . , decreasing a m. However, the maximum change was only about ~15%

increase as the model was moved a maximum distance of 26.7 in. in Tun-

nel D and 20.2 in Tunnel E.

Estimated Re t locations obtained from the computer program de-

veloped in Appendix D are shown in Figure X-7 for large axial locations

in three different wind tunnels. I t is seen that a negligible change in

Re t with changes in a m were computed for the AEDC-VKF Tunnels D and E

and Tunnel B and M= = 4.5, 5.0, and 8.0, respectively.

Therefore, i t can be concluded from the results presented in

Figures X-6 and X-7 that the variations of model axial positions within

a test section wi l l produce only small changes in model transition loca-

tions. I t is of course assumed that the model wi l l remain within the

test rhombus and that uniform flow (that is, free from shock waves or

compression or expansion waves) exists over the model.

IV. Re t TRENDS WITH MACH NUMBER AND UNIT REYNOLDS NUMBER

Presented in Figures Xm8 and X-9 are plots of planar and cone

model Re t data as a funct ion of un i t Reynolds numbers (Re/ in.)= for a

wide range of Mach numbers (M=). The Re t data exh ib i t an increase with

increasing un i t Reynolds number. This trend is as expected and has

been previously reported, e .g . , see References (37) and (1.08). The data

in Figures X-8 and X-9 show that the variation of Re t with unit Reynolds

number is not strongly dependent on ~ch number and tunnel size. It

264

A E D C - T R - 7 7 - 1 0 7

Sym ~m, in.

o 59. 8 :, 54. 8 [] 39. 6 0 48.5 [7 47. 0

10 x 106 8 6 5

Re t 4 3

Source Method-of-Detection

Present Study Maximum pp

L i Figure V I-1 Ref. 119 Maximum T s

. _, I ' l , l , , ' i , l , l C f " t ' _

-

-Z

~ I T l-Adjusted (Ret)max. pp = I. 15 (Ret)ma x Tw

, I , I , I , , , I , I , I , 0 0.1 0.2 0.4 1.0 2 3xlO 6

Re/in.

a. AEDC-VKF Tunnel E, M = 5.0

Re t

Sym Reference ~m, in.

o Present Research 40. 2

A 1 45. 2 [] 61.9 0 66. 9

- - 37 48. 5 6_ , I I I ' I ' I ' ] 5[ O01 in i 4

?

- - Data Fairing

I t I I [ z I ~ [ l / 0.1 0.2 0.3 0.4 0.6 l. Ox I06

IRe/i n. )co

b. AEDC-VKF Tunnel D, M = 4.5

Figure X-6. Effect of model axial locations on Re t data (hollow- cyl inder model).

265

AE DC-TR-77-107

Predicted, Equation (10) and Appendix C

Test Section

8 l-- ~. 8 / ( 5 0 in . Diam)

Ret 4 ~m = sg.~,..-~ ~ (1~ ~1

0.i 0,2 0.3 0.4 0.6 0.8 1.0 x I0 b

(Re/in.)=

Figure X-7. Computed values of Re t with varying model (~m) locations (planar models).

266

AEDC-TR-77-1'07

(Tw/Taw)tunnel S_ym M= wall

o 3.0 1.0

o 4.0 1 O 5.0 <~ 5.0 A 6.0 0.8

7.0 0.7 o 8.0 0.6

Tunnel AEDC-VKF-D (12 by 12 in.)

,L AEDC-VKF-E

Reference

Present Investigation

1 169

Computed, Eq. (10) and Appendix C

o

1 ~ 3

0.1 1.0 (Re/i n. )~o

7x 1o °

Figure X-8.

a. Small Size Tunnels

Ef fec t o f Rach number and un i t Reynolds number on planar model t r ans i t i on data.

26"I

AEDC-TR-77-107

S_,vm Reference Mo) Tunnel

o 123 3.7 JPL-SWT (18 by 20 in.) a 123 4.6 JPL-SWT (18 by 20 in.) 0 126 6.0 NASA Langley (20 by 20 in. )

Computed, Eq. (10) and Appendix C

10 x 10 6

Re t

m

8 - B

6 - 5 -

4

3

1 0.03 0.04

Planar Models b=O

0.06 0 .08 0 .1

I l l L i l I I [ I , 1 , 1 , 1 0.2 0.3 0.4

(Relin.) m

(Tw/Taw)tu nnel wall

1.0 1.0 0.8

, 1 1 , I , 0.6 0.8 1.0x 10 6

b. Hedium Size Tunnels

Figure X-8. (Cont inued).

268

A EDC-TR-77-107

AEDC (Tw/raw)tu nnel Sym Model Reference Mco Tunnel wall

o HC Present Study 3.0 VKF-A 1.0(40by4Oin.)

[] 5.0 0 170 6.0 VKF-B 0.8 (50 in. Diameter)

Experimental C] 108 8. 0 1 O. 5 | Data "C] FP 170 8. 0 t 0. 5

o Present Study 8.0 VKF-F 0.3 (40in. Diameter) G' 63 5. 0 VKF-A 1. 0 (40 by 40 in. ) Cr 63 8.0 VKF-B 0.5(50in. Diameter) 0 63 10.2 VKF-C 0.3(50in. Diameter)

- - Computed, Eq. (10) and Appendix C 20 x 106

Mco

10

6

5 10

4 8

3 6

2

Planar Models b:O

I , l , , i l J I l l m I , , i l i , l l ' I l l

0.030.04 0.06 0.080.1 0.2 0.4 0.6 0.81.0 1.5x106 (Re l i n. )co

c. Large Size Tunnels

Figure X-8. (Continued).

269

A E DC-TR-77 -107

Sym

0

[ ]

0

tO0 x 10 6

AEDC (TwlTaw)tunnel Reference M~o 0 c, deg Tunnel wall

Present Study 3. 0 5.0 VKF-D 1.0 Present Study 4. 5 5. 0 VKF-D 1.0

137 6. 0 I0. 0 VKF-E 0. 8 137 8. 0 lO. 0 VKF-E O. 6

Computed ~ l O . O . . . . . . 0.35 12. 0 . . . . . . O. 25 116.0 . . . . . . 0.20

Tunnel Test Section Size

(12 by 12 in. )

I i [

(Ret)b

10

1

0. I

- M=

" 12

10 o - 8 [ ] 7

6

3 5

- o Symbols - Experimental Data

~ C o m p u t e d Eq. (l l) and Appendix C

i I , I I I I I I I I I I I f

1.0

(Re/in.) OD

I I

7x1¢

Figure X-9. a. Small S i ze Tunne ls

Effect of Mach number and unit Reynolds number on sharp-cone transit ion data.

270

A E DC-TR-77-t 07

Experimental I Data

I00 x 106

Sym

0

[]

Reference M m 8 c, deg

Present Study =7.5 10

26 8.0 5, 10, I6

Tunnel

AEDC-VKF-F (40 in. Diameter) NASA Langley (18.3 in. Diameter)

Computed Using Eq. (ll) and Appendix C

(TwlTaw)tunnel wall

0.3

0.6

m

B

m

m

D

w

(Ret / 6

10--

m

1 0.1

Sharp Cones

i I i I I I I I I I I i I , I 1.0

(Re/i n, )co

I I I 7xlO 6

b. Hedium Stze Tunnels

F igure X-9. (Cont inued) .

271

AEDC-TR-77-107

Sym Reference Me__ Bc' deg

o Present Study 3. 0 5. O o 4.0 .5.0 ¢ 5.0 5.0

AEDC Tunnel

VKF-A 140 by 40 in. )

1 Experimental ,.' ix 5. 9 5. 0 Data • 137 6. 0 6. 0 VKF-B (50 in. Diameter)

• 137 8.0 6.0 VKF-B (50in. Diameter) o 165 I0. 0 6. 0 VKF-C 150 jn. Diameter)

21 14.2 9.0 VKF-F (54.in. Diameter) Computed, Eq. (11) and Appendix C

100 x 106 . . . . . .

(Pet)~ 14

10 6 10 L38 5.q

(TwlTaw) tunnel wall

1.0 1.O 1.0 0.9 0.8 0.5 O. 35 0.2

1 O.

Sharp Cones

i I t I I I I I I I I , I , I

1.0 (Re/in.)

O0

C. Large S ize Tunne ls

F igu re X-9. (Con t i nued ) .

I I I

7xlO 6

272

AEDC-TR-77-107

should be noted that the planar Re t data presented in Figure X-8 have a

slightly steeper slope compared to the cone data in Figure x-g.

The variations of Re t data with Mach number for several different

size tunnels are shown in Figures X-tO and X-11 for planar models and

sharp cone models, respectively. Variation in Re t with M= is not

strongly influenced by tunnel size for either planar or cone models.

These data also indicate that the changes in Re t data with changing M

is significantly greater for planar models than sharp-cone models. The

estimated values of Re t obtained from the computer code are in good

agreement with the experimental data as shown in Figures X-tO and X-11

except for the AEDC-VKF Tunnel D cone data at M® ~ 4. A contributing

factor to this discrepancy between the experimental data and computed

values at M ~ 4 is the disagreement between the measured tunnel wall 6*

and the theoretical value of 6* used in the computer code (see Figure B-7

in Appendix B, page 339).

I t is obvious from the results presented in Figures X-IO and X-11

that transition data from different sizes of supersonic-hypersonic wind

tunnels cannot be used to establish "true" Mach number trends.

Figure X-12 presents (Ret) ~ data as a function of cone local

Mach number for a free-stream Mach number of eight. The data for the

7.5- and 15.8-deg cones were published in Reference (130), and all the

data shown in Figure X-12 were later published in Reference (121). For

a given free-stream Mach number, there are two cone angles which will

produce equivalent local unit Reynolds numbers, but significantly di f -

ferent local cone surface Mach numbers (see Figure D-2 in Appendix D,

page 376). Figure X-12 shows that when the local Mach number was changed

273

A E D C - T R - 7 7 - t O7

Experimental Data

I0 x 10 6 g 8 7

6

5

Ret 4

3

2

Sym Reference

a 53 [] Present Study O' Present Study 0 Present Study

123 o Present Study

108 ,~ 170 0 Present Study

~ C a l c u l a t e d , Re t =

Model Configuration Tunnel

Flat Plate USSR Hollow Cylinder VKF-D Hollow Cylinder VKF-E Flat Plate VKF-E Flat Plate JPL-SWT Hollow Cylinder VKF-A Hollow Cylinder VKF-B Flat Plate VKF-B Hollow Cylinder PWT-16S

O. 0126 (CF 1-2" 55(~,)

b=O

Test Section Size

7.9 by 7.9 in. 12 by 12 in. 12 by 12 in. 12 by 12 in. 18 by 20 in. 40 by 40 in. 50 in. Diameter 50 in. Diameter 16 by 16 ft

, See Eq. (10) and Appendix C for Details of Digital Computer Program

J_ See Table 4 for T " Additional Information Obtained by Extrapolating Re t Values Re t Corresponds to Surface for Small Bluntness (b <0. 005 in. ) Peak Pressure Location Back to b = 0

r I 1 T r 1 I- l v T r I -

,,6 in. • ) = 0 . 2 0 x l u

18in. C ~ ~ o =0" ~ " 12in. b [] 0

7'9 i in" I I [ i I i I , I ,. I

3 4 5 6 7 8 M

(3O

] I

2 9

Figure X-t0. Variation of planar model transition Reynolds numbers with tunnel size and Mach number.

274

AEDC-TR-77-107

20 x 106

Experimental Data

Sym 0c' deg Tunnel Test Section Size Reference

x 7.5 RAE .Sin. by 5 in. 136 o 5.0 VKF-D 12 in. by 12 in. Present Study cr 10.0 VKF-E 12 in. by 12 in. 137 4~ 5. 0 VKF-A 40 in. by 40 in. Present Study • 6.0 VKF-B 50in. Diameter 137 ~t 9.0 VKF-B 50in. Diameter 137 • 6. 0 VKF-C 50 in. Diameter 143 K 3. 75 NASA 31 in. by 31 in. 171 or° 10.5"00 Laigley 18.3 in.i Diameter 2 i

z6.o • 9.0 VKF-F 54 in. Diameter 2I r~ lO, 0 VKF-F 25 in. Diameter Present Study o" 5. 0 JPL 9 in. by 12 in. 79

5. 0 Republic 30 in. Diameter I73 Av.

10 9 8 7 6

(Ret)6,

4

3

_ n= •

! C

.'- (Re/in) = O. 2 x 10 D "co c~ o. . , o ~ C o m p u t e d , Eq. (ll)and . , 3 ~ RA E Appendix C

×

! I ! 2 4 6

Sym Tunnel Size

x Very Small Open Symbols Small Half Solid Intermediate Solid Large

I I l I 8 10 12 14 16

M m

Figure X-l l . Variat ion of sharp-cone t r a n s i t i o n Reynolds numbers with tunne l s i ze and Hach number.

275

AE DC-TR -77-107

(Re/in.)6 Sym

o

0

107 9 - 8 -

7 -

6 -

5x 106 -

4 -

(Ret)6 3 -

2 - -

106 2

O c, deg 5, 20.1 7.5, 15.8

(Re/in.)oo (Re/in.)oo x 10 -6 x 10 "6

(Ret) 6 - (Re/in.)6 xt x 10 "6

O. 116 O. 224 O. 483 1.17

O. 092 O. 18 O. 38 0.93

O. 082 O. 16 .0.34 0.83

I

20. I

dXt determined from heat transfer ata obtained using fusible paint.

Data from References 130 and 121

e c, deg i

15.8 I I

7.5 5.0

o 8

t

O

O O O

I I I I i I i I , o I I 4 6

M 6

8

Figure X-12. Trans i t ion Reyn6lds numbers as a funct ion of local number fo r sharp cones, H= = 8.

Mach

276

A E DC-TR -77-107

from approximately 4 to 7 for constant free-stream conditions [constant

M=, constant (Re/in.)=], there was no significant change (upward trend)

with Mach number except at the lowest (Re/in.)= value. Recent data pub-

lished in Reference (26) using the same approach confirm the invariance

of (Ret) 6 with M 6 as shown in Figure X-13.

The experimental data presented in Figures X-12 and X-13 are par-

t icularly significant to the findings of the present research. The aero-

dynamic-noise-transition hypothesis formulated in this research and the

resulting empirical equation developed [Eqs. (10) and (11)] predict no

change in (Ret) ~ with changing M 6, provided the free-stream conditions

M and (Re/in.)= do not change. Predictions from the aerodynamic-noise-

transition computer code [Eq. (11) and Appendix D] are presented in Fig-

ure X-13 and the agreement with the data is considered excellent. Note

that the computer code predicted the slight increase in (Ret) 6 with in-

creasing M= that is evident in the data. This is a result of the e c

values not being selected to provide a constant (Re/in.) 6 value as was

the case for data shown in Figure X-12.

I t should be pointed out that the 5- and 20-deg cone angles pro-

duce equivalent local unit Reynolds numbers as do the 7.5- and 15.8-deg

cones for M = 8 (see Figure X-12). However, for the local unit Reynolds

number conditions to have been equivalent for both sets of cone data as

listed in Figure X-12, there would necessarily have been a 10% to 15%

difference in (Re/in.)=. A 15% difference in (Re/in.)= would produce a

maximum change in Re t of approximately 10%, and this is well within the

scatter of the data shown in Figure X-12. Consequently, i t seems just i -

fied to compare the four sets of data directly.

277

AE DC-TR-77-107

(Re/in.)6 _5 Sym Reference x 10 -6 (Relin.)oo o 26 O. 5 O. 385 m [ 1.O 0.769 z~ ~, 1. 5 1.154

m

B

1

10 x 106 -

Re 6 - m

m

2x10 6 3

Oc, deg

10 16

(Re/in.)oo (Re/in.)oo

0.32 O. 329 0.633 0.658 O. 95 0.987

Moo - 8.0

Data Adjusted to Equivalent PPmax Transition Location Using Figure IV-2 and Table 5

(Re/in.)G

_ ~ 1.5 ~ 1.0

ra o ~ . . ~ 0.5

O O

~Computed, Eq. (11)and Appendix C

I I 1 I I 4 5 6 7 8 9

M 6

Figure X-13. Comparisons o f predic ted ~nd measured (Ret) ~ values on sharp cones f o r various local Mach numbers,-H= = 8.

278

AEDC-TR-77-107

The results shown in Figures X-8 through X-13 strongly indicate

a la rge , i f not major, par t of Re t va r i a t ion with Mach number in wind

tunnels is r e l a t ed to the presence of f ree-s tream aerodynamic noise dis -

turbances. These results also indicate that transition data obtained in

wind tunnels cannot be used to establish true Mach number effects.

The standard deviation (~) for the Re t experimental data points

and the computed values shown in Figs. X-I through X-13 was determined.

Based on these 262 data points, the standard deviation was found

to be 11.6%. Figure X-14 presents a summary plot of the measured

versus the computed Re t values for the specified 262 data points. Two other

transition studies have estimated standard deviation values for

empirical prediction methods. Deem, et. al (Ref. 63), found a

standard deviation of 33% (based on 291 data points as shown in Fig.

II-lO) and Beckwith and Bertran (Ref. 81) found ~ = 35% (see Fig.

II-11) for empirical equations developed at NASA Langley.

Based on a direct comparison of the standard deviation values,

i t is seen that the current empirical equation provides a considerable

improved method for predicting the location of boundary-layer transition.

Dougherty and Steinle indicated in Reference (52) that the

aerodynamic-noise-transition correlation developed in this research (10)

could be applied down to M = 2. As discussed in Chapter IX, the pres-

ent aerodynamic-noise-transition correlation was restricted to M ~ 3 in

the present research. This restriction was applied because of possible

influences of velocity fluctuation disturbances (s t i l l i ng chamber vor-

t i c i t y fluctuations) which can be present to a significant degree in the

279

A E D C - T R - 7 7 - 1 0 7

ev,.

10( 80

60

40

20

15

E 10

x zo 6 I I I I I I I I I I I I I I I I I I

+20% /

I /

/ /> r / /

N = 262

= / 1 KRetca,- Retmeas.y

o = 11.6%

Retcal from Eqs. 10 and 11

I : ~ O / I I I I I I I I I I I I I I I I I I I / ],/ 2 4 6 8 10 15 20 40 60 100X

Re t

Fig. X-14 Comparison of Predicted and Measured Transition Reynolds Number from Current Method (Eqs. (10) and (11) and the Fortran Computer Program, Appendix C)

los

2 8 0

A E D C - T R - ? 7 - 1 0 7

Open Symbols Represent Experimental Data ,= • $ Computed Values, Eq. (10) and Appendix C

5 x 10 6 f u U , I u I t I i I i

Re/in. x tO -6 6 = O. 001P O. 1 5 , % . Re t Determined

from Peak Pitot 4 O. I O ~ , , ~ , , ~ Probe Value

Ret Data from Fi9ure 76

2 / z I , I , 7.,~ , I , t 1.5 2.0 2.5 3.0 3. P 4.0 4.5

Mm

a, AEDC-PWT Tunnel 16S Transition Data

4x 10 6

3 Re t

I

0.4

0.3

0.2

01

1

1.5

I ' I ' I ' I ' I ' I ' I

o~ Re/in. x 10 -6 Data from Reference (IL~) \ ~ - - - Flat Plate - I \ \

a \ \ Ret Determined f rom , ~ / - I \ \ ~ Maximum Surface ~ ~.~

.,.,.

0 ~ _ 9---- 2.0 2.5 3.0 3.5 4.0 4.5 5.0

hi m

Figure X-15.

b, JPL Transition Data

Variation of transit ion Reynolds Mach number,

numbers with Q

tunnel

281

AEDC-TR-77-107

tunnel free stream and which are not accounted for in the present corre-

lation. Wind tunnel Re t data also exhibit a reverse trend with Mach

number for M= ~ 3, as shown in Figure X-15. This trend is apparently

present in all sizes of wind tunnels. This assumes, of course, that the

data presented in Figure X-15 from the AEDC-PWT Tunnel 16S obtained in

the present research and data from the JPL 18- by 20-in. tunnel pub-

lished in Reference (123) are considered to be representative of all tun-

nels.

Included in Figure X-15b are the computed values of Re t obtained

from the computer code, Appendix C . . I t is seen from Figure X-15b that the

aerodynamic-noise-transition correlation developed in the present research

[Eq. (10) from Figure IX-8, page 249] and the resulting digital computer

code developed in Appendix C is not valid for M= ~ 3.0.

I t is of interest to point out that Doughertyand Steinle (52)

were able to correlate pressure fluctuation data (p/q=) from the AEDC-

PWT Tunnel 16S directly with the parameter C F q 6"/C for M® = 1.7 to 3.0.

They also were able to correlate the measured (Ret) 6 data from the AEDC-

PWT Tunnel 16S (Figure VII-3, page 186, and b = O) with the measured p/q=

values for M® = 2.0, 2.5, and 3.0.

V. COMPARISON OF TUNNEL AND BALLISTIC RANGE Re t DATA

Figure X-16 presents a direct and quantitative comparison of

transit ion data f¢om sharp slender cones obtained in wind tunnels and

from an aerobal l ist ic range at equivalent local Mach numbers using simi-

lar methods of t ransi t ion detection. At a comparable (Re/in.)6 value,

282

A E D C - T R - 7 7 - 1 0 7

Sym Facilit~ M._58 TwlTaw °

o VKF Range K 4.3 =0.18 ,,', VKFTunnel D 4.3 =1.0

(12 by 12 in. ) c~ VKFTunnel A 4.3 =1.0

(40 by 40 i n. )

-----PWT-Tunnel 16S 4.3 =1.0 (16 by 16 ft)

'Model Wall Temperature Ratio

9c, deg Source

10 Ref. 27 5 Present Study

5 Present Study

5 Present Study

Method of Detection

Shadowgraph - Schlieren Schlieren

Surface Pitot Probe Maximum Value Adjusted to Schlieren Location (Ret)schliere n = O. 82 (Ret)Pmax Estimated from Two-Dimensional Data Surface Probe Data

lOx 106 8 6

(Ret) 6 4 3

2

1.0

~Predicted (Eq. (11)) and Appendix C - Facility ~ J '

= Eq (11 o

- 0 0

"-" . t / / M 6 - 4. 3.

,I , " 1 ' ' ' ,!!!i~tee;enlp!o~!h I p s : I

O. 1 L 0 5 x 106 (Reli n. )6

F i g u r e X-16. Compar ison o f sha rp - cone t r a n s i t i o n Reynolds numbers from wind t u n n e l s and an a e r o b a l l i s t i c range .

283

AEDC-TR-77-107

these data suggest that the range (Ret) 6 data are s igni f icant ly lower

than the tunnel results, even for the 12-in. tunnel.

One major nonsimilarity between the tunnel and range experi-

mental conditions is in the surface temperature rat ios. Transition re-

versals have been predicted theoret ical ly (174) and verif ied experi-

mentally (175,176), and possible transit ion reversals have been shown

experimentally (176). However, to the author's knowledge, there are no

experimental data that show transit ion Reynolds number to decrease below

the adiabatic wall value for any degree of surface cooling. Therefore,

i f comparisons could be made where the model wall to free-stream tem-

perature ratios were comparable, then a larger difference between tunnel

and range (Ret) a data than suggested by Figure X-16 might exist.

One question that naturally arises is whether adverse environ-

mental or model disturbances could be affecting the range results. I t is

also of interest to note that the data in Figure X-16 indicate a s ign i f i -

cant difference between the tunnel and range Re t versus (Re/in.) 6 slope.

The significance of the unit Reynolds number effect evident in the range

data and the results of preliminary investigations on range noise dis-

turbances were reported by Potter (27).

Recently additional ba l l i s t i c range transit ion data have been

published by Potter (23). Potter conducted a thorough and systematic in-

vestigation of the possible effects of model nose-tip ablation, small

changes in angle of attack, range disturbances, model vibrations, and

model surface roughness. However, none of the above were ident i f ied as

being the cause of the unit Reynolds number effect or the low (Ret) 6

values exhibited in Figure X-16. A part icular ly interesting result oh-

284

AE DC-TR-77-107

tained by Potter was that (Ret) 6 data obtained on lO-deg cone models at

Hach numbers of ~ = 5,0 {H 6 - 4.3) and H= = 2,3 (H 6 = 2.1) exhibited no

Mach number effect, The range transition "anomaly" remains as one of the

most baffling and challenging of ground testing transition phenomena,

285

A EDC-TR-77-107

CHAPTER Xl

COMPARISONS OF PLANAR AND SHARP CONE TRANSITION REYNOLDS NUMBERS

Potter and Whitfield (1371 made a qualitative comparison of

(Ret) 6 data obtained on cones and planar bodies from several sources and

observed that the ratio of (Ret)6,cone/(Ret)6, planar appeared to de-

crease from a value of approximately 3 at M® ~ 3 to a value of about 1.1

at M® ~ 8. Based on the results of Pate and Schueler (101 and Pate (111,

Whitfield and lannuzzi (211 concluded that attempts at a comparison of

(Ret) 6 data from various high-speed fac i l i t ies as done in Reference (1371

must now be viewed with reservation, and the relationship between cone

and planar (Ret) ~ results could not be established from presently avail-

able data.

Therefore, one of the objectives of this research was to attempt

to establish a quantitative correlation of sharp slender cones (axisym-

metric) and f lat-plate, hollow-cylinder (planar) transition Reynolds num-

bers at supersonic and hypersonic speeds.

Based on the results of the present investigation, i t was con-

cluded that a correlation was possible only i f cone and f lat-plate data

were obtained in the same test fac i l i t y , under identical test conditions,

using equivalent methods of transition detection. There are no avail-

able investigations of the receptivity of a laminar boundary layer to

radiated noise. Consequently, i t was necessary to obtain (Ret) 6 data

exposed to various intensity levels of radiated noise while continuing

to maintain a constant free-stream unit Reynolds number and Mach number

286

AEDC-TR-77-107

i f the cone-planar (Ret) 6 relation was to be determined. This was ac-

complished by obtaining test data in signif icantly different-sized tun-

nels (AEDC-VKF Tunnels A and D). The large variation of (Ret) 6 with

tunnel size has been shown in F~gures Vl l l ,20, page 216~ VIII-Z1, page

217, X-I, page 257, and X-2, page 258. The increase in cone (Ret)~

values above f lat-plate values was shown in the basic data presented in

Figures VIII-20, page 216, VIII-21, page 217, VII-5, page 173, and VII-6,

page 175.

Presented in Figure XI-1 is a correlation of cone and f lat-plate

(Ret) 6 data developed from the data obtained in this study (AEDC-VKF Tun-

nels A and D) and data from three other test fac i l i t ies . I t can be

argued that various procedures are available for reducing this type of

data. The three procedures used are outlined in the legend of Figure

XI-1. The significant conclusions to be drawn from Figure XI-1 are:

Ca) the (Ret) 6 ratio appears to be about 2.2 to 2.5 at M® = 3, (b) the

trend decreases monotonically with increasing Mach number to a value of

approximately 1.0 to 1.1 at M® = 8, (c) close inspection of these results

at a given Mach number (M = 3 to 5) suggests a decrease in the (Ret) ®

ratio with increasing tunnel size, and (d) the (Ret) 6 ratio is also

sl ight ly dependent on the method of analysis.

An empirical equation for the cone-planar (Ret) 6 ratios can be

obtained by ratioing Eqs. (10) and (11). Then

(Ret)6, cone

(Ret)~, planar

Eq. (10) .15 (c-')c°ne = F.q. (11) = 3880 (CF)1

(c--) f la t pl ate ( 1 2 )

287

A E D C - T R - 7 7 - 1 0 7

Sym Configuration gc. deg Mm M 6

Sharp Cone 5 3 to4.5 2.9to4.3

O Hollow Cylinder 3 to 4.5 3 to 4..5 (b- OI

Sharp Cone .5 3to.5 2.91o4.7

,e, Hollow Cylinder - - - 3 to3 3 to 5 (b • OI

Sharp Cone 5, 6 6 5.5

O "l:-Ia-t-I~l; t'e - . . . . . . . . . . "--6- . . . . . 6- . . . . . . ( b " OI

Sharp Cone 6,9 8 7.0, 6.4

Heflow Cylinder 8 8 i Ib • O)

Sharp Cone 6,9 8 7.0, 6.4

Flat Plate 8 8 i (b = OI

Sharp Cone 5 3.1 2. g8

Hollow Cylinder --- 3. l 3.1

Sharp Cone 2. 5 5. 0 4. 90

Hollow Cylinder --- 5. 0 5. 0

Method -of - (Re/in.)6 x 10 "6 Range Factlity Cetection Source

O. i.5 to 0. 4 VKF-D Maximum Present Study 1 l12byllEin.) PitotPressure andReference(3l)

0.1.5 to O. 6 VKF-A Maximum ! Present Study (40 by 40 in. I Pitot Pressure

Ira, in.

44

48,.5

215

231

OL 15 !o0.4

l V K F - A Shadowgraph Present Study VKF 215

V K F - 8 q m a x i m u m Reference (170l 232 (50-in. D=aml

0.2, 0.3 VKF-B (SO-in. Diam)

0.2 V~-B (50-in. Dlam)

qrrax and Refer'ence (137) 245 Shadovajraph and VKF

ITwlma x and Reference (37) 232 Pitot Pressure

qmax and Reference (1371 245 Shadowgraph and VKF

Pitot Pressure Reference1631 232 P

0. l to O. 6 NACA-Le,ls Tw max Reference (12Ol =40 112 by 12 in. ) -4"~5---

0. 15 to 0. 5 NASA-Lewis Tw max Reference Illg) 47 112 by 12 In. I . . . . . . .

47

Flagged Symbols - Evaluated at Equivalent IRe/in. )6 and M 6 Values ((Rehn.)6 "0. 2 x 106 Open Symbols - Evaluated at Equivalent (Rekn. I E and I~', m Values

Solid Symbols - Evaluated at Equivalent (Re/in. leo and M 6 Values (From Data Cross Plols)

2 (Ret)6 cone

(Ret)6 planar

1

I i I i I

3 4 5

r3 e O" e

I i l ~ I

6 l 8

Mach Number

Figure XI-1. Correlation of axisymmetric and planar transition Reynolds number ratios.

288

AEDC-TR-77-107

Predicted transition ratios using Eq. (12) are presented in Fig-

ure XIZ2 for a large range of tunnel sizes, Mach numbers, and (Re/in.).

values. The experimental data for the 40- and 50-in. tunnels (3 ~ M® ~8)

are in good agreement with the empirically predicted ratios. The data

also indicate, qualitatively at least, a decrease in the transition ratio

with an increase in tunnel size.

Many investigators have referenced the analytical analysis of

Tetervin (138,139) and Battin and Lin (140) when attempting to explain

the cone-planar (Ret) ~ ratios of approximately three that were observed

experimentally.

Battin and Lin (140) concluded that the minimum cri t ical Reynolds

number (Rx,cr) for a cone was three times greater than for a f la t plate.

However, the agreement between the ratio of approximately three exhibited

by previously published transition data at moderate supersonic Mach num-

bers and the stabi l i ty theory ratio of three is perhaps only fortuitous,

as demonstrated by the data correlations presented in Figures XI-I and

Xl-2.

From Tetervin's theoretical analysis (138)

(Ret)6, planar-minimum (Ret)~, cone = 1 + 2 (13) (Ret)~, planar (Ret)6, planar

The (Ret)~, planar-minimum values represent the theoret ical mini~

mum t rans i t ion Reynolds number that can occur on a f l a t p late, and these

values are presented as a function of Mach number and model surface tem-

perature in Reference (138).

289

t J

Q

innel

I Variation of Experimental Data with Re/in.

Symbols Are Identified in Figure X I-2b

o

(Re/in.)m x 10 -6

0.4 ~Predicted Eq. (11) 0.2 - - - - ( ' ~

)) m 0 c) .h ~u ' ,4

0 ,,,J

3 4 5 6 7 8 9 lO

Figure XI-2.

a.

Compari son of

Variation with Mach Number

predicted and measured cone planar transition ratios.

Experimental Data Evaluated at Equivalent (Re/in.)oo and Moo Values

~o

Sym Configuration 0c, deg Moo M 6 (Re/in.)oo x 10 -6 Range

Sharp Cone 5 3to 4.5 2.9 to 4.3 O. 15 to 0.5

o Holl0w Cylinder - 3 to 4.5 3to 4.5 0.15 to 0.5 (b = 0)

SharpCone 5 3to5 2.9to4.7 0.].5 to 0.5

• Hollow Cylinder 3 to5 3to5 0.]5 to 0.5 (b = 0)

Sharp Cone 5 5.9 5.5 0.2

L' "HOI'I~ Cyl"i n(/er- . . . . . . . . 5-9 . . . . 5-9 . . . . . . . . . . ().2 . . . . . . . . . . . (b = 0)

it

Sharp Cone 6 6 5.5 O. 2

Flat P late 6 6 O. 2 (b = O)

SharpCone 6, 9 8 7.0, 6.4 0. ]5to0.3

Facility Method of x t Detection Source

VKF-D 112 by 12 in. )

VKF-A (40by 40 in.)

VKF-A (40 by 40 in.)

VKF-B (50-in. Dial)

Maximum Surface Pitot Probe Pressure

Maximum Surface Pitot P robe P ressu re

Schlieren

Present Study

Present Study and Reference (37)

Present Study

-R-e)erence Ft'IF ....

Present Study . . . . . . . . . . . . . . . . . d . . . . . . . . . . . . . . . .

Schlieren Present Study

Adjusted Max. Heat Transfer Reference (137 (Adjusted by 1.08) and VKF

.................................

Maximum Pitot Press. Present Study and Reference (170)

Maximum Heat Trans. Reference (137) VKF-B (No Adjustment) and VKF

....................................................... (50-in. Dial) .................................. Hollow Cylinder 8 8 O. 15 to O. 3 Maximum Pitot Press. Reference (108) (b = 0)

Sharp Cone 10 6, 8 5.0, 6. 2 0. 3 to 1.0, 0. 35 to 0. 55 VKF-E

....................................................... (12 by 12 in.) Flat Plate 6, 8 6, 8 O.3to 1.0, (b - O) 0.35 to 0.55

Shadowgraph Reference (137) • (_A_dj ._st . . . . . . . . . . . . . . . . . . . . .

Maximum Pitot Press. Reference (169)

b. Specific Information

Figure Xl-2. {Continued).

m O o

"n

, , , j

O . , , j

AE DC-TR -77-107

Tetervin's theoretical transition ratio [Eq. (12)] was derived

using linear stability theory. As shown by Eq. (12) when (Ret)6, planar

is near the minimum possible value, then the cone-planar ratio approaches

a value of three. As (Ret)6, planar moves farther downstream then Eq.

(12) approaches a value of unity. The assumptions that must be applied

to Tetervin's analysis are: (a) free-stream disturbances are nonexistent,

or (b) the disturbances affect only the laminar region of instability up-

stream of the respective (Ret)6, planar-minimum locations, or (c) the

absorptivity characteristics of the laminar layers on both the cone and

f lat plate downstream of the (Xt)planar_minimum locations are identical.

There are no available experimental supersonic data that comply with as-

sumption Ca), and with disturbances present there is no evidence to

support assumptions (b) and (c). Nevertheless, i t appears to be of

interest to use Eq. (12) and the theoretical (Ret)~,planar_minimum values

of Reference (138) in conjunction with the experimental (Ret)6, planar

values presented in Figure X-IO, page 258, of this study to estimate a

few cone-planar transition ratios. The results are listed in column six

of Table 7.

An increased value for Eq. (12) can be obtained i f experimentally

measured minimum critical Reynolds number [Figure 3 of Reference (139),

showing the stability data of Schubauer and Skramstad, Laufer and

Vrebalovich, and Demetriades] is used instead of the theoretical esti-

mates of Tetervin. Also the (Ret) 6 values presented in Figure X-tO,

page 258, [and used in the evaluation of Eq. (12), i .e. , column 6] cor-

respond to the maximum pitot probe pressure location which is on the

order of a factor of two downstream of what one might consider as a

292

Tab le 7. Es t ima ted c o n e - p l a n a r t r a n s i t i o n r a t i o s .

~0

AEDC Tunnel

6 7

2 3 4 5 1 + 2/-~-- ) 1 + 2 ( ~ / 2 /

Free-Stream Exper imenta l Theoretical Estimated, Eq. (13) Conditions (Figure X-J0) [Reference (139)]

Mm (Re/in.)m x 10 "6

D 3 0.2 A 3 0.2

165 3 0. 2 D 5 0.2 A 5 0.2 B 8 0.2

(Ret)6, Planar x I0 -6

1.42

2.25 3.35 2.05 2.95 6.15

Critical Reynolds Number from Stability Experiments [Reference 1139)]

Ret)6. Planar-Minimum x I0-6

0. 016 0. 016 0. 016 0.044 0.044 0.145

-:0.08 ~0. 08 :0.08 -~0.5 =0.5

Estimated, Eq. (13) with Adjustments

(Ret)6. CQne

(Ret)6..Planar

1.1~2 1. 014

1. 010 1.042

1. 030

1.048

1.23

1.14 1.10

1.98

1 68

> m O O

=D

L, O

AEDC-TR-77-107

"measurable" beginning of t ransi t ion. Incorporating these adjustments

into Eq. (12) produces the cone-planar ratios tabulated in column seven.

For a factor of three to exist in the estimated cone-planar tran-

s i t ion rat io at M = 3 would require, depending on the method of analy-

sis, a two-dimensional (Ret)a,planar value of 16,000 to 80,000. To the

author's knowledge, these values are on the order of a factor of 10 to

50 below any published data. Therefore, i t would seem that the cone-to-

f la t -p la te rat io of three quoted by many investigators as being theo-

re t i ca l l y predicted by Eq. (I2) is perhaps without adequate foundation,

and the apparent agreement with experimental data that appeared to exist

is perhaps only fortui tous. Similarly, the decrease to approximately

one exhibited by the experimental data in Figures XI-1 and XI-2 as the

Mach number approaches eight does not appear, based on the results in

Table 7, to be explained by Eq. (12). Based on the available informa-

tion i t is suggested that the absolute values produced by Eq. (12) are,

at best, not adequate for accurate predictions or for laying a founda-

t ion for analyzing experimental t ransi t ion results. However, i t is of

interest to note the trend predicted by Eq. (12) for a constant ~ch

number when the value of (Ret)a,planar_minimum is assumed constant. The

cone-planar (Ret) ~ rat io as given by Eq. (13) is seen to decrease with

increasing experimental (Ret)a,planar values--which wi l l occur with in-

creasing tunnel size or increasing (Re/in.)am-and this trend is in agree-

ment with the experimental results shown in Figures XI-1 and XI-2.

294

AEDC-TR~7-107

CHAPTER XlI

CONCLUSIONS

Signif icant results obtained from this experimental research

program, which was directed toward investigating the relationship be-

tween free-stream disturbances and boundary-layer transit ion on sharp

f l a t plates and sharp slender cones in conventional supersonic-hypersonic

wind tunnels, can be sumarized as follows:

1. A set of unique experiments using a "shroud model" concept

has demonstrated conclusively that radiated noise emanating

from the turbulent boundary layer on wind tunnel walls can

dominate the transit ion process.

2. Transition Reynolds numbers are strongly dependent on tunnel

size. Boundary-layer transit ion data measured in supersonic

wind tunnels (M= ~ 3) having test section heights from 0.5

to 16 f t have demonstrated a signi f icant and monatonic in-

crease in transit ion Reynolds numbers with increasing tunnel

size. Free-stream radiated noise measurements measured on a

f la t -p la te microphone model have shown that the intensity

levels decrease with increasing tunnel size.

3. Model transit ion Reynolds number data have been shown to cor-

relate with the free-stream radiated noise intensit ies levels.

4. Correlations of transit ion Reynolds numbers as a function of

the radiated noise parameters [tunnel wall C F and 6" values

and tunnel circumference (c)] have been developed.

295

A ED C-TR-77-107

a .

b.

.

Sharp-flat-plate transition Reynolds number data from

13 different wind tunnels having test section sizes from

7.9 in. to 16 f t , for Mach numbers from 3 to 8, and a

unit Reynolds number per inch range from 0.1 x 106 to

1.9 x 106 were successfully correlated and the following

empirical equation developed:

0.0126 (CFII)-2"55 (~ Re t =

Sharp-slender-cone transition Reynolds number data from

17 wind tunnels varying in size from 5 to 54 in. for a

Mach number range from 3 to 14 and a unit Reynolds num-

ber per inch range from 0.1 x 106 to 2.75 x 106 were

successfully correlated and the following empirical

equation developed:

-1.40 48.5 (CFI I) (~)

(Ret)cone =

A FORTRAN IV digital computer code that wil l accurately pre-

dict transition locations on sharp f la t plates and cones in

all sizes of conventional supersonic-hypersonic wind tunnels

has been developed. Based on comparisons of standard devia-

tions, the accuracy of this technique is considerable better

than previously published methods. The standard deviation

(a), based on the difference between the calculated and

measured Re t values for 262 data points, using the present

296

AE DC-TR-77-107

method was l l .6gwhereas other published methods give values

a between 30 and 40%.

6. The rat io of cone t rans i t ion Reynolds numbers to f l a t - p l a t e

values does not have a constant value of three, as often as-

sumed. The ratio wi l l vary from a value of near three at

M® = 3 to near one at M® = 8. The exact value is unit

Reynolds number and tunnel size dependent. The aerodynamic-

noise- t ransi t ion empirical equations predict that for

M ~ 10 and (Re/in.) ~ 0.4 x 106 , the ra t io w i l l be less

than one.

7. Radiated noise dominance of the t rans i t ion process offers an

explanation for the uni t Reynolds number e f fec t in conven-

t ional supersonic-hypersonic wind tunnels.

8. The ef fec t of tunnel size on t rans i t ion Reynolds numbers

must be considered in the development of data corre lat ions,

in the evaluation of theoret ical math models, and in the

analysis of t rans i t ion sensit ive aerodynamic data.

g. I f a true Mach number e f fec t ex ists, i t is doubtful that i t

can be determined from data obtained in conventional super-

sonic-hypersonic wind tunnels because of the adverse e f fec t

of radiated noise.

10. The boundary-layer t r i p correlat ion developed by van Driest

and Blumer (wherein the ef fect ive t rans i t ion locat ion "knee"

can be predicted) has been shown to be val id for d i f fe ren t

sizes of wind tunnels and not dependent on the free-stream

297

AEDC-TR-77-107

1I.

12.

radiated noise levels (see Appendix E). The t r ip correla-

t ion developed by Potter and Whitfield remains valid i f the

effect of tunnel size on the smooth body transi t ion location

is taken into account (see Appendix E).

Wind tunnel t ransi t ion Reynolds numbers have been shown to

be s igni f icant ly higher than ba l l i s t i c range values.

Radiated noise intensit ies (pressure f luctuations) measured

with a hot wire in the tunnel free stream wi l l be s ign i f i -

cantly lower than pressure f luctuation levels measured by a

microphone flush mounted in a f l a t plate. Caution should be

exercised when comparing free-stream pressure fluctuations

obtained from hot wires positioned in the free-stream and a

plate-mounted microphone.

298

A E DC-TR-77-107

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Adams, John C. "Implicit Finite-Difference Analysis of Compressible Laminar, Transitional, and Turbulent Boundary Layers along the Windward Streamline of a Sharp Slender Cone at Incidence," AEDC-TR-71-235 (AD734535), December 1971.

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Lewis, Thomas L. and Banner, Richard D. "Boundary-Layer Transition Detection on the X-15 Vertical Fin Using Surface Pressure Fluc- tuation Measurements," NASA TM-X-2466, December 1971.

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Coles, Donald. "Measurements of Turbulent Friction on a Smooth Flat Plate in Supersonic Flow," Journal of the Aeronautical Sciences, Vol. 21, No. 7, July 1954, pp. 433-448.

Matthews, R. K., Eaves, R. H., Jr. , and Martindale, W. R. "Heat- Transfer and Flow-Field Tests of the McDonnell Douglas-Martin Marietta Space Shuttle Configurations," AEDC-TR-73-53 (AD759176), April 1973.

Masaki, M. and Yakura, J. K. "Transitional Boundary-Layer Con- siderations for the Heating Analysis of Lifting Re-Entry Ve- hicles," Journal of Spacecraft and Rockets, Vol. 6, No. 9, September 1969, pp. 1048-1059.

Holloway, Paul F. and Sterrett, James R. "Effect on Controlled Sur- face Roughness on Boundary-Layer Transition and Heat Transfer at Mach Numbers 4.8 and 6.0," NASA TN D 2054, April 1964.

Mateer, George G. "A Comparison of Boundary-Layer Transition Data from Temperature Sensitive Paint and Thermocouple Techniques.," AIAA Journal, Vol. 8, No. 12, December 1970, pp. 2299-2300.

Kendall, James M., Jr. "Wind Tunnel Experiments Relating to Super- sonic and Hypersonic Boundary-Layer Transition," AIAA Paper No. 74-143.

Miller, Charles G. and Maddalon, Del V. "Errors in Free-Stream Reynolds Number of Helium Wind Tunnels," AIAA Journal, Vol. 8 No. 5, May 1970, pp. 968-970.

Stainback, P. Calvin. "Some Effects of Roughness and Variable En- tropy on Transition at a Mach Number of 8," AIAA Paper No. 67-132, January 1967.

Mateer, G. G. and Larsen, H. K. "Unusual Boundary-Layer Transition Results on Cones in Hypersonic Flow," AIAA Journal, Vol. 7, No. 4, April 1969, pp. 660-664.

Stainback, P. Calvin, Wagner, Richard D., (]wen, F. Kevin, and Horstman, Clifford C. "Experimental Studies of Hypersonic Boundary-Layer Transition and Effects of Wind-Tunnel Distur- bances," NASA TN D-7453, March 1974.

Richards, B. E. "Transit ional and Turbulent Boundary Layers on a Cold Flat Plate in Hypersonic Flow," The Aeronautical Quarterly, Vol. XVIII, August 1967, pp. 237-258.

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van Driest, E. R. "Turbulent Boundary Layer in Compressible Fluids," Journal of the Aeronautical Sciences, Vol. 18, No. 3, March 1951, pp. 145-160.

Rogers, Ruth H. "Boundary Layer Development in Supersonic Shear Flow," AGARD Report 269, April 1960.

Potter, J. Leith and Whitfield, Jack D. "Boundary-Layer Transition under Hypersonic Conditions," AGARD Specialists Mtg. on Recent Developments in Boundary Layer Research, AGARDograph 97, Part I I I . (Also AEDC-TR-65-99 (AD462716), 1965.)

Tetervin, N. "A Discussion of Cone and Flat-Plate Reynolds Numbers for Equal Ratios of the Laminar Shear to the Shear Caused by Small Velocity Fluctuations in a Laminar Boundary Layer," NACA TN 4078, August 1957.

Tetervin, Neal. "An Estimate of the Minimum Reynolds Number for Transition from Laminar to Turbulent Flow by Means of Energy Considerations," Journal of the Aerospace Sciences, Vol. 28, No. 2, February 1961, pp. 160-161. (Also NAVORD Report 6854 (AD437345), January 1961.)

Battin, R. H. and Lin, C. C. "On the Stability of the Boundary Layer over a Cone," Journal of the Aeronautical Sciences, Vol. 17, No. 7, July 1950, pp. 453-454.

Spaulding, D. B. and Chi, S.W. "The Drag of a Compressible Turbu- lent Boundary Layer on a Smooth Flat Plate with and without Heat Transfer," Journal of Fluid Mechanics, Vol. 18, Pt. I , January 1964, pp. 117-143.

van Driest, E. R. "The +oblem of Aerodynamic Heating," Aero- nautical Engineering Review, Vol. 15, No. 10, October 1956, pp. 26-41.

Komar, James J. "Skin-Friction Predictions in Turbulent Compres- sible Flow," AIAA Journal, Vol. 4, No. 7, July 1966, pp. 1307- 1308.

Moore, D. R. and Harkness, J. "Experimental Investigations of the Compressible Turbulent Boundary Layer at Very High Reynolds Numbers," AIAA Journal, Vol. 3, No. 4, April 1965, pp 631-638.

Winter, K. G., Smith, K. G., and Gaudet, L. "Measurements of Tur- bulent Skin Friction at High Reynolds Numbers at Mach Numbers

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Cary, Aubrey, M., Jr. and Bertram, Mitchel H. "Engineering Predic- t ion of Turbulent Skin Friction and Heat Transfer in High-Speed Flow," NASA TN D-7507, July 1974.

Hastings, R. C. and Sawyer, W. G. "Turbulent Boundary Layers on a Large Flat Plate at M = 4," R&M No. 3678, Aeronautical Re- search Council, Aerodynamics Department, RAE Bedford, England, March 1970.

Harvey, W. D. and Clark, F. L. "Measurements of Skin Friction on the Wall of a Hypersonic Nozzle," AIAA Journal, Vol. 10, No. 9, September 1972, pp. 1256-1258.

Samuels, Richard D., Peterson, John B., J r . , and Adcock, Jerry B. "Experimental Investigation of the Turbulent Boundary Layer at a Mach Number of 6 with Heat Transfer at High Reynolds Numbers," NASA TN D-3858, March 1967.

Hopkins, E. J. , Rubesin, Morris W., Inouye, M., Keener, Earl R., Mateer, G. C., and Polek, Thomas E. "Summary and Correlation of Skin-Friction and Heat-Transfer Data for a Hypersonic Turbu- lent Boundary Layer on Simple Shapes," NASA TN D-5089, June 1969.

Miles, John B. and Kim, Jong Hyun. "Evaluation of roles' Turbulent Compressible Boundary-Layer Theory," AIAA Journal, Vol. 6, No. 6, June 1968, pp. 1187-1189.

Hopkins, Edward J. and Inouye, Mamoru. "An Evaluation of Theories for Predicting Turbulent Skin Friction and Heat Transfer on Flat Plates at Supersonic and Hypersonic Mach Numbers," AIAA Journal, Vol. 9, No. 6, June 1971, pp. 993-1003.

Coats, Jack Do "Flow Characteristics of a 40-inch Wind Tunnel at Mach Numbers 1.5 to 6," AEDC-TDR-62-130 (AD277289), June 1962.

Jones, J. H. "An Investigation of the Boundary-Layer Character- is t ics in the Test Section of a 40- by 40-inch Supersonic Tun- nel," AEDC-TN-50-189 (AD245362), October 1960.

Ames Research Staff. "Equations, Tables, and Charts for Compres- sible Flow," NACA Report 1135, 1953.

Maxwell, H. and Jacocks, J. L. "Nondimensional Calculation of Tur- bulent Boundary-Layer Development in Two-Dimensional Nozzles of Supersonic Wind Tunnels," AEDC-TN-61-153 (AD270596), January 1962.

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157. Tucker, Maurice. "Approximate Calculation of Turbulent Boundary- Layer Development in Compressible Flow," NACA TN 2337, April 1951.

158. Edenfield, E. E. "Contoured Nozzle Design and Evaluation for Hot- shot Wind Tunnels," AIAA Paper No. 68-369, presented at AIAA 3rd Testing Conference, April 1968.

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160. Rasmussen, M. L. "On Hypersonic Flow Past an Unyawed Cone," AIAA Journal, Vol. 5, No. 8, August 1967, pp. 1495-1497.

161. Jones, D. J. "Tables of Inviscid Supersonic Flow about Circular Cones of Incidence y = 1.4," AGARDograph 137, Parts I, I I , 196g, Part I I I , 1971, North Atlantic Treaty Organization (NATO).

162. Sims, J. L. "Tables for Supersonic Flow around Right Circular Cones at Zero Angle of Attack," NASA SP-3004, 1964.

163. van Driest, E. R. and Blumer, C. B. "Boundary-Layer Transition at Supersonic Speeds--Three-Dimensional Roughness Effects (Spheres)," Journal of the Aeronautical Sciences, Vol. 29, No. 8, August 1962, pp. 909-g16.

164. Nagamatsu, H. T., Sheer, R. E., Jr., and Graber, B. C. "Hypersonic Laminar Boundary-Layer Transition on 8-Foot-Long, 100 Cone, M 1 = 9.1 - 16," AIAA Journal, Vol. 5, No. 7, July 1967, pp. 1245-1252.

165. McCauley, W. D., Saydah, A. R., and Bueche, J. F. "Effect of Spherical Roughness on Hypersonic Boundary-Layer Transition," AIAA Journal, Vol. 4, No. 12, December 1966, pp. 2142-2148.

166. Mack, Leslie, M. "Calculation of the Laminar Boundary Layer on an Insulated Flat Plate by the Klunker-McLeon Method," JPL/CIT- PR-20-352, July 1958.

167. Braslow, A. L. and Knox, E. C. "Simplified Method for Determination of Critical Height of Distributed Roughness Particles for Boundary-Layer Transition at Mach Numbers 0 to 5," NACA TN- 4363, September 1958.

168. Dayman, Bain, Jr. "Comparison of Calculated with Measured Boundary- Layer Thickness on the Curved Walls of the JPL-20 in. Supersonic Wind Tunnel Two Dimensional Nozzle," JPL Technical Report No. 32-249, March 1963.

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Senator, R. J., DeCarlo, J. P., and Torr i l lo , D. T. "Hypersonic Boundary-Layer Transition Data for a Cold-Wall Slender Cone," AIAA Journal, Vo]. 3, No. 4, April 1965, pp. 758-760.

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Wisniewski, R. J. and Jack, J. R. "Recent Studies on the Effect of Cooling on Boundary Layer Transition at Mach 4," Journal of the Aeronautical Sciences, Vol. 28, No. 25, 1961.

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APPENDIX A

TURBULENT BOUNDARY-LAYER SKIN FRICTION

In the in i t i a l phases of this research (10,11), the method of

van Driest-I (135) was used to compute the mean, adiabatic, turbulent

skin-fr ict ion coefficient for the boundary layer on supersonic-hypersonic

wind tunnel walls. These skin-fr ict ion coefficients were then used in

the aerodynamic-noise-transition empirical equations developed in Chap-

ter IX [Eqs. (10) and (11), pages 248 and 252].

As a part of the present research effort , a review of available

methods was conducted to establish i f the method of van Driest-I (135)

should be retained. This review included the evaluation of twelve sur-

vey papers, References (141 through 152) which in turn evaluated many

different techniques. Based on this evaluation, the method of van

Driest-II was selected as a suitable technique for computing tunnel wall,

mean skin-fr ict ion values.

I. REVIEW OF THEORETICAL METHODS

The now widely accepted and often referenced work of Spaulding

and Chi (141) compared 20 d i f ferent theoretical methods, including the i r

own semi-empirical method, with exist ing experimental data. They con-

cluded the best method was the i r own which gave a root-mean-square (rms)

error of the difference in predicted and measured sk in - f r i c t i on data of

8.6) for adiabatic walls and 12.5% for flows with heat transfer with an

overall error of 9.9). The second best method was van Driest-ll which

gave a g.7) error for adiabatic flow and a 13.6) error for flows with

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heat t ransfer with an overall error of 11.0%. van Dr ies t - I (135) had

errors of 13.3% for adiabatic f low, 17.3% for heat t ransfer , and 14.7%

overal l error. Thus, there was not an extreme dif ference between van

Dr iest - I and I I , and van Dr iest - I f in ished f i f t h in the f i e l d of 21.

The f l a t - p l a t e data used by Spaulding and Chi for the evaluation covered

a Mach number range from zero to 10 and a temperature range (Tw/T =) from

1.0 to ~18.

Komar (143) concluded that although the theoretical method of

van Driest-II was in good agreement with the semi-empirical method of

Spaulding and Chi, there was a significant difference (as much as 35%)

at high heat-transfer rates. Consequently, Komar recomended the use of

the Spaulding-Chi method as the preferred method and presented a mono-

graph to assist in rapid calculations of local and/or mean skin-fr ict ion

coefficients.

Moore and Harkness (144) investigated skin-fr ict ion data at M® =

2.8 for an adiabatic flow and high Reynolds numbers (2.3 x 107 ~Re x

1.4 x 109). The model geometry was a 10-ft-long f la t plate and the f loor

of a supersonic wind tunnel. They compared the experimental data with

three theoretical methods and found the best agreement with van Driest-II

(142).

Winter, Smith, and Gaudet (145) used the sidewall of the R.A.E.

8- by 8- f t wind tunnel to provide experimental skin-fr ict ion data over

the range 0.2 ~M® ~ 2.2 and Reynolds numbers up to Re x = 200 x 106 .

They found good agreement between the experimental data and the semi-

empirical method of Spaulding and Chi.

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Cary and Bertram (146) evaluated a large col lect ion of experi-

mental turbulent-skin friction and heat-transfer data for flat plates

and cones to determine the most accurate of six popular prediction

methods (Eckert, Spaulding and Chi, Coles, van Driest, White and

Christoph and Moore). They concluded that for M < I0, Spaulding and

Chi gave the best overall predictions. For M® > 10, Coles' method was

rated best.

An experimental study was conducted by Hastings and Sawyer (147)

at R= = 4 using a f la t -p la te model with length Reynolds numbers up to

Re x = 34 x 106. Measured sk in- f r ic t ion data were compared to f ive d i f -

ferent prediction techniques (the reference temperature method of Sommer

and Short, the semi-empirical method of Spaulding and Chi, the theory of

van Dr iest - I I , the theory of Coles, and the empirical method of Winter

and Gaudet). They found that the method of Spaulding and Chi gave the

best estimate. The predictions by van Dr iest- I I (142) were high by

about 10%.

Experimental sk in- f r ic t ion data measured on the wall of a R ~ 20

wind tunnel was compared with eight di f ferent turbulent theories (Eckert,

Spaulding-Chi, Soniner-Short, van Dr iest - I I , Harkness, Barontt-Libby,

Coles, and Moore) by Harvey and Clark (148). They concluded that the

methods of Coles, Moore, and van Driest- I I gave the best overall agree-

ment with the experimental data. They also concluded that the turbulent

boundary layer of a cold wall nozzle rapidly adjusts to local gradients

and can be predicted by f la t -p la te theories such as van Driest- I I (142).

Samuels, Peterson, and Adcock (149) compared experimental turbu-

lent boundary-layer data taken on a hollow-cylinder model at X = 6 with w

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heat transfer with five theories (van Driest, Monaghan, Johnson, Somer

and Short and Spaulding and Chi) and concluded that Spaulding and Chi

(141) gave the best agreement which was judged as fa i r .

Hopkins, et al. (150) conducted experimental studies of turbulent

skin f r ic t ion on f la t plates, cones, and a wind tunnel wall over the

Mach number range from 5 to 7.4 and temperature ratios (Tw/Taw) from 0.1

to 0.6. They compared their experimental results with four theoretical

methods (Sommer and Short, Spaulding and Chi, van Driest-I I , and Coles)

and concluded that Coles' theory underpredicts at the higher Reynolds

numbers by 10%. At M > 6 the method of Spaulding and Chi (141) under-

predicted by 20% to 30%. The theory of van Driest-II (142) under-

predicted the local skin-fr ict ion data by about 10% for nonadiabatic

wal I s.

Miles and Kim (151) noted that Spaulding and Chi (141) had not

included the method of Coles in their evaluation of 20 theories. Miles

and Kim evaluated Coles' theory in a manner similar to the analysis of

Spaulding and Chi and concluded that Coles' theory was competitive with

the method of Spaulding and Chi.

Hopkins and Inouye (152) evaluated the ab i l i t y of four theo-

retical methods (van Driest-II, Soniner-Short, Spaulding-Chi, and Coles)

to predict the skin f r ic t ion and heat transfer on adiabatic and non-

adiabatic f la t plates and wind tunnel walls. The experimental data

covered a range of Mach numbers from 1.5 to 8.6 and Tw/Taw from 0.14 to

1.0. Their conclusion was that the method of van Driest-If (142) was

the best method for predicting turbulent skin f r ic t ion at supersonic-

hypersonic speeds.

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Edenfield (I05), based on his efforts to design a M = 8 high

Reynolds number axisymmetric nozzle,concluded that the theory of Coles

(and others) would underpredict the wall skin fr ict ion. Although his

work was done independently of the work by Hopkins and Inouye (152),

Edenfield noted in his summary report (105) that the extensive studies

by Hopkins and Inouye gave confirmation to his conclusions.

In summary, based on the results of References (141), (143),

(145), (146), (147), and (149), i t appears that the semi-empirical method

of Spaulding and Chi is the best technique for predicting the skin f r ic-

tion on f lat plates and wind tunnel walls, with the method of van

Driest-II being a close second. However, i f one accepts the results of

References (142), (148), and (150) and the latest study by Hopkins and

Inouye (152) then the order of preference would be reversed.

The method van Driest-II (142) was the method selected to com-

pute the tunnel wall skin-friction coefficients used in the aerodynamic-

noise-transition correlation developed in this dissertation. The method

of van Driest-If was selected for three reasons:

1. I t is among the best and perhaps the best method.

2. I t is a "theoretical" method as opposed to an empirical or

semi-empirical method, and the analytical expression,

although implicit in C F, can be programmed fair ly easily for

a digital computer, and

3. The author is more familiar with the method and personally

likes i t .

319

AEDC-TR-77-107

I I . METHOD OF VAN DRIEST-II

The method of van D r i es t - I I was used to compute the wind tunnel

wall mean turbulent skin-fr ict ion coefficients used in the aerodynamic-

noise-transition correlations developed in Chapter IX, Figures IX-8,

page 233, and Ix-g, page 235.

Van Driest published in 1951 a theory for turbulent, compressible

flow co,only referred to as van Driest-I (135). This theory was devel-

oped specif ically for f lat-plate flows and ut i l ized the Prandtl mixing

length hypothesis (¢ = ky) as the principal assumption as discussed in

Reference (135). In I956, van Driest (142) published a second theory,

comonly referred to as van Driest. I f . In this theory the von K~rnkln

mixing length hypothesis, ~ = k(du/dy)/(d2u/dy2), was used. At certain

flow conditions, particularly for M® ~ 5, there can be significant d i f -

ferences in C F, as shown in Figure A-l, depending on which method is

used. At the time the theories were published, van Driest saw no theo-

retical reasons to prefer one method over the other and stated that a

preferred theory would have to wait for experimental verif ication. Based

on comparisons with experimental data (as discussed in the last section),

i t is now generally accepted that van Driest-II (142) provides the best

predictions.

Included in Figure A-1 are the experimental skin-fr ict ion coeffi-

cients obtained in this research on the walls of the AEDC-PWT Tunnel 16S.

Experimental data from several other sources are also included. Reason-

able agreement between the experimental data and the theory of van

Driest-II exists.

320

A E D C - T R - ? 7 - 1 0 7

S~. H

Experimental Values

Cr' in. Source Reference

x -h 0 0 0 D

0.2 2.2 3.0 3.0 3.0 2.6 3.7 4.5

~530 R.A.E. 8 f t x 8 f t Tunnel (Straight Wall) (147) ~350 R.A.E. 8 f t x 8 f t Tunnel (Straight Wall) (147)

56 AEDC-VKF 12 in. x 12 in. Tunnel (D) (Straight Wall) (97) 238 AEDC-VKF 40 in. x 40 in. Tunnel (A) (Straight Wall) (154) 839 AEDC-PWT 16 f t x 16 f t Supersonic Tunnel (Straight Wall) Present Study - - - F la t Plate (123) - - - F la t Plate (123) - - - F la t Plate (123)

C F

CFI --- Theoretical Values i l CFI I --- Theoretical Values (See Appendix C)

0.006 I~" ' I t I ' I ' ' ' I ' I ' I ' I ' I ' I ' ' ' I I I ' I

0.005 /

0.004

0.003

0.002

0.001

0.0008

0,0006

0.0004

0.0003

" " I ~ A I J ~ r I l i l ~ f l 5 a I ~r

, I , I ,lJ,,l , I,I , I

2 3 4 6 8 10 20

(13s) (142)

, I ,lJ,,l

30 40 60 80 100

I I I m

0 .5

2 3 3 4 5 " 5

7 9 9

I l l l I I I I I 200 300 400x 106

Re~ r

Figure A-I. Adiabatic, mean turbulent skin-fr ict ion coefficients as a function of Mach number and length Reynolds number.

321

AEDC-TR-77-107

Presented in Figure A-2 are calculations using the method of van

Driest- I I (as developed in Appendix C, page 343) to i l lus t ra te the sig-

ni f icant effects of nonadiabatic wall conditions at high Mach numbers

and/or high Reynolds numbers. The method of van Driest- I I is discussed

in detail in Appendix C, page 343.

322

0.01 I

O. 001

CFII

O. 0001

D ~

Sym Tw%w

L ~ " = " ~ , - =

0.5 1.0

~. Moo

6 8 12

Figure A-2.

See Appendix C for Method of Computation

I I m m mm=i~ I I i t mtmtl , m m m mmmmi i I I m lliml

10 ? 10 8 10 9 1010 Rej~

Mean, turbulent skin-friction coefficient computed using the method of van Driest-ll.

m D O

O

A EDC-TR-77-107

APPENDIX B

TUNNEL WALL BOUNDARY-LAYER CHARACTERISTICS

The aerodynamic-noise-transition correlations developed in

Chapter IX [see Eq. (10), page 232, and Eq. (11), page 235] are dependent

on the boundary-layer displacement thickness (6") and the mean turbulent

skin-friction coefficient (CF). Part of this research program included

making boundary measurements in three of the AEDC wind tunnels (AEDC-

VKF A, AEDC-VKF E, and AEDC-PWT 16S) to determine the values of 6*. The

measurements in the AEDC-PWT 16S were the f i r s t boundary-layer data mea-

sured in that fac i l i ty . The data from the AEDC-VKF Tunnel E was the

f i r s t for M = 5. The AEDC-VKF Tunnel A test section boundary was re-

surveyed in this research to establish i f a modification to the tunnel

wall flexible plates upstream of the throat region (153) that occurred

after the tunnel was in i t ia l l y calibrated (154) affected the test section

boundary layer.

This section presents the basic, experimental boundary-layer

characteristics obtained in this research. Correlations that are ade-

quate for predicting tunnel wall boundary-layer displacement thickness

values for two-dimensional supersonic nozzles and axisymmetric hyper-

sonic nozzles are presented.

I. DATA REDUCTION PROCEDURES

The two-dimensional boOndary-layer displacement thickness (6")

(mass defect) and momentum thickness (e) (momentum defect) for a compres-

sible flow are defined by Eqs. (B-I) and (B-2), respectively.

324

A EDC-TR-77-107

, ou( o) o ~ 1 - ~ ~ (8-2)

Subscript e denotes values at edge of boundary layer.

Equations (B-l) and (B-2) were evaluated using the standard as-

sumptions that the stat ic pressure and the total temperature remain con-

stant across the boundary layer. By employing a p i tot pressure rake to

measure the impact pressure across the boundary layer in conjunction with

a measured wall stat ic pressure at the rake location allows the local

boundary-layer prof i le conditions to be determined. Writing Eqs. (B-l)

and (B-2) in terms of local Hach number gives

= - - ~ dy (B-3) 0 ~ee I + ~ M e

e = / . M dy (B-4) 2 o re

For subsonic flow, P/Po >- 0.528, Eq. (B-5) is used to compute the local

Mach number:

H [] 5 - - - ~ (B-5)

For supersonic flow, P/Po < 0.528, the local Hach number was determined

using the impl ic i t Rayleigh-Pitot Formula (155).

325

A E DC-TR-77-107

2 +1 1 (B-6)

where y = ratio of specific heats = 1.4 for air or nitrogen.

The integrands of Eqs. (B-I) and (B-2) were plotted at the re-

spective probe height (y) and then 6* and e were determined from graph-

ical integration using a planimeter.

I f i t is assumed that the boundary layer begins at the tunnel

throat and that a uniform flow constant Mach number ( i .e . , zero pressure)

flow exists over the ful l length of the nozzle, then the skin-frictlon

coefficient is readily determined from the two-dimensional von K~rm~n

momentum integral.

de M 2 e dUe = ~ + ( 2 + H - ) Ue ~ (B-7)

H = T ~ shape parameter (B-8)

x = axial distance

where

for uniform zero pressure gradient flow du/dx = 0 and Eq. (B-7) becomes

Cf _ de (B~9) T-B~

Upon integrating Eq. (B-g) becomes

x B Cf dx = 2 /

By definition

i /x Cf dx CF=~" 0

de (B-iO)

(B-II)

326

then

and

2 fi d e - 2e CF = ~ 0 - ~

_ 2e c F -

A EDC-TR-77-107

(B-12)

I I . AEDC-PWT TUNNEL 16S DATA

The displacement thickness (6*) and momentum thickness measured

on the f lexible plate in the 16- by 16-ft test section at M = 2.0, 2.5,

and 3.0 are shown in Figure B-I. The geometry of the fourteen-probe

boundary-layer rake used to obtain these data is shown in Figure B-2a.

The rake location in the test section is shown in Chapter IV, Figure

IV-11, page 90. There was a small difference in the straight wall and

f lexible plate data as evident in the data presented in Figure B-I.

The computed momentum thickness was determined from e = (CFX)/2

where C F was determined using the theory of van Driest-If (see Appendix C).

The agreement between the experimental e and the " f la t plate" theoretical

values for e is seen to be fa i r l y 9ood.

I l l . AEDC-VKF TUNNEL A DATA

The f lex ib le plate which forms the lower nozzle wall in the Tun-

he1A was damaged on October 10, 1961. The damage, Figure B-3, occurred

in the converging region of the nozzle upstream of the throat where

several of the lugs which connected the f lex ib le plate to automatically

controlled actuators were broken or cracked. Repair of the plate

327

t , ,J OO

J~r = 839 in. Experimental S o t~ o Straight Wall

Data 1 q z~ c~ Flexible Plate

5 ' I ' I ' I I I I I '

4 M_.m_

6", in. 3 2.5

, I , I , I I I I I

" ~ ~ : : ~ [ L =--2"5 !

------(Theoretical 0 Estimate, Tw/Taw - 1. 0 /

~ 8-CFH J~r;CFl, from Figure A-2

1.0 0.9 0.8 0.7 0.6 0.5

'" 0.4

0, in. 0.~ O. 0.6

2.21-, i , l , , , i , , ' ! 0.5

0.6 1 . 5 ~ 0.5 0.03 0.04 0.06 0.10 0.15 0.2x106

Re/in.

' I ' I ' 1 I I I I

: M._9_ = -

- - - - ~ 3.0 -

, I , I , I I I I I

I - - - ~ - - 2.5 -

, ,

i - ' - - - - ~ _ . . . : . . ~ 2 . 0 -

, , , , , , , ,

0.030.IN 0.06 0.10 0.15 0.20x106 Re/in.

m O o

',,4

O

a. Displacement Thickness b. Momentum TMckness Figure B-1. AEDC-PgT Tunnel 165 boundary-layer character is t ics .

AEDC-TR-77-107

10 deg

1.5o 6.o Typ.

Sharp Leading Edqe

~ 1.0 R

Probe l ) No. y, in.

14 : 12.0

13 11.0

12 10.0

11 9.0

10 8.0

g 7.0

8 6.0

7 5.0

6 4.0

5 3.0

4 2.0

. 3 1.5

I 2 1.0

NOTE: y is Distance to Centerl ine of Probe.

a. AEDC-PWT Tunnel 16S Boundary-Layer Rake

Probe No. y , in.

1 0.20 2 0.25

3 0.30

4 0.35

5 0.40

6 0.45

7 0.55

8 0.60

9 0.65

10 0.75

11 0.95

NOTE :

Probe I No. y, in.

13 1.50 i

14 1.75

15 2.00

16 2.25

17 2.50

18 2.75

19 2.95

20 3.50

21 4.00

22 4.45

23 4.95

y is Nominal Distance to Centerline of Probe. Tube Size: 0.042 0D x 0.027 ID

Y

m ~

~ m m

m

23--

lO-deg Included Angle

O. 625 m

~ 3 . 0 " - - ~ O N

k

5

r

Figure B-2. b. AEDC-VKF Tunnel A Boundary-Layer Rake

Boundary-layer rakes used in the AEDC-PWT 16S Tunnel and the AEDC-VKF Tunnel A to measure tunnel wall boundary- layer profiles.

329

AE DC-TR-77-107

Removable Rubber Bolt Heads - , _ I ,: ~r " 208 in,

Stilling F I o ~ Chamber

f L 160 Permanent Steel " Nozzle Hexagonal Bolt Heads Plate 0. ]58-in. Height by 0.58-in. Width ISee Reference (153)]

AEDC-VKF Tunnel A Profile

Station 0 -J ~ >- Bou ndary-Layer Rake

Fledble '%-Test Section

Rake Locatio n Remarks o n o Top Plate With Rubber Bolt Heads • • • Top Plate Without Rubber Bolt Heads o' z~ o' Bottom Plate With Steel Bolt Heads

• r= Bottom Plate Before Plate Repair, Reference (154)

2.5 f . M ~ 0.25 2.0 0.20

.=_. I. 5 ~ v ~ ,: 0.15

*,o" 1.0 I ~ l ~'0.10

o.s o.o8

0.6 ~ 0.06 O.l 0.2 0.3 0.40.50.60.7 0.1 0.2 0.3 0.40.50.6

Re/in. x 10 .6 Re/in. x 10 .6

a. Displacement Thickness b. Momentum Thickness

Figure B-3. AEDC-VKF Tunnel A boundary-layer character ist ics.

330

AE DC-T R-77-107

required new lugs to be bolted to the plate. A total of 160 steel bol t

heads, protruding O.158-in. above the plate surface, was required (Fig-

ure B-3). Details of the replacement lugs, bol t heads, and plate damage

can be found in Reference (153).

Test results presented in Reference (153) showed that the con-

necting bol t heads had no s ign i f i cant ef fect on the uniformity of the

free-stream flow but increased the boundary-layer displacement thickness

(6*) on the repaired plate by a factor of approximately 1.5 at a free-

stream Mach number (M) of 1.5 and had no ef fect on 6* at M = 5.0.

To obtain more information on the effects of the bol t heads on

the bottom plate boundary-layer growth and to provide information on 6*

to be used in the t rans i t ion correlat ion (discussed in Chapter IX), addi-

t ional boundary-layer p ro f i le measurements were made on the repaired bot-

tom f l ex ib le plate using the rake shown in Figure B-Eb. The experimental

data are presented in Figure B-3 and confirm the results of Reference

(153) which showed no bolt-head effects on the bottom plate at M = 5.0.

Likewise, there was no ef fect at M® = 4.0 and only about a six-percent

increase in 6" at M = 3.0 when compared with the results from Reference

(Z54).

Since this research was directed toward investigat ing the effects

of radiated aerodynamic noise on t rans i t ion , i t was f e l t necessary to de-

termine i f the plate repair produced any noticeable differences on model

t rans i t ion. Therefore, duplicate rubber bol t heads were glued to the top

f l ex ib le plate, and the boundary-layer characterist ics on the top plate

and the t rans i t ion location on the 3.0-in.-diam hol low-cyl inder model

were measured with and without these rubber bol t heads. These results

331

AE DC-TR-77-107

were presented in Figure VII-2, page 170. The data presented in Figure

B-3 show no s ign i f i cant ef fect o f the plate repair and the upstream pro-

tuberances on the test section 6" and e for H = 3, 4, and 5.

IV. AEDC-VKF TUNNEL E DATA

Studies were conducted in the AEDC-VKF Tunnel E (12- by 1Z-in.

test section) to determine i f the axial location of the model in the test

section had a s ign i f icant ef fect on the location of t rans i t ion as dis-

cussed in Chapter X. An e f fo r t was also made to cool the walls of the

tunnel using l iqu id nitrogen in an attempt to maintain laminar flow on

the tunnel walls and thereby reduce (el iminate) the radiated aerodynamic

noise. The boundary-layer p ro f i le was measured at the d i f fe rent model

locations to establish i f cooling was ef fect ive in producing laminar

flow and to define the displacement thickness. Figure X-5, page 263.

presented in Chapter X, shows the model and rake posit ions. An eighteen-

probe rake was used to measure the p i to t pressure d is t r ibu t ion through

the boundary layer on the bottom f lex ib le plate. The s ta t ic pressure

was computed using the free-stream Nach number at the edge of the bound-

ary (computed using the edge p~ measurement) and the tunnel s t i l l i n g

chamber pressure.

Figure B-4 presents the p i to t pressure prof i les obtained at the

two axial stations (£r = 39.6 and 56.0 in . ) for several tunnel stagnation

pressure levels. These data are for the uncooled tunnel wall condition

and exhib i t the mean value characterist ics of a turbulent boundary layer.

The prof i les at ~r = 39.6 in. exhib i t a p/pj maximum value greater than

1.0 and also show a decrease in p i to t pressure with increasing y distance

332

A EDC-TR-77-107

1 4

12

lO

. 0.8 ,..r._

Po 0.6

O.4

¢2

0

FLOW C~DfflONS

5~rn d_r, m Po, psu To, ~ Re#in. x00 .5 Me Xtm o 3~.6 99 (6 6}) A3718 4.79 4.99 • ". 39.6 q8.7) 679 0.3315 4.76 4.99 o 39 6 100.8 663 0 35~ 4,16 4 99 7 568 ~.M 660 rt 3453 499 4.99 0 56.8 150.8 666 0.5211 4.97 ~Lq9 0 56.8 l q 8 (68 O. 7000 4.99 4.99 = 56.8 2i'5. 6 689 0 . ~ ~99 ~gg

Wa:P Number Grldlent f rm Expandl~ Fbu Field - -~

p • Probe Pitot • " " • Free-Slream Pit" Pressure , ~ / " Po WMo.5. 0

I i ~ , I I , I , I , [ I l i l I I

02 0.4 0~6 0.8 lO i 2 14 16 18 20 22 2.4 y, Irl

a. Adiabatic Wall

1.2

LO

G 8

.L ~ 0.6

114

D

6

,8 J ~ / / eta FLOW CONDITIONS

0 4 0 # 204,1 659 0 . 1 1 7 4 . W 4 , 9 9

, I l I , i . I • I i I , I i I I I I I I

0.2 0.4 0.6 0.8 ] 0 ) 2 ) 4 ).6 ).8 2 0 Z.2 Z.4 y. in.

b. Cooled Wall

Figure B-4. Pilot pressure profiles from AEDC-VKF Tunnel E, M = 5.0.

333

AE DC-TR-77-107

outside the boundary layer. This is a direct result of the probe (~r =

39.6 in.) being located in the expanding flow field of the tunnel (see

Figure X-5, page 263) where the boundary-layer-edge Mach number was ap-

proximately 4.8. The table included in Figure B-4 l ists the flow condi-

tions.

Figure B-4 allows a comparison between the cooled and uncooled

wall pitot pressure profiles at station t r = 39.6 in. These data show

that the wall cooling for these test conditions had a negligible effect

on the development of the turbulent profile.

The boundary-layer displacement thickness (6*) values for star

tions t r = 39.6 and 56.8 are presented in Figure B-5 for both the cooled

and uncooled wall case. These data again show no appreciable effect of

cooling. Comparisons with the AEDC-VKF 12-in. Tunnel D data from Refer~

ence (97) and the theoretical values of 6* calculated using Reference

(156) show good agreement.

I t should be mentioned that the information necessary to provide

an exact location of the last tunnel characteristic for M = 5 in Tun-

nel E was not available. However, the rake data show a negligible Mach

number gradient existing outside the boundary layer at station t r = 56.8

in., and this location is thought to be the approximate axial station

for cancellation of the last characteristic for M [] 5. Therefore, i t

is assumed that the last characteristic is cancelled at t r • 56.8 in.,

and this value is used with Reference (156) to calculate the theoretical

6* values. A knowledge of the last characteristic is also required to

provide a meaningful analysis of the transition data.

334

AE DC-TR-77-107

Sym Jr , in. To, OR Plate Conditions

o , 56. 8 = 660 Uncooled z~ 39. 6 = 660 Uncooled A 39. 6 = 660 Cooled

2 . 0 [ ' I I I ' I I I I I l l ' I ' I ' I

/ l. 0 From Reference (97)

[~ F (AEDC-VKF Tunnel D 12- by I2-in. Test Section - O. 8 IZ.. ~ . . J~r = 56 in., T o = 500°R)

0.6 I - ~ /FThe°ry , - ~_ v ~ , ~ ¢ / , , ~ . . . . . . . , ~ . / Reference (156)_

6', in. / .... . o ~ ; - . (Uncooled)

0.3 I

0.2

0.1 0.1

Flexible Plate Data

I I , I , I I I I I I I ' I I I i f

0.2 0.3 0.4 0.6 0.81.0 2 3 4 5xlO 6

Re/in.

F i g u r e B -5 . AEDC-VKF Tunne l E t u r b u l e n t b o u n d a r y - l a y e r d i s p l a c e m e n t t h i c k n e s s ( 6 * ) f o r H = 5 . 0 .

335

AE DC-T R-77-107

Presented in Figure B-6 is a summary of the 6- and B values de-

termined from the experimental boundary-layer pitot pressure profiles

measured in the AEDC-VKF Tunnels A and D and AEDC-PWT Tunnel 16S at

M =3.0. oo

The experimental displacement thickness (a*) was evaluated em-

ploying the usual assumptions of constant total temperature and constant

static pressure through the boundary layer at a particular station.

V. CORRELATIONS OF BOUNDARY-LAYER DISPLACEMENT THICKNESS

Some data sets used in verifying the aerodynamic-noise-transition

correlation presented in Chapter IX required an estimate of a*. Analyti-

cal relationships for a* are also required in the FORTRAN Computer Pro-

gram that will be developed in Appendix C for predicting the location of

transition on sharp flat plates and sharp cones using the aerodynamic-

noise-transition empirical equations [Eqs. {I0) and {II)] that were de-

veloped in Chapter IX.

In this section the experimental values of a* are compared with

existing correlations to establish if applicable correlations exist, or

can be developed, for a wide Mach number range (3 2M 215) for both

two-dimensional and axisymmetric wind tunnel nozzles.

For 1.5 2M2 5 the theory developed by Maxwell and Jacocks {156)

allows a good correlation of displacement thickness. The following non-

dimensional correlating parameters were developed by Maxwell and Jacocks

{156) by rearranging the theoretical equation presented by Tucker {157)

[obtained by integrating the momentum integral equation].

336

UJ

S_,ym J~r, in. Source

o • 839 This Investigation • 208 This Investigation

,, 208 Reference (154) Open Symbols - Tunnel Straight Wall a • 56 Reference (97) Solid Symbols - Tunnel Flexible Wall

5 . 0 ~ _ , , , , , , , , , , , , , , , , , , , , , , , ~ 1.0 L, , " , ' , , , ' , ' , . ' , ' " , ' , ' , - 4._t. ~ Tunnel ~ O. 8 ~-- Tunnel -

2. O.

. ~ ~ ~ l , ~ / 1 I" ' AEDC-VKFA "

• ii °~" ~" O.

°:2 ° " : 0. O.

0.03 ~- 0 . 1 - - ' i , i , l i l l l i I , I , I , , , I , I , I 0 . 0 2 , I , , I , I , I , I , I , I , , , I , 1 1

0.03 0.06 0.1 0.2 0.30.4 0.6 1.0x106 0.03 0.06 0.1 0.2 0.30.4 0.6 1.0x 106 Re/in. Re/in.

Figure B-6.

Displacement Thickness a. Displacement Thickness Turbulent boundary-layer characteristics at R= = 3.0 for AEDC Tunnels PWT-16S, VKF-A and VKF-D.

m 0 ¢3

-11

0 ,,,d

AE DC-T R-77-107

where

and

- - -- ~ *

+. K(xE)617 (B-13)

K=O. 0131 ~/p_~o/1/7 (B-13A)

a o = Speed of sound at stagnation conditions, f t /sec

X E = Longitudinal distance from tunnel throat to nozzle

aerodynamic exi t plane, f t

6* = Boundary-layer displacement thickness, f t

Po = Coefficient of viscosity at stagnation conditions,

lb-sec/ f t 2

Po = Density at stagnation conditions, lb-sec2/f t 4

Data from nine wind tunnels are presented in Figure B-7 for

1.5 ~ M= ~ 10. Up to M = 5, the experimental data are in good agreement

with the theoretical estimate of Maxwell and Oacocks (156). One s ign i f i -

cant trend of the present data at H = 5 is the dependence of 6* on the

Re/in. value. The AEDC-VKF Tunnel D (97) and Tunnel E data obtained in

the present research show a decreasing value of~-~wi th increasing Re/in,

values over the range 0.1 x 106 to 1.3 x 106 . The theory of Reference

(157) assumed a 1/7-power-law prof i le existed (u/U = (y/~) l /N, N = 7),

and the large Re/in. range of these data could ref lect a variation in N.

Although the correlation method developed by Maxwell and Jacocks is con-

sidered good, there can s t i l l be as much as a 10~ difference in the pre-

dicted value using the mean correlation curve (theory curve) and the

actual data value.

338

AE DC-TR-77-107

Sym Facility Test Section Size ~r, in. Source

! o AEDC - VKF (A) 40 in. x 40 in. - - - Reference (156) z~ AEDC - PWT (SMll 12 in. x 12 in. - - - Reference (]56) o A E D C - VKF (D) 12 in. x 12 in. 56 Reference (97)

* P' A E D C - PWT - 16S 16ft x 16ft 839 Present Invest. * • A E D C - VKF (A) 40 in. x 40 in. 208 Present I nvest. * x JPL - 20-in. SWT 18 in. x 20 in. 66-118 Reference (93)

Cooled Walls * • JPL - 21-in. HWT = 20 in. x 21 in. ]59 Reference(93) * • AEDC - VKF (E) 12 in. x 12 in. 64 Unpublished VKF Data * 0 A E D C - VKF (B) 50-in. Diam 244 Figure B-8 " • AEDC - VKF (E) 12 in. x 12 in. 57 Present Invest.

¢' AEDC-VKF (B) 50-in. D i a m 242-302 Figure B-8

~* Computed at Aerodynamic Exit Plane if, E ) * 8" Computed at Rake Location (J~r)

20 - -Maxwel l and. Jacocks. Theoretical ' I ' / ' I ' I ' I ,JP' I Value (Adiabatic Wall, Reference / • / .~ ,~

18 ]56) Two D i m e n s i o n a l ~ / , , A , " ~ ' 9 - - - ~ v . ~'C'.- ~

16' Re/in. x 10 -6 ~ / / ~ . ~ ~ " - ~ - 0 10," ~ .,.,~".~, ~ : ' ; ' 4 ~ ~ - D a t a -

14 • ~,-.~ _.\ . -

Iz o . 3 2 _ • -

O. 5 1 ~ ~, lo o. 98yQ z ~

-

6 -

2 -

~ I i I i I I I i i I E i I J I L I I - 2 3 4 5 6 7 8 9 10 II

Moo

F i g u r e B -7 . F l e x i b l e p l a t e d i s p l a c e m e n t t h i c k n e s s c o r r e l a t i o n s f o r M = I to 10.

Oo

3 3 9

AE DC-TR-77-107

Data for Mach numbers greater than f ive do not fo l low the Maxwell-

dacocks curve as shown in Figure B-7. This is not unexpected since the

power-law p ro f i l e changes a~ higher Mach numbers (7 < N < 11) [Edenfield

(105)]; also there are cold wall effects. However, use of the parameter

6* does allow a correlat ion for cold wal l , contoured two-dimensional and

axisymmetric nozzles to be developed in the range 5 < M < 10 as shown

in Figure B-7. Note that two sets of data were available for the two-

dimensional case and three sets for the axisynmnetric case. Since axisym-

metric ( i . e . , conical) boundary layers are thinner than two-di~nsional

boundary layers, i t would be expected that the axisyninetric 6* data cor-

re lat ion would be lower than the two-dimensional data, and this is in-

deed the case as evident in Figure B-7. Empirical equations for the

fa i r ings of the 6* data shown in Figure B-7 are presented in Appendix C

for use in the FORTRAN Computer Program.

Edenfield (105,158) reviewed d i f ferent techniques for correlat ing

and predicting 6" in hypersonic axisymmetric nozzles. This work showed

that s ign i f i cant differences exist between the various methods, and no

one method was c lear ly superior to the others over a large H= and Re=

range. In order to select a method that was exp l i c i t in nature and pro-

duced consistent and reasonable resul ts, the techniques discussed by

Edenfield were reviewed and the method of Whit f ie ld was selected as an

acceptable method for hypersonic nozzles in the range H= ~ 10. Data from

seven d i f fe rent hypersonic nozzles over a Mach number range from 6 to 16

and a large Reynolds number are presented in Figure B-8. The empirical

equation of Whit f ie ld is also presented and the agreement with the data

is considered f a i r l y good. The equation shown in Figure B-8 is the

340

AEDC Sym Tunnel o VKF-B z~ VKF-B [] VKF-C 9 VKF-F • VKF-F I VKF-F

0.1

Moo 6 9 14, 10 8

O. 01 6 '

O. 001 lO 6

Figure B-8.

Moo X, in. 6 242 8 249

10 302 8 375

12 375 14 39O

I I I I I 1 1 1 I

X = ~v

Type Nozzle Type 6 ° Data

Contoured Experimental Contoured Experimental Contoured Experimental Contoured t (Computed Using Momentum Contoured~ ~ Integral or Finite Difference Conical ) ~Technique, Reference (105)

m I , , , m , m I , , m m , , , , I

References (101), (105). and VKF Data

x

O. 22 (Mm) ~ 5

(Rex)O. 25 , [ Reference (105)]

I I I m i l l ] i I I m m , r o l l , I m , m , m m , l , m m m z m l

10 / 10 8 10 9 1010

Rex = pooUooX Poo

Correlation of hypersonic wind tunnel wall displacement thickness (6*).

)> m 0 0 :4 7)

0

A EDC-TR -77 -107

method used in the FORTRAN Computer Program developed in Appendix C fo r

H= > 10 and/or H= > 8 and Re x > 200 x 106 .

342

AE DC-TR-77"107

APPENDIX C

DEVELOPMENT OF FORTRAN IV COMPUTER PROGRAM FOR

PREDICTING TRANSITION LOCATIONS USING THE

AERODYNAMIC-NOISE-TRANSITION CORRELATION

I. METHOD OF APPROACH (

The algorithm developed to solve the aerodynamic-noise-transition

empirical equations for a sharp f la t plate, Eq. (10), page 248, and sharp

slender cone, Eq. (11), page 252, at zero angle of attack are presented

and discussed in this section. At f i rs t glance, Eqs. (10) and (11) ap-

pear fair ly simple;

Sharp Flat Plate at Zero Angle of Attack (Eq. (10), page 248)

0.0126 (CFII)'2"55 (~-) -- ( c - i ) (Ret) FP

Sharp Slender Cone at Zero Angle of Attack (Eq. (11), page 252).

48.5 (CFII)-1"40 (~) • = ( c - 2 ) {Ret)c°ne

however, computation of the tunnel wall turbulent-boundary-layer dis-

placement thickness (6*), tunnel wall skin-friction coefficient (CF),

along with the tunnel free-stream unit Reynolds number and flow proper-

ties at the surface of an inviscid cone, become a fair ly involved and

lengthy process. In order to provide a systematic approach and to aide

343

A E DC-T R-77-107

persons who might be interested in the details of the computer program,

the equations required to execute each individual program option are pre-

sented in this section. A special effort has been made to include many

comment statements in the FORTRAN Program so that the program wi l l be

essentially self explanatory. A program l is t ing is provided in Section

IV.

There are four program options (KOPT). These options were de-

veloped in a manner considered most beneficial to potential users and ¢

are described in detail in the program l is t ing. Only a br ief description

wi l l be given here.

KOPT = I and 3

Calculations of transition Reynolds numbers and locations

on sharp f la t plates at zero angle of attack are provided.

KOPT = 1

KOPT = 3

KOPT = 2 and 4

3 ~ M ~ 10 (ideal gas flow)

M R; 10 (real gas flow)

Calculations of transition Reynolds numbers and locations

on sharp slender cones at zero angle of attack are provided.

KOPT = 2 3 ~ M ~ 10 (ideal gas flow)

KOPT = 4 M ~ 10 (real gas flow)

Required input data for all programs options are defined in the

program l is t ing (Section IV) and i l lustrated in the included check prob-

lems (Section V).

344

I I . BASIC EQUATIONS

AEDC-TR-77-107

The following equations were used in the development of KOPT = I

and KOPT = 2.

Tunnel Test Section Conditions (Free Stream)

The tunnel test section static temperature (T®) and pressure (P®)

are computed using perfect gas, one-dimensional isentropic flow relation-

ships (155) with y = 1.4.

T o T o T = = (C-3) ® 1 + y - 1 M 2 1 + 0.2 M 2

and

P ¢o

Po Po

2

U® = M®A® = M® ~/yRT® =

G + 0 . 2 M2®) 3"5 (C-4)

(M®)(49) ~ (C-5)

The value of the absolute viscosity (~) is temperature dependent,

and consequently two different viscosity laws (linear and Sutherland)

are used to compute this parameter. A recent discussion of viscosity

laws is given by Fiore in Reference (15g).

For temperature below 216°R, the viscosity varies l inearly with

temperature:

Linear Viscosity' Law for Air

, = (0.0805)(T)(10 "8) l b - sec / f t 2 (C-6)

For temperature above 216°R and up to about 5.000°K. the Suther-

land equation provides the best estimate:

345

AE DC-TR-77-107

Sutherland Viscosit), Law for Air

(2.270)(T) 1"5 P = 198.6 + T x 10 .8 Ib-sec/ft 2 (C-7)

The free-stream Reynolds number is computed using Eq. {C-8):

p=U® 144 P=U= Re=- "= - T.=R (C-8)

P= ~ Ib/ in. 2

U ~ f t / s e c

p= ~ Ib-sec/ft2; Eqs. (C-6) or (C-7)

T w ~ OR

R ~ 1,716 ft2/sec2-°R

Len9th Reynolds Number

The Reynolds number based on tunnel free-stream conditions and

the nozzle length is required in the computation of C F and 6* and is com-

puted using the free-stream unit Reynolds number and the tunnel length (~):

Re~ = Re=,~ = (Re®)(~)/(12) (c-g)

where

Re ~ f t - I Oo

~in.

NOTE: ¢ = Cm

where ~m = model leading-edge location

Boundary-Layer Displacement Thickness

The turbulent boundarymlayer displacement thickness used in Eqs.

(C-1) and (C-2) is the tunnel wall value computed at the model leading-

edge position (~m).

346

AE DC-TR-77-107

Four separate analytical expressions are required to provide ade-

quate calculation of ~* for the Mach number range from 3 to 20 for two-

dimensional, axisymetric contoured nozzles and conical nozzles. The

development of these correlations were discussed in Appendix B (see Fig-

ures B-7, page 339, and B-8, page 341).

For two-dimensional nozzles and 2 ~ M ~ 5, the following em-

pirical equation developed by Maxwell and Jacocks is applicable:

~o ~ computed from Eq. (C-7)

~ nozzle length, f t

(c-1o)

144 Po I b-sec 2 - , (C-lOa)

Po RT o f t 2

where

a 0 = ~/ 1.4 RT 0 = 49 V~O, f t / sec

Po ~ l b / i n ' 2

T O ~ OR

R = 1,717 f t2 /sec2-°R

The value 6* is computed from a third-degree polynomial curve f i t of the

theoretical curve in Figure B-7, page 339:

Adiabatic ~-~ = 1.1408 M® + 0.08813 + 0.02698 M3®; 2 <_ M® <__ 5 Nozzl es

(c-11i Equation (C-11) matches the curve in Figure B-7, page 339, to w i t h i n

+1.8% for 2 < M < 6.

347

AEDC-TR-77-107

For two-dimensional and axisymmetric nozzles and 5 < M=<IO (see

Figure B-7, page 339) the following linear equations are used to compute

6*:

5 < M < 1 0 ,'

Coo1 Wall I ~¥= 2 .0+ 1.8333 M= : Non-Adiabatic) ~ 0.167 + 1.833 M: Nozzles {,

For the following special conditions

two-dimensional nozzle

axisymmetric nozzles f (C,-12a) (C-12b)

1. Contoured or conical nozzle with 10 < M C 15

2. Very high Reynolds number flow, Re= ~ 2.0 x 106,

and 7 < M < 10 =

~* is computed using Whitfield's empirical formula. A discussion of this

empirical equation is given in Reference (105) and compared with experi-

mental data in Figure B-8, page 341. Whitfield's empirical equation is

(0.22)(¢)(M®) 0"5 6* = (C-13) (Re=,~) 0"25

Turbulent Skin-Friction Coefficient

The method of van Driest-II (see Appendix B) was used to compute

the turbulent flow mean-skin fr ict ion coefficient for the tunnel wall at

the model location in the test section.

The van Driest-II mean skin-friction formula is

0.242 (sin -I a + sin -I B) = loglO(Re~CF) + 1.5 log10 (Te/T w) A'~F '~w/T®

198.6 + T w +

I°glO 198.6 + T e

(C-14)

T w = tunnel wall temperature

Re~ ~ determined by Eq. (C-9)

348

AE DC-TR-77-107

A = r ~ww ; r = recovery factor : 0.9 (C-14a)

(C-14b)

= (2A 2 - B)/~JB 2 + 4A 2 (C-14c)

B = B/ ~ B 2 + 4A 2 (C-14d)

y = 1.4

Since Eq. (C-14) is imp l i c i t in C F, the Newton-Raphson method

was used to solve for C F when H , Re t , T w, and an i n i t i a l value of C F

are specif ied. Equation (C-14) can be rewri t ten as

FCF = ~ F (C2 + C 3 + loglo C F) - C 4 (C-15)

where

O~ C4=0.242 (s~n'~w/T ~ sin-lB) (C-15a)

C 2 = loglo Re t (C-15b)

C 3 = 1.5 loglo ~ww + l °g lO \ 1 9 8 . 6 + T e (c-15c)

Application of the Newtonian-Raphson method gives

_ FCF/dFcF cFi = cFi .1 (c-z6)

dFCF dC F

- - i s the derivat ive of FCF with respect to C F.

~--m 015 (CF)m~ [C2 + C 3 + lOglo C F + 018686] (C-17)

349

AEOC-TR-77-107

By computing an in i t ia l value of CFI I using CFI I = O.O050/M,

Eqs. (C-15) and (C-17) are solved and a new value of the C F term (CFi)

is computed from Eq. (C-16)

This process is repeated using the newly computed C F term in the

right side of Eq. (C-16) until the difference in successive calculations

of C F are within the specified l imi t of 0.0000010:

(ICFi - CFi.1 [ ~ 0.0000010)

This value of C F is then used along with the computed 6* value [Eqs.

(C-12) or (C-13)] to calculate the transition Reynolds number from Eqs.

(C-I) or (C-2).

Program Option I (Sharp Flat Plate at ~ = O)

The location of transition on a flat plate is determined by

X t [] (Ret/Re®)(12); in. (C-18)

where Re t is computed from Eq. (C-1) and Re® from Eq. (C-8).

Program Option 2 (Sharp Slender Cone at a = O)

The analytical expressions required to determine the transi t ion

location on a sharp cone are presented in this section.

The values for CFI I and 6" are computed exactly as in Program

Option 1 [Eqs. (C-9) through (C-17)]. With known values of CFI I , 6", and

the tunnel coordinates C, ~, then the transit ion Reynolds number is com-

puted using Eq. (C-2). However, what one usually wants to know is the

location of transit ion on the cone surface and this requires knowing the

cone surface inviscid Reynolds number, i . e . , the local free-stream Reyn-

olds number at the edge of the boundary layer on the cone surface.

350

AEDC-TR-77-107

For a f la t plate at zero angle of attack, the plate surface in-

viscid parameters are assumed equal to the free-stream parameters, e.g.,

plate boundary-layer edge conditions equal M, Re, T , p., etc. How-

ever, in order to determine the inviscid surface parameters for a sharp

cone, relationships between the surface values and free-stream values

are required.

Cone Surface Static Pressure

The static pressure on the surface of a sharp cone at zero angle

of attack is computed by the "approximate" analytical expression devel-

oped by Rasmussen (160). The cone surface pressure coefficient from

Reference (160) is

cp i[ ] s _ (y + I)K 2 + 2 In - I + + ( c - l g )

(y - I)K 2 + 2

where

K = M s in ~c

~c = ~ the cone included angle

y = ratio of specific heats = 1.4

and Cps is the pressure coefficient defined as

Ps " P- 2(Ps - P-) - - z ( c - 2 o ) Cps q- p M

and

P.

is defined as the free-stream dynamic pressure.

(c-21)

351

AEDC-TR-77-107

Using Eqs. (C-19), (C-20), and (C-21) the cone surface static

pressure (ps) can be expressed as

p - I + sin 2 i + In ® L(Y - I) M 2 sin 2 6 + 2

oo

+ I ) f (c-zz) M 2 sin 2

Cone Shock Wave Angle

A formula for the bow shock angle (¢) as developed by Rasmussen

(160) is

sin 6 c (C-23)

Cone Surface Velocities and Static Temperature

The velocity and temperature at the cone surface is found by us-

ing oblique shock wave theory and isentropic flow theory in conjunction

with the known cone surface pressure and shock wave angle computed from

Eqs. (C-22) and (C-23), respectively.

Oblique Shock Wave Theory

The static pressure (p2) and temperature (T 2) are computed using

oblique shock wave equations (155). For y = 1.4, these equations are

P2= 7 M 2® sin 2 ¢ - 1

P® 6 (c-z4)

T 2 : (7 M 2® sin 2 ¢ - 1)(M= 2 sin 2 ¢ + 5) (C-25)

T® 36 M 2 sin 2 ¢

where P2 and T 2 are the static pressure and temperature immediately down-

stream of the oblique shock wave.

352

A E DC-TR-77-107

Isentropic flow theory is valid between downstream of the bow

shock wave and the cone surface since the flow f i e l d in th is region ts

free from shock waves and consists of an tsentropic compression process.

Using the isentropic f low re la t ionship

-P--= constant (C-26) pY

and the ideal gas equation of state

p = pRT (C-27)

one obtains

T--2 - (C-28)

T s can be computed d~rect ly from Eq. (C-28) since Ps' P2' and T 2 are

known quant i t ies determined from Eqs. (C-20), (C-24), and (C-25), respec-

t i v e l y , and y = 1.4 for a i r .

Cone Surface Veloci t ies

The ve loc i ty at the cone surface is computed using the equation

for to ta l entha lw and the basic physical law that energy ( to ta l entha lw)

is conserved.

since

and

2

Hoo = = Ho2 = Hos = h s + - ~ (C-29)

Ho = Cp T O (C-30)

h s = Cp T s (C-31)

353

AE DC-T R-77-107

where for an ideal gas, Cp = constant = 6,006 ft2/sec2-OR.

Eqs. (C-28), (c-2g), (C-30, and (C~31), one gets

and

I o_ U S

Ms -~/yRTs

Then from

(c-3z)

(C-33)

Cone Surface Reynolds Number

The unit Reynolds number at the surface of an inviscid cone is

computed from

PS US PS Us = ~ - - (C-34) Res = ~s RTs ~s

using Eqs. (C-22), (C-25), (C-28), and (C-32) with Ps computed from

either Eqs. (C-6) or (C-7), depending on the value of T s-

The location of transition on the cone surface is computed from

(Ret)c(12) (Xt) c Re s , in. (C-3S)

using Eqs. (C-2) and (C-34).

Cone Surface Reynolds Number Ratios

Results obtained using the methods developed in the preceding

section for computing inviscid cone surface flow properties and surface

Reynolds number are compared in Figure C-I with the "exact" numerical

technique as developed by Jones (161) and used by Sims (162) to compute

extensive tables of cone properties and by applying the appropriate

354

AE DC-TR-77-107

(Re6) c Re=

Sym M® T o, OR

"Approximate" Computed as Described in Appendix C and D Section I

3 530 4 530

O 5 600 A 6 800

8 1,300 10 1,900

"Exact" Values, References (161) and (162) and Eq. (D-3)

1.8 ~.__ ' I ' I ' l ' [ ' I ' I , I , I , I ,_~

1.7 M=

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8 . a = 0

' l , I , I i I , I , i , I , I , I ,

0 2 4 6 8 10 12 14 16 18 20

B c

T O , OR

600 800 540

1,300 540

1,900 540

5 4 0

Figure C-1. Comparisons o f approximate and exact cone surface Reynolds number r a t i o s .

355

AE DC-T R-77-107

viscosity law [Eqs. (C-6) or (C~7)]. The results presented in Figure C-1

show that the approximate theories of Rasmussen (160) in conjunction

with constant total enthalpy and isentropic flow theory as developed in

the previous section adequately predicts the Reynolds number on the sur-

face of inviscid cones for M ~ 3 and ~ ~ 5 deg.

Program Options 3 and 4

Transition Reynolds numbers are computed using Eqs. (C-1) or

(C-2), page 326, in conjunction with Eqs. (C~13) and (C-14). The free-

stream unit Reynolds number (Re = p® U®/~®) is a required manual input

and not computed using the ideal gas equations [Eqs. (C-3) through (C-8)].

KOPTS 3 and 4 are designed to accommodate wind tunnels having a real gas

nozzle expansion. Sharp cone surface Reynolds numbers are also a re-

quired manual input and can be obtained from Figure D-2, page 358.

Section IV provides a detailed description of Program Options

1, 2, 3, and 4 and specifies all required input data.

I I I . COMPUTER CODE NOMENCLATURE

S,ymbol s

Computer Conventional

A m ~

AO a o

ALPHA

B _ . _

D e f i n i t i o n

V a r i a b l e in S k i n - F r i c t i o n Formula, - - -

Eq. (c-14a)

Tunnel S t i l l i ng Chamber Speed of Sound

Variable in Skin-Fr ict ion Formula, - - -

Eq. (C-14c)

Variable in Skin-Frict ion Formula, - - -

Eq. (C-14b)

U n i t s

ftlsec

356

Sy.mbol s

Computer

BC

BFP

Conventional

C

C

m

BARDEL 6

BETA

C C

CC - - - CFP

CF C F

CP Cp

Cl C 1

C2,C3, C4

C2,C3,C 4

DELS 6*

DELTA 6 e C' C

FCF FC F

FPRIME dFCF dC F

AEDC-TR-77-107

Def in i t ion Units

Tunnel Size Parameter fo r Cones, Eq. (11) - - -

Tunnel Size Parameter for Flat Plates, - - -

Eq. (10)

Tunnel Wall Boundary Displacement Thick . . . .

hess Parameter, Eq. (C-11)

Variable in Skin-Friction Formula, - - -

Eq. (C-14b)

Tunnel Test Section Circumference in.

Aerodynamic-Noise-Transition Correlation - - -

Parameter, Eq. (10), CC =

Mean Turbulent Skin-Friction Coefficient, - - -

Eq. (C-14), (C F = CFII)

Specific Heat of Air at Constant Pres- f t 2

sure, Cp = 6,006 ft2/sec2-OR sec2-OR

Test Section Circumference of 12- by in.

1Z-in. Tunnel, C 1 = 48 in.

Variables in Sk in-Fr ic t ion Formula,

Eq. (C-15)

Tunnel Wall Boundary-Layer Displacement in.

Thickness

Cone Hal f-Angle deg

See Eq. (C-15) - - -

See Eq. (C-17) - - -

357

AEDC-TR-77-107

Symbols

Computer

GAF~4A

K

Conventional

Y

- - - - m

KOPT

KGEOH

Option

Geometry

OK OK

PHI ¢

PO Po

PSl,PS2, - - - PS3,PS4, - - -

PS5 - - -

P1 p®

RT r,n r

REL ReCm

Definit ion

Ratio of Specific Heats (y = 1.4 for Air) - - -

Counter in Number of Loops Used to ~--

Satisfy C F Convergence Cri ter ia, I f

K ~ 100 Program Will Be Terminated.

Program Option - - -

Wind Tunnel Nozzle Geometry - - -

Kgeo m = I , Two-Dimensional Nozzle - - -

Kgeo m = 2, Axisymmetric Nozzle - - -

K [] 3, Conical Nozzle - - - geom

Variable in 6* Equation, Eq. (C-10), ( f t ) I/7

OK = 0.0131 (~®/Po ao)I/7

Sharp Cone Bow Shock Angle, Eq. (C~23) radians

Tunnel S t i l l i ng Chamber Pressure psia

Variables in Cone Surface Static Pres . . . .

sure Equation, Eq. (C-22) - - -

Free-Stream Static Pressure in Wind psia

Tunnel Test Section, Eq. (C-4)

Gas Constant, R = 1,716 ft2/sec2-OR

Temperature Recovery Factor

r = (Taw - T~)/(T ° - T~)

Reynolds Number Based on Distance to

Model Leading-Edge Location,

Ream = p®U®~m/U ®, Eq. (c-g)

Units

ft2/sec 2_ OR

358

AEDC-TR-77-107

S~mbols

Computer Conventional

RES,RESC (Re~) c

RHO Po

RClC C 1 C

RP21 P2 P

RTS1 T s

T®

RT21 T 2 T

REINF Re

RETFP

RETSC

Re t

(Ret)FP

(Ret) c, (Ret) 6

RMACH M

RMACHS M 6

Definition

Cone Surface Unit Reynolds Number

Re s = PsUs/Ps , Eq. (C-,34)

Tunnel Sti l l ing Chamber Density,

Eq. (C-10a)

Ratio of Tunnel Circumference to

Reference Value

Ratio of Static Pressure Immediately

Behind Cone Bow Shock Wave to Free-

Stream Static Pressure, Eq. (C-24)

Ratio of Cone Surface Static Tempera-

ture to Free-Stream Value

Ratio of Static Temperature Immediately

Downstream of Cone Bow Shock Wave to

Free-Stream Value, Eq. (C-25)

Tunnel Test Section Free-Stream Unit

Reynolds Number, Eq. (C-8)

Flat-Plate Transition Reynolds Number

Re t = p®U® xt/~ ®, Eq. (C-I)

Cone Transition Reynolds Number

(Ret) 6 = p~U 6 xt/p 6, Eq. (C-2)

Tunnel Test Section Free-Stream Mach

Number

Cone Surface Reynolds Number, Eq. (C-33)

Units

( f t ) 'Z

I b-sec 2

( f t ) - I

359

AE DC-T R-7 7-107

Computer

RPSl

S~nnbols

Conventional

Ps P®

Definition

Ratio of Cone Surface Static Pressure

to Tunnel Free-Stream Value, Eq. (C-22)

Units

RRHOSI PS P~

Ratio of Cone Surface Static Density to

Tunnel Test Section Free-Stream Value

RRESC RRES1

Re s Re

c o

Ratio of Cone Surface Unit Reynolds

Number to Tunnel-Stream Value

RTWTAW

TO

TS

TW

TI

TAW

US

U1

T W

Taw

T O

T s

Tw T

Taw

U s

U oo

Ratio of Wall Temperature to Adiabatic ---

Wall Temperature

Tunnel St i l l ing Chamber Temperature OR

Cone Surface Static Temperature, Eq. (28) OR

Wall Temperature OR

Tunnel Test Section Free-Stream Static OR

Temperature, Eq. (C-3) J

Adiabatic Wall Temperature

Flow Velocity at Cone Surface, Eq. (C-32)

Tunnel Test Section Free-Stream Velocity,

Eq. (C-5)

ft/sec

ft/sec

VISO PO Tunnel St i l l ing Chamber Absolute Vis- Ib-sec

cosity, Eq. (C-7) ft~

VISS Cone Surface Absolute Viscosity Based

on Linear Law, Eq. (C-6)

lb-sec

VlSl Tunnel Test Section Free-Stream Vis-

cosi ty, Eqs. (C-6) or (C-7)

lb-sec

f t ~

XL X~ Distance from Tunnel Throat to Model

Leading Edge

in.

360

Computer

XTFP

XTSC

Symbols

Conventional Definition

x t Transition Location on Flat Plate~

(Xt)Fp Eq. (C-18)

(xt) c Transition Location on Cone Surface,

(xt)~ Eq. (C-35)

AEDC-TR-77-107

Units

in,

in.

IV. COMPUTER PROGRAM LISTING OOmQOOOOOQOOOOO~OOJO,OO,OOOOQQOOOOOOOOOOOOOQOQJOOOQQQOOOQOOOQOOOQQ

eeeeeeettPREOICTION OF BOUNDARY LAYER TRANS;TIONeeeeteeeeeeoeeeee eeeeeeeeeON SHARP FLAT PLATES AND SHARP CONES USING eoee teeeeeeee eteeeeeeePATEtS AbRUDYNAMIC-NOIS~-TRANSIT|ON CORH(LAT|ONeeeeeeeeee eeeeeeeeeeeeoeeeteeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

eeeeeeeeeeeeeeeeeeee GENERAL COMMLNTS eeeeeeeeeeQeoeeeeeeeeeeeeeee eeTHIS COMPUTER COOE ALLOWS MEASONABLY ACCURATE

PREDICTIONb OF TRANSITION RLYNULOS NUMBENS AND LOCATIONS TO BE MADE ON SHAHP FLAT PLATES AND SLENDER CONES AT ZERO INCIUbNCk FOH ALL SIZE WIND TUNNELS AND 3 ¢N< 20.

eeTHIS COMPUTER CODE IS VALIU FOR A|R OR NITROGEN

eeTHE AEROOYNAMIC-NOISE-TRANS|TIUN CORRELATION AND CONSEGUENTLY oTHIS COMPUTER PROGRAM IS APPLICABLE ONLY TO CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS HAVING TURBULENT ~OUNOARY LAYERS ON THE NOZZLE WALLS AND 3 <M <20 ,

eOTHE PREDICIEU LOCATION OF IHANSIT|ON CORRESPONDS TO THE END OF TRANSITION AS UbFINED BY THE PEAK IN A SUHFAC( PITOT PROBE PRESSURE TRACE

eeTHE VALUE UF THE TUNNEL WALL MEAN TURBULENT SKIN FRICIION CUEFFICINT USED I;¢ THL AERODYNAMIC-NOISE TRANSITION CORRELATION IS COMPUTED USING THE METHOD OF VAN DHILST- I I oINCLUOXNG NON-ADIABATXC WALL EFFECTS

ee THE TUNNEL TEST SECTION WALL TURBULENT BOUNDARY LAYER DISPLACEMENT THICKNESS USED IN THE AERODYNAMIC- NOISE-TRANSITION CORRELATIUN IS COMP~TED USING CORRELATION DEVELOPEO FROM Z-D AND 3-0 NOZZLE DATA

eetouR PROG~AH OPTIONS ARE AVAILABLE eKOPT : I ANU 2 ARE FOR IOEAL GASESpGAMMAa|o¢ eKOPT m 3 AND 4 ARE FOR REAL GAS NOZZLE EXPANSIONS

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeegeeeeeeeeeeeeeeeeeeeeeeeee PROGRAM OPTIONS

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeteeeeeeeeee

KOPT : I eeTRANSITION REYNOLDS NUMBERS AND LOCATIONS ON SHARP

FLA1 PLATE OR HOLLOW CYLINDER AT ZERO INCIOENCE eeIDEAL GASt GAMMA : 1 , 4 ee3 • RMACH < 10 eeee REOU~REO INPUT DATA eeee

• KOPT : | • KGEUM = | OR 2 e C:~UNNEL TEST SECTION CIRCUMFERENCE • XL: AXIAL DISTANCE FHOM TUNNEL THROAT

ro MODEL LEAOIN~ [OGE LOCATIONoINCHES

361

A E D C - T R - 7 7 - 1 0 7

C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

• P08 TUNNEL ST ILL ING CHAHBEH PHESSUREePSIA • TO m IUNNEL S T I L L I N G CHAMBER TEMPERATURE eOLQ R • RMACH• TUNNEL TEST bLCT|ON HACH NUMBER • TW:TUNNEL WALL TEMPEHATUREo OEG R

KOPT 8 2 • •TNANSIT |UN HEYNOLDS NUHBEMS AND LOCATIONS ON

SHARP SLENDER CONES AT ZERO INCIDENCE • • IOEAL GASI GAMMA = 1 e ¢ De3 ( RMACH < | 0 0 • 0 • REQUIRED INPUT DATA • D e •

• KOPT • Z • KBEOH • I OR 2 • C:TU~NbL TEST SECTIUJq CIHCUMFERENCE • XL m AAIAL DISTANCE F~OM TUNNEL THROAT

TO MODEL LEADIN~ ~DGE LOCATION,INCHES P0• TUNNEL S T I L L I N G CHAMBER PRE$SUREePSIA TOm [UNNEL S T I L L I N G CHAMBER TEMPERATURE 90EG R RMACHm TUNNEL TEST SECTION MACH NUMBER DELTA = CONE HALF ANKLE 9DEG TMaTUNNEL MALL TEMPEHATURE¢ OE~ R e

K O P T u 3 e e T R A N S I T I O N REYNOLOS NUMBERS ANU L O C A T I O N S

ON SHARP FLAT PLATES AT ZERO INCIDENCE ee REAL GAS EFFECTS CONSIUEREO IN NOZZLE EXPANSION

PROCESS ee 7 < RMACH • 20 • PO • ~000 PSIA eo FREE-S|REAM STATIC TEMPe SET EQUAL TO 90 DEC R

e e e e REUUIHED INPUT OATA o d e • e KOPT m 3 e KGEOM • 3 • Cm TUNNEL TEST SECTIUN CIRCUMFERENCE • XLmAXIAL DISTANCE FNON TUNNEL THROAT TO

HOOEL LEADING EDGE LOCATION•INCHES • HMACH

• REINF • TUNNEL TEST SECTION UNIT REYNOLDS NUMBER ( OBTAIN FROM FIG )

• TM : TUNNEL MALL TEHPERATUREtUEG R KOPT w 4

0 • TRAN$ITIUN REYNOLDS NUMBERS ANO LOCATIONS ON SHARP SLENOER CONES AT ZERO INCIDENCE

e • REAL GAS EFFECTS CONSIDERED IN NOZZLE EXPANSION PROCESS

• 0 7 < RMACH • 2 0 9 PP • SO00 PSIA • 0 FREE-STREAM STATIC TEMPERATURE SET EQUAL

TO 90 UEG R • • • • REQUIRED INPUT DATA e e o c

• KOPT s 4 oKGEOM • 3 • Ca TUNNEL TEST SECTIUN CIRCUMFERENCE • XLmAAIAL DISTANCE FROM TUNNEL THROAT TO

MODEL LEADING EO~E LOCATIONoINCMES • RMACH

• REZNF s TUNNEL TEST S E C T I O N U N I T REYNOLDS NUMBER ( OBTAIN FROM FIG )

• RRESG • RATIO OF CONE SURFACE UNIT REYNOLDS

362

AE DC-TR-77 -107

NUNHER TO FHLE-STREAM VALUE (USE FIG )

• TW = TUNNEL WALL TkMPERATUNEoUEG R • OELTAs CONE HALF ANbLE OEG

•eeoeeeoee•o•oeoeo•eeoeopeo•teee•eoee••eeeee•oeoee•eee•ee•eeeeeeee TUNNEL NO/ZLL bbONETRIES

KbEOM • I • FO~ T ~ O - D I H E N S I O N A L CONTOUH~U NOZZLES • l t b < RMACH•S ADIAUATIC NALLS • ~ • RMACH • lO NON-AOIAGA;]C WALLS e METHOD OF MAXWELL Ib USED TO COMPUTE

BOUNOARY LAYER DLSPLACEMLNT THICKNESS ON TUNNEL TEST SECTION •ALL

• IOEAL GAS tGAMMA • L . 4 • USk WITH KOPT n I UH

KUEON • 2 • FON AA|SYMMETRIC CUI~TOUHED NOZZLES • 5 • MMACH • lO • NON-AOIASAT|C WALL

K~EOM • 3 • FO~ GONICAL AND CONTUUREO AA|SYMMETRIC NOZZLES

• NON-ADIABATIC WALL • T • RMACH • 20 • USL WITH KOPT • 3 UN 4 • NETHOu OF WHITFZELS UbEO TO CONPUTE BOUNUANY

LAYEN DISPLACEMENT THICKNESS ON TUNNEL TEST SECTAON MALL

• •FOR CONTINUOUS FLOW ANO INIEHM|TTENT MIND-TUNNELS- WITHOUT WALL CUOLIN~ ASSUeCE TV • TAW r - ~ M ~ • 6 Td • |DO * Uog•(GAMMA+ 1DO ) • ( R N A C M • • 2 o O ) / 2DO TM • leO * OeIS•RMACH••2oO

eeFOR F A C I L I T I E S WITH COMPL~Ik MATEH COOLED NOZZLES ASSUME T~ • WATER TENR. • ~30 DEG R

• •FOR IMPULSk F A C | L I T I ( S ASSUME TWo AIR TEMPe=b30 DEG R

| HkAO (Se2tENDaSUO0) KOPTt K~EON 2 F U N N A T C | I t i J ) 3 I F I K O P T ' 2 ) 4 ; 100 . 200

@@@@@OO@~OQ@O@@Q@OOOOQQOQOQOOOOOOOtOQOQOOQOO@OeQO@QQ@ODOQmQOOQ@O

KOPT • 1 wd|TE COLUMN HEAD|NUS

4 • ~ I T E ( b + 1 2 1 K O P | t KGEOM 12 FUHNAT | ;1 o • o L S [ I M A r I O N OF BUUNDAHV-LAVER TRANSITION ON SHAHP

IFLAT PLATES o / / 2 t ~ X ; ; l N CONVENTIONAL SUPENSONIC-MYPEHSON|C l I N D TUNNELS U S I N G ; / / 3 ; l A D o PATES AEHUUYNAM|C NOISE TRANSITION CORRELATION t / / 4o~AoeKOPTaOtl~t3AoeKGEOMaO+|2o// St~XooColNeOo2XooXLtlNeOoZAttRMACHOo2AoePOtPSIAOt3X. tTOoRO~4XteTdoR 6ot3AmtRkINF/FTOobAt;RELeoBXtoCFIt~AteOELS+IN.Oo3XoeRETFP;tSAe 7 e A T F P , | N e O o 2 X t t T ~ / T A W e )

~4 H~AU (5o lboEND= I ) Co ALtPOtTU;RMACHoTW 16 FUHMAT ¢ 6 F 1 0 . 0 ) 16 CX • 4 8 . 0

363

A E Dc. ' r R-77-107

GARMA • 1 , 4 R • 1716

¢ COMPUTE FREE-STREAM TEMPERATURE T I=TO/ I I ,O+Oe2e IRNACHee2,U) I

C COMPUTE FREE-STREAM VELOCITY U|uRNACHeSORT(GAMMAeIReTI|I

C COMPUTE FREE-STREAM ABSOLUTE VISCOSITY C USE $UTNERLANDS VISCOSITY LAM lT17216 OEG R)

1F IT | ,LEe 216) GO TO 30 VISlm 2,270*(TleeI,S)e(IO,Oe*(-8,U))/CI98,6*TI) 60 TO 32

C USE LINEAR VISCOSITY LAW |T1<216 UEG R) 30 VlSlx(O,OGOGeTl)e(lOeOee(-8,O)) 3Z CUNTINUE

C COMPUTE FREE'STREAM STATIC PRESSURE PlaPO/((X,O*Ot2e(RMACHee2,0))et3eb)

C COMPUTE FREE-STREAM UNIT REYNOLDS NUMGER REXNFmi(144,0eP;)tUI)/((ReTI)eVIS~|

C COMPUTE REYNOLDS NUMBER BASED ON TUNNEL NOZZLE LENGTH(ALl 34 REL • REINF • (XL /12 .O)

IF (KGEOM'3) 3 5 t 9 0 t 8 0 0 0 35 CONTINUE

C CUMPuTE TUNNEL TLST SECTION WALL TURBULENT BOUNDARY LAYER C DISPLACEMENT THICKNESS COMPUTED USING MAAWELLIS CORRELATION C ABSOLUTE VISCOSTY (VIS) COMPUTED USING SUTHERLANDiS LAd C VALID FOR 216<T< SO00 tOEG R

36 VISO:(2*270)e(TOeeI*S)eiIO,O•e(-B*O))/(198*btTO) C RMO IS STILLING CHAMBER DENSITY

38 RHO x ( I # A • PO) / (Re TO ) C AU IS STILLING CHAMBER SPEED OF SOUND

40 AO • SGRT((GANNA•R) • TO) C OK IS THE VARIABLE IN MAXdELL;S EU,

42 OK • (O ,0131 ) • ( (V |SU/CRHO• A O ) ) e e ( O . | 4 2 B 6 ) ) C 8AROEL IS MAXWELL CORRELATION PARANETER C IBARDEL IS COMPUTED USING A THIRD UEGREE POLYNOMINAL CURVE FIT OF C |MAXWELLeS ORIGINAL CORRELATION FON RNACN ,LE , 6 . 0

IF (RNACH - S.O ) 4b t 46g 50 46 IF (KGEON ,GT, I ) GO TO 8000 48 BAROEL m 1 , | 4 0 0 2 ~ • RMACH * O,UUG|32e((RMACH)e•2,0)

1 t 0*026978 • ( (RMACH)e •3 ,0 ) 80 TO 56

60 IF ( RMACHeGT, lO,O ) GO TO 8000 IV (KGEOM - 2 ) 6~g S4t BOO0

C IF 64 RNACHClO ANU KGEON • I THEN BARDEL a 2*0 * I.G333•RNACH ~2 BAROEL • 2 . 0 * 1*8333 • RNACN

GO TO 56 54 BARUEL • 0 .167 * | ,B33•RNACH

C DELS [$ TUNNEL dALL DISPLACEMENT THICKNESS IN IN , 56 O~LS•IOKIe(BARDEL)eIIXL/12,0)eeO.B~YI43)eI2.O

C COMPUTE MEAN TURBULENT SKIN FRICTION|CF) USING VAN O R I E S T - i l MITH C TM IS INPUT DATA • DEG, RANK|NE C RT IS THE RECOVERY FACTOR FOR A TURBULENT BOUNDARY LAYER

57 ~Tm 0*90 68 AxSURT((((GANMA-IeOI/2,0)eRTe(RNACHei2,0))e(TI/TW))

B • |TX/TW) * ( A e • 2 . 0 ) - l , O 8 ; • B * * 2

364

A EDC-TR-77-107

BnSU~T(UI} ALPHAmL~oUe(AeO2oU)-O)/SURTIBee2oU*~.Oe(Aee~oO)) B~TA m U/SQHT C(Bee2o~) *4oO° (Ae~2eO) ) C~ m (Uo242)O(ARS|N(ALPHA) , ARS |~CBLTA) ) / (A • S U R T i T N / T | ) ) C~ : ALUGIO(REL) m : O,?b ¢Jg I o b e A L U G | O ( T I / T w ) * A L O G I O ( ( | V 6 o b o T M ) / ( | 9 8 , b * T | ) )

C STAHTZNU VALUE uF CF |50eOOSU/RMACH CF=(OeOOSU)/~MACH K=O

70 FCF = S~HT(CF)eCG~*C3 * ALOG|O(LF)) - C4 RsK- I Z~ CK . b T . 100) ~U ro BOO0

C FPH|ME | 5 THE DERAVAT|V( OF FCF M|TH HESPECT TO CF FPg|ME = ( 0 , 5 0 / bURT(CF) )e ( C2*Cd t ALOG|O(CF) ,O,8bBb)

C THE hEMTON-~APHSUN M~THOO |5 CF : CF - (FCF / FPHIHE)

C INT~RAT[ UNTZL SUCCLSS|VE APPROX|MAT[ONS UF ROOT IS LESS THAN C 10 ,0000010

HUOT m A B S ( F C F / F P ~ | ~ E ) IF C~UO! .GT, O,OUUOUIO) ~0 TO ?O C1=48.~ |F (KOPT eEU, 2) GO TU ]5~ |F |KOPT eEO~ 4) GO TO 22Z AFP:CCF)eo( -2oSS) RGIC : C | / C IF (RC|G - 1o0 ) T i t ? I t 72

T] BFP : OeSb t i O ° 4 ~ ) e C I /C ~U TO T3

72 8#P • | , 0 0 73 ¢F# : SURT (OELS/ C )

u F P : ( O I U | 2 b ) e A F P R(TFPm|BFPeOFP)/CFP ATFP• (RLTFP/RL |NF)e I2eO

C TA~m TUNNEL MALL K~COVEHY TEMPERATURE TAwa T | e ( | ° O * O°|Ue(RNACHee2oO)) RrwTAMa TM/TAM |F | KUPT e[Q~ 3) GO TO 210

BO WHILE ( b t 8 2 ) CtXLeRMACH+POoTOoT~oH(INFtRELtCFeDELStRETFPoXTFPe IRT~TAM

82 FU~MATILH~FB,|tFT,LoFU,l~Fq,~o2F~o|~LPEIIe~o|PE||,~tOPF|Oebt

GO TO l~ C CUMPUTE OELS USIN~ MH|TF|ELOS CORHELAT|ON FOR CON|CA| NOZZLES OR C REAL GAS AX|SYNH~T~|C NUZZLES C x~EN 7< RMACH (~O

90 ULLSB(Oe22)eSQRT(HMACM)/SORT(PEL) 60 TO SU

C ee~eeeeeeoeeeeeeeeeeeeeeeeeee~eeeeeeeeeeteeeeeeeeeeeeeeeeeeeeeeeee C KUPT :

~UO ~ I T E ( b t l O ; ] KUP1t KGEOH | U I FUkHAT ( o |o~ ° [ST|MAT|ON OF OUUNUARY LAYER TRANS|TZON ON SHARP SL

|E,~UER CUNES |N CONVENT]ONAL SUPE~ON|C-HYP~RSONICee/ / | t L X t O ~ | N O TUNNELS USXNO THE AEROUYNAM|C NOISE CORREL&TIONS BY PATE i t ~ / / | o | X t o K O P T moo12~3X~tKSEUM a t t | 2 o / /

365

A E DC-TR-77-107

l ; ~ X t e C + l N , t t 2 X , e X L l l N , et2XttRMACHel3XeePOtPSIAtt|XveTO;Rll4At 2oTntRoo3X+OREINF/FTOo3X+ODELTA+DkbOtZXmoRTSOo4X+IRPSOo3Aoe~NACHS t 3uAA;IRRESCO.4AItRLTSCep3XeeXTSCtINOI~AIITff/TAVl)

102 HEAU(be IO* tENO: I ) CgXL; POt TOI RMACH; OELT&+ TM ;04 FURMAT ( 7 F l O e O )

C COMPUTE CONE SURFACE STATIC PRESSURE RATIO (RPS| • P S / P | ) US|NS DELTA • DELTA/ 5 7 . ~ 9 6

C IRASMUSSENIS eEO, P b l : (SIN(UELTA)ee2oO)e(Ie4eIRMA~Hee2+O))/ZeO P b 2 : 2e40(RMACHeeZeO)e(S;N(OELTA)eo2eO) • 2eO PS3 m U.4O(RNACHeo~,OIe(SIN(DELTA)ee210) + 2cO PS~m A~OG(Ie20 • ;eO/C(RMACHee2oO)e(SIN(UELTA)ee2eO))) PbSo(PSZ/PS3)oP$# HPSImI .O+PSIe ( I+U*PS5) GAMMA • 1 .40 Hm1716.O

C COMPUTE CONE BOW SHOCK ANGLE(PHI) | 10 PHI : ARSIN( S I N ( D E L T A ) • E l i + 2 0 • I . O / ( ( R M A C H e S I N t D E L T A I ) e e 2 , 0 ) ) ee

I Q , S U ) ) C COMPUTE STATIC PHESSURE ANO TEMPEHATURE BEHINO BOW SHOCK USING C 2-D OBLIQUE SHOCK WAVE THEORY C RT21 • T2 / TI

X I2 R(2X • ( 7 . 0 e ( (RMACHeSIN(PHI ) )ee~eQ) - I e Q ) e ( I I R N A C H e S | N ( P H | ) ) e o 2 e O l ) * 5eO)/C3b.Oe((HMACHISIN(PHI))ee2.0))

C RP21 a P21PI | 1 4 AP21 m (T.Oe(CRMACH • S I N ( P H I ) ) e e 2 . 0 ) - I . O ) / 6 . 0

C COMPUTE PRESSURE AND tEMPERATURE UN CONE SUHFACE BY USING CONDITIO C BEHIND SHOCK ~AVE AND |SENTROPIC GQMPMESS|ON PROCESS C HTSX • T S t T |

116 HrS | : HT21 e( (HVS| / RP2 I )eeOe2BST|4 ) C CUMPUTE FREE-STREAM TEMPERATURE(T1)

118 T I : T 0 / ( 1 . 0 • OI~•(RNACH)ee2eO) 120 TS :T IeRTSI

C COMPUTE VELOCITY AT CONE SURFACE (US) C RATIO OF SPECIFIC HEAT IS CPm6006 F T . S O . / SECe SOe-DEGR

CP = 600G | 2 2 US m(SQHT(2.0 • CP))eSQRT( TO " (TIeRT2|Je((RPSI/RP21)eeO,28§?|4))'

C COMPUTE MACH NUMBER AT CONE SURFACE (HMACHS) 1~4 RMACNS = US / ( 4 9 e 0 e SQRTCTS))

C COMPUTE DENSITY AT CONE SURFACE (RHOS) R:1716.0

C COMPUTE FREE'STReAM STATIC PRESSURE ( P I ) 12b PI : PO/ (11o0 + O . 2 e ( R M A C H e e 2 . 0 ) | e t 3 e S )

C COMPUTE DENSITY HAT|O AT CONE SUHFAC( (RRHOSI m RHOS/RHDI) 128 ~ H O S I : ( R P S I / R T S I )

C CUMPUTE REYNOLDS NUMBER AT CONE SURFACE iRRESI • RES/REI) C CUMPUTE FREE-STREAM VELOCITY (UI )

130 UI : |RMACH • 49eO) e SOHT(TI) | 3 2 IF ( TI . b E . 2 | b ) GO TO 138

C CUMPUTE FREE-STHEAM ABSOLUTE V I S C O S I T Y ( V I S I ) USING LINEAR LAW V/S1 = 10 .0805 • T I ) e ( l O , O ) e e ( - B . U )

136 ~ TO 140 C CUMPUTE FREE-STREAM ABSOLUTE VISCOS|TY USING SUTHERLANDS LAM

138 V I S I • (2e270•lTleeloSO|)e(lO.Oee(-BeO))/(|~Be6 • T I ) C ~L I : RE|NF : RHOJ • | J I / V | S | C CUMPUTE FREE-STREAM-UNIT REYNOLDS NUMBER(REI •REINF)

366

AEOC-TR-77-107

|~0 RE INFmIU IeP Ie I#4 .U ) / (ReTI e V | S i ) 142 IF (TS oGE. 216) bU TO |46

C CUMPUT( CONE SURFACE VISCOS|TY V ies USING LINEAR LAW ITS) 216 OEOR 144 V|SS • |0+0605 • T S ) • ( | O o O • • l ' 8 o O ) )

6U TO 14G C COMPUTE CONE SURFACE VISCUS|TY USING SUTMERLANOS LAM ITS>216 OEGR)

l a b VISS x |2o270•(TSet|.SO))el|OeOee¢-6.0))l(19646 • TS) C COMPUTE CONE SURFACE REYNOLOS NUMBER iRES)

148 MESu|RPS]eP|eI44.0eUS)/(ReTSeV|SS) C COMPUTE REYNOLOS NUMBER RATIO(RREb| • RES/RE|NF)

149 R~ESI u RES/REINF 150 GO TO 3 4 i b 2 CUNTINUE

OkLTA • OELTA • 51oE96 C COMPUTE TRANSIT|ON REYNOLDS NUMBER ON CONE SURFACE (RETSC)

153 AC • i C F ) e e ( - | e A O ) RCZC • C1/ C IF CRCIC - 1 .0 I l b 4 t I S 4 o ISS

154 G+ • 0 . 8 0 + 0,20•1C1/C1 80 TO 1~6

155 BC • 1 .00 156 CC • S U R T |OELS/C)

RETSCxIABoS)o(AC • BC ) / CC ATSC •(HETSC / RES) • 12 .0

C TAM• TUNNEL WALL RLCOVERY TEMPERATURE TAWs T I • ( I . O . OI ;U•(RMACHe•210)) RYWTAW• TW/TAW WA]TE (bolSG) CeXLoRMACHoPO eTOtT~ ,RE|NFtOELTAIRTSI tRPSI t

2RMACflStRRESIoRETSCwATSCoRTMTAW 158 FORMAT ( IHtFbeZIFTeltFSoIIFgolgF~o|eFToIt|PE|20490PFGe2

21F8 .3 oFTe3oFT,2oF/o3elPEl2oAtOPFToZoFGe3) 60 TO 102

C •o•••••oeoooo•••ooo••••••••••••••••••oe••••••••ooo••oeeOeoO•••••e• C KUPT • 3 C

200 IFIKOPT-4) 201o 214e G000 201 IF IKGEOH - 3 ) 8000 9 202 m 8000 ~02 mRITE ( 69 204) KOPl9 KGEOM 204 FORMAT | o l e e ePREU/CTION OF BOUNUARY LAYER TRANS|TION ON SHARP

1FLAT PLATES• / / | •2S t •FOR NON ;OEAL GAS NOZZLE EXPANSION PROCESS•// Im~Xt°RHACH • |0 OH RMACM > G o REINF • 15•i0oo6 ,SEE F16 0 / / lobAr •USiNG PATES AEROOYNAM|C NOISE TRANSITION CORRELATIONt// 19dXg IKOPT • o.IZtSXBeKGEOMm e m l ~ t / / |94~9 l C l I N I I I S X I I~LI INI I I4XI IRMACHI95KI ITMeg$XgeREINFeeGK9 eCFe 193XeeOELSoIN. le§Xo eRETFPee5Xo eX[FPelNeeoSXoeTW/TAM o)

2U6 REAblSo 2089 END• I ) Co XLm RMACMo REINF~ TW ~06 FOHMAT ISFIOeO)

H~L • R ( I N F • ( X L / | Z e O ) C COMPUTE DELS US|NO ~HITFZELOS FORMULAS

DkLS • XLOIOo22)oSGMTIRMACM)/(RELe•O.25) C C6MPUTE TUNNEL ~ALL SKIN FRICTION USING VAN OR|EST- | |

GAMMAmIoAO C SOT FREE-STREAM STAT|N TEMPERATURE EAUAL TO 90 DEC R

TI • 9 0 , 0 C TAUm TUNNEL WALL RECOVERY TEMPERAIURE

367

A E DC-TR-77-107

TAW= T I e ( | , O * OoZ~(RMACHe*2oO)) RTWTAW= Tff/TAW GO TO 57

~10 CUNTINUb wHITE ( b , 2 l l ) CtXLoRMACHtTWoREINFoCFoUELStRETFPtXTFPoHTWTAW

~11 FORMAT (|Ht|F8.1tlFIO.191F�IItIFGo|oIPEI~.4*OPFIO.btIFB.tolPE16.4, IOPFIOB2oFUo2)

Z12 GU TO ~ 0 6 QOQ40~mQOO~OOOQOOQOQOlIO~O~OOOOQIgOQOQQO~O~Q~OOQIOQQOOQ~OQOQ60~00

C KUPT= 4 C

Z14 IF (KGEUN - 3 ) 8000 o 21S , 8000 ~15 MR|TE ( 89 2 |b ) KOPTo KGEON ~16 FURMAI ( OlOt tEST|NAT|ON OF BOUNUARY LAYER TRANSIT|ON ON SHARP

1SLENDER CONESO//= | I~X~ OFOR MACH NUMBERS GREATER THAN |0 ON VERY HZGH REYNOLOSO// | ~ X : O A T NACH HUMBER EQUAL APPROX 8(HELNF>ZOeeT) t / / |o~X~oUS|NG PATES AERODYNAN|C NUISE TRANSZT|ON CORRELAT|ONO// | g ~ X ~ ºKOPT m * I IZ~bX~ *KGEOMN t . | ~ t / / | o I A ~ ; C , I N . O t S X , * X L ~ Z N . oe4XoORMACHO~3X,~TM.DEGRI~4X,tRE|NF/FTO 2*JAooRESC/REINFOo~X,oUELStZN.o~TA~OHETSCO,SAgeXTSC~IN.o~3X. 3°OELTA.UEGO.SX. OlW/TA~ o )

218 REAUISo~20~ENU= | ) C*XL~RNACH~HEXNFoRRE$CeT~OELTA 220'FOHMAT (TFIO.O)

REL = Rb |NFe |XL / I~ .O) C COMPUTE OELS USZN~ dHITFIELU°S FO~MULS

D[LS = XLeIO.22|ebQHTIRMACH)/{REL~eO.~5) C COMPUTE TUNNEL ~ALL SKIN FRICTION USING VAN DR|EST- I ]

GAMMA~I,~O C SET FREE'STREAM bTATZG TEMPERATUHE EQUAL TO 90 DE8 R

TI : 90,0 C TAM= TUNNEL MALL ~COVERY TEMPEHATURE

TA*~ T | * I I . O * OeIGI(RHACHte2.O)) RT~TAV~ Td/TAM GO TO Sl

Z22 CONTINUE C COMPUTE TRANSIT|ON REYNOLOS NUMBEH ON CONE

AC : ( C F ) I I ( - | . ~ U ) RCIC ~ Cl IC IF (RCZC - 1.0 ) ~24~ ~ , 2~5

224 BC = 0.80 * O,~O*(C l /C | GU TO 2~b

225 BC = 1.00 226 CC • SQRT IDELS/ C )

RETSC = (48 .S ) * (AC * BC ) I c e R£SC~RRESCeREZNF LTSClIRETSC/RESC)e12.0 W4IT~(b~Z3OICtXLgRHACM~T~tREINFoR~ESC~OELS,HETSC~XTSC.OELTA,RTMTAN

230 FOHMAT(IH~FS.|,ZFIOo2~F|O.2,|PE|3o~OPF�.3,F|Z.3o|PE|bo4~OPFIO.3~ |F ;Oo3 ,F~3 .2 ) GO TO 2~8

8000 CUNTINU~ SlOP END

368

V. INPUT DATA FORMAT AND CHECK PROBLEMS

CARD

1 ~11111111111111111111111111111111111111111111111111111111111 IllxIIIIIIII.Jlllllllllllllllllllllllllllllllllllllilllllllllllll

17' Icl,lIINl.I I I I I IxlLI,IIINI.I I I I IPIoI,IPIsIIIAI I I ITIoI,IOIRI I I I IRk"IAIcIHI=k'I=I I I h'l"l'lOl'q I I I I I I IxlxlxI'Ixl I I I I IxlxlxI'Ixl I I I I IxlxlxlxI'Ixlxl I I IxlxlxlxI'Ixl I I I IxlxI'Ixlxl I I I I IxIxlxlxI'ixl I I I 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61

L~

ESTIMATION OF BOUNDARY-LAYER TRANSITION ON SHARP FLAT PLATES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 1 KGEOM = 1 C, IN. XL, IN. RMACH PO,PSIA TO,R TW,R REINF/FT 160.0 213.0 4.0 40.00 540.0 495.0 3.6932E 06

REL CF DELS,IN. RETFP XTFP,IN. TW/TAW 6.5554E 07 0.001172 1.3061 2.8744E 06 9.34 0.992

ESTIMATION OF BOUNDARY-LAYER TRANSITION ON SHARP FLAT PLATES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 1 KGEOM = 1 C, IN. XL, IN. RMACH PO,PSIA TO, R TW,R REINFIFT 157.0 300.0 8.0 450.00 1400.0 530.0 1.8438E 06

REL CF DELS, IN. RETFP 4.6096E 07 0.000857 3.1547 4.0874E 06

XTFP,IN. 26.60

ll~/TAW 0.417

ESTINATION OF BOUNDARY-LMER TRANSITION ON SHARP FLAT PLATES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING PATES AERODYNANIC NOISE TRANSITION CORRELATION KOPT = 1 KGEOM = 2 C, IN. XL, IN. RMACH PO,PSIA TO, R TW,R REINF/FT 157.0 300.0 8.0 450.00 1400.0 530.0 1.8438E 06

REL CF DELS, IN. RETFP 4.6096E 07 0.000857 2.8073 4.3329E 06

XTFP, IN. 28.20

"I'WTAW 0.417

m o

-11

,,4

o ,,J

CARD I- o 1 I~lllllllllllllllllllllllll[lllllllllll[lllllllllllllllllllilllll[lllll

121xlllllllllllillltllllllllllllllllllllllllllllllllllllllllllllllllllllll

I! lcl, lzlNI I I I ! I IXILI,IIINILI I I [ IPI01,1PIslIIAI I I ITIOI ,I P H I l IRIMIAIcIHI=H=[ I IOIEILITIAI.IDIEIGI I ITS~I ,PIRI I i I I I I Ixlxlxl-lxl I I I I Ix[xlxl Ixl I I I i Ixixlxlxl,lxlxl I I Ixlxlxlxl Ixl I I I Ixlxl,lxlxl I I I I Ixlxl IxlxI I I I I Ixixlxlxl Ixl I I I

~> m

.h

.-n

..,,i

o

-, .4

ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING THE AERODYNAMIC NOISE CORRELATIONS BY PATE KOPT = 2 KGEOM = 1 C,IN. XL,IN. PJ4ACH PO,PSIA TO,R TW,R REINF/FT DELTA,DEG RTS RPS RMAClIS RRESC RETSC 160.0 213.0 4.0 40.0 540.0 495.0 3.6921E 06 5.00 1.078 1.299 3.81 1.105 5.8567E 06

XISC,IN. TW/TAW 17.23 0.992

ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING THE AERODYNAMIC NOISE CORRELATIONS BY PATE KOPT = 2 KGEOM = 1 C,IN. XL,IN. RMACH PO,PSIA TO,R TW,R REINF/FT DELTA,DEG RTS RPS RMACHS RRESC RETSC 157.0 300.0 8.0 450.0 1400.0 530.0 1.~33E 06 5.00 1.210 1.920 7.22 1.302 5.7956E 06

XTSC,IN. TW/TAW 28.99 0.417

ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES IN CONVENTIONAL SUPERSONIC-HYPERSONIC WIND TUNNELS USING THE AERODYNAMIC NOISE CORRELATIONS BY PATE KOPT = 2 KGEOM = 2 C,IN. XL,IN. PJvIACH PO,PSIA T O , R TW,R REINF/FT DELTA,DEG RTS RPS RMACHS RRESC RETSC 157.0 300.0 8.0 450.0 1400.0 530.0 1.8433E 06 5.00 1.210 1.920 7.22 1.302 6.1437E 06

XTSC,IN. TW/TAW 30.73 0.417

,.,.,j i , , l *

PREDICTION OF BOUNDARY LAYER TRANSITION ON SHARP FLAT PLATES FOR NON IDEAL GAS NOZZLE EXPANSION PROCESS RMACH > 10 OR RMACH > 8 . REINF > 15"10"'6 *SEE FIG. USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 3 KGEOM = 3 C, IN. XL,IN. RMACH TW REINF CF DELS,IN. 157.0 300.0 8.0 530.0 3.0000E 06 0.000771 2.0060

RETFP XTFP,IN. "II~/TAW 6.7141E 06 26.86 0.47

CARD ~ p,

1 B~IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIlIIIIIIIIIIIIIIIIII 131311111111111111111111111111111111111111111111111111 1 3 5 7 9 1113 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

2 4 6 8 10 12 . 16 18 20 , , 24 26 28 30 32 34 36 38 40 42 44 46 48 50 I I Icl.lIINI 1 ! I I I IXILI,IIINI.I I I I IRI, IAIcbI=i,I®IRIEIIINIFI,IFITI'Ill I ITIwI.IOIRI I 1 I I I1 IxIxlxI IXl I I I I IxlxlxI.Ixl I I I I IxlxI.Ixlxl J I Ixlxlxlxlxlxlxlxl Ixl I Ixlxlxlxl Ixl I I I

ESTIMATION OF BOUNDARY LAYER TRANSITION ON SHARP SLENDER CONES FOR MACH NUMBERS GREATER THAN 10 ON VERY HIGH REYNOLDS AT MACH NUMBER EQUAL APPROX 8(REINF>IO**7) USING PATES AERODYNAMIC NOISE TRANSITION CORRELATION KOPT = 4 KGEOM = 3 C, IN. XL,IN. RMACH TW,DEGR REINF/FT RESC/REINF DELS,IN. 157.0 300.00 8.00 530.00 3.0000E 06 1.500 2.006

REISC XTSC,IN. DELTA,DEG TW/TAW 8.4295E 06 21.341 10.000 0.47

CARD ~ 4 6 8 10 12 1,4 16 18 20 22 24 26 28 30 32 ~ 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 71) 72

1 I~l~lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 141311111111111111111111111111111111111111111111111111111111111111111111111

I I Icl.iIINl.I I I I I IXlLI,IIINI'I I I I IRI"IAIclHI I I I HEIIINIFI,IflTI'11 I IRIRIEIslcl I-I I I ITIwI,PIRI I I I IolEILITIAI,IDIEIGI.I I I I IxlxlxI'Ixl I I I I IxlxlxI'Ixl I I I I Ixlxl Ixlxl I I IXlXlxlxlxlxlxlxl Ixl i Ixlxl Ixlxl I I I I Ixlxlxlxl Ixl I I I I I I I I I I I I I I

m

-h -n

,,,J

0 ",,4

-.,.1

VI.

I~OPT • 2

p

L .. . . . . . t STATIC PR[SSulU! I~TI .SIN~ P.ASAqUSS£N'S FORm.I.A, Eq. (C-?ZI

1 C~Ull C(I~ ~ SHOCK ANr,~ ~ING t~SMUS~N'5

I 80W SHOCK USING Ott~l~(J[ HOCK WAW TI~Y

• .~-%;,~ I II m. ~,.. o. ~s,.,, I I I

""T '..-.I L

L w , m

|

m

L . . . . .o,.~ vo~,glW ~ ' 5 COIT ION (Q. (C-t~

Flow Chart for Fortran Computer Program

5¢U--

iK~OM • !

VAN OeEST - U 11)ImUU~

m O F

qPT-4

t*l~lSt

U U I~,TA ¢ N t

i L ct~vtLtl[ i ° uslm ] V~ITI~It~'S K~UmI~MI~ F~ iC-UQ

I*'.m~.l IlfjLI t i l l

m 0 c)

|

o

AEDC-TR-77-107

APPENDIX D

EFFECTS OF DIFFERENT VISCOSITY LAWS ON INVISClD

FLOW CONE SURFACE REYNOLDS NUMBER RATIOS

In reviewing published transition results, it became apparent

that inconsistencies existed in the calculation of tunnel unit Reynolds

number and more often for cone surface values. These differences were

traceable primarily to different viscosity relationships used.*

Using two different viscosity laws, Eqs. (C-6) and (C-7), pages

345 and 347, for air, three methods for computing the Reynolds number at

the surface of unyawed cones were investigated.

I. Using the linear viscosity law {p ~ T) which is valid in air

and nitrogen for temperatures below approximately 216OK, then

pc,c ~ Jlinear p® M®

.

(D-I)

Using Sutherland's viscosity law which is valid for tempera-

tures above approximately 216°R, then

3.

r e ,cl pc ,c (: )' (:: " LK -JSutherland - ~ ~ ~cc + 198. (D-2)

Using a combination of the linear law and Sutherland's law,

then

*In addition to the linear law [Eq. (C-6)] and Sutherland's law [Eq. {C-7)], the power law ~ ~ {T)W, when w ~ 0.76, is also often used.

373

Pc L ~ "..J l inear and- g ~ \ T c / P~c (D-3)

Sutherl and

where ~® and ~c are computed from Eqs. (C-6) or (C-7) depend-

ing on the value of T.

Equation (D-3) combines the two viscosity laws and therefore pro-

vides a more general method for calculat ing Reynolds number rat ios. A

combination of the viscosity laws allows the free-stream viscosity to be

determined using the l inear law and the cone surface value to be com-

puted using Sutherland's law, which is often the condition exist ing in

wind tunnels at high supersonic and hypersonic Mach numbers.

Presented in Figure Dml are the Reynolds number rat ios computed

using cone surface pressure, temperature, and veloci t ies from Reference

(162) for M® = 2, 5, and 12 and cone half-angles from 0 to 35 deg. I t

is evident from Figure D-2 that the two viscosity laws and the three

methods can produce s ign i f icant differences depending on the combined

effects of cone angle and flow conditions.

A family of Reynolds number rat ios calculated using Eq. (D-3)

and the cone surface properties from Reference (162) are presented in

Figure D-2. I t should be noted that the rat ios are temperature depen-

dent at flow conditions where Sutherland's viscosity law was applicable.

The range of temperatures (To) was selected to represent the range of

total temperatures usually available in wind tunnels.

All of the t ransi t ion data generated in this research were calcu-

lated using Eq. (D-3). Data from other sources were corrected i f i t was

established that a relat ionship other than Eq. (D-3) was used.

Note that Figure D-2 can be used to determine values for (Rea)c/

Re which is a required input for Program Options 3 and 4.

374

AEDC-TR-77-107

( R e 6 ) c

Re m

1 8 ~ _ ' I ' I ' j ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' 1 ' I T • , OR

NCl) , , ° e a l • °

1.4 12 " "'L' I'm •,1 • °

1.2 ' ~ . . q

' 2 ..!~ 1.0 :

0 .8

0.6

0.4

0.2 0

' 1 ' 1 1

2,400 600

t ..m

i • l o • , o • • o e o Do • • o e •

(D-2) and (D-3)

Legend :'L" F (D-l) . . . . Linear Viscosity Law

"(D-2) ......... Sutherland's Viscmity Law """ ~ " •

- ( D - 3 ) ~ Combined Linear-Sutherland Viscosity Law

,I,I,P,f,t,rl,V,Y,f,lrlrr,r,l,l,l,r, 4 8 12 16 20 24 28 32

0 c, deg 36

Figure D-I Sensitivity of the Reynolds number ratio to various viscosity laws.

375

A E D C - T R - 7 7 - 1 0 7

l'8i_' I ' t ' i ' I '

L-- Moo

i . 6 1 - - - . i 4 > - ; . ~

i , i , I , I ' I ' :1.o' ' ~ R ' l ' t ' i ' i ' J i I i 4

--t 9OO F "=J -J

lr ® °,4o 7 1.4

1.2

(Re5)c

Rein l. 0 ~ . , = ~ - . . . . . . TO , OR

0.8

21,4l

2

Moo = 1.5 to 4. 5, T O = 540°R 4, O. 6 Except as Indicated for Moo = 3

(Re 6 )c/Rein Evaluated Using O. 4 Combined Linear-Sutherland Viscosity Law

,

0.2 l 0 4 8 12 16 20 24 28 32 36

B c, deg

Figure D-2. Var ia t ion ot: Reynolds number r a t i o w i th cone ha l f - ang le , Mach number, and temperature.

376

A E D C-TR -77-107

APPENDIX E

COMBINED EFFECTS OF AERODYNAMIC NOISE AND

SURFACE ROUGHNESS ON TRANSITION

The literature provides abundant documentation for the necessity

of providing effective boundary-loer tripping mechanisms for application

in wind tunnel experiments. The effectiveness of surface roughness for

inducing laminar boundary-layer transition on planar and coniGal, bodies

at supersonic and hypersonic speeds has been extensively reported in

References (16), (17), (20), {21), (37), {47), (7g), and {163) through

{165). Although there may remain considerable doubt about the effective-

ness of surface roughness in promoting "early" transition at hypersonic

speeds (20, 21, 164, 165), the evidence to date would indicate that some

confidence should be expected in estimating and predicting trip perform-

ance in the supersonic speed range (16, 17, 37, 141).

However, there may be some cause for concern when consideration

is given to the absence of experimental data on the potential coupling

between the radiated aerodynamic noise free-stream disturbances at super-

sonic speeds (M® g 3), as discussed in Chapters III and VIII and the dis-

turbance generated by the controlled surface roughness.

This section presents the experimental results of an investiga-

tion undertaken to determine if boundary-IQer trip effectiveness is re-

lated to the tunnel size and the tunnel disturbance levels, per se. The

studies were conducted in the AEDC-VKF 12- and 40-in. supersonic wind

tunnels at M = 3 and 4 on an adiabatic wall lO-deg total-angle sharp

cone. Basic results are presented, analyzed, and compared with the two

377

A E DC-TR-77-107

well-known and widely used tr ip correlations developed by van Driest-

Blumer (163) and Potter-Whitfield (37).

Transition Models and Apparatus

The transitional model was the lO-deg total-angle, stainless

steel cone as described in Chapter IV and shown in Figure IV-14, page

ll2.

The boundary-l~er trip mechanism consisted of a single row of

precision steel balls having diameters of 0.010 and 0.015 in. and at-

tached with epoxy resin to a ~-in.-wide steel band having a thickness

less than 0.002 in. as illustrated in Figure E-I. Ball spacing on the

band was maintained constant at 1/16 in. between centers, and the band

centerline was positioned approximately 4.9 in. from the cone apex. The

trip bands were machined to match the cone surface angle and,were at-

tached to the surface using very small amounts of glue. Variations in

the two sets of ball heights above the band were approximately ±2% to

±3%, and the average heights from the cone surface to the top of the

0.010- and O.Ol5-in.-diam spheres were 0.0117 and 0.0172 in., respec-

tively.

Initially some difficulty was experienced in gluing the steel

balls to the band because of an unacceptable accumulation of glue as de-

termined by visual inspection with a ten-power eyeglass. However, satis-

factory results were obtained with practice, as illustrated by the photo-

graph in Figure E-Ic. The spheres remained attached quite satisfactorily

even after several hours of test time. Also the loss of several balls

{provided they were not adjacent) did not noticeably affect the test

378

Trip Details b.

a. Trip Location

Figure E-1.

Enlanjed View of Sphere Glued to Band

Boundary- layer trip geometry.

m cp

o

AE DC-TR-77-107

data. I t is probable that every other ball could have been lost without

affecting the tr ip results since References (37) and (7g) suggest that /

the allowable spacing could have been increased from 1/16 to 1/8 in.

The minimum spacing as reported in References (16), (37), (39), and (163)

has been established as about 4k.

I t was demonstrated in Reference (163) that for test conditions

similar to those of the present experiments a band height less than 0.002

in. had a negligible effect on the smooth wall transition data, and con-

sequently the tr ip performance, provided the band was located 5 in.

downstream of the cone tr ip.

A remotely controlled, electrically driven, surface pitot probe,

as discussed in Chapter IV, provided a continuous trace of the probe

pressure on an X-Y plotter from which the location of transition was de-

termined. Tests in Tunnel A using different sizes of probes established

that probe size effects on the location of transition (Xto) were negli-

gible (see Chapter VI, Figure VI-5, page 151.

Schlieren photography was also utilized as a secondary method

for detecting the location of transition in Tunnel D.

Transit ion Dependency on Tunnel Size

The purpose of this research was to determine i f spherical rough-

ness t r ips were equally ef fect ive in d i f fe rent sizes of supersonic

(M= ~ 3) wind tunnels where the differences in free-stream disturbances

were suf f ic ien t to a l te r the smooth surface (Ret) 6 values. The re la t ion-

ship between free-stream disturbances which radiate from the tunnel wall

boundary layer and the i r ef fect on the location of t rans i t ion were shown

380

AEDC-TR-77-107

in Chapters VIII and X. Variations in (Ret) a with tunnel size as a re-

sult of these radiated noise effects are very significant, as exempli-

fied by the data presented in Figure VIII-20, page 216, for both planar

and sharp cones. The cone data presented in Figures VII-5, page 151,

VII-6, page 175, and VIII-20, page 216, were obtained on the test model

used for the current trip experiments, and these basic data will appear

in different forms in later sections. It will be shown that the aero-

dynamic-noise-transition correlations presented in Figures IX-8, page

249, and Ix-g, page 251, are useful for providing basic smooth wall

(Ret) a values for application with the Potter-Whitfield trip correlation.

Transition Detection and Identification

A series of basic transition profiles obtained with the tra-

versing surface probe is presented in Figures E-2 and E-3. These data

show that the surface probe was able to detect and provide a distinct

transition profile very near the trip position. Transition locations

determined using the surface probe {with the x t location selected at the

pressure peak as shown in Figures E-2 and E-3) were also consistent with

the location of transition determined from schlieren photographs, as

illustrated in Figure E-2. Additional comparison between probe and

schlieren results will be presented in the following section.

Basic Results

Basic t r a n s i t i o n locat ions for the conditions of smooth surface

andwith spherical roughness elements positioned at 4.9 in. from the

cone t ip are presented in Figures E-4 through E-6 for M® = 3 and 4.

381

A E D C - T R - 7 7 - 1 0 7

, . - s.o M 4 - 2 . 8 9

6 . 9 • x t

°1 I!

u

L

a. Schlieren Photograph

x t - 13.6 x t - 19.3 X t 7.O

~, ; , N ~t " g . s ® ~ - - k - 0 . o i o In . |l~,* t ~ -, ~ k " 0.015 In . A l

t ~ ~..~_ "",,,.0.343 / "N Note: Traces a r e not necessarily p l o t t e d ~ " x • 9 f f ~ " ~ 0 375 J --~, x " 19 4 to equ iva lent pressure scale.

t "~.L,." " : , : - C . Z . . l ".. t / "

" V " ' , " " " " " x - 19.~ ~ - • 260 ~ t •

, _ ~ 0 . 1 7 7 j ' , t x t " 9,6 . . . . . . "

o I ! I I I I I I I P i I I I I | I 4 6 8 10 12 14 16 18 20 22

X, tn .

b. Surface Pitot'Probe Traces

Figure E-2. Methods of transit ion detection, M= = 3.0, AEDC-VKF Tunnel D.

382

A E D C - T R - 7 7 - 1 0 7

v

Q L

L

w~

~L

0

L I

4

= 11.8 x t = 18.7 x t = 39.2 X t

A ~ (Re/ in : )6 x 10-6 /

/ I I l I I I I I I I I I I I m m m n m 8 12 16 20 24 28 32 36 40 44

X, .in.

a. Smooth Surfaces

!

e 8

# x t ~d 7.0

{t = 7.4

K t ~ 8.3

(Relln.)6 x 10 -6

0.386 M= = 3.0

:Trace M6 = 2.89 (Traces are not necessar.ily

0.343 plotted to equivalent pressure scales.)

~ # x t

0.137 ) = 36.5

1 i t I ' I I I I I I I 1 I I I I I . I I 8 12 16 20 24 28 32 36 40 44

X, "in.

b. With Tr ip , k = 0.010 in.

Figure E-3. Surface probe t rans i t i on p ro f i l e s , M = 3.0, AEDC-VKF Tunnel A. =

383

AE DC-TR-77-107

24

22

20

18

16

• 7 14

10

8

6

4

0

Sym $

o Smooth Wall (Xto) • 0.010-tn.-diam Spheres

~. • 0.015-in.-diam Spheres | x t Less Than Indicated

l~b Flagged symbols represent • | ~. data obtained with physically

$ "~Reg_ ion different trip ring.

M6 ~ I] • I l l • \

Effective Point- ~TTri, p Location, Xk = 4.95 in.

, l n l i I i I 0.1 0.2 0.3 0.4 0.5 x 106 •

(Re/in.) 6

a. Surface Probe Results

i Sym 0 Top Surface, Smooth Wall (Xto)

24 \ A Bottom Surface, Smooth Wall (Xto) 22 ~ • Top Surface, O.OlO-in.-diam Spheres

| ~ • Bottom Surface, O.OlO-in.-diam Spheres 20 ~ ~ [] Top Surface, O.OlS-in.-diam Spheres 18 ~ ~ 0 Bottom Surface, O.Ol5-in.-dlam Spheres

.~ 16 ~ l k . ' ~ - - - - -Sur face Pitot Probe x t 14 ~ , ~Jm~A~"~ x Locations from Figure E-4a

.+=3.0 . . / - t o

10 Effective ~ ~ ~ P ° i n t - ~ . ~ L Location, W/--Trip

~ x k = 4.95 in. 0 " ~ m I i I m I , m i

0 0.1 0.2 0.3 0.4 0o5 x 106 (Re/in.) 6

b. Schlieren Results

Figure E-4. Ef fect of spherical roughness on t r ans i t i on loca t ion , M 6 = 2.89, AEDC-VKF Tunnel D.

384

A E DC-TR-77-107

If.--

;=

40 - m

38

36

34 m

32 m

30 m

28 m

26

24

22

20

18 m

16

14

~12

I0

8

6

4

o 7 ,

Figure E-5.

O A t

Smooth Wall 0.010-in.-diam Spheres x t Less than Indicated

Nagged Symbols, 0 ~, TDp <~ 35°F

Unflagged Symbols, -18 < TDp < 0°F

I-A

I

d

II ~ . / ~ Xto

Effective Point I I I

L T r t p Location, x k = 4.9 in. I , I , I , I , I , I , l

0.1 0.2 0.3 0.4 0.5 0.6 0.7 x 106

(Re/in.) 6 .

Ef fec t o f spher ica l roughness on t r a n s i t i o n l o c a t i o n , M 6 = 2.89, AEDC-VKF Tunnel A.

3 8 5

AE DC-T R-77-107

22

20

18

16

, r -

. 14 #

12

10

8

20

18

16

• 7 14

10

8

5

\ ~ \ 0 Smooth Wall (Xto)

6 Trip Location x k = 4.9 in. 7 ¥

0 ~ , m , I i I m I a 0 0.1 0.2 0.3 0.4

(Re/in.)~

o~

Figure E-6.

a. Surface Probe Results

I 0,5 x 106

s_~

f i 'x*°, Bottom Surface, Smooth Hall (Xto) . Top Surface, O,015-in.-diam Spheres

O lk ~ & Bottom Surface, O.015-in,-diam Spheres

ns from Figure E-6a

M 6

TripLocation, x k = 4.95 in.-~

' I i I i I i I , I 0.1 0.2 0.3 0.4 0.5 x 106

(Re/in.) 6

b. Sch l le ren Results

E f fec t o f spher ica l roughness on t r a n s i t i o n l o c a t i o n , M 6 = 3.82, AEDC-VKF Tunnel D.

386

AEDC~R-77-107

These data were obtained in the AEDC-VKF 12-in. Tunnel D and 40-in. Tun-

nel A using sphere diameters of 0.010 and 0.015 in. attached to a 0.002-

i n . - th i ck band.

The various regions of interest which exist in a t r ipped- t rans i -

t ion location p ro f i le are presented in Figures E-4a and E-5. Region I

i l lustrates the variations in the smooth surface transition location as

a function of the tunnel unit Reynolds number. A trend of this form is

quite common (163), and the level has recently been shown to increase

significantly with increasing tunnel size as discussed in the preceding

section.

Region I-A is dominated by the free-stream disturbance levels,

although tr ip disturbances are also being introduced into the transition

process. Region II is a region of multiple dominance, and Region I I I

(which represents the region between the "effective point" or "knee" and

the tr ip) is dominated by the tr ip. The classification of the various

parts of the tripped profile is taken from the definitions proposed by

van Driest and Blumer (163). The "effective point" is by definition (163)

the point where the transition Reynolds number is a minimum, as i l lus-

trated in Figure E-7. The author agrees with this interpretation of the

phenomenon and chose to apply these criteria to the present study.

I t is of interest to note that the schlieren transition loca-

tion results presented in Figures E-4b and E-6b are about 10% to 20%

lower than the probe locations in Region I, but as the tripped values of

x t approach x k then the transition locations are about equal. One

conclusion to be deduced from this observation is that the "effective

387

A E DC-TR-77-107

7 x 1 0 6

6

5

4 (Ret) 6

3

2

I

0 0

5 x 106

(Ret) 6

Figure E-7.

Sym Tunnel Xk/k k, in. x k, in.

O D 493 0.010 4.93 A A 490 0.010 4.90

- rSmooth Surface - /Tunne l A _ Region j ~ . . . .

- I ~. - "¢~- - - Z)I~_~T. I-A Smooth Surface - ~ / T u n n e l O

_ ~ . . ~ I l I A ~ - - - - - -T r io • ~J-!-A ~ ~ T r i p (Rexk) -"Effecti v e ~ - Point, ,~ ~ / 'Ret Less Tha n Indicated

. . . ~ I i l i I , I i I , l , I m l 1 2 3 4 5 6 7 8

Re k x 10 -3

a. M 6 = 3.89

Sym Tunnel M 6 Xk/k

o D 2.89 327 0.015 4.91 Zl O 3.82 327 0.015 4.91

k, in. x k, in.

o A x t Determined with Probe

I • x t Determined with Schlieren

(Ret) 6 Less Than Indicated

F Region .~-"~ Smooth Surface

...- Trip 2 ~,Effective~=~Tril (Rexk)

0 0 1 2 3 4 5 6 7 8

Re k x 10 -3

b. M 6 = 2.89 and 3.82

Variation of transition Reynolds numbers with trip Reynolds number for Hi - 2.89 and 3.82, AEDC-VKF Tunnels D and A.

388

AE DC-T R-77-I 07

point" locations when determined from conventional schlieren photographs

are not as distinguishable as the probe x t locations.

Composite plots of the tripped data from Tunnels A and D for

M = 3 and 4 are shown in Figure E-7 as a function of (Ret) 6 and the

t r ip Reynolds number (Rek). Data presented in this form allow the Re-

gions I - I l l to be i l lustrated in a different form. Also, data presented

in this form are convenient for comparison with the results of van Driest

(16,79,163). Once again the large variation of the smooth cone (Ret) 6

values with tunnel size is demonstrated. The data also show that a sig-

nif icant difference in t r ip effectiveness in Regions I-A and II exists.

This avenue wi l l be pursued in the following sections.

Van Driest, et al. Trip Correlation

Van Driest, et al. (16,79,163) conducted a systematic experi-

mental and analytical program that resulted in a spherical roughness cor-

relation of "effective" point Reynolds numbers that is applicable to

both planar models and sharp cones. This correlation incorporated the

effects of surface ~ch number from zero to approximately four and the

effects of surface cooling.

Results from the present investigation are compared in Figure E-8

with results of van Driest and BlunTner (16,163). The agreement is con-

sidered good, and the author feels these results provide additional con-

firmation to the conclusions of References (IG) and (163). It should be

specifically noted that all the data presented in Figure E-8 are based

on the "effective point" concept. The "effective point" roughness cri-

teria are based on the hypothesis that all x t locations upstream of the

389

A E DC-TR-77-107

Facil i ty

JPL

AEDC-VKF D

1 AEDC-VKF A

Sym M~ Source

0 1.90 Adiabatic and Wall Cooling to References (16) and (163)

3.67 • 2.89 Present Study, Adiabatic Wa11,

k = 0.010 A 2.89 Present Study, Adiabat ic H a l l ,

k = 0.015 • 3.82 Present Study, Adiabatic Wall,

k = 0.015 2.89 Present Study, Adiabatic Wall,

k = 0.010

4 x 106, -

m

3

I m

i

o I

0 I

van Driest and Blumer nqA [Reference (16)]

500 1000 1500 2000

a. Correlation of Effective Trip Location

b.

Fi gure E-8.

3

x ~ 2 From Reference (163) Adiabatic Wall

~- 1 - t

ol I 0 1 2 3 4 5 6

M 6

Interval Between Effective Point and Trip Location Reynolds Numbers Correlation of tripped results using the methods of van Driest-Blumer.

390

AE DC-TR-77-107

"effective point" location are tr ip dominated and controlled, but down-

stream of this location the x t values are significantly influenced by

the combined effects of surface tr ip disturbances and free-stream dis-

turbances (whatever the mode).

When evaluating the comparison between the two independent sets

of data, i t should be kept in mind that the test models, tr ip sizes, and

general test conditions were nearly identical. Therefore, agreement

would be expected provided the data were valid and all extraneous sources

of error had been eliminated (or were identical) in both experiments. I t

is nevertheless reassuring to observe that different investigators can

produce reproducible and repeatable results even in the very uncertain

areas of boundary-layer tripping. In addition to the agreement exhibited

in Figure E-8, direct comparison of the tripped transition locations

[x t versus (Re/in.) 6] in the 12-in. Tunnel D data with the 12-in. JPL

tunnel results in Reference (7g) also show reasonable agreement. I t was

additionally encouraging to establish that the traversing probe produced

results comparable in quality to the surface temperature and the magni-

fied schlieren technique of References (16), (79), and (163).

Potter and Whitfield Trip Correlation

The tr ip correlation of Potter and Whitfield f i rs t appeared in

References (37) and (137) and was further extended to include higher Mach

numbers in Reference (21). To the author's knowledge, this correlation

is without question the most comprehensive of any published to date. The

correlation incorporates, as did the correlation of van Driest and Blumer,

the effects of heat transfer and Mach number, and is applicable to both

391

A E DC-TR-77-107

planar models and sharp cones. However, the local Mach number range e x -

tends to approximately 10, and the correlat ion provides values of the

t r i p size required to locate t rans i t ion anywhere between the undisturbed

smooth surface and t r i p location. The correlat ion also predicts the ef-

fectiveness of single two-dimensional surface wires in addit ion to single

rows of spheres.

Data from the present investigation are presented in Figure E-g

using the correlat ion of Potter and Whit f ie ld. The current data are

seen to l i e within the data band used in Reference (37) to establish a

suggested curve. One observation is that the suggested correlat ion

curve w i l l not predict the "effect ive point" or "knee" location of the

present data. However, the most s ign i f icant resul t to note is that the

correlat ing parameters provided a nearly identical collapse of the M 6 =

2 . 8 9 , k = O.010-in. data from the AEDC-VKF Tunnels A and D. I t should

be remembered that the only difference in these data ( in terms of tunnel

conditions and model and t r i p geometry) is the large difference in the

smooth wall Xto locations. A tentat ive conclusion to be inferred from

these results is that the Xto normalizing parameter in the Potter-

Whit f ield correlat ion w i l l allow data from various sizes of supersonic-

hypersonic tunnels to be successfully correlated.

Application of the Potter-Whftf ield correlat ion parameters re-

quires that the Hach number (Yr~) in undisturbed laminar flow at height k

be known. Values of Yr~were obtained using the f l a t -p la te s im i la r i t y

parameter [n = (Y/Xk)(~/Rexk)] divided by the ~ i n conjunction with

the results of Reference (144). Values of H~for sharp cones can also be

obtained d i rec t ly from graphical results presented in Reference (145).

392

AE DC-TR-77-107

Sym M 6 Roughness AEDC Tunnel Model Reference

od 2.89 Spheres D Cone Present Investigation d 3.82 Spheres D Cone Present Investigation • 2.89 Spheres A Cone Present Investigation

0-5 /Spheres\ - /Cone,\ Reference (37) |Wires J |Cyl. | \Grit I \Plate/

1.0~ Suggested Curve [Reference (37)] I

0.9

O.B

0.7

"~ O.6

~'~ '0 .5

I 0 . 4 o F1

0.3 F Unflagged Symbols, k = 0.010 in., k- = 0.0117 in.

0 . 2 ~

0.1

0 0.03 0.06 0.10 0.20 0.40 0.60 1.0

Re-~'/c

Figure E-9. Correlation of tripped results using the method of Potter-Whi t f i e l d.

393

A E D C ~ R - 7 7 - 1 0 7

In determining the boundary-layer thickness i t has been assumed

that the entropy layer generated by the bow shock has been "swallowed"

by the boundary layer, and the cone acts as an "aerodynamically" sharp

cone. This is a reasonable assumption, since the ratio at the tr ip loca~

tion distance to the nose radius is approximately 2,000.

Inspection of the correlation parameters of Potter and Whitfield

in Figure E-9 reveals that the smooth surface value of the transition

location must be known. Therefore, when transition locations for M® ~ 3

are desired for application in the Potter-Whitfield tr ip correlation,

and measured values of Xto from the faci l i ty under consideration are not

available, the correlations presented in Figures IX-8, page 249, and

Ix-g, page 251, can be utilized to obtain estimated smooth wall (Ret) ~

values for either f la t plates (or hollow cylinders) and sharp slender

cones .

Direct comparisons between the experimental data and the esti-

mated x t locations using the correlation of Potter and Whitfield (37)

for the specified spherical roughness heights of 0.0117 and 0.0172 in.

for a local cone surface Mach number of 2.89 are provided in Figure E-IO.

The methods of van Driest and Blumer as presented in Figure E-8b, page

390, enabled the "effective point" location to be estimated. Estimates

of tripped x t locations to be expected in very large supersonic tunnels,

such as the AEDC-PWT Tunnel 16S, are included in addition to the experi-

mental data from the AEDC-VKF Tunnels D and A.

I t is evident that when the Potter-Whitfield suggested curve

from Figure E-g is used, the "effective point" or "knee" location is not

predicted. This deficiency could, of course, be eliminated i f a

394

A E DC-TR-77-107

x t, in.

a. M 6

40

32

24

16

0 0

= 2.89, k = 0.010

Fairing of Experimental Data - ~ ~k ------Predicted Effect of Trip Reference (37i _VKF-A I \ \ X Predicted "Effective Point" - \ \ X Loca'tion References (16) and (163)

- ". ' X Smoot Wall (Xto)

: " - . ~ ) K - ~ _With T r i p ,_ ~ . ~ -k = O.OlO i n . J x

~ T r i p Location (Xk) a I , I , l , l , I , I

0.I 0.2 O.3 0.4 0.5 0.6 x 106 (Re/in.)6

i n . , k = 0.0117 i n . , x k = 4.9 in.

x t, in.

b . M 6

Figure E-IO.

/---Estimated Using Figure E-9 and Eq. 11

V r ~unnel ~. I(Ret), -- xi ~ c//

m [ ~ ~ Fairing of Experimental Data 40 - ~ k -----Predicted Effect of Trip Reference (37)

- ~ \ X Predicted "Effective Point" . 32- \ ~ Location References (16) and (163)

- X \ ~ " FSmooth Wall (Xto)

-.it, / < -

8 - x k__ -"--.j2>

O I I I I I O 0.1 0.2 0.3 0.4 0.5 x 106

(Re/in.)~

= 2.89, k = 0.015 i n . , k = 0.0172 i n . , x k = 4.9 in.

Comparisons of corre la t ion predict ions with experimental resul ts .

395

AE DC-TR-77-107

d i f fe rent "suggested curve" were used. 20 However, upon inspection of

the data band in Figure E-g i t is not immediately evident that a d i f f e r -

ent "suggested curve" would be j u s t i f i e d . This disagreement in terms of

physical distance (inches) also increases with tunnel size. The method

of van Driest and Blumer predicts the "ef fect ive point" x t location

quite adequately, but misses the (Re/in.) 6 value at which the knee oc+

curs. However, the agreement between predictions and measurements using

both methods is considered good and wi th in the correlat ion scatter of

the methods (e.g. , see Figures E-8 and E-9).

Although perhaps somewhat l imi ted in scope the present study has

provided results which are considered to be s ign i f icant . The mode] con-

f igurat ion was a sharp slender cone, but the results can also be ex-

pected to apply to spherical roughness on plates. The test Hach numbers

of 3 and 4, although not covering a large Hach number range are Hach num-

bers of prime interest in many wind tunnel test programs. The data in

Figures E-7 and E-IO indicate that the t rans i t ion location between the

t r i p and the "ef fect ive point" location is a function of the free-stream

20In a personal comunication, J. L. Potter has told the author that he o r i g i na l l y looked for evidence that the suggested curve in Fig- ure E-9 should exhib i t a "knee" or asymptotic approach to the abscissa in the region x t ÷ x k, but could not j u s t i f y presenting the curve in

that form [on the basis of the data used in Reference (37)] even though he thought some change in shape near the r ight side of the curve had p l aus i b i l i t y .

396

A E DC-T R -77-I 07

disturbance level, but indicate that the Potter-Whitfield correlation

through the use of the Xto term successfully collapsed the tripped data.

The present data support the "effective point" criteria proposed by van

Driest and Blumer and suggest this location wil l be valid for all sizes

of supersonic wind tunnels.

An observation which seems to merit mention is the absence of

evidence of the "effective point" in the published hypersonic tripped

data (21,137,164,165). I f the hypersonic data represent the I-A and I I

regions, i l lustrated in Figures E-4, page 384, and E-5, page 385, then

one might question whether the published results were t r ip dominated or

whether the data could also have been significantly influenced by free-

stream disturbance effects (either radiated noise or temperature spotti-

ness).

I t has been shown that the absolute effectiveness of spherical

roughness can be influenced by the free-stream disturbances (aerodynamic

noise) present. I t is therefore concluded that to a s igni f icant degree

the tripped transit ion location at supersonic speeds (M® ~ 3) is depen-

dent on the tunnel size or more precisely the free-stream disturbances.

Thus, i t appears appropriate to relate roughness effects to the smooth

wall transit ion location (Xto), as done by Potter and Whitfield (37),

when attempting to normalize tunnel flow effects. These results have

further demonstrated that the tr ip correlation parameters developed by

Potter and Whitfield successfully correlated the tripped transition data

obtained in two significantly different sizes of supersonic tunnels hav-

ing significantly different Xto values. These studies also confirmed the

397

AE DC-TR-77-107

"effective point" criteria proposed by van Driest, et al. (163) and

verified that the "effective point" is tr ip disturbance dominated and

essentially independent of the tunnel disturbance levels (Xto location)

at supersonic speeds.

398

APPENDIX F

A E D C - T R o 7 7 - 1 0 7

TABULATIONS OF BASIC EXPERIMENTAL TRANSITION DATA

FROM THE AEDC SUPERSONIC-HYPERSONIC WIND TUNNELS

Table F-1. AEDC-VKF Tunnel D transition Reynolds number data, 3 .0 - in . - diam hollow cylinder.

To, Re/tn. *xt , Ret OLE, 14= psta OR x 10 -6 t~." x 10 "5 b, tn. deg Remrks

0.0036 2.98 7.3 536 14.0 2.99 11.3 539 11.3 2.99 14.4 540 10.0 3.00 23.8 539 8.3 3.00 30.7 537 7.0 3.00 37.8 533 6.3 3,00 44.5 528 5.5 2.98 7.3 532 14.0 2.99 11.4 535 11.0 3.00 14.9 537 10.0 3.00 22.8 536 8.25 3.~0 29.9 534 7.0 3.00 37.8 526 5.1 3.00 44.9 518 5.5

2.98 7.5 529 11.7 3.00 23.0 533 6.8 3.00 29.9 534 6.1 3.00 37.9 530 5.4" 3.00 44.9 527 4.9

2.98 7.5 523 13.2 2.99 11.5 527 11.2 2.99 15.0 529 9.8 3.00 22.8 529 8.0 3.00 31.1 523 6.8 3.00 37.9 515 5.1 3.00 45.0 510 5.4

2.98 7.6 523 11.2 2.98 11.6 517 9.4 2.99 15.1 612 8.3 3.00 22.9 511 6.6 3.00 30.0 515 5.9 3.C0 38.0 515 5.3 3.00 44.9 514 4.9 2.98 7.7 613 11.2 2.99 11.6 511 9,8 2.99 15.1 519 8,5 3.00 23.0 527 7.0 3.00 30.0 528 5.0 3.00 38.0 525 5.3 3.00 45.0 520 4.7

2.98 11.7 511 9.6 2.99 15.1 517 8,5 3.00 23.0 529 7.0 3.00 30.0 529 5.0 3.00 38.1 626 5.2 3.00 45.2 515 4.7

3.0 - - - ~30 ---

4.0

5.0

1

~540

0.097 0.148 0.188 0.311 0.402 0.501 0.598 0.097 0.151 0.195 0.300 0.394 0.511 0.820

0,102 0.305 0.396 0.507 0.505

0.103 O. 155 O. 201 O. 305 0.423 0.525 0.635

0.105 0.162 0,213 0.323 0.419 0.530 0.626 0.109 0.165 0.209 0.309 0.403 0.513 0.620

0.155 0.211 0.308 0.401 0.514 0.530

0.1 0.2 0.3 3,~ 0,5 0.6

0.] 0.2 0.3 0.4 0.5 0.6

0,1 0,2 0.3 0.4

1.36 1.57 1.88 2.58 2.81 3.16 3,29 1.36 1.66 1.95 2.47 2.76 3.12 3.41

1.19 2.07 2.41 2.74 2.96

1,35 1.74 1.97 2.44 2.87 3.21 3.44

1.18 1,52 1.77 2.13 2.47 2.81 3.07 1.22 1.62 1.78 2.16 2.42 2.72 2.91

1.58 1.79 2.16 2.41 2.57 2.95

1,10 1.43 1.70 1.93 2.09 2.24

1.~.2 1.51 1.76 1 96 2.15 2.31

1 4O 2.05 2.55 3.10

0.0023 12 Probe A

1 l 1 0.0035 6 **

0,0021 Probe

0.0021

Probe A . 1 5 I°) 0.032

Probe B 0.007 x 0.C~37 t r . I

1 Extrapolated Values of Re t f ror Figure P[-I

1 Extrapo'ated Values of Ret from Figure VI-1

*x t Oetemtned wtth a Surface Pltot Probe Peak Value

*~Joandary-Layer Trtp Located on Inside Bevel Angle )/8-~n. fron Hollow-Cylinder Leadtng Edge.

399

Table F-2. AEDC-VKF Tunnel E 3.0-in.-diam hollowmcylinder transition data.

i n o ? -4 3D

0 . j

Data Potnt M=

Po' P®' Re/tn. * (Xt)min. (Ret)min. pp * ( X t ) m x . (Ret)max. pp Wall psia psia T o, OR x 10 .6 in . PP' x 10 -6 in . PP' x 10 -6 ~m, i n . Condit ion b, tn .

4~ C~ 0

1 4.99 2 5.00 3 5.03 4 5.00 5 5.04 6 4.99 7 5.03 8 5.00 9 5.04

10 4.99 11 4.99 12 5.03 13 4.99 14 5.04 15 4.99 16 5.03 17 4.99 18 5.04 41 5 42 5 43 5

101.1 0.193 666 0.349 . . . . . . 8.1 2.83 200.2 0.378 665 0.690 3.4 2.34 6.7 4.63 303.5 0.554 681 0.996 3.1 3.09 5.4 5.38 142.9 0.270 680 0.477 4.0 1.91 8.0 ± 0.3 3.81 + 0.14 399.1 0.720 672 1.329 . . . . . . 5.5 ± 0.3 7.30 ± 0.4 94.2 0.180 668 0.324 4.0 1.30 9.0 2.92

296.5 0.541 680 0.975 . . . . . . 5.9 5.75 147.1 0.278 662 0.511 3.5 1.79 7.6 3.88 398.1 0.718 692 1.270 . . . . . . 5.5 6.99 137.9 0.264 660 0.483 . . . . . . . . . . . . 101.2 0.194 660 0.355 4.75 ± 0.75 1.69 ± 0.27 10.5 ± 0.2 3.73

• 300 ~0.55 ~680 ~0.98 4.0 3.92 7.2 7.1 150.4 0.288 664 0.522 4.5 2.35 9.3 4.86 399.5 0.721 676 1.319 - - - 5.28 6.5 8.58 97.4 0.186 664 0.338 . . . . . . 12.3 4.16

300.2 0.548 677 0.994 . . . . . . 7.8 7.75 154.4 0.295 658 0.543 5.5 ± 0.5 2.98 ± 0.27 10.5 5.71 409.8 0.739 690 1.312 . . . . . . . . . . . . 101.8 0.19 658 0.36 . . . . . . 13.0 4.66 305.3 0.56 686 0.99 3.0 2.97 5.25 ± 0.25 5.20 ± 0.25 54.6 0.10 495 0.29 . . . . . . 14.5 ± 0.5 4.20 ± 0.14

54.8

1 59,8

l 39,6

34.6

J 34.6

Uncooled 0.0023

Cool ed

1 *X t Detemtned wi th a Surface P i t o t Probe; pp = P i t o t Probe.

AE D C - T R - 7 7 - 1 0 7

Table F-3. AEDC-VKF Tunnel A transition Reynolds number data, 3.0-in.-diam hollow cylinder.

Po" T O , P~/tn. *x t , Ret eLE, N psta OR x 10 -6 tn. x 10 -6 b, tn. deg Remarks

0.0021 2.98 2.99 2.99 2.90 3.00 4.02 4.02 4.02 4.02 4.02 5.04 5.04 5.06

2.98 2.99 2.99 2.99 2.99 3.00

4.02 4.02 4.02 4.02 4.02 5.06 5.06 5.06 5.05 3.00 2.99 2.99 2.08

5.06 5.04

2.98

2.99 2.99

2.98 2.99 2.99 2.99 3.00 2.99 2.99

3.0

1 4.0

5.0

16.6 20.5 24.8 32.8 40.7

28.0 34.1 41.0 58.5 64.5 50.95 81.96

136.7

16.2 20.5 25.6 33.3 41.4 49.2 28.4 34.3 41.6 56.3 73.4 81.5

109.9 137.1 150.5

41.0 32.9 24.8 16.7

136.4 82.3

16.5 32.7 24.7

16.2 25.4 33.6 40.9 48.7 33.1 25.0 . . .

1 . . .

1

56O 56O 564 565 566

565 563 565 562 565

6O3 64O 644

572 571 57O 571 573 575 563 561 561 562 567 638 645 647 649

563 563 562 562 842 640

565

563 562 566 5.66 568 57L 573 564 565

*.560

~c560

l

0,206 13.3 2.74 0,253 11.5 2,91 0,303 10.5 3.18 0,400 8.6 3.44 0.493 7.5 3.69 0,200 14.6 2.02 0.244 12.8 3.00 0.292 11.0 3.22 0.405 9.1 3.69 0.459 8.4 3.85 0.200 17.0 3.40 0.294 13.6 4.00 0.484 lO.q 5.26

0.195 16.0 3,12 0.246 13.5 3.32 0.300 11.7 3.60 0,400 10.0 4.00 0.494 9.0 4.45 0.581 8.3 4.82 0.203 15.0 3.04 0.246 14.0 3.44 0.298 13.5 4.02 0.404 11.3 4.56 0.518 lO.O 5.18 0.292 16.0 4.67 0,386 14.5 5.60 0.478 14.0 6.69 0.520 13.8 7.26 0.503 6.5 3.27 0.403 7.6 3.00 0.305 9.2 2.81 0.206 12.5 2.58 0.483 9.9 4.78 0.296 12.7 3.76 0.203 13.4 2.72 0.401 8.4 3.37 0.304 10,0 3.04 0.198 15.0 2.97 0.309 10.7 3.31 0.407 9.2 3.74 0.491 8.0 3.93 0.578 7.3 4.22 0.404 9.3 3.76 0.30g 10.6 3.24

0.15 --- 2.10 0.2 L 2.25 0.3 2.49 0.4 2.68 0.5 2.82 0.6 2.96

0.15 --- 2.37 0.20 ] 2.60 0.30 2.92 0.40 3.20 0.50 3.41 0.60 3.60

0.15 - - - 2.64

0.20 1 2.91 0.30 3.38 0.40 3.80 0.50 4.12 0.60 4.40

0.0036 I

0.0013 12

0.0023 12

1 l 0.0030 12

Extrapolated Value of Re t From Figure V)-2

*x t Oetemtned fron Sur%ce Pitot Probe Peak Value.

40l

AEDC-TR-77-107

Table F-4. AEDC-PWT-165 Tunnel basic transition Reyno]ds number data, 12.0-in.-diam hollow cylinder.

* * ** ** ** Average Dew Potn¢ Average Referenced to Po' To' Re/in. Retl Ret2 Ret3 Ret4 Re t ~, Atmospheric

N psta OR x 10 .6 x 10 .6 x 10 .6 x 10 -6 x 10 .6 x 10 .6 tn. Pressure, OF

0.0015 3.00 3.00 3.01 3.01 3.00 3.00 3.00 3.00

3.00 3.00 3.00 3,00

3.00 3.00 3.03 3.00 3.03

2.50 2,51 2.50 2.50 2.50 2,50 2,50

2.50 2.50 2.50

2.00 2.00

3.0

l 2.6

l 2.0

1

5.23 647 2.16 2.16 - - - 2.12 6.21 666 2.26 2.26 - - - 2.26 7.09 656 2.42 2.40 2.47 2,32 7.06 653 2.48 2.43 2.46 2.34 7.93 669 2.43 2.42 2.54 2.40 9.27 671 2.57 2.59 2.62 2.53 9.27 669 2.59 2.63 2.72 2.54

10.92 667 2.85 2.88 2,91 2.68

5.09 645 - - - 2.30 2.36 2.32 7.12 649 2.64 - - - 2.64 2,54 7.17 655 - - - 2.82 - - - 2.88 9.28 664 - - - 2.81 2.84 2.77

6.22 658 2.53 2.63 2.77 2.63 7.05 657 2.75 2.81 - - - 2.75 8.36 659 2.94 3,05 3.08 2.91 9.20 644 3.26 3.36 3.40 3.18

10.52 659 3.19 3.39 3.36 3.23

4.06 641 2.52 2.52 . . . . . . 4.62 642 2.54 2.60 2.64 - - - 5.34 654 2.71 2.81 2.81 2,81 5.46 655 2.66 2.70 2.77 - - - 6.31 657 2.76 2.71 2.87 - - - 7.82 654 3.18 3.08 3.29 3.12 8.57 658 3.32 3.16 3.38 3.16

5.38 658 2.82 2.93 2.93 2.98 6.26 655 3.04 3.14 3.12 2.98 8.65 656 3.68 3.65 3.80 3.76

5.62 632 3.68 3.40 3.83 3,64 7.45 631 4.12 3.73 4.38 4.12

0.0516 0.0591 0.0686 0.0689 0,0748 0.0873 0.0876 0.104

0.0517 0.0701 0.0700 0.0888

0.0603 0.0686 0.0794 0.0920 0.0998

0.0535 0.0605 0.0685 0.0694 0.0798 0.1003 0.1089

0.0684 0.0799 0.1105

0.0970 0.1286

0.050 0.070 0.090 0.11

0.050 0.070 0.090 0.11

0.090 0.11 0.13

2.15 2.26 2.40 2.43 2.45 2.58 2.62 2.83

2.33 2.61 2.85 2.81

2.64 2.77 2.99 3.27 3.29

2.52 2.59 2.78 2.71 2,78 3.16 3.25

2.91 3.07 3.72

3.64 4.09

2.09 2,32 2.54 2.71

2.38 2.64 2.89 3.09

3.40 3.65 3.86

0.0050 0.0042 0.0050 0.0050

0.0090

1 0.0015

0.0050

0-.0015 0.0015

O*

0 -13 -18 -18 -13 - t4 -14 - 2

+25 0

+12 + 7

- 4 + 1 - 8 + 1 - 9

+ 5 - 4 + 7 -16 -16 +11 + 7

+ 6 + 6 + 6

+13 +13

*Extrapolated Values of Re t from Figure Vl-4.

* ' 1 , 2, 3, 4 Correspond to the Four Surface Probes; x t Detemtned from Surface P i t o t Probe Peak Value.

402

AE DC-TR -77-1 07

Table F-5. AEDC-VKF Tunnel D transit ion Reynolds number, lO-deg total-angle sharp cone.

H Hc = H6 Po' psta T O , OR (Re / in . ) . x 10 -6 (Re/tn.) 6 x 10 -6 x t , * in. (Ret) 6 x 10 -6

2.98 2.87 9.93 533 0.133 0.141 ~21 ~2.97 2.99 2.88 14.9 524 0.204 0.217 18.7 3.62 3.00 2.89 20.0 523 0.272 0.289 13.6 3.93 2.98 2.87 9.86 532 0.133 0.~41 ~21 ~2.96 2.99 2.88 12.4 544 0.160 0.170 19.3 3.28 2.99 2.88 14.9 548 0.191 0.203 17.8 3.61 3.00 2.89 17.4 549 0.220 0.234 15.7 3.67 3.00 2.89 20.0 549 0.253 0.269 14.8 3.98

3.48 3.34 15.0 520 0.180 0.172 10.5 3.18 3.48 3.34 20.0 516 0.215 0.232 15.3 3.54 3.48 3.34 24.8 514 0.269 0.289 13.2 3.82 3.48 3.34 30.0 513 0.326 0.350 12.0 4.20

3.99 3.81 17.5 580 0.139 0.152 19.1 2.91 4.00 3.82 20.0 528 0.159 0.174 17.6 3.07 4.00 3.82 22.5 526 0.180 0.197 15.8 3.12 4.00 3.82 24.9 523 0.201 0.220 14.7 3.24 4.00 3.82 29.9 521 0.242 0.265 13.1 3.47 4.00 3.82 34.9 518 0.288 0.313 11.5 3.60 3.99 3.81 39.9 518 0.328 0.359 10.5 3.77 3.99 3.81 45.0 517 0.371 0.407 9.4 3.83 3.99 3.81 50.0 518 0.411 0.451 8.4 3.78

4.55 4.32 24.9 539 0.146 0.163 ~20.5 3.34 4.56 4.33 27.4 540 0.159 0.177 19.5 3.48 4.56 4.33 29.9 542 0.173 0.193 18.9 3.65 4.56 4.33 34.9 543 0.202 0.225 16.6 3.74 4.56 4.33 39.9 544 0.229 0.255 15.6 3.98 4.56 4.33 45.0 546 0.258 0.288 14,5 4.17 4.56 4.33 49.9 547 0.285 0.318 13.5 4.29 4.56 4.33 55.0 548 0.312 0.348 12.6 4.38 4.55 4.32 60.0 546 0.345 0.385 11.7 4.50

*x t Determined from Surface Probe Peak Pressure.

403

4~ C~ 4~

2.99 2.99 2.99 2.98 3.00 3.00 3.00 3.00 2.99 2.99 2.99 2.99 2.98

4.02 4.02 4.02 4 . 0 1

4.00

4.54 4.53 4.53 4.53 4.52 4.50

5.04 5.06 5.05 5,05 5.04 5.02 5.00 5.00

Table F-6. AEDC-VKF Tunnel A transit ion Reynolds number, lO-deg total-angle sharp cone.

Hc = H6 Po' psia T O , OR (Re/|n.)® x 10 -6 (Re/in.)~ x 10 -6 xt,* tn. (Ret) ~ x 10 .6

DeW Point Referenced to AtmosphePi¢ Pressure, OF

2.88 19.8 562 0.243 0.258 23.2 6.01 2.88 29.7 562 0.364 0.38? 17.0 6.57 2.88 14.8 565 O. 181 O. 192 29.0 5.57 2.88 10.1 561 0.126 0.134 39.2 5.25 2.89 49.9 566 0.603 0.640 9.5 6.08 2.89 49.6 569 0.596 0.633 9.3 5.89 2.89 39.8 568 0.479 0.509 11.8 6.00 2.89 35.0 566 0.424 0.450 13.3 5.99 2.88 29.6 565 0.362 0.384 15.8 6.07 2.88 24.7 563 0.303 0.322 18.7 6.02 2.88 19.7 568 0.238 0.253 22.5 5.69 2.88 15.1 562 0.186 0.198 28.0 5.53 2.87 12.6 561 0.156 0.166 33.2 5.51

3.84 69.9 569 0.493 0.540 10.5 5.67 3.84 50.0 562 0.359 0.394 14.6 5.75 3.84 34.6 565 0.246 0.269 20.0 5.38 3.83 24.7 563 0.178 0.195 27.0 5.25 3.82 19.8 564 0.143 0.157 31.6 4.95

4.31 115 573 0.623 0.695 10.0 6.95 4.30 89.6 573 0.483 0.539 12.2 6.57 4.30 59.7 568 0.327 0.365 16.4 5.98 4.30 39.5 565 0.218 0.243 22.3 5.42 4.29 29.8 564 0.166 0.185 ~28 :~5.2 4.27 19.7 563 0.111 0.124 438 qJ4.7

4.75 150 646 0.532 0.612 13.8 8.44 4.77 120 644 0.420 0.483 15.8 7.63 4.76 101 645 0,354 0.407 17.5 7.12 4.76 79.9 646 0.281 0.323 20.2 6.53 4.75 59.9 645 0.212 0.244 25.2 6.14 4.73 40.2 616 0.154 0.177 31.2 5.53 4.71 29.9 600 0.120 0.138 37.0 5.11 4.71 24.9 602 0,100 0.115 :~44 5,06

14.5 5.5

14.0 35

- 1.5 - 1 -18 -11 - 9.5 - 2.5

2.5 13 19

-10.5 -10 - 4 . 5

8.0 12

-19.5 -23 -19 -12 - 3.5

8 . 0

- 1 8 -14 -17 -13.5 -12 - 2.5

5.5 1 4 . 5

> m o ? -4 -n

. j

0 ~J

*x t Detemined from Surface Pt to t Probe Peak Pressure

AE DC-TR-77-107

Table F-7. AEDC-VKF Tunnel A long- and short-shroud t rans i t ion results.

Conftgu- Po' To' Re/in. Ret H ratton psta oR x 10 .6 x t * * , in. x 10 "6 b, in. e, deg

Long 0.0021 6 Shroud

2.98 2.99 2.99 2.99 2.99 2.99 2.98 2.98

4.02 4.00 3.99 4.02 4.02 4.02 4.02 4.02

5.04 5.04 5.06 5.06 5.05 5.04 5.04

5.04 5.04 5.04 5.06

5.04 5.04 5.04

2.98 2.98 2.99 2.99 2.99

3.0

4.02 4.02 4.02 4.02 4.02 4.02

5.05 5.06 5.06 5.05

Long Shroud wlth Trtp

1 Short Shroud

16.6 563 0.203 12.7 2.58 20.4 562 0.252 10.2 2.57 24.7 562 0.304 8.0 2.43 32.7 563 0.401 5.5 2.21 28.1 562 0.345 6.6 2.28 18.2 561 0.225 11.5 2.59 14.2 562 0.176 14.5 2.55 15.3 561 0.191 13.5 2.58

28.4 566 0.202 9.5 1.92 21.3 564 0.154 14.0 2.16 17.7 564 0.128 * . . . . . . 34.0 564 0.243 8.0 1.94 41.1 564 0.293 6.7 1.96 56.3 564 0.403 5.2 2.09 64.5 562 0.463 4.7 2.17 73.4 563 0.525 4.4 2.31

50.9 601 0.201 12.5 2.51 82.0 638 0.296 9.0 2.66

110.1 539 0.392 7.2 2.82 136.5 645 0.480 6.2 2.98 150.0 644 0.531 6.0 3.19 66.6 641 0.238 10.5 2.50 39.2 606 0.153 16.1 2.46

39.1 604 0.153 15.5 2.37 50.6 603 0.199 11.5 2.29 82.0 638 0.296 8.2 2.43

138.9 638 0.490 5.7 2.79

39.4 603 0.155 16.0 2.48 50.8 601 0.200 12.0 2.40 82.2 639 0.296 9.0 2.66

14.3 564 0.176 9.0 1.58 16,6 563 0.205 6.6 1.35 20.5 565 0.250 5.5 1.37 26.1 563 0.324 5.3 1.72- 32.8 564 0.39 4.8 1.87

28.2 564 0.202 * . . . . . . 34.4 564 0.245 * . . . . . .

41.3 562 0.296 11.2 3.31 56.4 565 0.401 9.5 3.81 64.7 569 0.457 8.7 3.98 73.5 565 0.524 8.0 4.19

150.6 643 0.532 10.8 5.75 136.9 643 0.484 11.1 5.37 109.9 643 0.389 11.7 4.55 82.4 645 0.292 14.0 4.09

0.0013 12

I 1 0.0021 6

0.0021 6

*Shroud Ltp Shock Wave Interference.

**x t Measured on 3.0-in.-dtam Hollow-Cyl|nder Trans|tton Hodel Using Surface Ptt6t Probe Peak Value.

405

AE DC-TR-7 7-107

Table F-8. AEDC-VKF Tunnel F transition Reynolds number data.

Flat Plate, = = 0

M® T o, OR (Re/in.). x 10 -6 Xt,* in. Re t x 10 -6 b, in. Remarks

R~.O ~1900 0.54 16.0 8.6 0.0006 40-in. Diam 1 1 0.80 13.3 10.6 ~ Contoured

1.07 11.7 12.5 Nozzle

Sharp 10-deg Half-Angle Cone, ~ = 0

M® T O , OR (Re/in.). x 10 -6 Xt,* in. (Ret) 6 x 10 -6 Remarks

~7.5 ~1800 25-in. Diam Contoured Nozzle

0.51 7.5 5.9 0.62 6.3 6.1 0.70 6.0 6.5 0.88 5.6 7.7 2.56 2.2 8.6 2.42 2.5 9.4

*X t Determined from Maximum q Value.

406

A EDC-TR-77-107

NOMENCLATURE

A

A o

Ar

aij b

b

C

C!

CF

CF I

CFII

Cf

Ch

C

e

e "

F(w)

f

H, h

k

k

Amplitude of boundary-layer disturbance fluctuations

Amplitude of disturbance at the neutral stability point

Reference amplitude for boundary-l~er disturbance (determined at M = 1.3

i

Coefficients in Eq. (1)

Model leading-edge thickness at a specif ic location

Average value of model leading-edge thickness

Tunnel test section circumference

Tunnel test section circumference of 12- x 12-in. tunnel (C 1 = 48 in. )

Mean turbulent sk in - f r i c t i on coef f ic ient

Mean turbulent sk in - f r i c t ion coef f ic ient calculated using method of van Driest- I

Mean turbulent sk in - f r i c t ion coef f ic ient calculated using method of van Dr iest - I I

Local sk in - f r i c t ion coef f ic ient , Cf = ~w/q®

Heat-transfer coef f ic ient , C h = ~/(T o - T w)

Aerodynamic-noise-transition correlat ion size parameter [see Eq. (10)]

Root-mean-square of the hot-wire voltage f luctuat ion

Instantaneous value of hot-wire f luctuat ion voltage

Power spectral density (psia)2/radian/sec

Frequency, cycles/sec

Enthalpy

Diameter of roughness element (sphere diameter)

Total height of roughness element above model surface (sphere diameter plus band thickness)

407

A E DC-TR-77-107

£

Cm

~ r

M

M 6

m

m

m"

Pr

P n~ n~

P' PRMS p"

PC

PO

Po

Pp

Ps

p®

qo

q6

q®

R

Reference length

Axial distance from tunnel throat to model nose

Axial distance from tunnel throat to wall boundary- layer rake

Mach number

Local Mach number outside boundary layer

Root-mean-square of the mass flow f luctuat ion

Mean mass flow value

Instantaneous mass flow f luctuat ion value

Prandtl number, Pr = Cp ~/k

Stat ic pressure

Root-mean-square value of radiated pressure f luctuat ion

Instantaneous f luctuat ing pressure

Cone surface s tat ic pressure

Tunnel s t i l l i n g chamber total pressure

Total pressure downstream of a normal shock wave ( f ree- stream)

Surface probe pitot pressure

Model surface static pressure

Free,stream static pressure

Heat-transfer rate

Stagnation heat-transfer rate on a 1.0-in.-diam hemisphere probe

Dynamic pressure based on local condition at edge of boundary layer, q~ = ½ % U~

Free-stream dynamic pressure, psia

Shroud internal radius, in. (R = 5.72 in.)

408

Re Re/in., Re, (Re/in.).

Ree, e

Re k

Re "

Re a, Re, a

Rea m

Rea r

Re t

Retef f

(Ret) 6

Re x

A EDC-TR-77-107

Reynolds number

Free-stream Reynolds number, per in. (p~ U/u®)

Reynolds number based on edge conditions and momentum thickness at the transition location, x t

Trip Reynolds number (Re k p.U. k

Potter-Whitfield trip correlation Reynolds number

V s+o Re~'= ~kk

For adiabatic wall

Re['= g ~v~]~M~J + + (Y" I) n r M

Length Reynolds number p. U a

Re

I p. U aml Length Reynolds number Re&m m

I p. U &rl Length Reynolds number Rear-

Flat plate or hollow-cylinder transition Reynolds number based on free-stream conditions,

U X t Re t = (Re/in.). (X t) = v

Effective point transition Reynolds number (p~U8 Xteff/~6)

Cone t rans i t ion Reynolds number (based on local condi- t ions) ,

U 6 X t (Ret) 6 = (Re/in.)6 (X t ) - v6

Length Reynolds number (Re x = p 8 U 6 x/g 6)

409

AEDC-TR-77-107

Rex k

Re6, (Re/in.) 6

Re6*,t

S T , ST=

T

T

TDp

(Te/T6)corr

T; TT U

U c U L

U

U

~b U

U~

X s

X t

Xteff

Xt o

X

Trip position Reynolds number, Rexx = P6 U6 Xk/U6

Inviscid flow local surface unit Reynolds number per in. (P 6 U~l~ 6)

Reynolds number based on the boundary-layer displacement thickness at the transition location, x t

Stanton'number [(q/p= U=) (H o - Hw)]

Temperature

Adiabatic wall temperature, Taw T +---~--r

Root-mean-square of the temperature fluctuation

Dewpoint temperature at atmospheric pressure

Corrected effective temperature ratio as defined in Reference (163)

Instantaneous value of the total temperature fluctuation

Mean total temperature value

Velocity outside the boundary layer

Source convection velocity

Local velocity outside the long shroud inner wall boundary layer

Free-stream velocity

Velocity in the boundary layer

Root-mean-square velocity fluctuation

Instantaneous velocity fluctuation

Shroud l ip shock impingement location

Surface distance location of boundary-layer transition

Effective point transition location

Transition location on smooth body

Surface distance from model nose

410

x k

Y

Y

ACp ,ACprms

AeT,Ae m

(z

6

6*

6 c

6 k

nr,r

B

8 C

BLE

Ii

V

p

p

T W

+

[0

A E D C-T R -77-107

Distance from cone t ip to center.of-roughness sphere

Distance normal to model surface

Ratio of specific heats

Dynamic pressure coefficient, ACp = p/q,

Hot-wire sensitivity coefficients

Speed of sound

Boundary-layer thickness

Boundary-layer displacement thickness

Boundary-layer displacement thickness parameter (Eq. B-13)

Cone half angle

Boundary-layer displacement thickness at k location

Value of Re~" where X t = Xk; c = f (~ ) as shown in

Reference (37J

Temperature recovery factor (Taw - TJT o - T 6)

Boundary-layer momentum thickness

Cone half-angle

Planar model leading-edge bevel angle

Absolute viscosity

Kinematic viscosity, v = ~/p

Density

Instantaneous fluctuating density

Wall local shear stress

Cone bow shock wave angle

Power spectral density, ~2 = $ 0

~df, psia2/Hz

Angular frequency (radians/sec) and exponent in viscosity-temperature relat ion (m = 0.76)

411

AEDC-TR-77-107

Subscripts

Z

AW, aw

Beg.

C

End

e

FP

K

k

L

max

min

0

planar

S

t

W

X

6

¢0

Conditions immediately downstream of an oblique shock wa v e

Adiabatic wall

Beginning of transition location

Cone configuration

End of transition location

Boundary-layer edge conditions

Flat p] ate

At height k in undisturbed laminar boundary layer

Trip location

At total height k in undisturbed laminar boundary layer

Local conditions at edge of boundary layer

Peak value

Minimum value

Stagnation conditions

Two-dimensional configuration, either hollow cylinder or f la t plate

Cone surface inviscid values

Transition

Wall

Surface distance

Local inviscid flow properties at edge of boundary layer

Momentum thickness

Free stream

412

II B . B zy AEDC-TR-77-107 ARCHIVE coPY DO Nor LOAN › dtic › tr › fulltext › u2 ›...

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Transcript of II B . B zy AEDC-TR-77-107 ARCHIVE coPY DO Nor LOAN › dtic › tr › fulltext › u2 ›...