AEDC-TR-79-39

c./ ARCHIVECOPY DO NOT LOAN

Application of the Multistage Axial-Flow Compressor Time-Dependent Mathematical Modeling Technique to the TF41-A-I Modified (Block 76) Compressor

C. E. Chamblee ARO, Inc.

September 1979

Final Report for Period January 1978 - March 1979

Approved for pubhc release; distribution unlimited.

Property of U A,c.~..~ . . S. Air FO~ e

~ m F¢~;,: UO,?4~v

~ _ _ , ( _ ~ r r l I

= - ~ l - e m i l ARNOLD ENGINEERING DEVELOPMENT CENTER

- ~ , , , ARNOLD AIR FORCE STATION, TENNESSEE

AIR FORCE SYSTEMS COMMAND

, UNITED STATES AIR FORCE

NOTICES

When U. S. Government drawings, specifications, or other data are used for any purpose other than a def'mitely related Government procurement operation, the Government thereby incurs 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.

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This report has been reviewed by the Information Office ((31) 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.

SALVADOR REZA, 2d Lt, USAF Project Manager, Analysis and Evaluation Division Directorate of Test Engineering

Approved for publication:

FOR THE COMMANDER

MARION L. LASTER Director of Test Engineering Deputy for Operations

UNCLASSIFIED PEPORT.DOCUMENTATION PAGE

I . REPORT NUMBER 12 GOVT ACCESSION NO.

AEDC-TR-79-39 4 T ITLE ( ~ d Subt l t l~ APPLICATION OF THE MULTISTAGE AXIAL-FLOW COMPRESSOR TIME-DEPENDENT MATHEMATICAL MODELING TECHNIQUE TO THE TF41-A-I MODIFIED (BLOCK 76) COMPRESSOR 7. AUTHOR(e)

C. E. Chamblee, ARO, I n c . , a Sverdrup Corporation Company-

9 PERFORMING ORGANIZATION NAME AND ADDRESS

Arnold Engineering Development Center/DOTA Air Force Systems Command Arnold Air Force Station, Tennessee 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 Deve lopmen t Cen te r /DOS A i r Force S y s t e m s Command Arnold Air Force Station, Tennessee 37389 14 MONITORING AGENCY NAME & AODRESS~I! dllferenf Item ConfrolllnE OHiee.)

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 f o r P e r i o d - J a n u a r y 1978 - March 197E 6. PERFORMING ORG. REPORT NUMBER

8. CONTRACT OR GRANT NUMBER(el

10. PROGRAM ELEMENT. PROJECT. TASK AREA & WORK UNIT NUMBERS

P r o g r a m E l e m e n t 27121F

12. REPORT DATE

S e p t e m b e r 1979 13. NUMBER OF PAGES

97 IS. SECURITY CLASS. (ol thie ~&pGr;)

UNCLASSIFIED

lea. DECL ASSI FIC ATION / OOWNGRADIN G scN,~ou-s N/A

16 DISTRIBUTION STATEMENT ro f th le Report)

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 (OI the abe/reel turreted In Block 20. i f dl(laronf Itom RopoTt,)

IB SUPPLEMENTARy NOTES

Available in DDC

19 KEY WORDS (Conl~uo ~ roverae eldo i f necaa la~ ~ d I ~ n t i ~ ~ block numbo~

h i g h p r e s s u r e c o m p r e s s o r s p e r f o r m a n c e ( e n g i n e e r i n g ) TF41-A-1 t u r b o f a n e n g i n e s mathematical models . 20 ABSTRACT (C~ l l nuo ~ rev~ao aide I f naceaaa~ ~ d Identify by block numbo~

The o v e r a l l o b j e c t i v e o f t h e work d e s c r i b e d h e r e i n was t o c o n s t r u c t a v a l i d a t e d m a t h e m a t i c a l mode l o f t h e h i g h - p r e s s u r e c o m p r e s s o r o f t h e TF41-A-1 t u r b o f a n e n g i n e and t o p r o v i d e t h e r e b y a new a n a l y s i s t o o l f o r a s s e s s i n g i n f l u e n c e s o f e x t e r n a l d i s t u r b a n c e s and com- p r e s s o r m o d i f i c a t i o n s on p e r f o r m a n c e and s t a b i l i t y . T h e s e o b j e c - t i v e s w e r e a c c o m p l i s h e d t h r o u g h t h e d e v e l o p m e n t o f a o n e - d i m e n s i o n a l , s t e a d y - s t a t e TF41-A-1 c o m p r e s s o r m a t h e m a t i ' c a l m o d e l

J

DD FORM 1473 EDITION OF ' .OV 'S IS OBSOLETE I J AN ?3

UNCLASSIFIED

UNCLASSIFIED

20. A b s t r a c t ( C o n t i n u e d )

f o r s t a b i l i t y a s s e s s m e n t w i t h u n d i s t u r b e d £1ow, and a t h r e e - d i m e n s i o n a l , t i m e - d e p e n d e n t TF41-A-1 c o m p r e s s o r m a t h e m a t i c a l mode l f o r a n a l y s i s o f d i s t o r t e d i n f l o w s and t r a n s i e n t and dynamic d i s t u r b a n c e s . Example p r o b l e m s and c o m p a r i s o n s t o e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d f o r b o t h m o d e l s . The p r o b l e m s u s i n g t h e o n e - d i m e n s i o n a l , s t e a d y - s t a t e mode l c o n s i s t e d o f d e t e r m i n a t i o n o f t h e s t e a d y - s t a t e s t a b i l i t y l i m i t s ( s u r g e l i n e s ) w i t h u n d i s t u r b e d f l o w f o r t h r e e d i s t i n c t i n l e t g u i d e v a n e s c h e d u l e s . T h o s e p r .ob lems u s i n g t h e t h r e e - d i m e n s i o n a l , t i m e - d e p e n d e n t mode l i n c l u d e d d e t e r - m i n a t i o n o f t h e s t a b i l i t y l i m i t ( s u r g e l i n e ) r e d u c t i o n c a u s e d by p u r e r a d i a l p r e s s u r e i n l e t d i s t o r t i o n , p u r e c i r c u m f e r e n t i a l p r e s - s u r e , and p u r e c i r c u m f e r e n t i a l t e m p e r a t u r e i n l e t d i s t o r t i o n . The e f f e c t s o£ r a p i d u p w a r d ramps o f i n l e t t e m p e r a t u r e on c o m p r e s s o r s t a b i l i t y w e r e a l s o i n v e s t i g a t e d . The TF41-A-1 c o m p r e s s o r m o d e l s c o m p u t e d t h e c o m p r e s s o r s t a b i l i t y l i m i t s w i t h r e a s o n a b l e a c c u r a c y .

A F'S t . A r - ~ l ¢ ! A ] ' . I T e n r

UNCLASSIFIED

f

A E D C-T R -79-39

PREFACE

The research reported herein was conducted by the Arnold Engine.ering Development Center (AEDC), Air Force Systems Command (AFSC), at the request of the Aeronautical Systems Division (ASD). The work and analysis for this research were done by personnel of ARO, Inc. (a Sverdrup Corporation Company), contract operator for AEDC, AFSC, Arnold Air Force Station, Tennessee, under ARO Project Nos. E43P-78A, E43Y-84, and E43P-79. The Air Force project manager was Lt. S. Reza, DOTA. The mahuscript was submitted for publication on April 27, 1979.

The author wishes to acknowledge William F. Kimzey, ARO, Inc., for his assistance during the model development; Grant T. Patterson, ARO, Inc., for his assistance in modifying computer programs required for this effort; William R. Warwick, ARO, inc., for his assistance in obtaining compressor stage characteristics; and Virgil K. Smith, University of Tennessee Space Institute, for assistance provided during the course of this work.

C O N T E N T S

A E DC-TR-79 -39

Page

1.0 I N T R O D U C T I O N ........................................................ 7 2.0 TF41-A-I T U R B O F A N ENGINE A L T I T U D E A E R O M E C H A N I C A L

TEST AND RESULTS

2.1 Engine Description .................................................... 8

2.2 Instrumentation ....................................................... 9

2.3 Procedure for High-Pressure Compressor

Stability Assessment ................................................... 10

2.4 Experimental Results .................................................. l0

3.0 D E S C R I P T I O N OF O N E - D I M E N S I O N A L , STEADY-STATE M O D E L

3.1 Model Concepts ....................................................... I l 3.2 TF41-A-I High-Pressure Compressor Steady-State

Stage Characteristics ................................................... 17

3.3 Model Verification .................................................... 19 4.0 DESCRIPTION OF T H R E E - D I M E N S I O N A L , T I M E - D E P E N D E N T M O D E L

4.1 Model Concepts ....................................................... 20

4.2 Three-Dimensional, Time-Dependent

Model Refinements .................................................... 23

4.3 Model Verification .................................................... 24

5.0 S U M M A R Y OF RESULTS ................................................ 27

REFERENCES ........................................................... 28

I L L U S T R A T I O N S

Figure

31 I. TF41-A-1 Turbofan Engine Schematic .......................................

2. Installation Schematic TF41-A-I in Propulsion

Development Test Cell {T-4) ................................................ 32

3. TF41-A-I (Block 76) H P Compressor Schematic ............................... 33

4. H P Compressor lnterstage Instrumentation ................................... 34

5. TF41-A-I IGV Schedules ................................................... 35

6. Effects o f IGV Schedule on TF41-A-I HP Compressor

Stability Limit at 30,000 fl, Mach Number 0.7 with

Seventh-Stage Bleed Valve Closed ........................................... 36

AEDC-TR-79-39

Figure Page I

7. Effects of IGV Schedule on TF41-A-I HP Compressor

Stability Limit at Sea-Level-Static Conditions with

Seventh-Stage Bleed Valve Open ............................................ 37 8. Surge Induced by Inbleed at NH = 11,500 rpm with Axial

IGV Schedule ............................................................ 38

9. Radial Total Pressure Profiles with Uniform Engine

Inlet Flow ............................................................... 39

10. Radial Total Temperature Profiles with Uniform Engine

Inlet Flow .............................................................. 42

I I. Station Locations (Computat'ional Planes) for One-

Dimensional, Steady-State Compressor Model ............................... 45

12. Elemental Control Volume with Application of Mass,

Momentum, and Energy Conservation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

13. Typical Temperature and Pressure Coefficients as

Functions of Flow Coefficient at Constant

Rotational Speed ........................................................ 47

14. TF41-A-I HP Compressor Stage Characteristics ............................... 48

15. Comparison of Model Computed Speed Characteristics and

Stability Limits with Experimental Measurements

at 30,000 It, MO = 0.7 .................................................... 59

16. Model Computed Effect of Corrected Rotor Speed Variation

for -0.3-deg IGV Line with Axial IGV Schedule

at 30,000 ft, MO -- 0.7 .................................................... 62

17. Comparison of Model Computed Speed Characteristics and

Stability Limits with Experimental Measurements with

Seventh-Stage Bleed Valve Open at

sea-level-static conditions .................................................. 63 18. Comparison of Model Computed Stage Flow Coefficients

Near Compressor Stability Limit with Experimental

Measurements, IGV at Full Axial Position

(-5.0 _+ 0.5 deg) ............................................................ 66

19." Comparison of Model Computed Stage Pressure Ratios Near

Compressor Stability Limit with Experimental

Measurements, IGV at Full Axial Position

(-5.0 _+ 0.5 deg) ........................................................... 69

4

A E D C-T R -79-39

Figure Page

20. Comparison of Model Computed Stage Temperature Ratios Near

Compressor Stability Limit with Experimental Measurements,

IGV at Full Axial'Position (-5.0 _+ 0.5 deg) ................................... 72

21. Division of Compressor into Control Volumes ................................. 75

22. Control Volume Velocities and Fluxes ........................................ 76

23. Schematic of Three-Dimensional, Time-Dependent Solution

Procedure for TF41-A-I H'P Compressor Model ............................... 77

24. Illustration of Effect of Incremental Averaging on

Numerical Instability ...................................................... 78

25. TF41-A-I HP Compressor Model Loaded to Stall, NH/V0 = 92.6

percent, IGV = 12 deg, No Distortion ....................................... 79

26. TF41-A-I HP Compressor Model Flow Breakdown in Terms of

Computed Stage Inlet Total Pressures Leading to

Instability, NH/x/O-= 92.6 percent, IGV = 12 deg, No

Distortion .............................................................. 80

27. Computed Radial Distortion Influences on Stability,

TF41-A-I HP Compressor ................................................. 81

28. Comparison of TF41-A-! HP Compressor Model Radial

Distortion Computations with Experimental Resuhs . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

29. Model Computed Influence of Circumferential Pressure

Distortion on Stability, TF41-A-1 HP Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

30. Comparison of TF41-A-I HP Compressor Model Circumferential

Distortion Computations with Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

31. Model Computed Influence of Circumfereritial Temperature

Distortion on Stability, TF41-A-1 HP Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

32. Comparison of Circumferential Temperature Distortion

Model Computations with Experimental Results ............................... 87

33. Effect of 5,000°R/see Uniform Inlet Temperature Ramp

on Compressor Stability as Computed by TF41-A-I

HP Compressor Model .................................................... 88

34. TF41-A-I HP Compressor Model Flow Breakdown with 5,000°R/

sec Inlet Temperature Ramp, Nominal IGV Schedule,

No Distortion ............................................................ 89

35. TF41-A-I HP Compressor Model Computed Influence of Uniform

Inlet Temperature Ramp Rates on Compressor Stability . . . . . . . . . . . . . . . . . . . . . . . . 90

A EOC-TR-79-39

Figure Page

36. Effect of 5,000°R/sec Uniform Inlet Temperature

Ramp on Compressor Inlet Corrected Airflow as

Computed by TF41-A-! HP Compressor Model ............................... 91

37. Effect of 5,000°R/sec Inlet Temperature Ramp (Imposed on , ' ° , "

90-deg-Arc Circumferential Section) on Compressor

Stability as Computed by TF41-A-I HP Compressor Model ................................................................... 92

NOMENCLATURE ...................................................... 93

o J

, , o

6

A EDC-TR-79-39

1.0 INTRODUCTION

Stable, aerodynamic operation of the compression system of a gas turbine engine is essential for the engine to perform satisfactorily. "Aerodynamically stable operation" refers

to the condition existing when the compressor delivers a desired quantity of airflow on a

continuous basis, compressed to a desired pressure , free of excessively large amplitude

fluctuations in the flow properties throughout the compressor. The aerodynamic stability

limit (surge line)--most commonly defined as a locus of points denoting maximum pressure

ratio for stable operation as a function of corrected airflow rate--is typically determined from experimental results. However, only limited amounts of experimental compressor

steady-state, transient, and stability limit data can be obtained during test programs because of test hardware and economic constraints. A validated mathematical model based on the

limited experimental data is needed to make performance and stability computations at operating conditions with inlet distortion patterns and with subcomponent hardware configurations different from those actually tested. The use of such a model would significantly enhance the usefulness of data from any given compressor test.

The objectives of the work described herein were to construct a validated mathematical

model of the high-pressure compressor of the TF41-A-1 turbofan engine and to provide thereby a new analysis tool for assessing the influence of external disturbances and

compressor modifications on performance and stability. The objectives were accomplished

through development of a one-dimensional, steady-state mathematical model for stability assessment with undisturbed flow and a three-dimensional, time-dependent mathematical model for analysis of distorted inflows and transient and dynamic disturbances.

For both models, example problems are presented and compared to experimental results. The problems using the one-dimensional, steady-state model consisted of determination of the steady-state stability limits (surge lines) with undisturbed flow for three distinct inlet

guide vane schedules. Those problems using the three-dimensional, time-dependent model included determination of the stability limit (surge line) reduction caused by pure radial inlet

pressure distortion, pure circumferential inlet pressure, and pure circumferential inlet temperature distortion. The effects of rapid upward ramps of inlet temperature on

compressor stability were also investigated. The models compute compressor stability limits with reasonable accuracy.

An altitude evaluation of the TF41-A-! turbofan engine with a highly instrumented, modified (Block 76) high-pressure compressor was conducted at the Arnold Engineering Development Center during the period September 15, 1977 through January 26,

1979. Pressure and temperature measurements obtained during this evaluation provided

7

A E D C-T R -79-39

experimental data for formulation of the compressor, stage characteristics and validation of

the models. I I

The technology required to construct compressor models applicable to predicting' compressor stability margin loss caused by external disturbance in flow conditions was

developed in Ref. I. This demonstrated the validity of the multidimensional form of a mathematical model for a four-stage, fixed-geometry compressor at one value of corrected rotor speed. In this program, refinements were introduced to the basic (Ref. l)model. These

refinements were introduced to improve the generality of the model, to accommodate the

variable rotor speed and the variable-geometry features of the TF41-A-I high-pressure

compressor, to increase accuracy, and to accommodate the inherently unstable numerical solutions caused by error buildup in the model calculations. This report describes the.

manner in which the models were constructed and the results obtained.

2.0 TF41-A-I TURBOFAN ENGINE ALTITUDE

AEROMECHANICAL TEST AND RESULTS

Because the information derived from the TF41-A-I turbofan engine altitude test is such

an integral part of the effort reported herein, a description of the engine and

instrumentation and pertinent results is presented.

2.1 ENGINE DESCRIPTION

The TF41-A-I, manufactured by the Detroit Diesel Allison (DDA) Division of the

General Motors Corporation, is a two-spool, low-bypass-ratio, nonaugmented turbofan engine (Fig. 1) in the 14,500-1bf-thrust class. The engine incorporates a three-stage fan and a two-stage, intermediate compressor driven by a two-stage, low-pressure turbine and an eleven-stage, high-pressure compressor driven by a two-stage, high-pressure turbine. The

engine incorporates a can-annular combustor, an engine-controlled, high-pressure

compressor interstage (seventh-stage) bleed system, and an annular fan duct. A schematic of

the engine installation in the T4 test cell is presented in Fig. 2. • - .

The fan, intermediate compressor, and high-pressure compressor pressure ratios at sea- level-static, intermediate power are 2.48, 1.41, and 6.20, respectively, for an overall pressure ratio of 21.7 at a rated engine airflow of 260 Ibm/sec, a high-pressure rotor speed, NH,;. of 12,840 rpm, and a fan rotor speed, NL, of 8,940 rpm. Airflow is split at the fan exit, and. the bypass air passes through the annular fan duct and mixes again with the gas generator airflow aft of the low-pressure turbine exit at the tailpipe inlet. The gas generator air'passes

8

• A E D C - T R - 7 9 - 3 9

through the intermediate compressor and into the high-pressure compressor through the variable-position inlet guide vanes. The high-pressure compressor incorporates a bleed

mariifold at the compressor exit in the outer compressor case for extraction of air for aircraft services. The fan has no inlet guide vanes, and the bulletnose rotates; there are no anti-icing provisions.

2.1.1 High-Pressure Compressor Modifications

The engine (S/N 141683/3) utilized a production high-pressure compressor that had been modified to include: (l) full-chord, clapperless, first-stage rotor blades with increased

thickness-to-chord ratio and revised taper, (2) "Eiffel Tower" stator vanes for stages 4, 5, and 6 having increased thickness near the root, looser dovetails, and glass bead peened

surfaces, and (3) modified spacer between stages 9 and 10. The first two modifications are refei'red to as "Block 76" design modifications. A detailed schematic of the high-pressure compressor is presented in Fig. 3.

2.1.2 High-Pressure Compressor Variable-Geometry Control System

The high-pressure compressor incorporates a hydromechanical control system to position the inlet guide vanes (IGV's) and the compressor bleed valve (BVP) by a common actuator through a system of linkages.

The inlet guide vanes are scheduled as functions of engine inlet air temperature and high- pressure rotor speed. The bleed valve is fully open when the guide vanes are at 35 deg and fully closed when the guide vanes reach 24 deg.

2.2 IINSTRUMENTATION

Instrumentation was provided to measure dynamic stresses and aerodynamic pressures and temperatures; rotor speeds; fuel system pressures, temperatures, and flow rates; lube oil and hydraulic system pressures and temperatures; and other engine and test cell system parameters required for proper operation of the engine.

The instrumentation providing data for this study was located in the high-pressure (HP) compressor. The HP compressor was heavily instrumented since one of the objectives of the altitude test program was to determine the detailed aerodynamic characteristics of the HP

compressor throughout the TF41-A-I engine operating envelope. In addition to the array of steady-state instrumentation, the HP compressor was also instrumented with high- response, wall-static pressure transducers. A diagram showing the type, number, and location of the HP compressor interstage instrumentation is presented in Fig. 4.

9 /

A E D C - T R - 7 9 - 3 9 •

2.3 PROCEDURE FOR HIGH-PRESSURE

COMPRESSOR STABILITY ASSESSMENT

Following setting of the desired simulated flight conditions the high-pressure rotor speed

was adjusted to yield a selected inlet guide vane position, IGV, thereby establishing the

baseline point. The HP compressor was then slowly back-pressured by opening the inbleed

air system valve until surge occurred; steady-state and trarisient data were obtained along the .

constant IGV line from baseline to the surge point. The power lever was moved during

compressor loading to maintain the selected HP IGV angle at a constant value. When the

HP compressor surged, the inbleed air system valve was closed to relieve the compressor and

to permit recovery.

The surge testing of interest to this report was conducted at 30,000 ft, Mach number 0.7

in the range of operation where the seventh-stage bleed valve was closed and, at sea-level-

static, where open seventh-stage bleed valve performance was obtained. To evaluate the

effects of severely off-schedule, HP compressor IGV geometry, three IGV schedules were

selected, representing extremes beyond which the TF41-A-I engine is not expected to

operate. These IGV schedules are defined as:

1. "Nomina l , " M72-3 vane schedule (Ref. 2),

2. "Axia l ," open approximately 10 deg at a given NH, and

3. "Cambered , " closed approximately 10 deg at a given NH.

These schedules are shown in Fig. 5. For each IGV schedule, a HP compressor map was obtained by inbleeding high-pressure air into the exit diffuser by the previously stated

procedure.

2.4 EXPERIMENTAL RESULTS

The following are results obtained during the TF41-A-1 altitude test pertinent to this

report. The normal operating and surge lines for the HP compressor at 30,000 ft, Mach

number 0.7, with nominal, axial, and cambered IGV schedules are presented in Fig. 6. The compressor surge margin was 26 percent at 46.0 lbm/sec corrected airflow. Misscheduling

the IGV approximately 10 deg axial and cambered had no measurable effect on the Block 76

compressor surge margin.

10

A E D C-TR -79-39

The normal operating and surge lines for the HP compressor at sea-level-static

conditions with nominal, axial, and cambered IGV schedules at low rotor sp6eds at which

the seventh-stage bleed valve is open are presented in Fig. 7. Compressor exit airflow

corrected to compressor inlet conditions was used as the abscissa of this curve because no provision ,,vas made to calculate seventh-stage bleed flow rate, and high-pressure

compressor inlet airflow is therefore undefined since compressor airflow was computed

downstream by assuming choked flow in the HP turbine vanes. The compressor surge

margin with the bleed valve 100 percent open was 41 percent at 24.5 Ibm/see corrected

airflow with the nominal IGV schedule and at 27 Ibm/see with the cambered IGV schedule.

Surge could not be induced with the bleed valve 100 percent open with the axial IGV

schedule.

lnterstage dynamic pressures during a typical surge sequence are presented in Fig. 8.

That the surge originated near the sixth stage is indicated by the pressure traces reflecting the

increase in dynamic pressure at stages I, 2, and 4 and by the corresponding decrease in dynamic pressure at stages 8 and 10 following the initiation of surge.

The aerodynamic pressures and temperatures from the HP compressor vane interstage

instrumentation (Fig. 4) are presented, respectively, in Figs. 9 and l0 as typical examples of

the total-pressure and total-temperature profiles existing during uniform engine inlet-flow

conditions.

Experimental data and results presented are compared to the mathematical model

predictions in follov,,ing sections.

3.0 DESCRIPTION OF ONE-DIMENSIONAl. , STEADY-STATE MODEL

A one-dimensional, steady-state model of the TF41-A- l H P compressor was developed,

based on compressor geometry provided by the engine manufacturer and on stage

characteristics formulated from the experiment data. The steady-state model makes use of

individual stage characteristics of pressure and temperature rise as functions of mass flow to

predict the quasi-steady uniform flow performance of the compressor.

3.1 MODEL CONCEPTS

A steady-state compressor model is simply a mathematical representation of the

compressor performance. Sufficient data are necessary to determine the total-pressure and

total-temperature ratios for the compressor as functions of corrected airflow and rotor

speed. Thus, modeling the overall steady-state performance of a compressor can be as

11

AEDC-TR-79-39

simple as reading a compressor map. However, for the model to predict stage performance

as well as overall performance, it is necessary to analyze the components or stages of the compression system to account for stage interactions. The steps for development of the one- dimensional, steady-state model are (I) defining control volumes, (2) writing governing

equations, and (3) giving the method of solution.

3.1.1 Control Volume Analysis

The TF41-A-I HP compressor system (overall control volume) was divided into twenty

elemental control volumes consisting of four inlet duct, eleven compressor, and five exit duct elemental control volumes (Fig. l i). The division of the inlet and exit ducting

permitted calculation of the flow properties in the dueling by applying conservation of mass, momentum, and energy laws. The division of the compressor into elemental control

volumes representing stage lengths in the axial direction was made because the pressure and temperature rise between stage entry and exit were obtained from experimentally determined

stage characteristics as discussed in Section 3.2. For the one-dimensional, steady-state

analysis, all flow properties are "bulked" in the radial and circumferential directions~ and

variations with the axial coordinate only are considered.

3.1.2 Governing Equations

An axial-flow compressor imparts kinetic energy to the flow of a fluid by a direct interaction between that fluid and the rotating machine elements. The fluid is then diffused

through the diverging flow passages between the blades, reducing the kinetic energy and

increasing the static pressure. The divergence of each passage is determined by the inlet and

exit air angles. Since the blades are most often closely spaced, the exit-air angle is approximately equal to the trailing-edge angle of the blades. The inlet-air angle, however, is

a function of the axial velocity entering the blades and their rotational speed. Thus, a stage

flow coefficient (~), as defined in Ref. l,

U

Uwh (1)

where U = axial velocity and U.h = wheel speed, was used to represent the inlet-air angle at

the entry of each compressor elemental control volume.

The flow coefficient, ~, is related to the blade angle of attack, or, by the stagger angle, X,

which is a constant for any given blade row through the relationship

12

A EDC-T R -79-39

--- cot (A '-4 (2)

Thus, ~ serves the same purpose in the compressor stage as ot does for aircraft wing

aerodynamics. It decreases with increasing t~; therefore, small ~ means large % and vice

versa.

The temperature rise across each compressor elemental control volume was represented

by the stage temperature coefficient, ¢,T, expre.ssed as

C ( T l l - I) ~T= P

I-I w h 2 / T ~

(3)

where TR is the stage or compressor elemental control volume temperature ratio, Cp is

specific heat at constant pressure, and T is the stagnation (total) temperature.

The temperature ratio of Eq. (3) for an ideal compressor stage is the isentropic

temperature ratio defined from stage entry and exit stagnation pressure. Using this ratio,

another stage parameter, the stage pressure coefficient, ~P, is defined,

,/,P= Cp R 1

|l wh2/ 'Ft

(4)

where PR is the stage or compressor elemental control volume pressure ratio,

C C p p

C Cp - R/J (5)

and where 3, is the ratio o f specific heats, C,. is the specific heat at constant volume, and R/J

is the gas constant/mechanical equivalent of heat. For this model, the specific heat at

constant pressure, Cp, was computed as a function of temperature from the empirical

equation:

Cp = 0.2318 4 0.104 x 10-4T 4- 0.7166 x 10-81,2 (6)

where the constants are based on the specific heats of the constituents of air.

13

AEDC-TR-79-39

The temperature and pressure coefficients (~,T and ~k p) are primarily functions of the flow coefficient, 0, and the flow direction (Ref. 1). Thus, a set of curves

f t,.b P [ (,~) (7)

is referred to as "stage characteristics," and, with flow direction information, fully defines a

stage's performance from a one-dimensional standpoint.

in principle, theoretical or experimental lift and drag coefficients could be used, along

with stage geometry, to compute the stage characteristics. However, corrections for blade row interference losses and secondary flows would be required. The method used in this study was to compute directly ~b ~-, 6P, and q~ by Eqs. (1), (3), and (4) from the experimental measurements of stage total temperature, flow rate, and total pressure at the stage entry and

exit. A discussion of the stage characteristics obtained is presented in Section 3.2.

Friction losses in the inlet and exit ducting, internal bleeds, and the forces acting on the fluid in the compressor must satisfy mass, momentum, and energy conservation principles

as they relate to any elemental control volume (Fig. 12).

3.1.2.1 Mass

Application of the mass conservation principle to the elemental control volume yields

~ ' a - - d z + ~ B = W 0,.

mass leaving mass entering control volume control volume (8)

where W is the mass flow rate and z is the axial component.

Equation (8) reduces to

Wexit = W tranc~ -- WB (9)

where bleed flow, WB, is assumed to cross the control volume boundary normal to the axial

direction.

14

t A E D C - T R - 7 9 - 3 9

3 . 1 . 2 . 2 M o m e n t u m

The summation of all forces in a given direction is equal to the change of momentum in

that direction, and gives

F dz + PS A - PS A + 0"--"-7--- d ~- PS dz - A \' az

, , /

axial forces acting on control volume

IW 0(wu) dz 1 _ WU = U + 0~.

• % , l

momentum leaving momentum entering control volume control volume (10)

where F is the force of compressor blading and cases acting on fluid, including wall pressure

area force; PS is the static pressure; and A is the area.

Equation (10) may be reduced to give

0(IMP) 0A = F + P S I

0z 0~

where the impulse function, IMP, is defined as

(11)

IMP = WU+PSA (12)

-The resultant axial force, F, is defined as

F = IMP - IMP

impulse leaving impulse entering control volume control volume (13)

and in the case of ducting control volumes, assuming adiabatic flow conditions, reduces to a

simple friction loss expressed as

F = -C dYPSAM 2 (14)

where Ca is the duct pressure loss coefficient and M is the Mach number. The value o f Co

was adjusted to give a reasonable stagnation pressure loss in the ducting.

1 5

A ED C-T R-79-39

3.1.2.3 Energy

Energy conservation gives

al l I1 4- - - dz = H + WS dr - Qdz

az

enthalpy leaving enthalpy entering shaft work heat added to fluid control volume control volume done on fluid in control volume

in control volume 05)

where H is the total enthalpy flux, WS is the stage staff work added to fluid in control

volume, and Q is the rate of heat addition to control volume. Equation (15) may be reduced

tO

~H _ _ = WS*Q 0z (16)

where

The shaft work, WS, is defined as

H =WC T p (17)

WS = WC p'r ('rR- I)

and is zero in the ducting control volumes.

(18)

3 . 1 . 2 . 4 State and A d d i t i o n a l E q u a t i o n s

Additional equations required include the perfect-gas equation of state,

PS = p R TS, (19)

where p is the density and R is the gas constant; stagnation (total) state temperature

equation,

U 2 T : TS + - - (20)

2Cp

16

A EDC-TR-79-39

and stagnation (total) state pressure equation,

P = PS

Also required is the Mach number,

T

Y

y - l

(21)

M U

fl (22)

where the acoustic velocity, a, is

a = R T S = y

P (23)

3.1.3 Method of Solution

The one-dimensional, steady-state model uses a "stacking" procedure to determine flow properties throughout the compressor and associated ducting. The one-dimensional model of the TF41-A-1 HP compression system uses segmented inlet and exit ducting as indicated

in Fig. ! l. The solution is begun with known air properties at the compressor inlet (total pressure, total temperature, and airflow), ducting geometry, and a coefficient of friction.

Flow properties throughout the inlet ducting are calculated using the one-dimensional,

steady-state conservation laws (see Section 3. i.2). Since the exit of one duct segment is the entrance to the next segment, the solution is marched upstream from the compressor inlet to

the duct inlet by an iterative procedure. For the compressor segments, with compressor inlet flow properties known, a stage-by-stage calculation downstream through the compressor

using the stage characteristics formulated from experimental data gives individual stage

pressure and temperature ratios so that overall compressor performance can be calculated.

Compressor aft-ducting flow properties are then calculated using the one-dimensional, steady-state conservation laws.

3.2 TF41-A-I HIGH-PRESSURE COMPRESSOR STEADY-STATE

STAGE CHARACTERISTICS

Representative stage characteristics (temperature and pressure coefficients as functions

of flow coefficient) are presented schematically in Fig. 13 for a fixed-geometry compressor operating at a single value of compressor corrected rotor speed.

17

AEDC-TR-79-39

Several problems had to be resolved because of the variable geometry of the TF41-A-I

HP compressor:

1. To allow investigation of off-nominal schedules, the model had to account for variable IGV effects without relating IGV position to rotor speed.

2. To determine the stage flow rates during bleed-valve open operation the seventh-

stage bleed flow rate had to be estimated.

3. Interpolation of stage characteristics between lines of the chosen dependent variables had to reflect the experimentally det.ermined results.

i

Assumptions were made, and procedures were established and incorporated into the

TF41-A-1 HP compressor models to meet these requirements. The steady-state stage

characteristics are utilized both in the one-dimensional, steady-state model and in the three- dimensional, time-dependent model; therefore, the following discussion will apply, to both

models.

The variation of the steady-state stage characteristics with rotor speed was assumed to be second order, with primary effect attributed to the IGV position. This relates the stage

characteristics to the single dependent variable, the IGV, and greatly simplifies their

formulation.

An empirical relationship between bleed valve position, BVP, and bleed flow rate, WB,

was developed, based on the reactions of various static-to-total-pressure ratios determined

from the interstage instrumentation (Fig. 4). This estimation of the seventh-stage bleed flow rate permitted calculation of the stage characteristics from experimental data dur!ng open

bleed-valve operation (see Section 2.1.2).

The stage characteristic parameters ¢,T, ~P, and ~ were computed from measurements of rotor speed, flow rate, total pressure, and total temperature for each stage entry by use of Eqs. (3), (4), and (1) respectively for all data obtained during the TF41-A-I test. The

stage characteristics were then generalized along lines of constant IGV angle over the full range of IGV operation (from -5.5 to 36 deg). The TF41-A-1 HP compressor stage

characteristics developed from this analysis are presented in Fig. 14.

The stage characteristics were incorporated by means of a series of second-order curve

fits. Frequently, a prediction of compressor performance is required at some value of IGV that is not equal to any of the values used to formulate the stage characteristics. Hence,

18

AEDC-TR-79-39

interpolation of the required parameter (~,-r or ¢,P) from the values of stage characteristics

between higher and lower guide vane positions is required. The interpolation procedure used in the models is based on a fixed value of ~. This procedure was adopted because the

variation of compressor mass flow with rotor speed is effectively represented by d~. Hence,

the same ~ can be used to determine g,T or g,P at the higher and lower guide vane positions.

The ~-r or ~b P can then be interpolated linearly to define the value at the desired IGV for a

given value of 6.

3.3 MODEL VERIFICATION

Figure 15 presents steady-state model computations of compressor performance at

30,000 ft and Mach number 0.7, with nominal, cambered, and axial inlet guide vane

schedules over the corrected rotor-speed range from 90 to 100 percent and compares them to experimental results. The steady-state model computes compressor surge pressure

ratios within 2.4 percent of the experimental stability limits for the nominal, cambered, and axial guide vane schedules. For these results (Fig. 15) the model computations represent

constant corrected rotor-speed lines at a constant IGV, whereas the experimental data were obtained with nearly constant IGV (+ 0.4 deg) while corrected HP rotor speed, NH/0,,/~24, varied as much as 3.6 percent.The procedure used to obtain the experimental data (see Section 2.3), by maintaining constant IGV during the HP compressor loading, resulted in

near constant NH (+ 1.0 percent). However, the increase in energy to the engine turbines resulted in increased fan rotor s.peed, NL. Thus, the inlet temperalure, T24, delivered to the HP compressor increased from the baseline point to the stall point with corresponding

decreases in NH/0x]~z4. Therefore, the model and experimental data represent different paths from baseline to stall point. This is illustrated in Fig. 16 in which the steady-state model predictions are presented at the corresponding corrected rotor-speeds of the experimental

data points for the -0.3-deg IGV line on the axial IGV schedule (Fig. 15c).

Steady-state model computations of overall compressor performance with seventh-stage

bleed valve open at sea-level-static conditions with nominal, cambered, and axial inlet guide

vane schedules, over the corrected rotor-speed range from 85 to 92 percent are presented and compared to experimental results in Fig. 17. The steady-state model computes compressor surge pressure ratios within 4.0 percent of the experimental stability limits for the

nominal, cambered, and axial guide vane schedules with seventh-stage bleed valve open.

The large quantity of steady-state temperature and pressure measurements made on the TF41-A-I HP compressor during testing allows detailed model-to-experiment

comparisons on a stage-by-stage basis. Figures 18, 19, and 20 show model computed and

experimentally determined stage flow coefficients, pressure ratios, and temperature ratios,

19

A E DC-TR-79 -39

respectively, as functions of corrected rotor speed near the compressor stability limit. Good

agreement was obtained {within 0.5 percent).

It is evident from Fig. 18 that the TF41-A-I HP compressor operates with forward stages

(1 through 3) below the stall value of stage flow coefficient at corrected rotor speeds below

approximately 91 percent. This operation reinforces previous theories and experiment observations (Refs. 1, 3, 4, and 5). At low corrected rotor speeds, the forward stages cannot

deliver their intended pressure ratio. The flow density provided to the aft stages is therefore

lower than that for which the compressor axial area distribution was designed. Thus, to maintain steady mass flow continuity, the flow coefficients (axial velocity) in the aft stages

must increase with decreasing corrected rotor speed. Indeed, at sufficiently low corrected

rotor speeds, the aft stages are even choked. At low corrected rotor speeds, as the load on

the compressor (the demanded pressure ratio) is increased by back-pressuring, the

compressor flow reduces, and the following occur: initially the aft stages may increase their

pressure ratio in response to the flow reduction at a greater rate than the rate of decrease in

pressure ratio occurring in the forward stages; thus, the increased load may be satisfied.

However, as the loading continues, the forward stages become more and more stalled, and a

point is eventually reached at which the aft stages can no longer compensate. At that point,

overall compressor instability occurs.

It is necessary to distinguish stage stalling from overall compressor stalling or

instability. Instability is always preceded by stage stall but is not always simultaneous with

stage stall.

4.0 DESCRIPTION OF THREE-DIMENSIONAL,

TIME-DEPENDENT MODEL

The three-dimensional, time-dependent model detailed in Ref. l was converted to the

TF41-A-I high-pressure compressor system by the incorporation of TF41-A-I compressor

geometry and stage characteristics formulated during the steady-state model investigation

discussed in Section 3. The time-dependent model utilizes a finite control volume, integral

approach to solve the full nonlinear form of the three-dimensional conservation laws of

mass, momentum, and energy by means of a finite difference technique. Thus, the model is

capable of computing the influences of transient and dynamic disturbances with either

uniform or distorted inflow. ¢

4.1 MODEL CONCEPTS

A detailed description of the concepts involved in the three-dimensional, time-dependent

model development is presented in Ref. 1 and summarized in this section."

20

A EDC-TR-79-39

The compressor was divided radially, circumferentially, and axially on a stage-by-stage

basis into control volumes (Figs. 21 and 22). The governing equations were developed from the three-dimensional, time-dependent mass, momentum, and energy equations for a finite control volume. The force and shaft work applied to the fluid are determined from empirical

steady-state stage characteristics modified for unsteady cascade airfdil effects. For simplification empirical crossflow relationships were used to replace the radial and circumferential momentum equations. The radial work distribution variation effect

necessary for treatment of radial distortion was approximated using average stage

characteristics modified as a function of radius by empirical total pressure and total

temperature profile correction. Crossflow and unsteady cascade effects for circumferential distortion were also built into the model.

4.1.1 Method of Solution

The three-dimensional, time-dependent compressor model is formulated as an initial condition problem. The values of the dependent variables (mass, momentum, and energy) are specified for every control volume location (axial, radial, and circumferential

coordinate) to start the solution. For simplicity, the solution is always started from a steady,

uniform flow condition, thus allowing determination of the initial conditions by use of the

one-dimensional, steady-state model. With dependent variables, p, pU, and X (representing mass, momentum, and energy) specified for every control volume location, ijk, for time

equal zero, the time derivatives are computed from the following equations:

4.1.1.1 Mass

aPipjk 1 [WZijk+WRijk't'WCijk - WBijk - WZipjk- WRi'lpk - ~,'Cijkp 1

at vo I ijk (24)

4.1.1.2 Axial Momentum

O(PlJ)i-ik ] [[7 ] = ilk + IMPiI k - IMPipI k (25)

0t VOLij k

The force, F, is obtained from stage characteristic information modified for unsteady

cascade airfoil effects. The impulse terms are

IMP = PSAZ+WZU (26)

where AZ is the control volume area normal to axial direction and WZ is the mass flux

across radially-facing control volume boundary.

21

A E D C-T R -79-39

4. I. 1.3 Energ).

~x i p j k 1 1

[- -1

~t Vol i j k

where WS is the stage shaft work added to fluid in control volume, Q is the rate of heat

addition to control volume, HZ is the total enthalpy flux transported across control volume

axial-facing boundary, and where

(28)

The radial and circumferential impulse and velocity terms neglected in Eqs. (25) and (28) are

second-order terms determined respectively by nondimensionalization and order-of-

magnitude analysis of the equations; therefore, their influence on the solution would have

been small. Also, including these terms caused the numerical solutions to be generally less stable and to oscillate with small amplitude when a steady-state condition was reached. Once

these calculations of the time derivatives of the dependent variables, p , ,oU, and X, are

carried out for all the volumes, the solution can be advanced in time through use of a fourth-

order Runge-Kutta numerical integration method (Ref. 6) that provides values of the

variables at the next time step. The sequence is then repeated, with boundary conditions

changing in accordance with the specified event simulation for as many time steps as are

required. A schematic of the computational process is presented in Fig. 23.

The system of equations constituting the model is for time-dependent, three-dimensional

subsonic flow and is hyperbolic in nature, with specified boundary conditions and initial

conditions. Thus, each integration step to compute the dependent variables at the new time (t + At) must be made within the region of influence of the known values at time, t. The

Courant-Friedrichs-Lewy maximum time step criterion (Ref. 7) I

Az m i l l

At m.x " + Umax (30)

must be observed. For AZmin = 0.111 ft, a = 1,625 ft/sec (values at TS = 1,100°R),

Urea x = a ,

A t = 3 .4 × ] 0 - 5 sec m . ~ x

22

A ED C-TR -79-39

A time step of 1.0 x 10 .5 sec was used for the TF41-A-I HP compressor model.

4.2 THREE-DIMENSIONAL, TIME-DEPENDENT MODEL REFINEMENTS

Before this study, the three-dimensional, time-dependent model concepts (Ref. 1)

summarized in the previous section had only been applied to a four-stage, fixed-geometry

compressor operating at a single rotor speed. During this investigation, a number of

refinements were introduced to the basic model to accommodate variable rotor speed and

variable-geometry features of the TF41-A-I HP compressor. In addition, refinements were

incorporated to improve accuracy, and to handle numerical solutions that were inherently unstable. (This instability was caused by error buildup in the model calculations.) These

refinements are discussed in the following paragraphs.

4.2.1 Variable Rotor Speed and Variable Geometr~

The variable-rotor-speed and variable geometry requirements were met by incorporating

the IGV-dependent, steady-state stage characteristics formulated during the one-

dimensional, steady-state model investigation (Section 3.2). With both NH and IGV

specified as inputs (boundary conditions), stage shaft work and forces could be determined for all IGV schedules.

4.2.2 Real-Gas Properties

As was done in the one-dimensional, steady-state model development, real-gas

properties were approximated by incorporation of an emperical relationship for the specific

heat at constant pressure, Cp, as a function of temperature and gas composition.

4.2.3 Modified Fourth-Order Runge-Kutta Numerical Integration Method

Conversion of the three-dimensional, time-dependent model to the TF41-A-I HP

compressor form with incorporation of the previously discussed refinements resulted in a

mathematical model that was numerically unstable at all conditions. All attempts to start the

model resulted in unsteady conditions that produced a model computation abort similar in

nature to a compressor surge. An analysis of the instability revealed that the fourth-order

Runge-Kutta numerical integration method was not convergent when applied to the

hyperbolic equations constituting the TF41-A-I HP compressor model. Further analysis

revealed that the divergence was of a series form, alternating around the desired solution.

Therefore, an average of the oscillations over at least one cycle approximates the desired solution.

23

A ED C-TR-79-39

A technique was developed an'd incorporated to average the oscillations of the dependent

variables (mass, momentum, and energy) over a predetermined time interval and restarting

the solution at the average value of the dependent variables. The averaging technique was

investigated for convergence by running various time intervals to determine the minimum interval at which convergence could be maintained. The minimum time interval for

satisfactory convergence was determined to be approximately 0.2 x i0 -3 sec. This time

interval was also effective at the time of actual compressor surge since the instabilities that

occur during the surge event fully develop and produce model computat ion abort within 0.2

x 10 3 sec. An illustration of the effect of the incremental averaging technique on numerical

instability is presented in Fig. 24.

4.3 MODEL VERIFICATION

The TF41-A-I HP compressor model was loaded to the stability limit by increasing the

exit static pressure until flow breakdown was indicated. Inlet stagnation pressure and temperature were constant. Corrected rotor speed was 92.6 percent of design, and IGV angle

was 12 deg (nominal IGV schedule). Figure 25 illustrates the loading and the resulting stall

process. Exit static pressure was ramped at a rapid rate to minimize the computer time

necessary for the computations. The rate was slow enough, however, that transient effects

were very small. Airflow at any stage never differed from compressor inlet airflow by more

than 0.6 percent during loading. As the load on the compressor increased, compressor

pressure ratio increased, and airflow decreased until flow breakdown was indicated.

Figure 26 presents the model computed stage inlet total pressures on an expanded time

scale covering the flow breakdown. Initiation of surge is indicated at t = 76.78 msec by

observation of the sixth- and seventh-stage inlet total pressures. The inlet total pressure at

stage seven decreases because stage six stalls, thereby limiting pumping capacity. The inlet total pressure of stage six increases in response to the sudden blockage to the flow produced by the stalling in stage six. The indication that compressor surge originated in the sixth stage

agrees with the experimental results reported in Section 2.4

The model solution thus indicated the following sequence leading to compressor

instability: The compressor is loaded and mass flow decreases until a stage somewhere in the compressor reaches its stall point (its maximum pressure coefficient point). The ability of

that stage to continue to pump flow (i.e., to help support the pressure gradient over the

length of the compressor imposed by the back pressure load) begins to diminish ~. As the flow reduction continues, the ability of the stage to pump diminishes even further because of the

increased load. Eventually, a point is reached where the flow into the stage becomes fully

24

AEDC-TR-79-39

stalled; thus, little force on the fluid is provided to pump the flow, and the flow path

through the compressor becomes blocked because of the highly separated condition of the

stalled flow in the channels.

in terms of the solution of the model equations, as the loading is increased, a point is reached where no stable solution to the. governing equations exists that will satisfy the

imposed load (boundary conditions); thus, the solution, like the flow through the

compressor, becomes unstable. However, the behavior of the model quickly becomes

nonrepresentative of the'compressor shortly after flow breakdown because the stage

characteristics are not valid for deeply stalled, dynamic situations.

4.3.1 Pure Radial and Circumferential Distortion Patterns

Three types of distortion patterns were computed to see the influence of pattern severity

and shape variations on the TF41-A-1 HP compressor. The patterns considered were pure

radial pressure distortion, pure circumferential pressure distortion, and pure circumferential

temperature distortion. No specific experimental data for the TF41-A-I HP compressor

were available for these cases. Therefore, only comparisons to experimental results from

other compressors could be made.

4.3.1.1 Radial Pressure Distortion

Figure 27a illustrates the results of loading (by increasing exit static pressure) the TF41- A-! HP compressor model to the stability limit with tip radial distortion (low pressure in the

tip region). Pattern severities (Pmax - Pmin/Pavg), of 5, 10, and 20 percent were considered. Figure 27b shows the results for the hub radial case and indicates that the TF41-A-i HP

compressor would be more sensitive to tip radial distortion than to hub radial distortion.

Figure 28 compares of the TF41-A-i HP compressor model results with experimental data

from a J85-13 engine test (Ref. 8). Similar results were obtained, except that the J85-13 engine was even less tolerant of tip radial distortion than the TF41-A-I HP compressor was

computed to be.

4.3.1.2 Circumferential Pressure Distortion

The effect of increasing the severity of a 180-deg-arc circumferential pressure distortion pattern is presented in Fig. 29. Compressor surge limit in terms of pressure ratio decreased 3.1, 4.8, and 7.9 percent, respectively, from the uniform flow (no distortion) surge limit at

pattern severities of 5, 10, and 20 percent. Figure 30 shows the TF41-A-I HP compressor

25

AEDC-TR-79-39

model results compared to a range of experimental data from other compressors (Refs. 8 and 9). The trend and magnitude predicted by the model agree well with the experimental

data.

4.3.1.3 Circumferential Temperature Distortion

Figure 31 shows the effect of varying the severity of 180-deg-arc total temperature

distortion on compressor stability. Temperature distortion destabilizes the compressor in

much the same manner as does pressure distortion. The higher temperature region operates

at reduced airflow, thus, at reduced flow coefficients compared to the low temperature

region of the compressor. As the load on the compressor is increased, the high temperature

region stalls first, eventually causing the entire compressor to become unstable.

For the example presented in Fig. 3 I, corrected rotor speed was held constant during the

loading (exit static pressure increase) by maintaining constant average temperature over the

face of the compressor.

Figure 32 shows a comparison of the TF41-A- 1 HP compressor model computed stability

limit pressure ratio reduction caused by circumferential temperature distortion to test results with other compressors (Refs. 8 and 10). The trend and magnitude predicted by the model

agree well with the, experimental data.

I 4.3.2 Rapid Inlet Temperature Ramp to Stall

The TF41-A-I HP compressor model was subjected to a series of uniform inlet

temperature ramp rates of 2,000, 5,000 and 10,000°R/see to simulate ingestion of hot gases

from gun or rocket fire. The effects of inlet temperature ramps were investigated for three

IGV schedules of the TF41-A-! HP compressor. Guide vane schedules investigated were

nominal, cambered (+ 10 deg from nominal), and axial (-10 deg from nominal). Mechanical

rotor speed and inlet total pressure were held constant while exit static pressure was

maintained at the level corresponding to experimentally determined operating line condition

for the respective guide vane angle investigated. The initial corrected rotor speed was 92.6 percent. Figure 33 shows the effect of 5,000OR/see uniform inlet temperature ramps with the

nominal, cambered (+ 10 deg from nominal); and axial (-10 deg from nominal), mechanical

. no significant changes in transient surge limit with IGV schedule; this is expected since both

steady-state model and experimental results indicated that misscheduling the inlet

guide vane had no measurable effect on the TF41-A-I compressor steady-state surge margin.

26

A EDC-TR-79-39

Analysis of the model computations (Fig. 34) indicate that the forward stages are rapidly

driven into stall by the reduction in airflow accompanying the rapid temperature rise at the compressor inlet. Initiation of surge and associated flow breakdown occured in the second

stage and propagated back through the compressor.

Figure 35 shows the TF41-A-! HP compressor model computed influence of uniform

inlet temperature ramp rates on compressor stability with nominal, cambered and axial IGV

schedules. The model results from Fig. 36 indicate that the nominal schedule produces

slightly less reduction in airflow for a given temperature rise at the inlet than the cambered

or axial schedules. This allowed stable compressor model operation with the nominal

schedule at approximately 15°R higher inlet temperatures than could be obtained with the

cambered or axial schedules for a given ramp rate.

Figure 37 shows the model predicted effect on compressor stability if the 5,000°R/see

inlet temperature ramp is imposed only on a 90-deg-arc circumferential section of the

compressor inlet. This case illustrates a combined effect of the temperature ramp and the

associated inlet temperature distortion. Model results presented in Fig. 37 indicate that

compressor surge occurs 15.2 percent below the steady-state stability limit at an inlet

temperature distortion level of 18.4 percent.

5.0 SUMMARY OF RESULTS

Validated TF41-A-! HP compressor mathematical models capable of aerodynamic stall

prediction were developed. The followirig summarize the specific efforts and analyses:

I.

.

.

A one-dimensional, steady-state model of the TF41-A-I high-pressure

compressor v+as developed based on compressor geometry and stage

characteristics formulated from experimental data for use in analyzing steady-

state compressor phenomena and compressor improvement. I=

The one-dimensional, steady-state model compu'tes compressor surge

pressure ratios within 2.4 percent of that observed experimentally for nominal, cambered, and axial IGV schedules over the corrected rotor-speed range of from

90 to 100 percent.

The one-dimensional, steady-state model computes compressor surge

pressure ratios within 4.0 percent of the experimental stability limits for nominal, cambered, and axial IGV schedules with seventh-stage bleed-valve-

open operation.

27

A EDC-TR-79-39

.

.

.

.

A three-dimensional, time-dependent TF41-A-1 HP compressor model was • /

developed for use in analyzing transient and dynamic d~sturbances with uniform

or distorted inflow.

The TF41-A-I three-dimensional, time-dependent model was subjected to pure

radial pressure distortion, pure circumferential pressure distortion, and pure

circumferential temperature distortion patterns of varying severity. Their influences on stability were computed. No specific experimental data for the

TF41-A-1 HP compressor subjected to these specific distortion patterns were available. Therefore, comparisons were made to experimental results from other

compressors• Trends and general magnitudes computed by the model agreed with the experimental results•

The TF41-A-i three-dimensional, time-dependent model was driven to instability by ramping inlet temperature at rates of 2,000, 5,000, and 10,000CR/sec to simulate ingestion of hot gases from gun or rocket fire. Ramp heights varied from 74 to 108°R with the 2,000 and 10,000°R/sec inlet

temperature ramp rates, respectively, at the cambered IGV schedule.

The aerodynamic instabilities that were encountered during model loading

simulations occurred in test surges and exhibited characteristics representing the actual physical instability.

R E F E R E N C E S

I. Kimzey, William F. "An Analysis of the Influence of Some External Disturbances

on the Aerodynamic Stability of Turbine Engine Axial Flow Fans and Compressors." AEDC-TR-77-80 (AD-A043543), August 1977.

2. "Maintenance Instructions, Intermediate, Technical Manual 2J-TF41-6." Detroit

Diesel Allison, October 1977.

3. Cohen, Henry, Rogers, G. F. C., and Saravanamuttoo, H . I . H . Gas Turbine Theory. Longman, London, 1972.

4. Pearson, H. and Bowmer, T. "Surging of Axial Compressors." The Aeronautical Quarterly, Vol. 1, No. l l, November 1949.

28

AEDC-TR-79-39

5. Goethert, B. H., Kimzey, William F., Huebschmann, Eugene C., Braun, Gerhard W., and Snyder, William T. "Research and Engineering Studies and Ai)alyses of a Fan Engine Stall, Dynamic Interaction with Other Subsystems and System Performance." AFAPL-TR-70-S1 (AD-872872), July 1970.

6. Cannahan, Brice, Luther, H. A., and Wilkes, James O. Applied Numerical Methods. John Wiley and Sons, New York, 1969.

7. Roache, Patrick J. Computational Fluid Dynamics. Hermosa Publishers, Albuquerque, New Mexico, 1972.

8. Distortion Induced Engine Instability. Neuilly Surseine (France), Advisory Group for Aerospace Research and Development, 1974.

9. Calogeras, James E., Mehalic, Charles M., and Burstadt, Paul L. "Experimental Investigation of the Effect of Screen-Induced Total-Pressure Distortion on Turbojet Stall Margin." NASA-TMX-2239, March 1971.

10. Mehalic, Charles M. and Lottig, Roy A. "Steady-State Inlet Temperature Distortion Effects on the Stall Limits of a J85-GE-13 Turbojet Engine." NASA-TMX-2290, February 1974.

29

No. 1

~0 w~

!

~ :3 0 . - ~

I I ' .l.a'" I F ~1 " l ~--Fuel • ~ ~ ~ Nozzle

2

-b

5 - . I

d

k

• ~ W.,4

-IP ,PI

// I I

I/

C u s t o m e r B l e e d P i p e - - J

Figure 1. TF41-A-1 turbofan engine schematic. m o o

-n

(D

Cooling Air Engine Inlet ^ . . . . . To¢l. ro,i /-~etl Cooling Air Manifotd Piping--~ uellmoum----~ ........ /

^ . ~.~. \ \ Cooling Air / [ Engine Support Mount ~emeru~i_~ t ~ \ r~ I / ~ nstirun~teted /~ /- l l th Stage Compressor I n-Bleed System

Test Cell ~ \ ] ~ / / ~ngens on-----, / / / /-TF41-A-1 /-Exhaust Ejector I nlet Duct Turbofan Engine -Test Cell

~ " ! ~ , , ~ - l ' x " l - - , ' ~ / - I I / I I I / k J ~ , . . . . i_m. I I m_ _ K i i l

\ "~ I ~ - I . - a b y r i n t h Seal / / / / / / I~ - ~ ,

i-k-- Jll . . . . .

Flow-Straightening Grid ~ ~ Z ~ o ~ _ S t r a i g \ w htening ~ ~nng:~ e-.I /_ FMl:xurt:d ~ , 1 i \111,1 i - i ~ i ~ - - " " ownstream B u l k h e a d ~ - O

\ " ".." • . . . . . . Thrust \ . . . . ~-Low-Pressure Turbine t, rtmary A~rT~ow- v~enum - ~mae~ . . . . • Cooling Air Discharge Line Measuring Venturi Stand Support (Replaced by 7-ft- Cart diam Duct When Removed)

m

-q -11

¢o

Figure 2. Installation schematic TF41-A-1 in Propulsion Development Test Cell (T-4).

I

I I

Telemetry Cooling Air Supply- -~

~.. . . ~ . -.

I , I

~ a t i o n 2 . 3 /

..... ~ ~ - - ~ ~

• /

1 / / I

/.-- Dyuami¢' Pressure L1,tes

./

!i

.~an D u c t

/ I 9-10 Spacer ----~

a n d A n t e n n a R x n g

No. 3 B e a r i n g

Figure 3. TF41-A-1 (Block 76) HP compressor schematic.

> I l l

c)

~0

tO

tO

L ~

4~

Sy__~m O Tota l P res su re X Tota l Temperature • S t a t i c Pressure • Dynamic P res su re

Airflow

343 deg 0 \ I

309

270 d e g - -

250 deg ~ ~

90 deg

124 deg

~-- HP Compressor Shaf t

I HP Compressor Case

] 80 deg

Four th-Stage Vane Row (Typica l )

m 0 0

Zl tO

Vane Tota l P re s su re (Leading Edge) Vane Wall S t a t i c Pressure

Vane Tota l Temperature (Leading Edge)

Vane High Response Wall S t a t i c P res su re

HLgh-Pressure Compressor

IGV 1 2 3 4 5

5 5 5 5 5

2 2 2 2 2

10 10 I0 I0 i0

1 1 1

6 7 8 9 10 11

6 6 6 6 6 6

2 2 2 2 2 2

6 6 6 6 6 6

1 1 1

Figure 4. HP compressor interstage instrumentation.

~ J

~J

3o b--4

0 .e4

20 .e4

0

°

10

.~,-4

r~ 0

40 -

m

m

-10 ' 8,000

Experimental Data

Sy___mm IGV Schedule

0 Nominal

Cambered (-I0 deg)

[] Axial (-10 dcg) ~--M72-3 Vane Schedule

/ ( R e £ . 2) Engine I n l e t ~ ~ ~ ~ ~ Temperature = 59°F

Open B l e ° d ~ - t ~ 0 ~ _ / I T e s t i n g ~ ~ ~

. . .T ( S e a - L e v e l - S t a t i c ) ~ ..

I I 8,400 8,800

~ Closed Bleed ~ ~ ~ Test ing ~ _ ~ ~ / - - - M 7 2 - 3 Vane Schedule (30 000 f t , , ~ ~ ~ / ( R e f . 2) Engine I n l e t MO -- O. 7) ~ ~ ~ / Temperature = -8°F

I I I I I I [ I 9,200 9,600 10,000 10,400 10,800 11,200 11,600 12,000

High-Pressure Rotor Speed, NH, rpm

Figure 5. TF41-A-1 IGV schedules.

m o o

tO

~N

4-~

==

O

a)

O*

O r~

8 ° 0

7.0

6 . 0 - -

5 . 0

4 . 0 - -

3 . 0

38

_'j

Experimental Data

Sy___mm IGV Schedule

O Nominal

Cambered (-10 deg)

O Axial (~]0 deg)

Solid Symbols: Surge Points

/-=- Stability Limit / (Surge Line)

/

L ~ N o r m a l Operating Line

26-percent Surge Margin

I I I I I I I I 40 42 44 46 48 50 52 54

HP Compressor C o r r e c t e d A i r f l o w , W24 ,~24/524 , lbm/sec

I 56

rn O ¢3 :4 -n

co ¢3 (D

Figure 6. Effects of IGV schedule on TF41-A-1 HP compressor stability limit at 30,000 ft, Mach number 0.7 with seventh-stage bleed valve closed.

~J

Experimental Da ta

Sym IGV Schedule

0 Nominal

6.0 ~ Cambered (-10 deg) j-=-Stability Limits Q Axial (~10 deg) ~ (Surge L i n e s )

So l i d Symbols: Surge P o i n t s / ~ 30

5.0 Bleed /// ' .~'~"'~"~" Valve P o s i t i o n 100 . ~ (Percent Open) ~"~'~8 00.~ "sl~" ~"

4.0 BVP ffi 1 0 0 8 . ~ ~ I ° v ~ 4 0 ~ 3 0

m - N Ormal

~-- 4 1 - p e r c e n t Surge Margin

2.0 ~- - 4 1 - p e r c e n t o s Surge Margin "

i i i i l i I i i 1.0 2 0 2 2 2 4 2 6 2 8 3 0 3 2 3 4 3 6 3 8

HP Compressor E x i t A i r f l o w C o r r e c t e d to Compressor Inlet,

I 40

W 3 ~ 2 4 / ~ 2 4 , l bm/sec

Figure 7. Effects of IGV schedule on TF41-A-1 HP compressor stability limit at sea-l.evel-static conditions with seventh~tage bleed valve open.

m o

;0

¢o

¢o

A E OC -T R -79-39 %

Time

+2.5 PDI

.~ (Stage I ) 0

- 2 . 5

d_~ +2.5 ~_ PD2 0

(Stage 2) -2.5 o u ~ +2.5

PD4 0 o (Stage 4)

m PD6 0 (Stage 6)

-2.5 r

+2 5 ~ • 4 •

PD8 0 (Stage 8) -2.5

u + 2 . 5 ~ ' 4

N PDIO 0 (Stage 10)

-2.5

~--Initation of Surge

Altitude = 30,000 ft ch Number = 0.7

Figure 8. Surge induced by inbleed at NH = 11,500 rpm with axial IGV schedule.

38

AEDC-TR-79-39

11[ 1.O

0 . 9

A l t i t u d e = 3 0 , 0 0 0 f t Mach Number = 0 . 7 NH = 1 0 , 3 2 5 rpm w i t h Nominal

IGV S c h e d u l e

S t a g e ] I n l e t

1 . 1 [ S t a g e 2

1 . 0 -1:9_ 0

"~ 0 . 9 ,r,I

S t a g e 3 0 C

0.

'I F S t a g e 4

I .O . 0 0

0 . 9 I I 0 20 40 60

Vane Span from lIub, percent

I 8O

- 0

I 100

a. Stages 1 through 4 Figure 9. Radial total pressure profiles with uniform engine inlet flow.

39

AEDC-TR-79-39

1 , 1 q' S t a g e 5 I n l e t

lO o 1 1 - o -

0 . 9

A l t i t u d e = 3 0 , 0 0 0 f t Mach N u m b e r = 0 . 7 NH = 1 0 , 3 2 5 r p m w i t h N o m i n a l

IGV S c h e d u l e

0 0

S t a g e 6

1 . 0

"~ 0 . 9

Stage 7 P4

1 . 0

0 . 9

~0 0 0

0 0 0

1, f , C ~ 1.O ~ 0

o.9 I I I I 0 20 40 60 80

Vane Span from Hub, percent

b. Stages 5 through 8 Figure 9. Continued.

I i00

40

A E DC-TR -79-39

..1[ 1 0

0 . 9

A l t i t u d e = 30 ,000 f t Mach Number = 0 .7 N}I = 10 ,325 rpm w i t h Nominal

IGV S c h e d u l e

S t age 9 I n l e t

~ O

"E 1 . 0

0 . 9 ,e4

m

Stage" 11

0 . 9

- O

~ O

i . I ~ D i s c h a r g e

l O

0 . 9 i 0 20

C ~ 0

I I 40 60

Vane Span from Hub, p e r c e n t

c. Stages 9 through discharge Figure 9. Concluded.

I 8O

~D

I 1 0 0

41

AEDC-TR-79-39

Altitude = 30,000 £t ~lach Number = 0.7 NH = 10.325 rpm with Nominal

IGV S c h e d u l e

1 . 1 F S t a g e 1 I n l e t

l O [ ~ 0

0 . 9

C 0 0

i.i ~ S t a g e 2

1,0

"~ 0 . 9 . r , l

1 . 1 ~v F S t a g e 3

2

L I.O C'~

0.9

0 O~ - G -

- 0

iI F S t a g e 4

l O C ~ 0 - -0

0 9 I I I I IO0 0 ' 20 40 60 80

Vane Span f rom Hub, p e r c e n t

a. S~ges 1 through 4 Figure 10. Radialtotaltemperature profiles with uniform engine inlet flow.

42

A EDC-TR-79-39

A l t i t u d e = 3 0 , 0 0 0 f t Mach Number = 0 . 7 N i l ffi 1 0 . 3 2 5 rpm w i t h N o m i n a l

IGV S c h e d u l e

1.1 F S t a g e 5 I n l e t

lO ~ C-- C~

0 . 9

0 - 0 -

I . I S t a g e 6

1 . 0 o - - l,J

'~ 0 . 9

S t a g e 7 - - 0

[.-, 1 . o ~ 0 --0-

0 . 9

1 . 1 F S t a g e 8

lO ~ 0 . 9 I I I

0 20 40 60

Vane Span f r o m Hub, p e r c e n t

b. Stages 5 through 8 Figure 10. Continued.

I 8O

0

I 100

43

AEDC-TR-79-39

1I f 1 . 0

0 . 9

A l t i t u d e = 3 0 , 0 0 0 f t Mach Number = 0 . 7 NH = 1 0 , 3 2 5 rpm w i t h N o m i n a l

IGV S c h e d u l e

S t a g e 9 I n l e t

- - " C - - O

1 . 1

>~ 1 . 0

0 . '9

~ I. i

1 . 0

0 . 9

S t a g e 10

S t a g e 11

11f Dis°barge 1 .0 O r

o . 9 I I I I 0 20 40 60 80

Vane Span f rom Hub, p e r c e n t

c. Stages 9 through discharge Figure 10. Concluded.

I i00

44

ID

t ~

1 2 3 4 5 6 7 8

i'ii 'r' ~- Inlet -~

Ducting r

~Stage Number

9 10 11 12 13 14 15 16 ]7 18 19 20 21

I [ II I I i J

High-Pressure Compressor - . . . ~ . ~ F J ( i t Ducting

Figure 11. Station locations (computational planes) for one<limensional, steady-state compressor model.

~>

m 0

-n

t o

t o

A EDC-TFt-79-39

A

W

PS

U

' H

l ~- dz ~~I WB

I

WS dz + Q dz

A +~dz bW .~ W +~--~ dz

~PS PS + ~ dz

~U U + ~-~ dz

~H ' H + ~-~ dz

Figure 12. Elemental control volume wi*.h application of mass, momentum, and energy conservation principles.

45

A E D C - T R - 7 9 - 3 9

e=

Q;q=l ,,~ ~,-~

• ~ 0

S t a g e Flow C o e £ ~ i c i e n t ,

a. Temperature coefficient

°pI ~ , . ~

. l - ~O c/} r,..~

S t a g e Flow C o e £ f i c i e n t ,

b. Pressure coefficient Figure 13. Typical temperature and pressure coefficients as functions

of flow coefficient at constant rotational speed.

47

A EDC-TR -79-39

0 . 5 m

%

0.4 -- ~ ~ ~ 5 --5. 3

0 3 - -

/ - - S e v e n t h - ~ # / 0 2 S tage Bleed V / St.~ge ~leed \ 11 ~ n l e t ~uide

| / v a lve ~ ± ± ~ f Vane Angle • = 'en \18 (IG,), deg

~ 6 0 1

0 4

% 0 3 -5.5

.o 4 0 3 0 2

| / Stage Bleed I / / ' In le t Guide L I Valve Full t __ ~ Vane Angle

~ 0 1 ~ ~ pen . . . . . I / ~ (IGV), deg

• ~ 36 ~ I I 0 0.48 0.52 0.56 0.60 0.64 0.68 0.72

Flow C o e f f i c i e n t ,

a. S tage 1

Figure 14. TF41-A-1 HP compressor stage characteristics.

48

A E D C-T R -79 -39

JcJ e.

¢J °~ ¢H q.d

0

a; [,-4

0.5

0.4

0.3

0.2

0.I

i 'l

S e v e n - 5 .

"--~;d 36 ~.IGV, deg

I I I I I I

0 . 4 ~

o . 3 - ,

¢J .Pi

0 .2 - O O r~

= 0 . 1 -

0 0 . 4 4

Seventh-Stage / \ \ ~ ~ 4 / Bleed Valve / ~ ~ " 0 / Full Open --...--J \ ~ _ 3 / ~ IGV, deg

-5.5J

I J i i I J 0 . 4 8 0 . 5 2 0 . 5 6 0 . 6 0 0 . 6 4 0 . 6 8

F l o w C o e f f i c i e n t ,

b. Stage 2 Figure 14. Continued.

49

A E D C-T R -79-39

0,5 --

J = 0.4 -

u .,~

o 0 . 3 c.)

0.2 -

E

0.I

1 8 -

/ ~6 -°'~ S e v e n t h - S t a g e / Bleed Valve / Full Open ----d

I i i I

I G V , d e g

I

0 , 4 ~

0 . 3 -

e. 0J

~. 0 . 2 - <9 o r~.

= 0 1 -

~..

0

0 . 4 8

• 1 1

-5.51

S e v e n t h - S t a g e / Bleed V a l v e / F u l l O p e n - - - - ~

I I I 0 . 5 2 O. 5 6 0 . 6 0

F l o w C o e f f i c i e n t , %

c. Stage 3 Figure 14. Continued.

I 0 . 6 4

, I G V , d e g

J 0 . 6 8

50

A E D C-T R -79-39

~ o . 4 -

.r4

,r4 ~ 0 . 3 -

0

0 . 2 - 4J

o~

E ~ O . 1 I I

S e v e n t h - S t a g e B l e e d V a l v e .

u l l O p e n

I ! I

deg

0 . 4

0 . 3 4~

,r4 U

0 . 2

0

0 . 1 LO

0 0 . 4 4

I J I 0 . 4 8 0 . 5 2 0 . 5 6

F l o w C o e f f i c i e n t ,

d. Stage 4 Figure 14. Cont inued.

S e v e n t h - S t a g e B l e e d V a l v e . F u l l Open

36

18j 11

:i I I

0 . 6 0 0 . 6 4

IGV, d e g

51

A EDC-TR-79-39

4 -

C

0

E

0 . 5 B

0 . 4 B

0 . 3 -

0 . 2 - -

0 . 1

S e v e n t h - S t a g e B l e e d \ V a l v e F u l l O p e n ~

I I I I I

36

181 11 4 0

-3 - - 5 .

IGV, deg

0 . 4 D

~ " 0 . 2 0 0

m O.I- Q)

0 0 . 4 0

Seven t h - Stage V a l v e F u l l Open 11

4 0

-3 - - 5 .

I I I I I I 0 . 4 4 0 . 4 8 0 . 5 2 0 . 5 6 0 . 6 0 0 . 6 4

Flow C o e f f i c i e n t ,

e. Stage 5 Figure 14. Continued.

IGV, deg

52

A E D C-T R-79-39

~ 0 .4

o.3

S e v e n t h - S t c~ / Bleed Valve- ~ ~ _

O. 2 3 IGV, • deg

E-, 0 . i

o~

. , - I ¢J

.,.~ ¢I-I

c @ D u}

0 , 3 m

0 . 2 B

0 . 1 -

0

O. 40

I

0.44

/ / L - S e v e n t h - S t a g e 4

/ "-- ~ F ~ i i d 0 ~ ve _~ . J

I I I I

0.48 0.52 0.56 0.60 0.64

Flow C o e f f i c i e n t ,

f . S t a g e 6 Figure 14. Continued.

IGV, deg

53

AE DC-TR-79-39

0 , 5 m

4,J = 0 . 4 --

v~

0 . 3 -

i.i

= 0 . 2 - -

E Q

0 . 1

S e v e n t h - S t a g e Va lve F u l l Open

l i

.5 L I I I

IGV, deg

0 . 3 m

O .,~ O . 2 - ¢J

o,4

O

0 . 1 -

w,

~ ~ o 0 . 4 0

I 0 . 4 4

is 1

S e v e n t h - S t a g e B l e e d / ~ 36 Va lve F u l l Open - - - J

I I I 0 . 4 8 0 . 5 2 0 . 5 6

F l o w C o e f f i c i e n t ,

g. Stage 7 Figure 14. Continued,

i I 0.60 0 .64

IGV, deg

54

A E D C-TR -79-39

E- 0 . 4 --

.4-..

~D

. r4 0 ,3 -

o

0 . 2 -

t~

~, 0 . 1

Valve F u l l O p e n - - - - - / X - 5 .

\ 36

I I I I l " J

IGV, de.~

• ~ O. 2

o~ F u l l Open IGV,

\El deg

0 . 1

o i I I I i I 0 .40 0 .44 0 . 4 8 O. 52 0 .56

Flow C o e f f i c i e n t .

h. Stage 8 Figure 14. Con t i nued .

0 . 6 0 0 . 6 4

55

A EDC-TR-79-39

[.., ~ 0.4 --

°P(

.~ 0.3 - o~

0

0 2 --

~ •

Seventh-Stage Bleed

Valve Ful l Open 7 _..._.36 1 1

- - 1 1

4 0

-3 ~ °

I I I ] I I

IGV, deg

0 . 4

0 . 3

r~

0 . 2 o r~

r~ 0.1 o r,.,,

0 O. 40

I

0 . 4 4

Seventh-Stal Bleed Valve Ful l Open--

I I I

0.48 0.52 0.56 Flow C o e f f i c i e n t ,

i. Stage 9 F igu re 14. C o n t i n u e d .

11

3 6

I

0 . 6 0

IGV, deg

I 0.64=,

55

A E D C - T R -79 -39

0 . 4 - -

~2 ID .r,i

u 0 . 3 - .H

0

¢ 0 . 2 -

4.J

0.i

11 4

_ I G V ,

- 5 . d e g

I I I I I I

0 . 3 --

,r,( u 0 . 2 -

.,-I ¢,-.l

O ¢.J

0 . 1 -

,.e

<V

~ 0 0 . 4 0

~ 3 6 "~

11 / B l e e d V a l v e 4 I G V ,

F u l l O p e n 0 d e g - 3 - - 5 .

i I I I 1 I

0 . 4 4 0 . 4 8 0 . 5 2 0 . 5 6 0 . 6 0 0 . 6 4

Flow C o e f f i c i e n t ,

j. Stage 10 Figure 14. Continued.

57

A EDC-TR-79-39

~" 0 . 4 ~

.~ O.

0 - o 18

4 o

Bleed Valve / ~ -3 0 Full Open---/ ~ -5.

36 o I I I I i

IGV, deg

o .,.i 0

.el

o o

u}

0.3

0 .2

0 . 1 m

o I 0.40 0 .44 0 .48

F S e v e n t h - S t a g e Bleed Valve F u l l Open a t 36 deg

'1 - - 5 °

18 I ] I 1 1 I

0 . 5 2 0 . 5 6 0 . 6 0

Flow Coefficient,

k. Stage 11 Figure 14. Concluded.

IGV, deg

I 0 . 6 4

5 8

t ~

8 . 0 - -

co

7 . 0 - o" ~a

6 . 0 -

5 . 0 -

o 00

4 . 0 -

3 . 0 38

E x p e r i m e n t a l D a t a

Sym IGV r d e g N H / ~ 2 4 p e r c e n t P

O 1 8 . 0 +_ o . 4 8 9 . 4 t o 9 2 . 2 A 1 3 . 0 + o . 2 9 1 . 9 t o 9 3 . 9 [] 4 . 0 + 0 . 1 9 2 . 8 t o 9 6 . 4 ~, - 3 . 0 + 0 . 2 9 5 . 9 t o 9 8 . 7 F E x p e r l m e n t a l S t a b i l i t y

S o l i d S y m b o l s : S u r g e P o i n t s / L i m i t - / 1 . 0 % " J .

i.i% / ..~_~---~"

o. 2% ~ - . . ~ []

, L~ ~ A ~ / - 3 deg

3 deg ~m/.~F'- q~ S t e a d y - S t a t e Mode l . . . . . . . ~A = 9 0 . 8 ~

~ C o m p u t e d C h a r a c t e r i s t i c s IGV = 18 d e g a n d S t a b i l i t y L i m i t s

( a t M i d - P o i n t o f

Figure 15.

40 42 44 46 48 50 52 54

I~P C o m p r e s s o r C o r r e c t e d A i r f l o w , W 2 4 ~ 2 4 / 5 2 4 , l b m / s e c

a. Nominal IGV schedule Comparison of model computed speed characteristics and stabil i ty l imits with Experimental measurements at 30,000 f t , MO = 0.7.

56

m

f~ q

tO

tO

O~ 0

E x p e r i m e n t a l Data

Sym IGV, deg N H / ~ 2 4 ' p e r c e n t

O 1 8 . 7 + 0 . 1 9 3 . 1 t o 9 5 . 9 A 1 1 . 0 + 0 . 2 9 5 . 4 t o 9 7 . 8 [] 1 0 . 8 + 0 . 1 9 8 . 0 t o 1 0 0 . 0

S o l i d S y m b o l s : S u r g e P o i n t s S . O -

¢q

0~ 7 . 0 -

d °r,I

6 . 0 - N

S,!

5.0 -- o u~

4 . 0 - E 0

~3

¢k =¢

3 . 0 38

/

oEXper i m e n t a l S t a b i l i t y L i m i t

,---1.5% .2% . ~ ~

0.1% J ~ ' T '

" _ ~ 99.0% ~ 0 96.6% / 1 0 . 8 deg

~H/,~.,~ 94.5~ ~ / ~ ~ S t e a d y - S t a t e Model Computed IGVffi 1 8 . 7 deg

C h a r a c t e r i s t i c s and S t a b i l i t y L i m i t s ( a t M i d - P o i n t o,' N H / ~ 2 4 V a r i a t i o n )

I I I I I I I I I 40 42 44 46 48 50 52 54 56

HP C o m p r e s s o r C o r r e c t e d A i r f l o w , W 2 4 ~ 2 4 / ~ 2 4 , ] h m / s e c

~> i l l o o

-n

to

t o

b. Cambered IGV schedule Figure 15. Continued.

cq

co

6 ,r4 J~

h

0

~n ~D

m.,

I=

E x p e r i m e n t a l D a t a

Sym IGV, deg

O 4 . 2 +_ 0 . 1 A - 0 . 3 + 0 . 1 [ ] -5.5 + 0.i tk - 5 . 4 + 0 . 1

8 . 0 - - O - 4 . 9 + 0 . 1 Solid Symbols :

7 . 0

6 . 0

5 . 0

4 . 0

3 . 0

N H / ~ 2 4 , p e r c e n t

8 9 . 9 t o 9 1 . 5 9 1 . 5 t o 9 3 . 3 9 2 . 8 to 9 4 . 8 9 5 . 1 t o 9 6 . 7 9 6 . 3 t o 9 8 . 3

S u r g e P o i n t s

38

0.6% Experimental Stability O. 7%

i A ~ ~ ' ° ",~ -I~ "1 °

/ O ' ~ ~ : 0 ~ 9 3 8: 955:49~$deg~ 7"'~%de6 k 9,.. ~,~",<5.5 d e ~

IGV= 4 . 2 deg Steady-State Model Computed Characteristics and Stability Limits (at Mid-Point of NH/4~2 4 Vat ia t ion )

[ I I I I I I I 40 42 44 46 48 50 52 54

HP C o m p r e s s o r C o r r e c t e d A i r f l o w , W24,~224/024 , l b m / s e c

c. Axial IGV schedule Figure 15. Concluded.

I 56

m

c) q

(D

O~ t J

8 . 0

cq

7.0

o" 4J

6 . 0

u~

5 . 0

O

4.0

Experimental Data

sym

O 9 3 . 3 A 9 2 . 3 I-I 9 1 . 6

9 1 . 5 Sol id Symbol :

NH/~24, percent

Surge Point f

J

9 3 . 3 ~ 92. 3 % - - 7 #

NH/, ,~24 = 91.

~ d y - S t a t e Model Computed Character i s t i cs and S t a b i l i t y Limits

O. 8% _ , , . , ¢ . -

0.7% 0. ,, - , 9 % ~ / r ~__Experimental 0 . ~ ~ ~ Stabt l tty Limit

/ /

3 . 0 ! I 1 I I I 1 I 38 40 42 44 46 48 50 52 54

HP Compressor Corrected Alrflow, W24~224/524 , lbm/sec

Figure 16. Model computed effect of corrected rotor speed variation for -0.3<leg IGV line axial IGV schedule at 30,000 ft, MO = 0.7.

m

-n

co

¢D

c ~

c~

o" .e4 4a

=¢

O

o~ O

6 . 0

5.0

4 . 0

3 .0

2 . 0 - -

1 •

2O

E x p e r i m e n t a l Data

Sym IGV, deg NH/~24 ' p e r c e n t

O 36 .0 ± 1 84 .7 to 85 .7 3 2 . 0 ± 2 8 7 . 0 t o 8 8 . 6

Q 2 6 . 7 ± 1 8 8 . 5 t o 9 0 . 9 S o l i d Symbols: Surge P o i n t s

BVP, p e r c e n t

1 0 0 8 0 30

) e r i m e n t a l S t a b i l i t y ~ i EXI

•NH•• _24 87. 26.7 deg

= 8 5 . 2 ~ a d y - S t a t e ~ Model Computed C h a r a c t e r i s t i c s and S t a b i l i t y

IGV ffi 36 deg L imi t s ( a t Mid -Po in t of NH/~24 V a r i a t i o n )

I I I I I I I , I I , J 22 2 4 26 2 8 3 0 3 2 3 4 3 6 3 8 4 0

HP Compressor E x i t A i r f l o w C o r r e c t e d to Compressor I n l e t , W3~24/~24, l bm/ sec

a. Nominal IGV schedule Figure 17. Comparison of model computed speed characteristics and stability limits

with experimental measurements with seventh-stage bleed valve open at sea-level-static conditions.

> rn o C~

-11

¢O

(D

o% 4~ o ~

C~4~ E O~ ~J

5 . 0

4 . 0

3 . 0 m

2 . 0 -

1.0 20

E x p e r i m e n t a l D a t a

Sym IGV~ d e g NH/~24' p e r c e n t

O 3 4 . 0 ± 2 . 0 9 0 . 0 t o 9 2 . 0

S o l i d S y m b o l s : S u r g e P o i n t s

BVP, p e r c e n t

1 0 0

E x p e r i m e n t a l Stability Limit

0 . 1 % ~ S t e a d y - S t a t e Model Computed C h a r a c t e r - i s t i c s a n d S t a b i l i t y Limits ~t Mid-Point of NH/4@~Varlation)

NH/8~24 = 91.0% IGV = 3 4 d e g

I 32

I I I I I 22 24 26 28 30

HP C o m p r e s s o r E x i t A i r f l o w C o r r e c t e d t o C o m p r e s s o r I n l e t , W 3 ~ 2 4 / 5 2 4 , l b m / s e c

b. Cambered s chedu le Figure 17. Continued.

m O

to

6 . 0

~¢~ 5 . 0

4~

4 . 0

3 . 0

0

u~

n . E 0

r.J

D

2 . 0 - -

1 . 0 2O

Experimental Data

Sym IGV, deg NHA~224' p e r c e n t

O 2 8 . 3 8 5 . 4

S o l i d Symbol: Surge P o i n t

BVP, p e r c e n t

40

Experimental Stability Limit .

4.0% ~ _ _ ~ - - - " . L I

i 41~ l~-~N~/~24 Steady-State Mode = 85. 4% Computed C h a r a c t e r i s t i c _ ~ _ ~ IGV 2 8 . 3 deg and S t a b i l i t y L i m i t s

I

N o t e :

I

22

Constant IGV could not be maintained experimentally with the axial schedule; therefore, only the surge point is presented.

I I I I I,, I 24 26 28 30 32 34

HP Compressor E x i t A i r f l o w C o r r e c t e d t o Compressor I n l e t , W 3 ~ 2 4 / 5 2 4 , l b m / s e c

I 36

c. Axial schedule Figure 17. Concluded.

I 38

m

c~

-n

t O

AEDC-TR-79-39

0.7

.; o 6 ,~1

0.5

• '~ 0 .4 . t - (

Altitude = 30,000 ft Mach Number = 0.7 Axial IGV Schedule

Sy__m_m

0 Exper imen ta l Measurement Nea res t Surge Line

[] Computed

Stage i

1 I I I

0"7 F / - - - ~ S t a l l /

~ == o . 6 ~ 0 . 5

o 0.4

0 . 7 [ - / - - - - .~ S t a l l Z

0.6 _ _ -

.~ 0 . 5 I S t ag ; 3 0 .4

0

o

bO c~

(/3

0 . 7 m

0.6 ~ S t a l l

0 .5 Stage 4

0 .4 I I 90 92 94

I I I

o__-o---o-

I I I 96 98 1 0 0

NH/~, p e r c e n t

Figure 18. a. Stages 1 through 4

Comparison of model computed stage f low coefficients near compressor stability l imit wi th experimental measurements, IGV at full axial position (-5.0 + 0.5 deg).

66

A E D C - T R - T 9 - 3 9

Altitude = 30,000 ft Mach Number = 0.7 Axial IGV Schedule

Sy__~m

0 Experimental D Computed

i 0.6

0 .5 Stage 5 • - O. 4 ,p,I ,m

rn ~ 0 . 7 ~

0.6

~ 0.5 Stage 6

o ~ 0 .4 CJ

0.7 -

Z

,~ * ~. 0.6 i Stage 7 u 0.5 , e l

~" 0 4 I c

0.7 O

r-4

~-' 0 .6 (9 b¢

0 5

0.4 9O

m

F .~ Stall

:e8 I 92

o_-o---a-

I l I f

o----a-----D-

l I I I

94 96 98 100

N]-[/.~@, percent

b. Stages 5 through 8 Figure 18. Continued.

67

A EID C-TR -79-39

A l t i t u d e = 3 0 , 0 0 0 f t Mach Number = 0 . 7 A x i a l IGV S c h e d u l e

Sy__~m O E x p e r i m e n t a l

0 . 7 C] . Computed

0 . 6 ~

0 . 5 S t a g e 9 i

, r 4

0 . 7 ,e.4 ~.r4 ~ 0 6

o.~ 0 . 5

~N o o 0 . 4 r,r.l ~1 ¢ ~ 0 . 7

~ o ~ 0 . 6

0 . 5

0 . 4 90

m

~ ~ S t a l l m

age 11 I

92 I I J

94 96 98

N H / ~ , p e r c e n t

I I 0 0

c. Stages 9 through 11 Figure 18. Concluded.

68

A E DC-'f R--/9-39

B

1 . 4 m

1 . 3

A l t i t u d e = 3 0 , 0 0 0 f t M a c h N u m b e r = 0 . 7 A x i a l I G V S c h e d u l e

Sy__.y_m

0 £]

E x p e r i m e n t a l M e a s u r e m e n t N e a r e s t S u r g e L i n e C o m p u t e d

. r 4

E "~ 1 . 2 ,-3

+~ 1 1 • p4 °

, " 4

1 . 4 -

1 . 3 - o

'~ 1 . 2 -

E 1 . 1 c L~

1.4 -

z 1.3 -

o .p4 4-" m 1 . 2 -

0~ 1.1

u)

1 4 -

c~ 1.3

- S t a g e 1

I

o~ 1 . 2

I I I I

S t a g e 2

I I I I

S t a g e 3

I I I I 1

- S t a g e 4

1.1 I I I I I 9 0 9 2 9 4 9 6 9 8 1 0 0

N H / ~ , p e r c e n t

a. Stages 1 through 4 Figure 19. Comparison of model computed stage pressure ratios near

compressor stability limit with experimental measurements, IGV at full ~xial position (-5.0 +- 0.5 deg).

69

A E D C-TR -79-39

E

4~

,F4

o

®

o

o

+~

a)

1 4 -

1 3 -

1 2 -

1 1

1 4 -

1 3 -

1 2 -

I.i

1.4 -

1.3 -

1.2 -

I.I

1.4

1.3

1.2 -

1.1

90

A l t i t u d e = 3 0 , 0 0 0 f t Mach Number = 0 . 7 A x i a l IG¥ S c h e d u l e

Sym

O E x p e r i m e n t a l [] C o m p u t e d

S t a g e 5

I I l I

S t a g e 6

-o-----c O----.o-----a- I I I I

S t a g e 7

I I I I

S t a g e 8

I I I I

92 94 96 98

NH/~@, p e r c e n t

b. Stages 5 through 8 Figure 19. Continued.

i /

I 100

O

70

A EDC-TR-79 -39

4-J

• ~ 1 . 4 - - . r 4

1 . 3 - 4-~

.e4

1 . 2 - .e4 e~

1 . 1 ~o

~ 1 . 4 -

~ 1 . 3 m.

o ~ 1 . 2

o 1 4 - , r , i •

4 -

el

~- 1 . 3 o N

o

I~ •

~ 1 . 0

"~ 9 0 r.¢l

S y m

0 [3

Altitude = 30,000 1"t Mach Number = 0.7 Axial IGV Schedule

Exper imen ta 1 Compu ted

S t a g e 9

-0---7--0 i I

- S t s g e 1 0

m

- S t a g e 1 1

B

- - - 0

I 9 2

I I I 9 4 9 6 9 8

N H / ~ , p e r c e n t

c. Stages 9 through 11 Figure 19. Concluded.

I 1 0 0

71

A EDC-TR -79-39

1.12

• ,4 1 . 0 8 E

.p4

1 . 0 4

4~ .el 1 . 0 0 ,~I

1 1 2 4-~ 0~

1 . 0 8 o m m ¢ 1.04

E o 1.00

1.12 Z

o 1.08 +~

= 1.04 i

m . 1 . 0 0 4~

m 1.12

1.08

1 . 0 4

0~

1 . 0 0

Figure 20.

A l t i t u d e = 3 0 , 0 0 0 f t M a c h N u m b e r = 0 . 7 A x i a l IGV S c h e d u l e

Sym

O []

E x p e r i m e n t a l M e a s u r e m e n t N e a r e s t S u r g e L i n e C o m p u t e d

J j G - - - - Q - - - - - o -

S t a g e 1

I I I I I

--(3 G

S t a g e 2

0 - - - - - 0 - - - - - - o -

S t a g e 3

l

G-- - - - -C O - -

I I I I

n

S t a g e 4

I 9 0 9 2

a.

I I 9 4 96

NH/~, p e r c e n t

Stages 1 through 4

I 1 98 I 00

Comparison of model computed stage temperature ratios near compressor stability limit with experimental measurements, IGV at full axial position (-5.0 + 0.5 deg~

72

AEDC-TR-79-39

1.12 -

+~ 1 . 0 8 - .pI

I . 0 4 -

J,.J • ,~ 1. O0 r-4

,r4

1 . 1 2 -

~ 1 . 0 8 - 0

~ 1 . 0 4 -

I O0 0 C~

I .12 -- o Z

o 1.08 --

J~

I .04 --

@

1. O0 J~

1.12 -

B ~_, 1.08

1.04 +J ¢n

1.00

Altitude = 30,000 ft Mach Number = 0.7 Axial IGV Schedule

Sym

O Experimental 0 Computed

J

-o--=--o op==.=Q.=..==, o

Stage 5

I I I I

Stage 6

u

I I I I

Stage 7

-c - 8 - - - 8 - - - - o - ~ r

I I I I

Stage 8

- - o - - - - o _o

I I I I 9 0 9 2 9 4 9 6 9 8

N H / ~ , p e r c e n t

b. Stages 5 through 8 Figure 20. Continued.

! I00

73

AEDC-TR-79-39

a).r4 Z~

O~ .,4

~.~

m 4~4~ ~D3

~O

I,i

1.12

1.08

1.04

1.00

Altitude = 30,000 ft Mach Number = 0.7 Axial IGV Schedule

Sy___~m O Experimental O Computed

S t a g e 9

~ O - - - - - O - - - - - e -

l I I I

1.12 -

1 . 0 8

1 . 0 4

1 . 0 0

_ S t a g e i0

_ . . ~ ~J

I

o - - - < z - - - - - o -

I I

1 . 1 2 -

1 . 0 8 - S t a g e 11

1 . 0 4 -

- - - 0 0 l .OO I

90 92

I I I 9 4 9 6 98

NH/,,~, p e r c e n t

I i00

c. Stages 9 through 11 Figure 20. Concluded.

74

AEDC-TR-79-39

/ / ~ ~ i Volume / ~ _ ~ ~ ~ j n ffi 4*

2 ~ ~ ~ ( ~ 6 kn ffi 6 .

p Denotes + 1 / / / ~ . ~ ~ m D e n o t e s - 1 I ~ ~ ~ " ' ) ~ ~ }

3 5

. F r o n t View

~ ~ . ~ 2 j ffi 1

I ~ 1 ~ ~ in = 5 (Example Presented) 3 f i = 1 2 in ffi 12 (TF41-A-1 Model)

- ¢ S i d e View

* i n a n d kn s e l e c t i o n i s on a c a s e - b y - c a s e b a s i s a s r e q u i r e d t o d e f i n e t h e d i s t o r t i o n p a t t e r n u n d e r i n v e s t i g a t i o n .

Figure 21. Division of compressor into control volumes.

75

A EDC-TR-79-39

WCi j kp HCi j kp wi j kp"

WZ. i j k

HZi j k

uij k

WRi jp k HRi jp k vi jp k

\ \ \

/

/ /

9'

~ m

I I

I

WZip j k

HZip j k Uip j k

/ "ci j k / wi j k

J HRi j k vi j k

AZi j k s

Figure 22. Control volume velocities and fluxes.

ACi j k

r

V

76

~J

Compute V a r i a b l e s a t Each Plane

E n t r y P lane C o n d i t i o n s

Wl J k " W(PU1 j k' A1 j k )

MZ j k m M(Pl 3 k' TI 3 k' wl J k' A1 3 k)

TS1 j k " TS(T1 j k ' MI J k )

PS1 3 k = PS(P1 j k ' M1 j k )

Pl J k " P(PS1 3 k ' 'PSI 3 k)

XI J k = X(PS1 3 k ' M1 j k )

I n t e r i o r P lane Va lues

Ui j k " U(Wt j k ' Pi 3 k ' At j k )

' l~i 3 k " TS(Xl 3 k ' Pl ,~ k ' Ui j k )

PSi j k = PS(Pi ,J k ' TSi j k )

Tt J k = T(TS£ j k ' UZ" ,,j k )

Pi 3 k = P(PSi 3 k ' 'Ci 3 k ' TSi 3 k )

Mi j k = M(Ux 3 k ' 'PSi 3 k )

IMPI j k = IMP(PSi J k ' At 3 k ' Mi J k ) = )

Hi 3 k H(Wi j k ' TI ,J k ' CPt j k

E x i t P lane C o n d i t i o n s

PSI2 J k " PS12 j k

M12 j k = M(Xi2 J k ' PSIp J k )

TSI2 J k " TS(PSI2 j k ' PI2 j k )

UI2 J k " U(M12 3 k ' TSI2 J k )

W12 j k = W(Pl2 3 k' U12 J k' AI2 J k )

41

i ]

At t - 0

At t > 0 I

I n i t i a l C o n d i t i o n s [

Pi J k ( t " 0 ) , pUt j k ( t - 0 ) , X i J k ( t = 0)

Mod i f ied Runge -Ku t t a I n t e g r a t i o n I

I P1 3 k ( t + At ) " g ( ( ~ p / ~ t ) i p j k ' Pi 3 k ( t ) )

cU1 3 k ( t + At) - g ( (~£U/~ t ) i 3 k ' PUi J k ( t ) )

X i j k ( t + ~ t ) - g ( ( ~ X / ~ t ) z P j k ' Xt J k ( t ) )

( ~P /~ t ) i p j k

(~PU/~ t ) i j k

( ~ x / ~ t ) i P S k m

Compute Time I k e r i v a t t v e s

( ~ P / ~ t ) ( w z t p J k" WZi j k ' WRi p 3 k '

WEt J k ' WC£ P j k ' wCi 3 k ' WBi J k )

= ( ~ P U / ~ t ) ( F i j k ' IMPt 3 k ' IMPi p J k )

= ( ~ X / ~ t ) ( w s l J k ' q l j k ' IlZl 3 k ' HZi p j k )

Compute F o r c e s and Work

¢ i j k

~ P J k

T V ' x j k

~I j k

7Rx 3 k

= ¢ ( u j j k' uw h )

= ~P(di 3 k ' IGV) p Curve F i t s w i t h Adjustment f o r

- ~T(¢i j k ' IGV) tUnsteadYEffects Cascade

- PR(,!~ j k' Uw h' Tt 3 k) Fi J k

= "I'R(gT 3 k ' Uw h ' Ti j k ) WSi j k

I

- F(PR[ 3 k' Mt 3 k' Ai p ~ k )

" WS(TRi j k ' Hi 3 k )

I n p u t s (Boundary C o n d i t i o n s )

p., j k + 'r iP"" I , n l s t p s , . , ' + I n P ' t l "-',+"t Ql .., k + I n p u t ,,' . - I n p u t I I

T1 3 k [ n i m t / T12 J k Input J WBi + k = Input IGV - Input

s

Figure 23. Schematic of three<limensional, time<lependent solution procedure for TF41-A-1 HP compressor model.

)> m

C)

"n

(O

6

0 -,~I~

~ I ~

N

. Sy_~m

C o r r e c t S o l u t i o n F o u r t h O r d e r R u n g e - K u t t a N u m e r i c a l I n t e g r a t i o n M e t h o d

: : : ~ : : : : Modified Fourth Order R u n g e - K u t t a Numerical Integration Method 0 Indicates Average of Previous 20 Time Steps

K. I

0o

Time Step, At ~ 0.01 msec

~ ' ~

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0

T i m e , m s e c

Figure 24. Illustration of effect of incremental averaging on numerical instability.

rn E~

0

~0

A EDC-TR-79-39

6 . 4 1 -

B

6 . 0 -

Time = 7 7 . 2 m s e c F low B r e a k d o w n

5 . 6 - -

0

= 5 . 2 -

0~

4 . 8 -

o

4 . 4 -

-

0

4 . 0 - -

3 , 6 - -

6 . 5 m

~6.0 - r-4

~5.5-

4~

• ,4 5 . 0 N

~ 4 . 5

4 . 0

Time = 0.5 to 20 msec

LTime ffi 0 I n i t i a l C o n d i t i o n s

P a n d T I n l e t ~ - I m p o s e d A f t H e l d C o n s t a n t V ~ y C o n d i t i o n

•

4 . 0 p s i a

- T i n l e t ffi 6 0 2 ° R

I I I I I I I I

0 10 20 30 40 50 60 70 80

Time , msec

3 . 2 4 3 . 6 4 4 . 0 4 4 . 4 4 4 . 8 4 5 . 2 4 5 . 6 4 6 . 0

C o r r e c t e d A i r f l o w , W ~ / 5 , l b m / s e c

F i g u r e 25. TF41-A-1 HP compressor model loaded to stall, NH/vfe "= 92.6 percent, IGV = 12 deg, no distortion.

79

A E D C -TR -79-39

, ,4 r/:

U~ c

r,4

o

e-

el 4.o m

1 0 0 . 0

90 .0

8 0 . 0

70.0

6 0 . 0

5 0 . 0 -

4 0 . 0 -

3 0 . 0 -

20 .O -

Stage II -/

S t a g e i0 J

Stage 9 - / 4

Stage 8 -24

S t age 7 J

S t age 6 - - ~

S t age 5 - ~

S t age 4 -24

S t age 3 L J 4

Stage 2 --4

Model Flow B r e a k d o w n - - ~

Initiation of Surge

Staff l-J I0.0 I I i I

7 6 . 4 7 6 . 6 7 6 . 8 7 7 . 0 7 7 , 2 7 7 . 6

Time, msec

Figure 26. TF41-A-1 HP compressor model flow breakdown in terms of computed stage inlet total pressures leading to instability, N H / v / 8 = 92.6 percent, IGV = 12 deg, no distortion.

80

A EDC-TR-79 -39

6.4 V s__~ 10"( Distortion, I ~

/ [] 20~ percent ~ ~

/ J ~ ~- -~o 0.0 / 115 rcent --/

~_ 0 percent -J ~ NH/~D = 92.6 percent ~ 5"6 I 20 p e r c e n t ~ ~ IGV = 12 deg

Tip

~, 5.2

4 . 8

I Hub' . • , ,l I 0 . 9 1.0 I . i

4 . 4 L IPl°°/Pav~l I I 42 43 44 45 46

Corrected Airflow, W~.~/5, ibm/see

Figure 27. a. Tip radial distortion

Computed radial distortion influences on stability, TF41-A-1 HP compressor.

81

A EDC-TR--79-39

6 , 4 ~

6 . 0

o ,,4

• 5 . 6

;:1

o~

~ 5 .2

N

c

4 . 8

4.4

42

/

Sym

0 A [3

5 I D i s t o r t i o n , i0 p e r c e n t 20

5 p e r c e n t

/ /

/ 10 p e r c e n t

f f

m

.v4 no ~d

/

No D i s t o r t i o n

NH/~ = 92 .6 p e r c e n t IGV = 12 deg

0ee Tip I

I

Hub I 0.9 1.0 I.i

P l o c / P a v g

[- I I 43 44 45

Corrected Airflow, W~/',, ibm/sec

b. Hub radial distortion Figure 27. Concluded.

I 46

82

AEDC-TR-79-39

1 .1

o p 4

0~ 4 J

o o

O .r~

e~

~ o

.r.I

1.0

0.9

0.8

/--Range of J85-13 Engine Test / D a t a £or Flow Range from 77

to 98 percent (Ref. 8)

- - ~ ] ~ / - - -Model Computations /for TF41 Compressor,

~ ~ ~/ NH/~= 92.6 percent _ ~ ~ deg

J I i J J 5 i0 15 20 25

Distortion Pattern Magnitude, (Pmax - Pmin)/Pavg ' percent

0

a. Tip radial distortion

.,4

~ i . i ~ /--Range of J85-13 .

r,,.i ,1~ • r,i .~-i

~ . r . i

Mode l C o m p u t a t i o n s , O TF41 Compresso r

o .~1

0 . 9 m

0 . s I I I I I 0 5 10 15 20 25

D i s t o r t i o n P a t t e r n M a g n i t u d e , (PH - P L ) / P a v g ' p e r c e n t

4~ ¢d

Figure 28. b. Hub radial distortion

Comparison of TF41-A-1 HP compressor model radial distortion computations with experimental results,

83

AEDC-TR-79-39

0 -,-4 4J ¢d

O)

O ~3 3~

E O

~3

6 , 4 --

6 . 0

5 , 6

5 2

4 . 8

4 . 4 42

Sym (PH - PL)/Pavg 0 5 percent

10 percent [] 20 percent f

f

~ f _ / / / ~ ~ N o Distortion

2

PB

180-deg Distortion

I I I I I I I I 43 44 45 46

Corrected Airflow, W~/6. ibm/sec

Figure 29. Model computed influence of circumferential pressure distortion on stability, TF41-A-1 HP compressor.

84

A EDC-TR-'/9-39

1 . 0 O r - -~ ~ - R a n g e o f | \ ~ / " ~ / ' ~ . . ~ / Experimental

\/PN///2 ~ I- Model

.~. c 0 . 9 0 - -

~ 0 . 8 5 - 0

l-l~g

• , - I f f l

• ,-I 4 - ' r - I . ~

• ,.4 I~ , , Q . ~

o 4-J

o o

. r 4 . . . l

0 . 8 0

0 . 7 5

0 . 7 0

0 . 6 5

Sym

0

O

O

Z~

Model C o m p u t a t i o n s , T F 4 1 - A - 1 HP C o m p r e s s o r , N H / ~ = 9 2 . 6 p e r c e n t , IGV = 12 d e g , W ~ / 5 = 8 5 . 3 p e r c e n t F o u r - S t a g e C o m p r e s s o r , W ~ / 5 = 101 p e r c e n t ( R e f . 8 ) F i v e - S t a g e C o m p r e s s o r , W,D/5 = 93 p e r c e n t ( R e f . 8 ) J 8 5 - 1 3 C o m p r e s s o r ( R e f . 9 )

I I I I I 5 10 15 20 25

D i s t o r t i o n P a t t e r n M a g n i t u d e , (PH - P L ) / P a v g ' p e r c e n t

Figure 30. Comparison of TF41-A-1 HP compressor model circumferential distortion computations with experimental results.

85

A E D C-T R -79-39

Sym (TH - T L ) / T a v g 6 . 4

O 5 p e r c e n t A I0 p e r c e n t / JZ] 20 p e r c e n t ~ /

6 . 0 ~ No o /// ~ < D i s t o r t i o n

5 p e r c e n t - - d

. . . . . . ~ _ / ~ t ~ l%'tt/~,~- 92 6 p e r c e n t o IGV = ~z de~

, o o cent

~ 5 . 2

g,

4 . 8

T L

4 . 4 l~O-de~I D i s ~ ° r t i ~ n I I '

42 43 44 45 46

C o r r e c t e d A i r f l o w , W4~/5, I b m / s e c

Figure 31, Model computed influence of circumferentialtemperature disto~ion on ~ability, TF41-A-1HP compressor,

86

A E D C - T R - 7 9 - 3 9

1 "00 r ~ /--Range of

I ~ 1 ~ I ~ ' ~ . / Experimental

~2 .,~ r~ | M o d e l . / "

~ 0 . 9 0 ~- C o m p u t a t i o n s - /

~ 0 . 8 5 ~0o

-.,4 h 0 80 E l = • ,~ r~

.e,I r - 4 4 a

• ,4.,~ 0 75 . ~E • ¢~ , , 4 + ~ o,~ C ¢ H . 4 ~

o

o O. 70 +J I

i

Sy__~m

0

0

<> A

\

Model C o m p u t a t i o n s , T F 4 1 - A - 1 HP C o m p r e s s o r , N H / ~ = 9 2 . 6 p e r c e n t C o r r e l a t i o n B a s e d o n F o u r C o m p r e s s o r s ( R e f . 8 ) J 8 5 - 1 3 , N/~B= 87 p e r c e n t ( R e f . 1 0 ) J 8 5 - 1 3 , N / ~ = 94 p e r c e n t ( R e f . 1 0 )

o . 6 5 I I I i 0 5 lO 15 20

D i s t o r t i o n P a t t e r n M a g n i t u d e , (T H - T L ) / T a v g , p e r c e n t

Figum 32. Comparison of circumferentialtemperature distoMion model computations with experimental resul~.

\

I 2 5

87

8 . 0

Sym IGV, deg Schedule

O 1 2 . 0 Nominal O 2 2 . 0 +10 deg Cambered

2 . 0 - i 0 dog A x i a l S o l i d Symbols: Surge P o i n t s

m ~3 t~

A -n

to

to

O0 O0

O

4~ ¢d

M

U} ~3

0

0 ~J

7 . 0

6 . 0

5 . 0

4 . 0

Time = 17 .0 msec c - -Exper imenta l NH/~ 8 6 . 7 p e r c e n t ~ S t a t e S t a b l l i Steady-ty

C----Time ffi 20 .6 msec ~ i m i t \ NH/~ ffi 85 .6 p e r c e n t ~ . ~ - " ~

\ U---Time - 17 .6 msec . . ~ ' ~ \ \ NH/,~ - s6.5 porcenb.. I \ \ i /

j t Time = 0 N H / ~ = 92 .6 p e r c e n t

3 . 0 I f I 34 36 38 40 42 44 46 48 50

J ~ - - E x p e r l m e n t a l Operat ing Line

I I I I . _ I I I

HP Compressor C o r r e c t e d A i r f l o w , W ~ / ~ , lbm/sec

Figure 33. Effect of-5,000°R/sec uniform inlet temperature ramp on compressor stability as computed by TF41-A-1 HP compressor model.

AEDC-TR-79-39

3 4 . 0

Initiation of Surge

3 3 . 0

ID

E 3 2 . 0

O P-4

k 3 1 . 0 .,'4

+~

r-4

c 3 0 . 0 I--t

00

2 9 . 0

28.0

19.0 19.4 19.8 20.2 20.6 21.0 21.4

Time, msec

Figure 34. TF41-A-1 HP compressor model flow breakdown with 5,000°R/sec inlet temperature ramp, nominal IGV schedule, no distortion.

89

0

160 r S___mm IC..V, deg Schedu" e

I 0 12.0 Nomlnal

I rl 22.0 +i0 deg Cambered Unstable

120 S t a b l e

L ~ 0 '

. ~ 80 ~ . ~ (D

~ 4o

Time

o| 1 i 1 1 1 1 0 2,000 4,000 6,000 8,000 10,000 12,000

I n l e t T e m p e r a t u r e R i s e R a t e , ° R / s e c

I 1 4 , 0 0 0

m o

to

to

Figure 35. TF41-A-1 HP compressor model computed influence of uniform inlet temperature ramp rates on compressor stability.

A E DC-TR -79-39

US

0@;

4J+J

0['-,

~ 0

~.~

°r,,I

O H

~ E ~ O

O ,I-) r..I I~q.4 ~ N

--4 --

- -8 --

-12 -

-16 -

-20 -

-24 -

-28

0

I o

Sym IGV, d e g S c h e d u l e

0 1 2 . 0 N o m i n a l

Q 2 2 . 0 +10 d e g C a m b e r e d

2.0 -I0 d e g Axial

S o l i d S y m b o l s : S u r g e P o i n t s

I I I I i I I 4 8 12 16 20 24 28

T ime f r o m I n i t i a t i o n o f T e m p e r a t u r e Ramp, m s e c

I I I I I I I 20 40 60 80 i 0 0 120 1 4 0

T e m p e r a t u r e R i s e a t C o m p r e s s o r I n l e t , °R

Figure 36. Effect of 5,000°R/sec uniform inlet temperature ramp on compressor inlet corrected airflow as computed by TF41-A-1 HP compressor model.

91

A E D C - T R -79-39

C .r4

(=

;3 m

r,.,

o m

E o r,j

6 , 4

6 . 0

5 . 6

5 . 2

4 . 8

4 . 4

Sym IGV, deg S c h e d u l e

O 1 2 . 0 Nomina l

S o l i d S y m b o l : S u r g e P o i n t

Experimental Steady-State Stability Limit

_ 15.2 percent Reduction

42

HP Compressor Corrected Airflow, W~@ls,

Time = 23.0 msec NH/~ffi 9 0 . 9 p e r c e n t ~TAv G 23 deg

~ TMA X = 115 deg

Time ffi 0 Temperature ~ NH/~= 92.6 percent D i ~ No Distortion

~Experimental ~ O p e r a t i n g L i n e

I I I i I 43 44 45 46 47

ibm/sec

Figure 37. Effect of 5,000°R/sec inlet temperature ramp (imposed on 90-deg-arc circumferential section) on compressor stability as computed by TF41-A-1 compressor model.

92

A

Az

a

BVP

Cd

Cp

C,

e

F

f (...)

g (...)

H

HC

HP

HR

HZ

IGV

IMP

IMPR

i

NOMENCLATURE

Area

Control volume area normal to axial direction

Acoustic velocity

Bleed valve position

Duct pressure loss friction coefficient

Specific heat at constant pressure

Specific heat at constant volume

Internal energy

A EDC-TR-79-39

Force of compressor blading and cases acting on fluid, including wall

pressure area force

A function of ...

A function of ...

Total enthalpy flux

Total enthalpy flux transported across control volume circumferentially-facing

boundary

High-pressure rotor

Total enthalpy flux transported across control volume radially-facing boundary

Total enthalpy flux transported across control volume axial-facing boundary

Inlet guide vane

Impulse function

Ratio of stage exit to stage entry impulse functions

Axial location index

93

A EDC-TR-79-39

ip

J

J

Jp

k

kp

M

N

NH

NL

P

PD

PR

PS

Q

R

T

TR

TS

U

Adjacent axial location, i + I

Mechanical equivalent of heat

Radial location index

Adjacent radial location, j + 1

Circumferential location index

Adjacent circumferential location, k + 1

Mach number

Compressor rotor speed

High-pressure compressor rotor speed

Low-pressure compressor rotor speed

Stagnation (total) pressure

Dynamic pressure measurement

Stage total pressure ratio

Static pressure

Rate of heat addition to control volume

Gas constant

Radius; coordinate in the radial direction

Coordinate in the circumferential direction

Stagnation (total) temperature

Stage total temperature ratio

Static temperature

Time

Axial velocity

94

AEDC-TR -79-39

V

vol

W

W B

WC

WR

WS

WZ

W

Radial velocity component in three-dimensional model development

Volume

Mass flow rate; airflow rate

Compressor bleed flow rate

Mass flux' across circumferentially-facing control volume boundary

Mass flux across radially-facing control volume boundary

Stage shaft work added to fluid in control volume

Mass flux across axially-facing control volume boundary

velocity component in three-dimensional Circumferent ia l development

Energy function

Axial coordinate

X

Z

G R E E K S Y M B O L S

Ot

3'

A

X

P

model

Angle of attack

Flow direction angle relative to axial direction

Ratio of specific heats

A difference

Ratio of compressor entry total pressure to standard day, sea-level-static pressure

Ratio of compressor inlet total temperature to standard day, sea-level- static temperature

Blade chord-to-axial direction angle or stagger angle J

Density

Stage flow coefficient

, 95

A EDC-TR-79-39

~P Stage pressure coefficient

1~ T Stage temperature coefficient (stage loading parameter)

SUPERSCRIPTS

P Pertaining to pressure

T Pertaining to temperature

SUBSCRIPTS

0,1,2 ...

avg

exit

H

i

ijk

ip

J

JP

k

kp

L

loc

max

rain

n

P

Location or station designators

Average value

Pertaining to compressor exit plane

High

Axial location index

Three-dimensional location index, refers to value at location, i, j, k

Adjacent axial location, i + I

Radial location index

Adjacent radial location, j + I

Circumferential location index

Adjacent circumferential location, k + I

Low

Local value

Maximum value

Minimum value

Last location, e.g., last axial location in control volume

Plus one

96

radial avg

ring avg

wh

Z

Average value along a radius

Average value along a circle, average at constant radius

Wheel

Axial component

A E D C-TR -79-39

97