NORTH ATLANTIC TREATY ORGANIZATION ADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT ...

8/12/2019 NORTH ATLANTIC TREATY ORGANIZATION ADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT CASCADE PLOW PROBLEMS by H. Schlichting

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ROYAL A LiSHMENTb i i I > J t ~ O h i O . REPORT 93oh-a iOQ_ VISORY GROUP FOR AER ON AUT ICRESEARCH AND DEVELOPMENT

REPORT 93

CASCADE FLOW PROBLEMS

by


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-

REPORT 93

NORTH ATLANTIC TREATY ORGANIZATIONADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT

CASCADE PLOW PROBLEMSby

H. Schlichting


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SUMMARY

In the Institute of Fluid Mechanics of the Engineering University ofBraunschweig a considerable amount of research work on cascades has beendone in recentyears. Some of this work is reported very briefly here.

(i) An extensiv e program of theoretical calculations of losscoefficients of two-dimensional cascades in incompressibleflow has been carried out, applying boundary layer theory tocascade flow. There is good agreement between theory andexperiment.

(ii) Using the results of (i) , and also results of secondary flowlosses,the characteristic curves of an axial flow compressor(pressure coefficient and efficiency coefficient against massflow coefficient) have been calculated purely theoretically.The tendency of these curves agrees with what is to beexpected.

(iii) Some results of pressure distribution measurements on cascades


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SOMMAIRE

L'Institut de la M^canique des Fluides de1 Ecoledes Arts et Metiersde Brunswick a effectue* beaucoup de recherches au sujet des grillesd aubes au cours de ces dernieres annees. Ce rapport donne un expose decertains des travaux entrepris.

(1) Determination par le calcul des coefficients de perte desgrilles planes en regime incompressible, avec application a1'ecoulement par les grilles de la theorie concernant la couchelimite. II existe un bon accord entre the'orie et expe'rience.

(ii) Determination th^orique des courbes caracteristiques d'uncompresseur axial (coefficients de pression et de rendementdonnes en fonction de 1* e'coulementmassique),en appliquantles re'sultats obtenus a (i) ainsi que ceux relatifs aux pertesen ecoulement secondaire. L allure de ces courbes corresponda celle a laquelle on doit s'attendre.

(iii) Expose de certains resultats suivant des mesures relatives ala repartition de pression sur des grilles d*aubes pour une


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CONTENTS

Page

SUMMARY ii

LIST OF FIGURES vNOTATION vi

1. INTRODUCTION 1

2. SCOPE OF INVESTIGATIONS 1

3. INCOMPRESSIBLE CASCAD E FLOW 1

4.COMPRESSIBL E CASCAD E FLOW 2

REFERENCES 4


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LIST OF FIGURES

Fig.l Loss coefficient =Ah/ ( & p w & 2 ) for cascades of various solidityratios d/c and v arious blade angles /L; blade section NACA 0010;Reynolds number R 2 = w2c/io =5xl0 5,fully turbulent boundary layer

Pig.2 Loss coefficients =A h/( & p w 2 ) of turbine cascades of varioussolidity ratios d/c and various blade angles/o^;blade sectionNACA 8410; Reynolds number R ? = w2c/io =5xl0 5

Pig.3 Blade sections of the single-stage axial flow compressor ofFigure 4

Pig.4 Characteristic curves of a single-stage axial flow compressor, ascalculated theoretically from cascade data, by N. Scholz 5. Pressurecoefficient = 2gH/ u A2and efficiency coefficient r)= H/H tn againstmass flow coefficient $ =V/(TTr 2u.)

Pig.5 Cascade geometry for pressure distribution measurements in the HighSpeed Cascade Wind Tunnel; blade section NACA 0010

Page

9Fig.6 Cascade geometry for pressure distribution measurements in the High

Speed Cascade Wind Tunnel; blade section NACA 8410 10Pig.7 Pressure distribution measurements of cascades in compressible flow;

blade section NACA 0010; Reynolds number R 2= w 2c/zo =3xl0 5 11


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NOTATIONd d i s t a n c e b e tw e en b l a d e sc blad e chord/3g b l a d e a n g l ej ^ a n g l e of i n f l o w3 a n g l e of o u t f l o w

w 1 v e l o c i t yof i n f l o ww ? v e l o c i t y o f o u t f l o ww a a x i a l c o m p o n e n t of v e l o c i t yA w u difference between circumferential velocity components behindand infrontof cascade^ wu^ wa deflectionof flow through cascadep d e n s i t yv kinematic viscosityAh lossin total head

2


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u A c i r c u m f e r e n t i a l v e l o c i t y o f r o t o r a t t i p , r = r AV v o l u m e f l o w p e r u n i t t i m eH , H j . n a c t u a l h e a d a n d t h e o r e t i c a l h e a d , r e s p e c t i v e l y

- \ / ( T 7 T p U p i ) , d i m e n s i o n l e s s f l o w c o e f f i c i e n tf = 2 g H / u | , p r e s s u r e c o e f f i c i e n t77 = H / H t h , e f f i c i e n c y c o e f f i c i e n t


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CASC ADE FLOW PROB LEMS

H. Schlichting*

1. INTRODUCTIONThe problemof theflow through cascadesis an importantone in thewhole fieldof

turbo-machinery,but it is a pure aerodynamic problem. The subject,in which considerable progresshas been madein recent years, seems important enoughto be discussedat a Meetingof theWind Tunnel Panel, perhaps partlyin conjunction withtheCombustionand Propulsion Panel.

Some research workin this fieldhas been donein Germanyin recent years,andsomenew equipmenthas been built,so that Germany wouldbe ableto contribute somepapers,if it isdecidedto discuss this subjectat a future meeting.

This paper gives, very briefly, some ideason the work doneon thesubjectatBraunschweig University inrecent years.

2. SCOPE OF INVESTIGATIONThe main incentiveof these Investigationsis that real progressin theflow prob

lemsof turbo-machines willbe achieved onlyby a deeper knowledgeof complex flowphenomena. This requires extensive theoretical calculations which, however, needcareful correlation with experiments. A general surveyof these Investigationshasbeen givenin previous papers

1'2.

The very complex cascade flow problemhas been splitup as follows:-


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2achievedby applying boundary layer theoryto thecascade flow. But before dealingwith this problem, it was necessaryto improvethe methodsof calculatingthe incompressibleand inviscid flow throughacascade. Convenient solutionsof the 'IndirectProblem'and the 'Direct Problem', have been published in two VDI-Forschungshefte 3,u.These solutions have been usedin an extensive programmeof theoretical calculationsof loss coefficients,in connection witha large amountof experimental work, mainlyto checkthe theoretical results. FiguresI and 2 show some examplesof the losscoefficient plotted againstthe dimensionless deflection. In theory fully turbulentflowin the boundary layerhas been assumed,and in the experiments thiswas achievedbya turbulence wire nearto theleading edgeof the blade. The resultsof Figure1arefor cascadesof blades withthe symmetrical profile NACA 0010, whereasin Figure2the blades havethe cambered profile NACA 8410. In both casesthe solidity ratiod/candthe blade angle/L have been varied. The agreement between theoryand experimentis very satisfactory.

These resultson two-dimensionalcascades,and some moreon secondary flow losses,have finally enabled calculation, purely theoretically,of thecharacteristic curvesofan axial flow compressor 5. An exampleof this kindof calculationsis giveninFigure3 and Figure4. in Figure3 the bladingand the velocity vectorsat differentcross sectionsare given. Figure4 showsthe pressure coefficient 51= 2gH/u 2and theefficiency coefficient r/for the single-stage compressor plotted againstthe dimensionless flow coefficientd) = \ / ( T T r A 2 u A . The general shapeof these curves agrees withwhatis expected,but no experimentsto compare with these theoretical calculationshaveyet been carriedout.

4. COMPRES SIBLE CASCADE FLOW*Inthe pasttwo yearswe have been engaged mainlyon problemsof three-dimensional


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geometry of the whole programme. The cascade geometry and the blade profile are thesame as in the earlier low speed investigations. Pressure distributions on all thesecascades were measured at different angles of inflow and for Mach numbers from M =0.2 to the choking Mach number. The Reynolds number is constant over the whole range

5 .to the three cascades marked in solid black in Figure 5 and 6.of Mach numbers, R 2 = w c / v = 3x10 . The results given in the following figures refer

In Figure 7 the cascade is unstaggered and of NACA 0010 profile, the angle ofinflow being J 3l= 90 (zero lift) and /31= 100. With increasing Mach number thepressure distribution remains quite normal up to about Mj = 0.65 following the Prandtl-Glauert rule. For /3 = 100 and Mj =0.6 5 a shock wave first appears on the suctionside of the blade. At Mx = 0.69 choking has occurred, and no further increase of Machnumber is possible. With the onset of choking the pressure distribution changes completely, as can be seen from Figure 7 for M x= 0.69. This is accompanied by a suddenincrease of the pressure difference across the cascade, Pj- P^ which is also given inFigure 7.

In Figure 8 similar results are presented for a compressor cascade of blade profileNACA 8410 and blade angle /L = 135. Here also the pressure distribution does notchange its character up to M = 0.7. The choking Mach number is rather different forthe two angles of inflow, being Mj = 0.75 for = 142. but Mx= 0.90 for /3 1= 148.Due to the considerable amount of stagger, the increase of the pressure drop throughthe cascade is not as steep as with the unstaggered cascade.

In Figure 9 some results for a turbine cascade are given, the blade angle being/Og = 45 and the blade profile NACA 8410 again. Here the change of the pressuredistribution, when approaching the choking Mach number, is not so abrupt as for the compressor cascade. This must be attributed to the favourable pressure gradient of theturbine cascade. If in this case the Mach number is referred to the outflow velocity,


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R EF ER EN C ES

1. Schlichting, H.

2. Schlichting, H.

Prob lems and R es u l t s o f I nv es t ig a t io ns on Cascade F low.Journal of the Aeronautical Sciences, Vol.21. 1954,p.163-178.Some Problems of Cascade Flow. Proceedings of the Conference on High Speed Aeronautics. Polytechnic Institute of Brooklyn, New York, Jan. 1955.

3. Scholz, N. S t r o m u n g s u n t e r s u c h u n g e n a n S c h a u f e l g i t t e r n .Forschungsheft 442, 1954.

VDI-

4. Schlichting, H. Berechnung de r r e ib ung s los en inkom press ib l en S t rbmungf u r e i n v o r g e ge b e n e s e b e n e s S c h a u f e l g i t t e r. VDI-PorschungsheftNo.447, 1955.

5. Scholz, N.

6. Schlichting, H.

B e r ec h nu n g d e r K e n n l m i e e i n e s A x i a l v e r d i c h t e r s a u f G r un dg r e n z s c h i c h t t h e o r e t i s c h e r G i t t e r u n t e r s u c h u n g e n . Jahrbuchder Wissenschaftlichen Gesellschaft fiir Luftfahrt (W.G.L.)1955, p.205-213, 1956; see also Porschung auf dem Gebietdes ingenieur Wesens,Vol.22, 1956, p.137-139.The V ar ia ble De ns i ty High Speed Cascade Wind Tunnel oft h e D e u t s c h e F o r s c h u n g s a n s t a l t f u r L u f t f a h r t , B r a u n s c h w e ig .Paper presented at the Agard Meeting in Rome, February1956;Agard-Report No.91.1957.


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0,4 OfiWa

=0,5A

- I-0,75

-0,8 -OAExperimentTheory

CompressorOA 0,8

Fig.l Loss coefficient = A h / ( ^ p w & 2)for cascadesof various solidity ratiosd/c andvarious blade angles/oL;blade section NACA 0010; Reynolds number R 2=w2c/iv=

5xl05, fully turbulent boundary layerThe circles with projected lineson the theoretical curves indicatethe beginning

of separation


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? Vv10-Ofl

i 1 rPB~30 Experiment

05

- V

0,5 7,6 3,2 4,0 4 r V UW 0

5

0,2 0,6 1.0 A 1,4Wa

Fig.2 Loss coefficients =A h/ ( & p w& 2) of turbine cascades of various solidity ratiosd/c and various blade angles / ; blade section NACA 8410: Reynolds number R 2=

w2c/v = 5x10


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SectionI (Tip) Section E SectionHI SectionIF (Hub)r/r 1.0 0,85 0,7 0,55d/c 1,30 1,11 0,91 0,71P 13V 12V 113 106{

ACjCm 0,575 0.5U7 0,589 0,695

i

c=vv-Pig.3 Blade sectionsof thesingle-stage axial flow compressorofFigure4


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m y y s y A Z ' .

777/CD

r^

v / / / / / / .

/ / / / / / / y / y / y

TpvyTTTTTTp r A

r w0 ^ Q4 Q5 ga

7? j (

(Thl: l f th=0.d }6=0.m

Pressure coefficient. Jf |p-

Section

r.y-0,55

Mass flow coefficient^jffijjDegree ofreaction, r/rj=^or^j=co/?s/.=Q5

Pig.4 Characteristic curvesof a single-stage axial flow compressor, ascalculated theoretically from cascade data,by N. Scholz 5. Pressurecoefficient$ = 2gH/u A2and efficiency coefficient TO = H/ H thagainst

mass flow coefficient$ = V/(wr A2u A)


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0.5

90' 120' 150'_

^C=

0,75

1.0

1,25



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30'

0.75

60' 9 0 120' 135'

1.0

1.25



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M, -0,2 5-Oi

- 04Priorf ir100\i XL

Shockwave ChokingFig.7 Pressure distribution measurementsof cascadesin compressible flow;blade section NACA 0010; Reynolds numberR, = W.C/TO=3x10 s;see Figure5

P-PP r e s s u r e c o e f f i c i e n t c n = P n-PMj_ = w1 / a 1

o r iMach number of inflo w.


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M ,' 0,20 0,60v 0 .70 075 A- c - t O0 , -M

M, 0t20 0,50 0/0 0,90C p o A 0,6PrP*WPo Pi 0.2 fr 2*o t W m M i

' shock wave-o.2Vyat r-M rf,i ichoking

Pig.8 Pressure distribution measurementsof compressor cascadesin compressibleHO; Reynoldssee Figure6

flow; blade section NACA 8410; Reynolds numberR 2=w 2c/ v=3xl0 5;


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Mi-0,12C P

P r 5 0 \8 *- i i-16

P,-70_

016 021Lt '4V

*


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M^0t25

fi=90w_Vt

1.00,8' 0

^

X 1c

/3=100VV '

o P1.2W

SuctionK ^ S i d e -

[Pressure0.8^Side'0 x_ 1c

055

0,8' 0

1.8

Sx 1c

ih1,2W

y

- 1 0 8f f lr*.' 0 x_ 1cTheory

0.60np f fm0,8o

1,6V1.11.21.0OS

% .

1

\ \ iJ '

N > i r *

^' 0 X 1

C

0.65 P , = s o H1,21.0

compr.^

X 1 ' 0cOtjyvoapt

3P r 1 0 0 \

x_ 1c

0 8 \ J K o r % r' 0 A 1c

Experiment

0,1Po Pi

- 0 1\ oyfsi *^ ^

TheorySr.-90100

0 0 2 Off 06 08

0 0,2 0,h Op 0,8Ms,Fig.10 Comparisonof theoreticaland experimental velocity distributionof cascades

in compressible flow. Theory from Prandtl-Glauertrule; experiments,seeFigure7. Blade section NACA 0010; Reynolds numberR = w c / v=3xl0 5


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DISTRIBUTION

Copiesof AGARD publicationsmay be obtainedin thevarious countries at theaddresses given below.

On peut se procurerdes exemplairesdes publicationsde1'AGARDaux adresses suivantes.

BELGIUMBELGIQUE

Centre National d'Etudeset deRecherches Aeronautiques11,rue d'EgmontBruxelles.

CANADA D i r e c t o r o f S c i e n t i f i c I n fo r m a ti o nServices , Defence Research BoardDepar tment of Nat ional Defence'A' B u i l d i n gOt tawa , Onta r io .

DENMARKDANEMARK

Mil i t a ry Resea rch Boa rdDefence StaffK a s t e l l e tCopenhagen 0.FRANCE 0 . N . E . R . A . ( D i r e c t i o n )


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LUXEMBURGLUXEMBOURG

Luxemburg Delegationto NATOPalaisde ChaillotParis16,

NETHERLANDSPAYSBAS

Netherlands Delegation to AGARD10 KanaalstraatDelft,Holland.

NORWAYNORVEGE

Chief Engineering DivisionRoyal NorwegianAir ForceDeputy Chiefof Staff/MaterialMyntgaten2Oslo.Attn: MajorS. Heglund

PORTUGAL Subsecretariadoda EstadodaAeronauticaAv.da Liberdade252Lisbon.Attn: Lt. Col.Jose Pereirado

NascimentoTURKEYTURQUIE

M. M. VekaletiErkan iha rb iye i Umumiye Riyase t iI lmi I s t i sa r e Kuru lu Mi idur lug i iAnkara.Attn: Colonel Fuat Ulug

UNITED KINGDOM Ministryof Supply


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