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ELSEVIER

E x p e r i m e n t a l I n v e s t i g a t i o n s o n T a n d e m

o m p r e s so r a s c ad e P e r f o rm a n c e a t

L o w S p e e d s

U K S a h a

B R o y

Department of Aerospace Engineering

Indian Institute of Technology

Bombay India

Min imiz ing the number o f ax ia l f low compressor s tages fo r a spec if ic

work ou tpu t , and the reby lowering the eng ine s ize and weigh t , has a lways

been the des igner ' s goa l . Recen t ly , wi th the emergence of low aspec t ra t io

b lades , the re has been a renewed in te res t in tandem b lad ing for maximiz ing

th e b l a d e lo a d in g fu r th e r b e s id e s imp ro v in g i t s o f f -d e s ig n p e r fo rma n c e

characteris tics .

T h i s p a p e r p re s e n t s a e ro d y n a mic p e r fo rma n c e e v a lu a t io n s o f t h re e a s -

sor ted c ascades o f s ing le (CD A 43) , tandem (CD A 21-21) , and a newly

deve loped tandem (CDA 32-21) b lad ing . Fundamenta l inves t iga t ion has

been a t tempted in a low speed cascade wind tunne l to f ind the h igh

d e f l e ct io n c a p a b i li t y o f t a n d e m c a s ca d e s. A l th o u g h l im i te d p e r fo rm a n c e o f

t a n d e m C D A 2 1 -2 1 h a s b e e n a f fe c t ed b y c e r ta in g re y a re a s c o v e r in g b o th

g e o me t r i c a n d a e ro d y n a mic s h o r tf a ll , t a n d e m C D A 3 2 -2 1 d e r ive d f ro m

CDA 43 and CDA 21-21 has shown h igh f low deflec t ion charac te r is t ic s and

hence h igh load ing over a wide range of ang le o f a t tack . Elsev ie r

Science Inc. , 1997

K e y w o r d s : a s p e c t r a tio a x ia l c o mp r e s s o r b o u n d a r y la ye r c a s c a d e

c o n t r o l l e d d i f fu s io n a i rfo il d i f fu s io n fa c to r lo s s c o e f f ic i e n t ta n d e m

b la d e

I N T R O D U C T I O N

F o r m o r e t h a n a d e c a d e , t h e q u e s t f o r i m p r o v e d a e r o

e n g i n e g a s t u r b i n e p o w e r a n d f u e l e c o n o m y h a s s t im u -

l a t e d m u c h r e s e a r c h i n t e r e s t i n t h e d e s i g n o f h i g h p e r f o r -

m a n c e c o m p r e s s o r a i r f o i l s . T h i s h a s h e l p e d t h e e v o l u t i o n

o f t h e m o d e r n a i r c r a f t g as t u r b i n e e n g i n e i n t o a n a t t r a c -

t i v e p o w e r p l a n t i n a s m a l l p a c k a g e . A x i a l f l o w - c o m p r e s -

s o r s o f c o m p a c t d e s i g n a r e o b t a i n e d b y i n c r e a s i n g t h e

s u c t i o n c a p a c i t y a n d t h e s t a g e p r e s s u r e r a t i o . A e r o d y -

n a m i c o p t i m i z a t i o n w i t h s u c h a d e s i g n i s a i m e d a t i n c r e a s -

i n g l o ad i n g t o a m a x i m u m , w i t h m i n i m u m p e n a l t y o f t o ta l

p r e s s u r e l o ss e s, l e ad i n g t o a m i n i m u m n u m b e r o f s ta g e s i n

a m u l ti s ta g e a r r a n g e m e n t a n d a m i n i m u m n u m b e r o f

b la d e s p e r s t a g e [1 -4 ] .

I n t e n s i v e r e s e a r c h t o o b t a i n c o m p r e s s o r b l a d e s e c t i o ns

c o n f o r m i n g t o p r e s c r i b e d v e l o c it y d i s t r ib u t i o n s o n c o m -

p r e s s o r b l a d e s h a s r e s u l t e d i n t h e d e v e l o p m e n t o f c o n -

t r o l l e d d i f f u si o n o f a ir f o il s [ 5 - 7 ] t o m e e t t h e r e q u i r e m e n t s

o f h ig h e f f i c i e n c y a n d h ig h b la d e lo a d in g c a p a b i l i t y , t h u s

l e a d i n g t o r e d u c e d d e v e l o p m e n t a l c o s t . C u r r e n t s t a g e

d e s ig n s a re , t h e re fo re , v e ry e f f i c i e n t (9 0 %) w i th r e l a t iv e ly

h i g h p r e s s u r e r a t i o s ( > 1 .6 ). H o w e v e r , i n c r e a si n g p r e s s u r e

Address correspondence to Dr. Bhaskar R oy, Departmen t o f Aerospace

Experimental Thermal and F luid Science

1997; 14:263-276

Elsevier Science Inc., 1997

655 Avenue of the Am ericas, New York, NY 10010

r a t i o s b e y o n d t h e p r e s e n t l i m i ts w i t h a m i n i m u m n u m b e r

o f b l a d e s f o r c e s h i g h e r a e r o d y n a m i c l o a d i n g a n d e v e n t h e

c o n t ro l l e d d i f fu s io n a i r fo i l s h o w s i t s l im i t a t io n d u e to th e

p re s e n c e o f in c ip i e n t f lo w s e p a ra t io n [8] .

T h i s h a s b r o u g h t a r e n e w e d i n t e r e s t i n t a n d e m b l a d i n g

[ 9 - 1 2 ] w h e r e b o u n d a r y l a y e r g r o w t h i s e x p e c t e d t o b e

e f f e c ti v e l y c o n t r o l l e d f o r t h e p r e v e n t i o n o f f l o w s e p a r a ti o n

a n d s u b s e q u e n t s t a l l . T h i s h a s b e e n p o s s ib l e w i th th e

in c e p t io n o f w id e c h o rd , l o w a s p e c t r a t io b l a d e s [13 , 14 ]

f o r h i g h e r M a c h n u m b e r f l o w r e g i m e w i t h t h e i n t e n ti o n o f

r a i si n g b l a d e l o a d i n g a n d i m p r o v i n g o f f - d es i g n p e r f o r -

ma n c e c h a ra c te r i s t i c s .

B e n e f i t s o f l o w a s p e c t r a t io b l a d e s , c o n t ro l l e d d i f fu s io n

a i r f o i l , a n d t a n d e m b l a d i n g h a v e b e e n a p p r e c i a t e d i n

t e rm s o f s t ru c tu ra l l i f e t ime , h ig h lo a d in g , a n d o f f -d e s ig n

f lo w c o n t ro l ; h o w e v e r , t h e s e in d iv id u a l e f fe c t s a re to b e

u n i f i e d to g e th e r in to a n e f f i c i e n t d e s ig n .

A n in n o v a t iv e d e s ig n o f a h ig h p re s s u re r a t io a x ia l f lo w

c o m p r e s s o r , h o w e v e r , r e q u i r e s s y s t e m a t i c s t u d y , a n d t o

b e g i n w i t h l o w s p e e d t e s t i n g p r o v i d e s q u a l i ta t i v e i n f o r m a -

t i o n w i th w h i c h t o c o n s t i tu t e a f r a m e w o r k f o r h i g h s p e e d

a n a ly s is . A n u n d e r s t a n d i n g o f t h e t w o - d i m e n s i o n a l l i n e a r

Engineering, Indian Institute o f Technology, Bom bay 400 076, India.

0894-1777/97/ 17.00

PII S0894-1777(96)00125-2

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2 6 4 U . K . S a h a a n d B . R o y

c a s c a d e m o d e l m a y p r o v i d e q u a l it a t iv e i n f o r m a t i o n f o r

p r e l i m i n a r y g u i d a n c e i n t h e d e s i g n o f t h r e e - d i m e n s i o n a l

c o m p r e s s o r b la d e s . T h e s e s t u d i e s m a y a ls o h e l p t o d e v e l o p

a n d v a l i d a t e c o m p u t a t i o n a l c o d e s [ 1 5 - 1 8 ] .

T h e w o r k r e p o r t e d h e r e w a s a i m e d a t fi n d i n g h i g h

d e f le c t io n c a p a b i li ty o f a d e v e l o p e d t a n d e m c a s c a d e ( C D A

3 2 -2 1 ) , c o m p a r e d w i t h t h a t o f a s in g l e ( C D A 4 3 ) a n d a n

e x i st i ng t a n d e m ( C D A 2 1 - 2 1 ) c a s c a d e . T h e m o t i v a t i o n

b e h i n d t h i s i n v e s t i g a t i o n w a s t o f i n d a b l a d e p r o f i l e t o

a c h i e v e a n a t t a c h e d f l ow b e h a v i o r o n t h e r e a r h a l f o f t h e

b l a d e u n d e r v a r y i n g o p e r a t i n g c o n d i t i o n s ( d e s i g n a n d

o f f - d e s i g n ) e i t h e r b y c o n t r o l l e d d i f f u s io n c h a r a c t e r i s t ic s o f

t h e a i r f o il o r b y s e t ti n g t w o b l a d e s i n t a n d e m , k e e p i n g

s i m i l a r a s p e c t r a t i o s .

T h e a u t h o r s ' e a r l i e r e x p e r i m e n t a l s t u d i e s [ 10 , 1 2] w i t h

s in g le a n d t a n d e m c a s c a d e s ( C D A 4 3 a n d C D A 2 1 -2 1 )

s h o w e d i n t e r e s t i n g c a p a b i l i t i e s o f t h e l a t t e r w i t h i n a l i m -

i t e d o p e r a t i n g r a n g e . T h i s m o t i v a t e d u s t o d e v e l o p a n e w

t a n d e m c o n f i g u r a t i o n s o a s t o h a v e a w i d e o p e r a t i n g r a n g e

w i t h g o o d l o a d i n g c ap a b i l it y . T h e d e v e l o p e d t a n d e m c a s -

c a d e w a s c o n f i g u r e d o u t o f a th i c k C D A b l a d e p r o f i le a t

t h e f r o n t ( f o r w i d e r o p e r a t i n g r a n g e ) , f o l l o w e d b y a s c a l e d

d o w n b l a d e p r o f i l e a t t h e r e a r , a s s h o w n i n F i g . 1. T h e

g a p - n o z z le g e o m e t r y w a s g iv e n a c u s p s h a p e t o p r o m o t e

n e c e s s a r y a n d s u f fi c i en t f l o w g u i d a n c e f o r e f f ic i e n t m o -

m e n t u m t r a n s f e r o n t h e r e a r b l a d e s u c t i o n o v e r a w i d e

r a n g e o f a n g l e o f a t t a c k . C D A 3 2 - 2 1 t a n d e m c a s c a d e w a s

c u t o u t f r o m a n e x i s t in g C D A b l a d e p r o f i le ( 4 3 c a m b e r )

t r u n c a t e d a t t h e m i d d l e , f o l l o w e d b y a n e x is t in g , C D A 2 1

c a m b e r b l a d e p r o fi le . D e t a i l ed b l a d e c o o r d i n a t e s o f C D A

3 2 -2 1 a r e p r e s e n t e d i n t h e A p p e n d i c e s . B l a d e c o o r d i n a t e s

o f C D A 4 3 a n d C D A 2 1 p ro f il e s h av e a l r e a d y b e e n

repor ted [7 , 19] .

I n b o t h c a s es , t a n d e m c a s c a d e s w e r e s e t a n d t e s t e d a t

4 8 c a m b e r ( o v e r a l l) t o f i n d a n e x t r a f l o w d e f l e c t i o n o f 5

c o m p a r e d w i t h t h e s i n gl e c a s c a d e w i t h 4 3 c a m b e r . I n t h e

p r e s e n t i n v e s ti g a t io n s , a t t e n t i o n w a s f o c u s e d o n l y u p o n

t h e b l a d e s u r f a c e a n d w a k e f l o w b e h a v i o r t o e v a l u a t e t h e

c a s c a d e p e r f o r m a n c e c h a r a c t e r i s t i c s . A d i r e c t c a s c a d e p e r -

f o r m a n c e a s s e s s m e n t w a s m a d e f o r a ll th r e e c o n f i g u r a -

t i o n s o n t h e b a s i s o f s ta t i c p r e s s u r e c o e f f i c ie n t C p ) dis t r i -

b u t i o n , d i f f u s i o n f a c t o r , s t a t i c p r e s s u r e r i s e c o e f f i c i e n t ,

l o s s c o e f f i c i e n t , a n d w a k e v e l o c i t y p r o f il e s , a s w e l l a s t o t a l

p r e s s u r e l o s s p r o fi l es . D e t a i l e d c a s c a d e b l a d e g e o m e t r y a s

g i v e n in T a b l e 1 , a n d t h e c a s c a d e n o t a t i o n s s h o w i n g

v a r i o u s g e o m e t r i c a n d f l o w p a r a m e t e r s a r e d e p i c t e d i n

F ig . 2 .

C D

3 2 2 1

igure 1 . B lade p ro f i l e s under p rese n t inves t iga t ions .

E X P E R I M E N T A L M E T H O D S

T e s t F a c i l i t y

T h e p r e s e n t i n v e s t ig a t i o n w a s c a r r i e d o u t i n a l ow s p e e d

c a s c a d e w i n d t u n n e l ( T a b l e 2 ) . E s s e n t i a l l y , t h e f l o w e n v i -

r o n m e n t u n d e r c o n s i d e r a t i o n i s i n c o m p r e s s i b l e . T h i s o p e n

c i r c u i t f a c i l i t y ( F i g . 3 ) i s d r i v e n b y a c e n t r i f u g a l b l o w e r

l o c a t e d a t t h e u p s t r e a m e n d , f o l l o w e d b y a d i ff u s e r , a

h e a d e r c o n t a i n in g a h o n e y c o m b a n d f o u r m e s h s c r ee n s ,

a n d t h e n a 1 2 - to - 1 c o n t r a c t i o n r a t i o n o z z l e . T h e n o z z l e

l e a d s t o t h e t e s t s e c ti o n o f a r e c t a n g u l a r d u c t e q u i p p e d

w i t h e n d - w a l l m o v a b l e f l ap s . T h e c a s c a d e a l o n g w i t h t h e

c i r c u l a r d i s k s c o u l d b e r o t a t e d i n t h e t e s t s e c t i o n a b o u t a

c o m m o n a x is t o v a r y t h e a n g l e o f a tt a c k . S u c t i o n s li ts w e r e

m a d e o n e i t h e r s i d e o f t h e s i d e w a l ls 0 . 2 5 t i m e s b l a d e

c h o r d u p s t r e a m f o r b o u n d a r y l a y e r r e m o v al . A d d i t io n a l

s u c t i o n w a s c r e a t e d b y e m p l o y i n g t w o c e n t ri f u g a l b l o w e r s ,

e a c h d r i v e n b y a 0 . 7 5 - k W m o t o r , o n e i t h e r s i de o f th e s i d e

w a l l s . E n d - w a l l m o v a b l e f l a p s w e r e u s e d t o i m p r o v e t h e

d e s i r e d f l ow u n i f o r m i t y a n d p e r i o d ic i t y .

M e a s u r e m e n t P r o c e d u r e

A l l t h e m e a s u r e m e n t s i n t h e p r e s e n t s t u d y w e r e m a d e

w i t h s t a n d a r d p i t o t s t a t i c p r o b e s a n d s t a t i c p r e s s u r e t a p -

p i n g s . W h i l e t h e u p s t r e a m p i t o t s t a t i c p r o b e w a s u s e d t o

r e c o r d t h e i n l e t f l o w c o n d i t i o n s a n d c h e c k f l o w u n i f o r m i t y ,

t h e d o w n s t r e a m p r o b e w a s u s e d t o r e c o r d w a k e t o t a l

p r e s s u r e a n d v e l o c i t y c o v e r i n g t w o b l a d e p a s s a g e s . S t a t i c

p r e s s u r e t a p p i n g s m a d e o n t h e b l a d e s u r f a c e s w e r e u s e d

t o r e c o r d s t a t i c p r e s s u r e s a n d v e l o c i t i e s ( w i t h r e s p e c t t o

T a b l e 1 . S i ng l e a n d T a n d e m C a s c a d e G e o m e t r y

B l a d e S i ng l e T a n d e m N e w T a n d e m

V a r ia b le s N o t a t i o n s C D A 4 3 C D A 2 1 - 21 C D A 3 2 -2 1

Ca m be r ang le (deg rees ) q~, ~p,, 43 48 (over al l) 48 (overal l)

S tagge r ang le (degrees ) 7 , Ye 22 220 (effect ive ) 22 (effect ive)

B l a d e c h o r d ( m m ) c 1 00 6 0 ( F B ) 6 0 ( F B )

c - - 4 0 ( R B ) 4 0 ( R B )

Blade p i t ch (mm ) s 50 50 50

Blade span (mm ) b 150 150 150

Sol id i ty c / s ) t r 2 1 .9 1 .9

A s p e c t r a t io

b / c )

A R 1.5 1.56 1.56

No. o f b lades N 10 2 10 = 20 2 10 = 20

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Experimental Investigations on Tandem Compressor Cascade 265

7 I

~ p l o n e

/ / ~ t , I

/ ~ IK I / ~ A x i o l d i r e c l i o n x l

Y

z

Figure 2. Cascade nomenclature.

inlet total pressure) at various chordwise positions to find

Cp distributions, the diffusion factor, and the static pres-

sure rise coefficient. The mass averaged loss coefficient

was evaluated by traversing the downstream total pressure

probe over a length of 150 mm covering the two blade

passages. Wake total velocity over the same length was

also recorded by the same probe.

RESULTS AND DISCUSSION

Low speed studies were attempted in the present investi-

gation to find qualitative information on the tested cas-

cades on the basis of fundamental aerodynamic perfor-

mance parameters.

Static Pressure Coefficient

Single Cascade (CDA 43) Static pressure coeffic ient

Cp) distributions of the single cascade (CDA 43) at

various angles of attack are presented in Fig. 4. At a = 0 ,

after an initial acceleration on the suction surface (up to

30 of the chord from the leading edge), flow starts

diffusing toward the trailing edge (Fig. 4a). This accelera-

tion and dece leration effect diminishes at a = 5 , showing

a flatter Cp distribution (Fig. 4b). At a = 10, steep

acceleration around the leading edge (LE) is followed by a

diffusion process at 6 of the chord from the LE, and

thereafter Cp remains constant (Fig. 4c). Between a = 0

W A K E

PROBE r'-CASCADE

2 0 x 2 0 M E S H

SCREEN -~

TRAVERSE PLANE UPSTREAM ALL TAPS

/ - 2 5 x 2 5 H O NE Y C O M B

- . ..F O R F L O W U N I F O R M I T Y ~ -

h . \

~ . E C . u ~ , , ~ , , ,~o w . . . - ~ , , , , ~ - t - . _ A S P L . ~ , o ~ L f l E~

I I I I I

' -

, i a i

I * - - / : S E C T I O N ', x , . . J I 1 1 I l l . L - - ~ ',

. . . . . . . . . . . . I o _ 1 . o o i J t l 2 s o i = w L s o . V = s o l .

S L I T S l S O e A C .

A L L D I M I E N S l O N 5 A R E I N r a m

igure 3. Low speed cascade wind tunnel.

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266 U. K. Saha and B. Roy

Table 2. Cascade Wind Tunnel Data

W i n d T u n n e l D r i v e S u c t i o n S y s t e m D r i v e T e s t S e c t io n D a t a

Blower type: radial Blower type: radial Size: rectan gular

I) : 3.30 m 3 / s 12:0.056 m3 /s Air velocity: 20.0 m / s

Press ure rise: 9.96 kPa Pres sure rise: 2.98 kPa Mach No.: 0.06

Motor power: 55 kW Moto r power: 0.75 kW Reyn olds No. 1.369 105

p

~ - 3 . 0

~ - 2 . 0

- I . 0

- 0 . 0

o~

o 1.0.

co 2.0

- S u c t i o n S u r f a c e

- - - - P r e s s u r e S u r f a c e

20 4O flO 80 100

P e r c e n t a g e o f C h o r d

( a ) A n g l e o f a t t a c k = 0

C p v s c~ P l o t s

S u c t i o n S u r f a c e

~ , A P r e s s u r e S u r f a c e

~E TE

20 40 60 80 I 0 0

P e r c e n t a g e

o f

Chord

b) Ang le o f a t t ack = 50

S u c t i o n

S u r f a c e

- , - P r e s s u r e S u r f a c e

I

. . . . . . . . . , . . . . . . . . . , . . . . . . . . . , . . . . . . . . . r . . . . . ~

0 20 40 60 BO 100


c) Ang le o f a t t ack = lO

C p

~ - 3 . 0

v

S u c t i o n

S u r f a c e

U ' ' P r e s s u r e S u r f a c e

~ - 2 , 0

~ - I . 0

m - 0 . 0

1 . 0 L E T E

2 o .......2'd ..... 'd ..... d'd ..... gd ..... 0 o


( d ) A n g l e o f a t t a c k = 1 5


A . . , P r e s s u r e S u r f a c e

0

20

40

60 80

100


e) Ang le o f a t t ac k : 180

= = S u c t i o n S u r f a c e

. 4 . . . P r e s s u r e S u r f a c e

1

o . . . . . . . ' 2 ' d . . . . . . ' i ' o . . . . . . ' g ' d .. . . . . g d ' ' T o o


( f ) A n g l e o f a t t a c k = 2 0

C p

~ - 3 . 0

ID

~ - 2 . 0

- 1 .1

0.0

1 . 0

o~ 2.0

~ Suct i on Surf ace

E TE

........ 2~ ...... 4~ ...... d d ......e~ .. ... f0o


(g) Angle of attack = 2 2 0

= = S u c t i o n S u r f a c e

A A A A P r e s s u r e S u r f a c e

t ........ ........ ........ ........ ........

0 20 40 60 80 100

P e r c e n t a g e of C h o r d

h) Ang le o f a t t ac k = 25 o

Suct ion Surf ace

I & . . A p r e s s u r e S u r f a c e

LE TE

1

. . . . . . . . . r . . . . . . . . v . . . . . . . . w... . . . . . , . . . . ~

0 20 40 60 80 100


( i) A n g l e o f a t t a c k = 3 0 o

Figure 4. Static pressure coefficient C p ) distributions of single cascade (CDA 43) at varying angles of

attack.

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Experimental Invest igat ions on Tandem Compressor Cascade 67

a n d a = 1 0 , t h e c a s c a d e i s o p e r a t i n g a t h i g h n e g a t i v e

i n c i d e n c e s. A s a r e s u lt , s h a r p a c c e l e r a t i o n a n d d i f f u s i o n

p r o c e s se s w e r e b e e n o b s e r v e d a n y w h e r e o n t h e b l a d e

s u r f a c e s . A t a = 1 5 t o 2 2 , t h i s i n i t i a l s t e e p a c c e l e r a t i o n

i s f o l l o w e d b y a s h a r p d i f f u s i o n p r o c e s s , w h i c h i s c o m -

p l e t e d w i t h i n 1 0 o f t h e c h o r d f r o m t h e l e a d i n g e d g e

( F ig s . 4 d - 4 g ) . T h i s s h a r p a c c e l e r a ti o n a n d d e c e l e r a t i o n

e v i d e n t l y c r e a t e d a s e p a r a t i o n b u b b l e . T h e s e p a r a t i o n

b u b b l e c a u s e d a l o c a l f l o w a c c e l e r a t i o n ( b e t w e e n 1 0 a n d

3 5 o f t h e c h o r d ) , f o l l o w e d b y a s t e a d y d i ff u s i o n o n t h e

r e s t o f t h e b l a d e s u c t i o n s u r f a c e . T h e l o c a l s e p a r a t i o n

b u b b l e , w h i l e a l t e r i n g t h e

p

d i s t r ib u t i o n , m a y h a v e i n -

d u c e d a n e a r l y t r a n s i t i o n , w h i c h i n t u r n , e f f e c t e d r e a t t a c h -

m e n t . A s e p a r a t i o n b u b b l e w a s a ls o c r e a t e d i n p a s t ex p e r i -

m e n t s w i t h C D A [ 2 0 , 2 1 ]. T h e s u c t i o n s u r f a c e p r e s s u r e

g r a d i e n t s t a rt s l e v e l i n g o f f w i t h a n i n c r e a s e i n t h e a n g l e o f

a t t a c k ( a = 2 5 a n d 3 0 ), w h i c h i s a p r e c u r s o r t o f l o w

s e p a r a t i o n ( F ig s . 4 h a n d 4 i ) . E v i d e n c e o f th e o n s e t o f

t r a i l i n g e d g e s e p a r a t i o n i s c l e a r l y o b s e r v e d i n t h i s r a n g e .

A t a = 3 0 , t h e

p

p l o t s t i ll s h o w s t h e e x i s t e n c e o f a

s e p a r a t i o n b u b b l e . A t t h is a n g l e o f a tt a c k , t h e s e p a r a t i o n

p o i n t h a s m o v e d t o w a r d t h e L E a n d m e r g e d w i th t h e

d e c a y i n g s e p a r a t i o n b u b b l e . T h e p r e s s u r e s u r f a c e

p

dis-

t r i b u t i o n r e m a i n s c o n s i s t e n t a t a l l a n g l es o f a t t a c k . T h i s

m a y b e d u e t o t h e c o n t r o l l e d d i f f u s i o n c h a r a c te r i s t ic s o f

t h e c a s c a d e p r o f i l e .

C p v s . x P t o t s

C p

~ - 3 0

~

~ - ~ . 0

- 1 .0

- 0 . 0

~ 1 . 0 .

m . Z . O


- - . . 6

P r e s s u r e S u r f a c e

LE

FR ONT B LADE

TE

2 0 4 0 6 0


R E A R B LADE

8 0 I t


S u c t i o n

Surface

4A4~A4 Presaure Surface

FR ONT B LADE DE

. . . . . . . . . l . . . . . . . . . i . . . . . . . . . I . . . . . . . . . . . . . . . . . .

2 0

4 0 6 0 8 0

1 0 0


b ) A n g l e o f a t t a c k = 5 0

I

= ~ = =

Suction Surface

- - * - -

Pressure

S u r f a c e

~LE

FRONT BL AD E JREARI R E A RLADE

0 2 0 4 0 6 0 8 0 1 00


( c ) A n g l e o f a t t a c k = 1 0

C p

- ~ - 3 . 0

..~

O

~ - 2 . 0

1 . 0

m - 0 . 0

o

1 0

~o 2 .0


- * * - - P r e s s u r e S u r f a c e

2 0

4 0 6 0 8 0 1 0 0


( d ) A n g l e o f a t t a c k = 1 5 0

I ~ S u c t i o n S u r f a c e

- ~ * , Pressure Surface

DE

o ....... 2~ ...... 'o ...... 66 ...... g'o ..... fo o


( e ) A n g l e o f a t t a c k ---

1 8 0

_ ~ = ~ S u c t i o n S u r f a c e



( f ) A n g l e o f a t t a c k = 2 0 o

~ - 3 .0 . = = S u c t i o n S u r f a c e S u c t i o n S u r f a c e S u c t i o n S u r f a c e

~ .'~ -2.0 - - * P r e s s u r e S u r f a c e ~ . . . A . P r e s s u r e S u r f a c e - - ~ - - P r e s s u r e S u r f a c e

L ] L ~ L

TE TE E

C p ~

m 0 . 0

c ~ F R O N T B L A D E R E A R B L A DE-~0 I 'O FR ON T B L AD E [R II .: ., I. . i~ . ,DE ] F R ON T B L AD E RL A D E ~F : I ,N . I I , .I ~ . I. E . P I ~ : . , B . ~

Z.O . . . . . . . , . . . . . . . . . , . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . .

2 0 4 0 6 0 8 0 1 0 0 0 Z 0 4 0 6 0 8 0 1 0 0 2 0 4 0 6 0 8 0 1 0 0

P e r c e n t a g e o f C h o r d P e r c e n t a g e o f C h o r d P e r c e n t a g e o f C h o r d

( g ) A n g l e o f a t t a c k = 2 2 0 ( h ) A n g l e o f a t t a c k = 2 5 0 ( i ) A n g l e o f a t t a c k = 3 0 0

F i g u r e 5 . S t a t i c p r e s s u r e c o e f f i c i e n t ( C p ) d i s t r i b u t i o n s o f t a n d e m c a s c a d e ( C D A 2 1 - 2 1 ) a t v a r y i n g a n g l e s o f

a t t a c k .

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2 6 8 U . K . S a h a a n d B . R o y

Tandem C a s c a d e ( C D A 2 1 - 21 ) S t a t i c p r e s s u r e co e ff i-

c i e nt d i st r ib u t io n s o f t h e t a n d e m c a s c a d e ( C D A 2 1 - 21 ) a r c

s h o w n i n F i g . 5 . A t a = 0 , s t e a d y a c c e l e r at i o n i s n o t i c e -

a b l e o n t h e fr o n t b l a d e s u ct i o n s u rf a c e u p t o 3 0 o f t h e

c h o r d ( t o t al ) r o m t h e L E ( F i g 5 a ) . T h e a c c el e r at i o n z o n e

d i m i n i s h e s g r a d u a l l y w i t h a n i n c r e a s e i n c ~ ( F i g s . 5 a - 5 c ) .

W i t h i n t h e r a n g e o f a = 0 t o I 0 , t h e f r o n t b l a d e p r es -

s u r e s ur f a ce s h o w s a l m o s t a c o n s t a n t

p

d i s t r i b u t i o n ; h i g h

d e f l e c ti o n o v e r t h e r e a r b l a d e s u c t i o n s u r f a c e d o e s n o t

s c c m t o b c e f f e c t iv e i n t h i s r a n g e o w i n g t o i n ef f ic i e nt

m o m e n t u m t r a n s f e r b y t h e g a p - n o z z l e f l o w f o r m e d b e -

t w e e n t h e b la d es . A t l o w e r a n g le s o f a t ta c k , o w i n g t o

m i n i m a l s t a t i c p r e s s u r e d i f f e r e n c e n e a r t h e t r a i l in g e d g e

( T E ) o f t h e f r o n t b l a d e s u c t i o n a n d p r e s s u r e s u r f a c e s , a

w e a k e r m o m e n t u m t r a n s f e r b y t h e g a p - n oz z l e fl o w w a s

e f f e c t e d .

T h e m i n i m a l d i f f e r e n c e o f s t a t ic p r e s s u r e a t lo w a n g l e s

o f a t t a c k w a s c a u s e d b y t h e i n c o m i n g f l o w , w h i c h i s

i n c i d e n t w e l l o n t o t h e b l a d e s u c t i o n s u r f a c e r a t h e r t h a n

o n t o t h e L E . T h e f l ow s e p a r a t i o n t e n d e n c y t o w a r d t h e T E

o f t h e f r o n t b l a d e s u c t i o n s u r f a c e o b s e r v e d e a r l i e r i s

p r e v e n t e d b y t h e g a p - n o z z l e f l o w a t c~ = 1 5 ( F i g . 5 d ) ,

f o r c i n g r e a t t a c h i n g o n t h e r e a r b l a d e s u c t i o n s u r f a c e . T h i s

f u r t h e r a i d s t h e d e c e l e r a t i o n p r o c e s s a l m o s t t o t h e r e a r

C p

~ 3 . 0

o

~_. 2.0

o

- l . 0

P

~ - 0 . 0

1.0,

w 2 . 0


- P r e s s u r e S u r f a c e

F R O N T BLADE

~ T E

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 0 4 0 8 0


R E A R

BLAD[

f lO t O 0


C p v s . G P l o t s

[ i I i I ~ u c ~ o n u r f a c e

- - - - - P r e s s u r e S u r f a c e

F R O N T B L A D E R E A R B L AD E

2 ~ f i i 6 d 6 ~ i o o


b ) A n g l e o f a t t a c k = 5 0

, , a . . S u c t i o n Surface

- - P r e s s u r e S u r f a c e

~ H E

1 ~

' ~

TE

F R O N T B L A D E R E A R ~ B ~ D E

0 2 0 4 0 6 0 80 I00


( C ) A n g l e o f a t t a c k = l O

p

J

~ . - 2 . 0

~J

- I . 0

- 0 , 0

e,

1.o

r . ~ 2 . 0

~ - 3 . 0 . , - , , = S u c t i o n S u r f a c e

* - - - -


H E

F R O N T B L A D E

. . . . . . . . . l . . . . . . . . . . . . . . . . .

R E A R B L A D E

2 0 40 60 80 I 0 0


d )

A n g l e o f a t t a c k

= 1 5 o

i l i l l

uction urface

- - - - P r e s s u r e S u r f a c e

I R O N T B L A D E R E A R B LA D E

t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .

0 20 40 8 0 80 100

Percentage of C h o r d

( e )

A n g l e

o f a t t a c k = 1 8

F R O N T B L A D E R E A R B L A D

......... ........

. . . . . . . . ~ . . . . . . . . . . . . . . . . . .

20 40 80 6 0 I00

Percentage

o f C h o r d

( f )

A n g l e o f a t t a c k

=

2 0 0

p

~ - 3 . 0 ~

' S u c U o n Sur fa c e

s s u r e S u r f a c e

~ 1 2 . o

v LE

~ L .O ~ ~ T

~ E

~ - 0 . 0

e~

o l . O . F R O N T B L A D E R E A R B L A D E

oq 2.0 ......... ........................... ........

0 20 40 60 O0 tO0

Percentage of Chord

g )

A n g l e o f a t t a c k = 2 2 o

' S u c t i o n Sur fa c e

- - - * , P r e s s u r e S u r a f c e

F R O N T BLADE

E

REAR B L A D E

........ ~'6 ...... gd ...... 8d ... ... go ..... i'oo

Percentage o f C h o r d

h ) A n g l e o f a t t a c k : 2 5 0

t l O , , o S u c t i o n S u r f a c e

, 8 * * , P r e s s u r e S u r f a c e

F R O N T B L A D E R E A R B L AD E

0 ..... . ~'6 ..... . ~'6 ..... . 8d .. .... S'0 ..... i'00


i ) A n g l e o f a t t a c k : 3 0 0

F i g u r e 6 . S t a t i c p r e s s u r e c o e f f i c i e n t C p ) d i s t r i b u t io n s o f n e w t a n d e m c a s c a d e ( C D A 3 2 - 21 ) a t v a r y i n g

a n g l e s o f a t t a c k .

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7/14

E x p e r i m e n t a l I n v e st i g a t io n s o n T a n d e m C o m p r e s s o r C a s c a d e 2 6 9

b l a d e T E . P r e s s u r e s u r f a c e C p d i s tr i b u t i o n a t t h e s a m e

a n g l e o f a t t a c k i n d i c a t e s c o n t i n u e d f l o w a t t a c h m e n t . D i f -

f u s i o n c h a r a c t e ri s t i c s o n t h e f r o n t b l a d e s u c t i o n s u r f a c e

i m p r o v e s i g n i f i c a n t l y a t a t = 1 8 a n d 2 0 (F i g s. 5 e a n d 5 f ) ;

t h e r e a r b l a d e s u c t i o n s u r f a c e a l s o i n d i c a t e s c o m p a r a t i v e l y

h i g h e r f l o w d i f f u s i o n . F r o m a t = 2 2 t o 3 0 , t h e d i f f u s i o n

p r o c e s s i s m i l d e r o n t h e f r o n t b l a d e s u c t i o n s u r f a c e ( F i g s .

5 g - 5 i ) , w h e r e a s t h e r e a r b l a d e s u c t i o n s u r f a c e s h o w s i ts

a t t a c h e d d i f f u s i o n c h a r a c t e r i s t i c s .

F l o w c o n t r o l , t o g e t h e r w i t h g o o d d i f f u s i o n c h a r a c t e r i s -

t ic s , e f f e c t e d b y t h e g a p - n o z z l e m o m e n t u m t r a n s f e r w a s

r e a l i z e d i n t h e r a n g e o f a n g l e s o f a t t a c k f r o m a t = 1 5 t o

at = 30 . T h e p d i s t r i b u t io n s o f C D A 2 1 - 2 1 w i t h i n t h e

a n g l e s o f a t t a c k f r o m a t = 1 5 t o 3 0 d o n o t i n d i c a t e t h e

p r e s e n c e o f a s e p a r a ti o n b u b b l e , w a s o b s e r v e d f o r C D A

4 3 . T h e a b s e n c e o f a s e p a r a t i o n b u b b l e i s p r e s u m a b l y d u e

t o t h e s u c t i o n c r e a t e d b y t h e g a p - n o z z l e e ff e c t .

N e w T a n d e m C a s c a d e C D A 32-21) pd i s t r i b u ti o n s o f t h e

n e w l y d e v e l o p e d t a n d e m c a s c a d e ( C D A 3 2 - 2 1 ) a r e p r e -

s e n t e d i n F i g . 6 . A t a t = 0 , s t e e p e r a c c e l e r a t i o n i s n o t i c e -

a b l e u p t o 4 0 o f t h e c h o r d (t o t a l ) o n t h e f r o n t b la d e

s u c t i o n s u r f a c e a f t e r w h i c h f l o w d e c e l e r a t e s u n t i l m o m e n -

t u m e x c h a n g e t a k e s p l a c e b y t h e g a p - n o z z l e a t 6 2 o f t h e

c h o r d ( F i g. 6 a ) . A k i n k b e l i e v e d t o b e d u e t o l o c a l f lo w

s e p a r a t io n a n d r e a t t a c h m e n t o n t h e r e a r b l a d e s u c t io n

s u r f a c e i s o b s e r v e d ; t h i s is c l e a r l y a n i n d i c a t i o n o f t h e

f o r m a t i o n o f a s e p a r a t i o n b u b b l e , a s o b s e r v e d i n th e

e a r l i e r i n v e s t i g a t i o n s [ 2 0 , 2 1 ] . C o n s t a n t p d i s t r i b u t i o n

w a s p r e d o m i n a n t o n t h e b l a d e p r e s s u r e s u r f a c e a t t h e

s a m e a n g l e o f a t t a c k . A t a t = 5 , f l o w a c c e l e r a t i o n r e a c h e s

t o 3 0 o f t h e c h o r d , f o l lo w e d b y c o n t i n u o u s d e c e l e r a t i o n

t o t h e r e a r b l a d e T E w i t h t h e i n t e r im e n e r g y t r a n s f e r b y

t h e g a p - n o z z l e fl o w ; p r e s s u r e s u r f a c e f l o w d e c e l e r a t e s o n

t h e f r o n t b l a d e , w h e r e a s i t a c c e l e r a t e s o n t h e r e a r b l a d e

( F i g. 6 b ) . T h e s a m e e f f e c t w i t h a m i l d e r a c c e l e r a t i o n a n d

d e c e l e r a t i o n i s t r a c e d o n t h e f r o n t b l a d e a t a t = 1 0 a n d

1 5 ( F i g s. 6 c a n d 6 d ) . A t a t = 1 8 a n d 2 0 t h e f l o w

u n d e r g o e s s h a r p a c c e l e r a ti o n a r o u n d t h e L E a n d t h e n

d e c e l e r a t e s o n b o t h s u c t i o n a n d p r e s s u r e s u r f a c e s o f t h e

f r o n t b l a d e , i n d i c a t i n g a s i g n i f ic a n t a m o u n t o f d if f u s i o n o n

t h e f r o n t b l a d e s u c t i o n s u r f a c e w h i l e t h e f l o w s u s t a in s t h e

d i f f u s i o n p r o c e s s o n t h e r e a r b l a d e s u c t i o n s u r f a c e ( F i g s .

6 e a n d 6 f ) . W i t h a n i n c r e a s e i n t h e a n g l e s o f a t t a c k f r o m

a = 2 2 to 3 0 , a s e p a r a t i o n t e n d e n c y o n t h e f r o n t b l a d e i s

i n i ti a t e d, t h u s l i m i t i n g t h e d i f f u s i o n p r o c e s s o n t h e s u c t i o n

s u r f a c e . H o w e v e r , f lo w b e h a v i o r o n t h e r e a r b l a d e s u c t i o n

s u r f a c e s h o w s c o n t i n u o u s d e c e l e r a t i o n , w h i c h i s i n d i c a ti v e

o f a n a t t a c h e d f l o w b e h a v i o r . T h i s i m p l i e s f lo w r e a t t a c h -

m e n t , s h o w i n g h i g h o v e r a l l f l o w d e f l e c t i o n a n d d i f f u s io n

c h a r a c t e r i s t i c s o f t h e c a s c a d e ( F i g s . 6 g t o 6 i ) . A t a = 3 0 ,

t h e l e a d i n g e d g e s e p a r a t i o n i s i n d i c a t e d o n t h e f r o n t

b l a d e , b u t , i n t e re s t i n g ly , t h i s f lo w h a s b e e n r e a t t a c h e d a n d

d i f f u s e d o n t h e r e a r b l a d e . I n t h e e n t i r e r a n g e o f a n g l e o f

a t t a c k , m i l d a c c e l e r a t i o n w a s o b s e r v e d n e a r t h e T I E o f th e

r e a r b l a d e p r e s s u r e s u r f a c e .

T h i s n e w l y d e v e l o p e d t a n d e m c a s c a d e s h o w s it s c a p a b i l -

i ty f o r p r e v e n t i n g f l o w s e p a r a t i o n u n d e r h i g h a n g l e s o f

a t t a c k . A l s o , t h e f o r m a t i o n o f a s e p a r a t i o n b u b b l e w a s

b e e n o b s e r v e d e x c e p t a t a t = 0 o n t h e f r o n t b l a d e , w h i c h

i s a c t ua l ly t h e f r o n t h a l f o f t h e C D A s t u d ie d u n d e r t h e

s i n g l e c a s c a d e s c h e m e . T h i s i n d i c a t e s t h a t t a n d e m e f f e c t

c r e a t e d a p s e u d o s u c t i o n a t t h e f r o n t b l a d e T E , w h i c h , i n

0 . 8

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U . K . S a h a a n d B. R o y

T w o d e f i n i t i o n s o f d i f f u s io n f a c t o r h a v e b e e n u s e d f o r

t h e t e s t e d t a n d e m c a s c a d e s : 1 ) D F g 1, b a s e d o n c l a s s i-

c a l d e f i n i t i o n , a n d 2 ) D F m o d i f i e d b a s e d o n s u m m a t i o n o f

l o c a l d if f u s i o n f a c t o r s o f t h e f r o n t a n d t h e r e a r b l a d e s .

F o r b o t h d e f i n i t io n s , t h e D F v a l u e s o f C D A 2 1 - 2 1 a r e

m u c h h i g h e r t h a n t h o s e o f C D A 4 3 w i t h in a r a n g e o f

a = 1 5 t o 2 0 F i g . 7 b ) T h e h i g h e s t m a g n i t u d e o f d i f f u -

s i o n f a c t o r D F g 1 = 0 .6 7 a n d D F m o d i f i ed = 0 . 7 5 i s o b -

s e r v e d a t a = 2 0 . D F v a l u e s d r o p s h a r p l y a f t e r 2 0 , w h i c h

i s a l s o n o t i c e a b l e f r o m t h e c o r r e s p o n d i n g p p l o t s . H i g h

b l a d e l o a d i n g c a n b e a c h i e v e d b y C D A 2 1 -2 1 w i t h i n a

r a n g e o f a = 1 5 t o 2 0

C D A 3 2 -2 1 s h o w s t h e h i g h e s t D F a t a = 1 8 a n d 2 0

F i g . 7c ) . DF ge ,~ ra l s h o w s a c o n s t a n t m a g n i t u d e o f D F =

0 . 4 2 a t a = 1 8 a n d 2 0 ; w h e r e a s , i n t h e s a m e r a n g e ,

D F m o d i f i ed s h o w s a c o n s t a n t m a g n i t u d e o f D F = 0 . 5 0. T h e

D F v s a p l o t o f C D A 3 2 - 2 1 tr a c e s a s i m i l a r v a r i a t i o n o f

d i f f u s i o n as t h a t o f C D A 4 3 w i t h a n g l e s o f a t t a c k , w i t h o u t

t h e p e a k y c h a r a c t e r i s t i c s o f C D A 2 1 -2 1 .

S t a t i c P r e s s u r e R i s e C o e f f i c i e n t

T h e s t a t i c p r e s s u r e r i s e c o e f f i c i e n t C a ) , w h i c h i s a l s o a

m e a s u r e o f t h e f l o w d i f f u s io n o r l o a d i n g c a p a b i l i t y , w a s

e v a l u a t e d f o r t h e t e s t e d c a s c a d e s F i g . 8 ). C D A 4 3 s h o w s a

r e a s o n a b l e a m o u n t o f l o a d in g c a p a b i li t y w i t h in t h e r a n g e

o f a n g l e a t t a c k f r o m a = 1 5 t o 2 5 F i g . 8 a ) . C D A 2 1 - 2 1

s h o w s h i g h e r v a l u e s o f C R w i t h i n a l i m i t e d r a n g e F i g .

8 b ) . C R v a l u e s f o r C D A 3 2 -2 1 F i g . 8 c ) t r a c e a s i m i l a r

p a t h a s t h o s e o f D F w i t h a n g l e s o f a t ta c k , a v o i d i n g t h e

p e a k y c h a r a c t e r i st i c s o f C D A 2 1 -2 1. T h e o b s e r v e d v a r i a -

t i o n o f C R w i t h D F f r o m a = 5 t o 1 5 w a s d u e t o t h e

v a r y i n g c h o r d w i s e l o c a t i o n o f V max o n t h e b l a d e s u c t i o n

s u r f a c e . A t a = 2 0 t o 3 0 , P l a n d Vmax are a t t h e s a m e

l o c a t i o n , a n d a s s u c h b o t h C R a n d D F s h o w s i m i l a r

l o a d i n g c h a r a c t e r i s ti c s .

L o s s C o e f f i c i e n t

M a s s a v e r a g e d l o s s c o e f f i c ie n t s w e r e c a l c u l a t e d f r o m t h e

w a k e s u r v e y b y m e a n s o f t r a v e r s i n g a t o t a l p r e s s u r e p r o b e .

T h e s u r v e y w a s p a r a l l e l t o t h e c a s c a d e a n d v e r y c l o se t o

t h e b l a d e T E , w h e r e t h e f l o w i s n o n u n i f o r m . D a t a w e r e

t a k e n a t c l o s e i n t e r v a l s i n th e w a k e r e g i o n a n d o v e r c o a r s e

i n t e r v a l s o u t s i d e t h e w a k e r e g i o n i .e . , f r e e - s t r e a m p a s s a g e

f l o w

T h e v a r i a t i o n o f l o ss c o e f f i ci e n t s w i t h a n g l e s o f a t t a c k

f o r t h e t e s t e d c a s c a d e s a r e s h o w n i n F i g . 9 . L o s s c o e f f i -

c i e n t v a l u e s a r e f o u n d t o b e l o w f o r s i n gl e C D A 4 3

c a s c a d e o v e r th e e n t i r e r a n g e . T h e t a n d e m C D A 2 1- 21

c a s c a d e , e v e n t h o u g h i t sh o w e d h i g h e r m a g n i t u d e s o f th e

d i f f u s i o n f a c t o r , g i v e s h i g h l o s s c o e f f i c i e n t s . T h i s m a y b e

d u e t o h i g h e r s u r f a c e f l o w v e l o c i ty , l e a d i n g t o h i g h e r s k i n

f r i c ti o n , a n d t o m i x i n g lo s s i n c u r r e d i n t h e p r o c e s s o f r e a r

b l a d e s u c t i o n s u r f a c e f l o w e n e r g i z a t i o n . T h e n e w t a n d e m

C D A 3 2 -2 1 s h o w e d l o w e r m a g n i t u d e s o f l o s s c o e f f i c ie n t s

t h a n d i d C D A 4 3 o v e r a r a n g e o f a = 5 t o 1 5 . T h e h i g h

l o s s c o e ff i c i e n ts o v e r t h e r e s t o f t h e a n g l e s o f a t t a c k a r e

d u e t o t h e t h i c k e r b u t a t t a c h e d g r o w t h o f b o u n d a r y l a y e r

s e t b y t h e t a n d e m c o n f i g u r a t i o n . T h i s i n d i c a te s t h a t t a n -

d e m c a s c a d e i s c a p a b le o f c o n t r o l li n g t h e b o u n d a r y l a y e r

g r o w t h , t h e r e b y p r e v e n t i n g t h e s e p a r a t i o n t e n d e n c y , a n d

t h e e x p e c t e d r i s e i n t h e l o s s c o e f f i c ie n t s a l s o is h e l d w i t h i n

t o l e r a b l e l i m i t s.

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c) N e w T a n d e m C D A 3 2 - 2 1

Figure 8 . V a r i a t i o n o f s ta t i c p r e s s u r e r i s e co e f f i c i e n t w i t h a n g l e s o f a t t a c k o f C D A 4 3 , C D A 2 1 -2 1 , a n d C D A

32-21 .

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d e g r e e s )

F i g u r e 9 . V a r i a t i o n o f l o ss c o e f f ic i e n t w i t h a n g l e s o f a t t a c k o f

C D A 4 3 , C D A 2 1 -2 1 , a n d C D A 3 2 -2 1 .

W a k e P r o f i l e C h a r a c t e r i s t i c s

N o r m a l i z e d w a k e v e l o c i t y a n d t o t a l p r e s s u r e l o s s p r o f i le s

a r e p l o t t e d f o r t h e t e s t e d c a s c a d e s i n F ig s . 1 0 - 1 5 . T h e

w a k e - m e a s u r i n g p l a n e w a s s e l e c t ed i n s u c h a w a y t h a t t h e

c e n t e r o f t h e h o r i z o n t a l a x is ( s h o w n i n t h e p l o t s ) c o r r e -

s p o n d s t o t h e c e n t e r o f t h e b l a d e p i t c h o f t h e m i d d l e t w o

b l ad e s . M e a s u r e m e n t s w e r e t a k e n c o v e r i n g th e t w o c e n -

t r a l b l a d e s i n e i t h e r c a s e . T h e w a k e v e l o c i t y m e a s u r e d a t a

d i s t a n c e o f 4 5 m m a f t o f t h e c a s c a d e l i n e i s n o r m a l i z e d b y

t h e r e f e r e n c e i n l e t f r e e - s t r e a m v e l o c it y . S i m i la r ly , t h e

w a k e t o t a l p r e s s u r e m e a s u r e d a t a d i s t a n c e o f 15 m m a f t

o f t h e c a s c a d e l i n e w a s n o r m a l i z e d b y t h e r e f e r e n c e t o t a l

p r e s s u r e .

W a k e v e l o c i t y p r o f i le s a t a ll a n g l e s o f a t ta c k f o r C D A

4 3 a r e a s y m m e t r i c a l a b o u t t h e w a k e c e n t e r , i n d i c a t i n g t h e

d i f f e r en t i a l g r o w t h o f b o u n d a r y l a y e r s d e v e l o p e d o n t h e

s u c t i o n a n d p r e s s u r e s u r f a c e s ( F i g . 1 0 ) . T h e d e f e c t i n t h e

w a k e v e l o c i t y p r o f i l e is l a r g e a t h i g h a n g l e s o f a t t a c k

( a = 3 0 ) .

T h e t o t a l p r e s s u r e l o s s c u r v e f o r C D A 4 3 e x h i b i te d

b e h a v i o r ( F i g . 1 1 ) s i m i l a r t o t h a t o f v e l o c i t y p r o f i l e s i n th e

e n t i r e r a n g e o f a n g l e s o f a t t a c k ( a = 0 to 3 0 ) . S u c t i o n

s u r f a c e a t a = 3 0 i n d i c a t es h i g h e r g r o w t h o f t h e b o u n d -

a r y l a y e r , w h i c h i s a l s o e v i d e n t f r o m t h e c o r r e s p o n d i n g

w a k e v e l o c i t y p r o f i l e .

T h e w a k e v e l o c i t y p r o f i le s f o r C D A 2 1 -2 1 a r e s y m m e t r i -

c a l a b o u t t h e w a k e c e n t e r f r o m a = 0 t o a = 1 0 , w h i c h

d i s t o r t s l o w l y a s t h e a n g l e o f a t t a c k i n c r e a s e s ( F i g . 1 2) .

H o w e v e r , t h e f l ow s e e m e d t o b e h i g h l y u n s t a b l e f r o m

c t = 2 2 t o a = 3 0

T h e l o s s d i s t r i b u t io n f o r C D A 2 1 -2 1 ( F ig . 1 3 ) i s s y m m e t -

r i ca l a b o u t t h e w a k e c e n t e r a t l o w e r v a lu e s o f a n g l e o f

a t t a c k ( a = 0 t o 1 0 ) . T h e w a k e p r o f i le b e c o m e s f l a t te r

a n d d i s t o r t s h i g h l y a s t h e a n g l e o f a t t a c k i n c r e a s e s . I t i s

p r o b a b l e t h a t t h e t w o a d j a c e n t w a k e s a r e c o a l e s c i n g t o -

g e t h e r i n t h e h i g h e r r a n g e o f a n g l e s o f a t t a c k ( a = 2 2 t o

30).

T h e w a k e v e l o c i ty p ro f il e s f o r C D A 3 2 -2 1 a r e m o r e

a s y m m e t r i c a l a b o u t t h e w a k e c e n t e r ( F ig . 1 4) a s c o m p a r e d

w i t h t h e v e l o c i t y p ro f i le s o f C D A 4 3 . B e y o n d a = 2 0 , t h e

w i d t h o f t h e w a k e i n c r e a s e s , i n d i c a t i n g a t h i c k e r g r o w t h o f

b o u n d a r y l a y e r o n th e s u c t i o n s u r f a c e . T h e i n c r e a s e i n

w a k e w i d t h c o u l d b e a s c r i b e d t o t h e a d d i t i o n a l 5 c a m b e r

o f th e n e w l y d e v e l o p e d c a s c a d e , w h e r e t h e b o u n d a r y l a y e r

g r e w b u t r e m a i n e d a t t a c h e d , g i v in g e ff i c ie n t d i f f us i o n .

T h e l o ss p r o f il e s f o r C D A 3 2 -2 1 ( F i g . 1 5 ) s h o w a t h i c k e r

w a k e p r o f i l e c o m p a r e d w i t h t h a t o f C D A 4 3 , i n d i c a t in g a

t h i c k e r g r o w t h o f s u c t io n s u r f a c e b o u n d a r y l a y e r a n d

h e n c e h i g h l o s se s o f th e c a s c a d e , w h i c h a r e r e f l e c t e d i n

t h e m a s s a v e r a g e d l o s s c o e f f i c i e n t .

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ang les o f a t t ack .

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F i g u r e I L W a k e t o t al p r es s u re l o s s p r of i le s o f C D A 4 3 a t

v a r y i n g a n g l e s o f a t t a c k .

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Figure 12. W a k e velocity profiles of CD A 21-21 at varying

angle s of attack.

1 . 8

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E x p er im en ta l In v es t i g a ti o n s o n T an d em C o m p resso r C ascad e 2 7 3

U N C E R T A I N T Y A N A L Y S I S

E x t r e m e c a r e w a s e x e r c i s e d t o e n s u r e t h e h i g h e s t p o s s i b l e

r e l ia b i l it y a n d a c c u r a c y o f t h e a c q u i r e d t e s t d a t a . E a c h

d a t a p o i n t o n t h e b l a d e s u r f a c e s r e p r e s e n t s a n a v e r a g e o f

t h r e e r e p e t i t i v e p r e s s u r e a n d v e l o c i t y r e a d i n g s . T h e t i m e

b e t w e e n s u c c e s s iv e r e a d i n g s w a s 5 s . I n s u r v e y i n g t h e

w a k e f l o w m a n u a l l y , e a c h t i m e t h e p r o b e w a s m o v e d t o a

n e w p o s i t i o n , w e a l l o w e d a s e t t l i n g t i m e o f 1 0 - 1 5 s t o

r e c o r d t h e d a t a . T h e a c c u r a c y o f th e m i c r o m a n o m e t e r w a s

0 .1 m m H 2 0 f o r t h e p r e s s u r e r e a d i n g a n d 0.1 m / s f o r th e

v e lo c i t y r ead in g .

T h e u n c e r t a i n t i e s r e l a t i v e t o c a s c a d e p a r a m e t e r s a r e a s

fo l lows: s tag ger ang le ~ / ) = _+0 .5 , a n g l e o f a t t a c k a ) =

+ 0 . 5 , o v e r a l l c a m b e r ~ P o ) = + 1 . 0 , b l a d e p i t c h s ) =

-+ 0 .5 m m , b l ad e p ro f i l e t o l e r an c e = -+ 0 . 25 m m .

P R A C T I C A L S I G N I F I C A N C E / U S E F U L N E S S

T h e r e s u l t s o f t h e p r e s e n t s t u d y w o u l d b e e x t r e m e l y u s e f u l

f r o m a p r a c t i c a l p o i n t o f v i e w b e c a u s e i t p r o v i d e s s ig n if i-

c a n t g u i d a n c e f o r d e s i g n i n g p r a c t i c a l m a c h i n e s m e a n t f o r

h i g h e r l o a d i n g l i m i t s . T h e p r e s e n t d a t a c o u l d b e u s e d a s

g u i d a n c e f o r d e s i g n i n g m a c h i n e s f o r l o w s p e e d a p p l i c a -

t i o ns , a s i n t h e c a s e o f a i r h a n d l i n g e q u i p m e n t , v e n t i l a t i o n

fan s , co o l in g f an s , an d so fo r th .

F o r h i g h s p e e d a p p l i c a t i o ns , f u r t h e r o p t i m i z a t i o n o f t h e

b l a d e s h a p e i s n e c e s s a r y t o t a k e i n t o a c c o u n t t h e f o r m a -

t i o n o f s h o c k s a n d c o m p r e s s i b i l i t y e f f e c ts . S u c h h i g h s p e e d

d a t a m a y b e u s e f u l f o r de s i g n i n g t a n d e m s t a t o r a n d r o t o r

b l a d e s f o r a i r c r a f t g a s t u r b i n e s , f o r v e h i c u l a r g a s t u r b i n e s

e . g . , ca r s , t r u ck s , h o v e rc ra f t s , sh ip s , e t c . ) , an d fo r i n d u s -

t r ia l p o w e r g e n e r a t i n g u n i t s . P o t e n t i a l c a n a l s o b e r e a l i z e d

i n t a n d e m v a n e d d i f f u s e r s o f c e n t r i f u g a l c o m p r e s s o r s a n d

i n t u r b o p u m p f e e d s y s t e m s in l iq u i d p r o p e l l a n t r o c k e t

en g in es .

C O N C L U S I O N S

I n t h e p r e s e n t i n v e s t i g a t i o n s , a n a t t e m p t h a s b e e n m a d e

t o a c h i e v e a n e x t r a f l o w d e fl e c t i o n o f 5 , u s i n g a t a n d e m

b l a d e c o n f i g u r a t io n , i n c o m p a r i s o n w i t h a s i n g le b l a d e

p r o f il e , w i t h m i n i m u m l o s s p e n a l t y . C D A 4 3 h a s s h o w n

g o o d d i f fu s io n cap ab i l i t y o v e r a r an g e o f t~ = 1 5 t o 2 5 ,

w h e r e a s C D A 2 1 - 2 1 h a s s h o w n h i g h e r d i f f u s i o n c a p a b i l i t y

w i th in a r a n g e o f a = 1 5 to 2 0 . T h in a i r fo i l ch a ra c t e r i s -

t i c s o f C D A 2 1 - 2 1 c o n f i g u r e d o u t o f t w o s c a l e d d o w n

C D A p r o f i l e s w e r e o b s e r v e d . A t h i n a i r f o i l i s c h a r a c t e r -

i z e d b y a n a r r o w r a n g e o f o p e r a t i o n . W h e n u s e d i n a

t a n d e m c o n f i g u r a t i o n , b o t h t h e f r o n t a n d t h e r e a r b l a d e s

h a v e a l o w l e a d i n g e d g e r a d i u s t o c h o r d t o t a l ) ra t i o .

H e n c e , f lo w g u i d a n ce o v e r b o t h f r o n t a n d r e a r b l a d e

l e a d i n g e d g e s i s l i m i t e d t o a n a r r o w i n c i d e n c e r a n g e . T h i s

w a s o b s e r v e d i n t h e p r e s e n t e x p e r i m e n t a l f i n d i n g s .

C D A 2 1 - 2 1 h a s a h i g h e r t o t a l p r e s s u r e l o s s c o e f f i c i e n t

t h a n t h a t o f C D A 4 3 . T h i s m a y b e c a u s e d b y th e m i x i n g

l o ss i n c u r r e d a s a r e s u l t o f t h e s u c t i o n s u r f a c e f l o w e n e r -

g i z a t i o n . T h e o t h e r r e a s o n c o u l d b e t h e l o w e r m a g n i t u d e

o f t h i c k n e s s t o t o t a l c h o r d r a t i o , y ie l d i n g p o o r f l ow g u id -

a n c e , e s p e c i a l l y n e a r t h e l e a d i n g e d g e s . W a k e f l o w is

a g g r a v a t e d f u r th e r b y a n e x t r a c a m b e r o f 5 F u r t h e r m o r e ,

s k i n f r i c t io n d r a g m a y b e h i g h b e c a u s e o f a h i g h e r m a g n i -

t u d e o f s u r f a c e v e l o c i t y , e s p e c i a l l y o n t h e r e a r b l a d e . I t

c o u l d b e s a i d t h a t , a f t e r a j u d i c io u s t r a d e - o f f b e t w e e n

h i g h e r b l a d e l o a d i n g a n d h i g h e r l o s s e s , C D A 2 1 - 2 1 h a s

t h e p o t e n t i a l c o m p a r e d w i t h C D A 4 3 o v e r a l i m i te d r a n g e

o f a n g l e s o f a t t a c k , a n d f u r t h e r o p t i m i z a t i o n w i t h t h e

c a s c a d e g e o m e t r y is r e q u i r e d f o r i t s i m p r o v e d p e r f o r -

m a n c e o v e r a w i d e r ra n g e . H o w e v e r , a c o m p r e s s o r m e a n t

o n l y f o r d e s i g n - p o i n t o p e r a t i o n m a y s t a n d t o g a i n b y t h e

u s e o f t h e C D A 2 1- 21 t a n d e m b l a d e .

T h e p o t e n t i a l o f C D A 3 2 -2 1 w a s o b s e r v e d i n m a i n t a i n -

i n g a s u s t a i n e d f l o w a t t a c h m e n t w i t h i n a r e a s o n a b l e r a n g e

o f an g le o f a t t a ck f r o m a = 5 t o a = 3 0 . T h i s i n d i ca t e s

th a t i t s f l o w d e f l ec t i o n cap ab i l i t y i s su p e r io r t o t h a t o f

C D A 4 3 . T h e r e a s o n f o r i ts e f fi c a c y c o u l d b e a t t r i b u t e d t o

a g u i d e d f l ow e n e r g i z a t i o n b y t h e c u s p - s h a p e d g a p - n o z z l e

f o r m e d b e t w e e n t h e b l a d es a n d t o h ig h e r m a g n i t u d e o f

f r o n t b l a d e l e a d i n g e d g e t h i c k n e s s t o t o t a l c h o r d r a t i o . A n

a d d i t i o n a l c a m b e r o f 5 w a s a d d e d f o r h i g h e r f l ow d e f l e c -

t i o n in t h e n e w l y d e v e l o p e d t a n d e m C D A 3 2 -2 1 c a s c a d e ,

w i t h a c c e p t a b l e l o s s c o e f f i c i e n t s o v e r t h i s r a n g e o f a n g l e s

o f a t t a c k .

F U T U R E R E S E A R C H

F u t u r e r e s e a r c h n e e d s t o a d d r e s s t h e c u s p s h a p e o f t h e

f r o n t b l a d e t ra i l in g e d g e a n d t h e c o n s e q u e n t g a p g e o m e t r y

m o r e a c c u r a t e l y . T h e f l o w c o n d i t i o n s n e a r t h e g a p a r e t o

b e a c c u r a t e l y a s s e s s e d t h r o u g h b o u n d a r y l a y e r s t u d i e s ,

a n d t h i s k n o w l e d g e c o u l d b e p u r s u e d f o r d e v e l o p i n g a

s u i t a b l e c o m p u t a t i o n a l c o d e . S u c h a n i n v e s t i g a t i o n w o u l d

n o t o n l y l e a d t o a c c u r a t e a n a l y si s o f t h e f l o w i n a n d

a r o u n d t h e t a n d e m c a s c a d e c o n f i g u r a t i o n s , b u t a l s o p r o -

v i d e g u i d e l i n e s f o r f u t u r e e x p e r i m e n t a t i o n .

T h e p r e s e n t w o r k h a s b e e n a d d r e s s e d m o r e t o t he

c o n t r o l o f d i f fu s i o n, w h i c h o c c u r s o n t h e r e a r h a l f o f t h e

b l a d e s u r f a c e . T h e f r o n t h a l f , w i t h h i g h a c c e l e r a t i o n , s e p a -

r a t i o n b u b b l e , a n d o n s e t o f s h a r p d i f f us i o n , w o u l d r e q u i r e

c l o s e i n v e s ti g a t io n , e s p e c i a l l y a t h i g h s p e e d w h e r e c o m -

p res s ib i l i t y , t u rb u l en ce , an d sh o ck in t e r ac t i o n s w o u ld b e

sign if ican t .

R e c e n t l y , r e s e a r c h h a s b e e n u n d e r t a k e n t o f i n d t h e

o p e r a t i o n a l f e a s i b il i ty o f th e d e v e l o p e d t a n d e m c a s c a d e

f o r t h e o f f - d e s i g n f l o w c o n d i t io n . K n o w l e d g e o f o f f -d e s i g n

p e r f o r m a n c e o f a h i g h p r e s s u r e r a t i o a x i a l f l o w c o m p r e s -

s o r i s e x t r e m e l y i m p o r t a n t b e c a u s e i t a f f e c t s o p e r a t i n g

c o s t s a n d c o m p o n e n t l i f e . I n c a s e o f a e r o e n g i n e s , i d l i n g ,

t ak e -o f f , an d c ru i se w i l l a lw ay s r e su l t i n d i f f e r en t f l o w

s i t u a t i o n s w i t h i n t h e c o m p r e s s o r s t a g e s . S i m i l a r l y , o t h e r

m o d e s o f p r o p u l s i o n , su c h a s m a r i n e a n d i n d u s t r i a l g a s

t u r b i n e s , w h e r e a x i a l c o m p r e s s o r s a r e e m p l o y e d o f t e n

n e e d t o o p e r a t e a w a y f r o m t h e d e s i g n p o i n t f o r s i g n if i c an t

l e n g t h s o f t i m e . T h u s t o m a i n t a i n t h e p e r f o r m a n c e o f th e

m a ch in e a t o f f -d es ig n co n d i t i o n , f l ex ib i li t y i n t h e o p e ra -

t i o n o f t h e c o m p o n e n t i s r e q u i r e d . O n e w a y t o i m p r o v e

t h i s s i t u a t i o n i s t o o p e r a t e t h e c a s c a d e i n a v a r i a b l e

c a m b e r m o d e . I n o u r n e x t e x p e r i m e n t a l v e n t u r e , t h e d e -

v e l o p e d t a n d e m c a s c a d e w i l l b e t e s t e d a t v a r i o u s c a m b e r

se t t i n g s t o a s ses s i t s o f f -d es ig n f l o w co n t ro l cap ab i l i t y .

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2 7 4 U . K . S a h a a n d B . R o y

A P P E N D I X A

B l a d e C o - o r d i n a t e s o f C D A 4 3 t r u n c a t e d )

xss ss xps

~

- 0 . 0 2 0 . 5 3 0 . 3 4 - 0 . 3 6

0 . 0 6 1 . 0 0 0 . 8 2 - 0 . 6 5

0 . 0 6 1 . 1 3 1 . 3 6 - 0 . 8 3

O. 1 0 1 . 9 0 2 . 0 0 - 0 . 8 9

0 . 2 8 2 . 7 4 2 . 7 1 - 0 . 9 0

0 . 5 9 3 . 5 6 3 . 4 9 - 0 . 8 6

1 . 1 2 4 . 2 6 4 . 3 2 - 0 . 7 4

2 . 1 6 5 . 2 0 5 . 2 4 - 0 . 5 3

3 . 4 6 6 . 1 9 6 . 3 0 - 0 . 3 4

5 . 1 7 3 . 3 7 7 . 3 6 - 0 . 1 2

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

9 . 2 8 9 . 9 0 9 . 7 0 0 . 4 2

1 1 . 5 8 1 1 . 1 9 1 0 . 9 8 0 . 7 2

1 3 . 8 6 1 2 . 3 9 1 2 . 2 9 1 . 0 6

1 5 . 9 6 1 3 . 4 3 1 3 . 6 0 1 . 4 5

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

1 9 . 4 1 1 4 . 9 9 1 6 . 6 7 2 . 1 8

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

2 2 . 0 3 1 6 . 0 6 1 9 . 9 2 3 . 0 3

2 3 . 1 5 1 6 . 4 8 2 1 . 6 4 3 . 4 8

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

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

2 6 . 0 7 1 7 . 4 6 2 7 . 2 8 4 . 8 7

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

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

2 8 . 6 3 1 8 . 1 8 3 3 . 6 3 6 . 2 7

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

3 0 . 2 1 1 8 . 5 6 3 8 . 3 6 8 . 2 0

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

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

3 2 . 4 3 1 9 . 0 0 4 3 . 0 0 1 0 . 0 9

3 3 . 1 3 1 9 . 1 1 4 5 . 0 0 1 1 . 1 8

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

3 4 . 4 6 1 9 . 2 9 4 9 . 0 0 1 3 . 0 2

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

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

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

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

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

3 8 . 9 1 1 9 . 5 0

4 0 . 2 2 1 9 . 5 2

4 1 . 5 6 1 9 . 4 7

4 3 . 0 1 1 9 . 3 8

4 4 . 4 5 1 9 . 2 5

4 5 . 9 4 1 9 . 0 9

4 7 . 4 4 1 8 . 8 9

4 8 . 9 7 1 8 . 6 6

5 2 . 1 1 1 8 . 0 8

5 5 . 3 9 1 7 . 3 6

5 8 . 7 7 1 6 . 5 2

6 1 . 0 0 1 5 . 5 8

A P P E N D I X B

B l a d e C o - o r d i n a t e s o f C D A 2 1 s o l id )

xs~ x~ x~

~s

- 0 . 4 2 0 . 6 9 - 0 . 3 9 0 . 5 1

- 0 . 4 1 0 . 9 0 - 0 . 3 5 0 . 3 5

- 0 . 3 9 1 . 1 3 - 0 . 2 8 0 . 2 3

- 0 . 3 1 1 . 4 2 - 0 . 2 0 0 . 1 2

0 . 1 2 1 . 8 9 0 . 0 0 0 . 0 0

0 . 0 7 2 . 2 4 O . 1 1 - 0 . 0 4

0 . 3 3 2 . 6 5 0 . 2 2 - 0 . 0 5

0 . 6 5 3 . 1 3 0 . 3 3 - 0 . 0 5

1 . 0 5 3 . 6 5 0 . 4 5 - 0 . 0 4

1 . 5 1 4 . 2 1 0 . 5 7 0 . 0 1

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

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

3 . 2 6 6 . 1 3 0 . 9 5 0 . 1 3

3 . 9 1 6 . 7 7 1 . 0 9 0 . 1 9

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

5 . 1 7 7 . 9 7 1 . 3 7 0 . 3 3

5 . 7 7 8 . 4 8 1 . 51 0 . 4 2

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

6 . 8 1 9 . 3 6 1 . 8 3 0 . 6 1

7 . 2 7 9 . 7 3 1 . 9 9 0 . 7 1

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

8 . 0 7 1 0 . 3 3 2 . 3 1 0 . 9 3

8 . 4 1 1 0 . 5 8 2 . 4 9 1 . 0 5

8 . 7 3 1 0 . 8 1 2 . 6 7 1 . 1 7

9 . 0 3 1 1 . 0 1 2 . 8 5 1 . 3 1

9 . 2 9 1 1 . 1 9 3 . 0 4 1 . 4 4

9 . 7 9 1 1 . 5 1 3 . 2 3 1 . 5 8

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

1 1 . 0 3 1 2 . 2 3 4 . 0 9 2 . 2 1

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

1 3 . 0 9 1 3 . 2 1 5 . 0 7 2 . 9 5

1 3 . 6 3 1 3 . 4 5 5 . 3 5 3 . 1 6

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

1 5 . 3 5 1 4 . 1 2 6 . 2 6 3 . 8 6

1 6 . 5 9 1 4 . 5 5 6 . 6 0 4 . 1 2

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

1 8 . 6 2 1 5 . 2 3 8 . 1 9 5 . 3 5

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

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

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

2 1 . 7 1 1 6 . 2 3 1 1 . 7 9 7 . 9 9

2 2 . 5 5 1 6 . 5 2 1 2 . 6 4 8 . 5 8

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

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

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

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

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

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

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

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

3 2 . 3 1 1 9 . 9 7 3 1 . 5 9 1 8 . 2 1

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

3 4 . 2 1 2 0 . 7 2 3 4 . 7 9 1 9 . 4 7

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Experim ental Investigations on Tan dem Compressor Cascade 275

. . . . . . . . . . . . . . ; ' - - ' 7 7 7 7 . . . . .

1 / . . . . . s .o i o s . .o e

- 1 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9

X - a x i s

C o n t r o l l e d D i f f u s i o n A i r f o i l ( 32 g C a m b e r )

or

q~

%

1,2

loc, ref

max

x, y,

solidity

c/ s ) ,

dimensionless

camber angle, degrees

overall camber angle (for tan dem blade), degrees

Subscripts

cascade inlet and outlet planes

local and reference conditions

maximum on the blade suction surface

axial, tangential, and spanwise directions

AR

b

p

CR

C DA

c

DF

FB

LE

N

P

/ 0

PS

Q

RB

SPRC

SS

TE

V

3

8

T

%

1

K

a e 0

to

~ t 0

Suction Surface

/ / -~--~-e= Pressu,'e Surface

- 0 q ~ l r , . , . . . . . . . . . . . . . . i

- I 10 20 30 40

X-axis

Controlled Diffusion Airfoil (210 Camber}

NOMENCLATURE

aspect ratio b / c ) , dimensionless

blade span, mm

static pressure coefficient

Cp

= Ploc - P1/Q1)

static pre ssu re rise coefficient (C R = P2 -

Pl/QI), dimensionless

controlled diffusion airfoil

blade chord, mm

diffusion factor (DF = Vm~ - V2 /V 1)

front blade

leading edge

number of blades

static pressure, kPa

total pressure, kPa

pressure surface

dynamic pressure, kPa

rear blade

static pressure rise coefficient, dimensionless

suction surface

blade pitch, mm

trailing edge

flow velocity, m/s

volume flow rate, Cu m/s

G r e e k S y m b o l s

angle of attack, degrees

flow angle, degrees

deviation angle, degrees

turning/d eflect i on angle (~ =/31 - / 3 2 , degrees

stagger angle, degrees

effective stagger angle (for tan dem blade),

degrees

incidence angle, degrees

blade angle, degrees

total pressure loss, kPa

loss coefficient (to = APo/Q1) dimensionless

REFERENCES

1. Wennerstrom, A. J., Highly Loaded Air Flow Compressors: His-

tory and Current Developments.

ASME J. Turbomachinery

112,

567-578, 1990.

2. Cumpsty, N. A.,

Compressor Aerodynamics.

Longman, Bombay,

India, 1989.

3. Starken, H., Performance of Controlled Diffusion Blades, Axial

Flow Compressors, VKI Lecture Series 1992-02, 1992.

4. Behlke, R. F., The Development of a Second Generation of

Controlled Diffusion Airfoils for Multistage Compressors.

ASME

J. Turbomachinery108, 32-41, 1986.

5. Stephens, H. E., and Hobbs, D. E., Design and Performance

Evaluation of Supercritical Airfoils for Axial Flow Compressors.

United Technologies Corporation Report FR 11455, 1979.

6. Hobbs, D. E., and Weingold, H. D., Development of Controlled

Diffusion Airfoil for Multistage Compressor Application.

ASME

J. Eng. Gas Turbines Power 106, 271-278, 1984.

7. Bledsoe, M. R., The Method of Complex Characteristics for

Design of Transonic Blade Sections. Paper No. D OE/ ER /

03077-273/UC-32, Elsevier Science, Inc., New York, 1986.

8. Sturm, W., Scheugenpflug, H., and Fottner, L., Performance

Improvements of Compressor Cascades by Controlling the Pro-

file and Sidewall Boundary Layers. ASMEJ. Turbomachinery114,

477-493, 1992.

9. Wu, C.-H., Zhuang, B., and Guo, B., Experimental Investigation

of Tandem Blade Cascades with Double Circular Arc Profiles.

ASME Paper No. 85-GT-94, 1985.

10. Roy, B., Marathe, B. V., and Gangal, D. B., Comparative Cas-

cade Studies of Some High Diffusion Compressor Bladings. Proc.

Ninth Int. Symp. on Air Breathing Engines,

Athens, Greece, pp.

1281-1289, 1989.

11. Sachmann, J., and Fottner, L., Highly Loaded Tandem Compres-

sor Cascades with Variable Camber and Stagger. ASME Paper

No. 93-GT-235, 1993.

12. Roy, B., Walvekar, A. K., Saha, U. K., and Marathe, B. V., Low

Speed Cascade Studies of Highly Cambered Single and Tandem

Compressor Blading. Int. J. Turbo Jet Engines 12, 129-137, 1995.

13. Gostelow, J. P., Cascade Aerodynamics. Pergamon, Oxford, 1984.

14. Wennerstrom, A. J., Low Aspect Ratio Axial Flow Compressors:

Why and What I t Means.

ASMEJ. Turbomachinery

111, 357-365,

1989.

15. Wisler, D. C., Loss Reduction in Axial F low Compressors

Through Low-Speed Model Testing.

ASME J. Gas Turbine Power

107, 354-363, 1985.

16. Hirsch, C., Advanced Methods for Cascade Testing. AGARD-

AG-328, 1993.

17. Yocum, A. M., and O'Brien, W. F., Separated Flow in a Low

Speed Two Dimensional Cascade I: Flow Visualization and Time

Mean Velocity Measurements.


115,

409-420, 1993.

18. Yocum, A. M., and O'Brien, W. F., Separated Flow in a Low

Speed Two Dimensional Cascade II: Cascade Performance.


115, 421-434, 1993.

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2 7 6 U . K . S a h a a n d B . R o y

1 9. M a ra t h e B . V . C a sc a d e S t u d i e s o f H i g h l y Lo a d e d C o mp re sso r

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Rece ived Apr i l 27 1995; rev ised August 30 1996

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