an examination of the flow and pressure losses in blade rows of axial-flow turbines

7/28/2019 An Examination of the Flow and Pressure Losses in Blade Rows of Axial-Flow Turbines

http://slidepdf.com/reader/full/an-examination-of-the-flow-and-pressure-losses-in-blade-rows-of-axial-flow 1/35



E x a m i n a t io n o f th e F l o w a n d P r es su r e L o s s es in

B la d e R o w s o f A x i a l -F l o w T u r b i n e s

D. G. AINLEY and G. C. R. MATHIESON

C O M M U N IC A T ED B Y T H E P R I N C I P A L D I R E C T O R O F S C I E N T I F I C R E SE A R CH ( A I R ) ,

M I N I S T R Y O F S U P P L Y

Rep or t s a n d M e~ n o r a n d a N o . 2 8 9 I

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i I g J U L 1 9 55 I

S u m m a r y . ~ T h e d e s ig n o f a x i a l- f lo ~ t u r b i n e s h a s b e e n h a m p e r e d i n t h e p a s t b y a l a c k o f c o m p r e h e n s i v e d a t as s es a n d g a s d e fl e ct io n s t h r o u g h r o w s o f t u r b i n e b l a d es . I n t h e p r e s e n t r e p o r t m u c h o f t h e a v a i l a b l e

r e l a t i n g t o t h i s s u b j e c t i s s t u d i e d a n d a n a l y s e d t o d e t e r m i n e m a g n i t u d e s o f g a s p r es s u r e lo s se s a n d d e f l e ct i o nst y o f b l a d e r o w s a n d a ls o t o d e t e r m i n e t h e s e p a r a t e i n fl u e nc e s o f v a r i a b l e s s u c h a s b l a d e s h a p e , b l a d e

n g , g a s M a c h n u m b e r , R e y n o l d s n u m b e r , i n c i d en c e , e tc . O f p a r t i c u l a r i m p o r t a n c e a r e t h e e f fe c t s o f s e c o n d a r yo w s o n t h e a e r o d y n a m i c p e r f o r m a n c e o f a b l a d e r o w a n d s p e c ia l a t t e n t i o n i s p a i d t o ' s e c o n d a r y l os s es ', w h i c h

d i f fe r e nc e b e tw e e n t h e t o t a l l o s se s o cc u r r i n g in a n a c t u a l t u r b i n e b l a d e r o w a n d t h e s m a l l e r tw o - d i m e n s i o n a l

w lo s s e s w h i c h a r e u s u a l l y m e a s u r e d i n a b l a d e c a s c a d e t u n n e l . E f f & ct s o f b l a d e t i p c l e a r a n c e a r e a ls o s t u d i e d .R e s u l t i n g f r o m t h i s a n a l y s i s a n u m b e r o f e m p i r i c a l g u i d i n g ru l e s a n d c h a r t s h a v e b e e n d e r i v e d f r o m w h i c h a p p r o x i -

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

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

s s b e i n g g e n e ra l l y f o u n d t o b e g r e a t w h e n t h e b l a d i n g h a s l o w r e a c ti o n .

1 . I n t r o d u c t i o n . - - I n early years of gas-turbine development absence of reliable data relating

stumbling block in the pa th of the design of high-efficiency turbines.

Inaccura te da ta or erroneous assumptions will inevitably lead to a poor compromise betweenefficiency of a turbine and the other impor tan t factors such as size, weight, cost and mechanical

During recent years the performances of several 7turbines have been accurately calibrated one Nationa l Gas Turbine Establishment and collaborating firms.

the r experimental work has accumula ted from. other sources such as cascade tunnels, de tailflow through nozzle rows, and earlier work carried out in the course of steam-

( e . g . , experiments conducted by the Steam.NoZzle Research Committee).

Much of this experimental evidence has been examined in detail and an attempt has been madethe various experimental results. This has been done with the prime purpose of

ning the magnitudes of the pressure losses and the gas efflux angles from rows of turbinelating them to those aerodynamic and geometric variables which exercise a dominant

* N . G . T . E . R e p o r t R . 8 6 , r e c e iv e d 1 3 t h S e p t e m b e r , 1 95 1.

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2 . L i m i t a t i o m . - - T h e g r e a t e s t d i f f ic u l t y t h a t a r is e s i n m a k i n g a n a n a l y s i s w h i c h i s s i m p l e t oc o m p r e h e n d a n d a p p l y i s c o n t e n d i n g w i t h t h e l a r g e n u m b e r o f v a r i a b l e s w h i c h p l a y a r o l e , l a r g eo r s m a l l , i n t h e o v e r a l l p e r f o r m a n c e o f a tu r b i n e s t a g e . I n o r d e r t o d e r i v e a n d p r e s e n t d a t aa p p e r t a i n i n g t o a n y a s p e c t o f t h e a e r o d y n a m i c o p e r a t i o n o f a b l a d e r o w i t b e c o m e s n e c e s s a r y t os e le c t, e i t h e r b y t h e o r e t i c a l r e a s o n i n g o r b y a b r o a d e x a m i n a t i o n o f e x i s t in g s t a t i s t i c a l e v id e n c e ,o n l y t h o s e v a r i a b l e s w h i c h e x e rc i se a d o m i n a n t i n f lu e n c e , a n d t o d i s c a r d t h e r e m a i n d e r . A n y

l a w s w h i c h m a y t h e n b e d e d uc e d a r e ne c e s s a ri l y a p p r o x i m a t e . T h e n u m b e r o f v a r i a b le s t h a ta r e s e l e c te d t o d e f in e t h e p e r f o r m a n c e o f a r o w o f b l a d e s w i l l d e p e n d u p o n , ( a) t h e a c c u r a c y t ow h i c h i t i s r e q u i r e d t o p r e d i c t t h e b e h a v i o u r o f t h e g a s w h e n i t f lo w s t h r o u g h a r o w of b l a d e s , a n d( b ) t h e n u m b e r o f v a r i a b l e s c o n c e r n i n g w h i c h t h e r e i s a d e q u a t e e x p e r i m e n t a l d a t a .

I n t h e p r e s e n t a n a l y s i s t h e a i m h a s b e e n t o d e r i v e b a s i c d a t a f o r p r e d i c t i n g m e a n t o t a l p r e s s u r el o ss in a b l a d e r o w w i t h a n e r r o r o f l es s t h a n ~ 1 5 p e r c e n t a n d m e a n g a s e f fl u x a n g l e w i t h a ne r r o r o f l e s s t h a n : ~ 0 . 0 2 c o s - ~ ( o p e n i n g / p i t c h ) . T h e s e t o l e r a n c e s w i l l e n a b l e a p r e d i c t i o n o fe f fi c ie n c y a n d f l o w t h r o u g h a t u r b i n e a t i t s d e s i g n s p e e d a n d p r e s s u r e r a t i o t o b e m a d e t o w i t h i n

2 p e r c e n t o f t h e t r u e v a l u e .

H o w e v e r , i t s h o u l d b e a p p r e c i a t e d t h a t t h i s is p o s s i b le o n l y w h e n t h e t u r b i n e i s d e s i g n e d to

c o n fo r m w i t h t h e t y p e o f b l a d i n g w h i c h is s u r v e y e d b y t h e a n a l ys i s. T h e r a n g e o f b la d e s h a p e sf o r w h i c h s t a t i s t i c a l d a t a e x i s t s i s b y n o m e a n s c o m p l e t e. F o r e x a m p l e , t h e r a n g e o f b l a d es e c t io n s t h a t h a v e b e e n u s e d u p t o t h e p r e s e n t t i m e f o r l o w r e a c t i o n s t a g e s h a v i n g h i g h g a sd e f l ec t i o n s h a v e s h o w n l o ss e s w h i c h a r e m a n y t i m e s t h e l o ss w h i c h i s n e c e s s i t a t e d b y c o n s i d e r a t i o no f s k i n fr i c t io n a lo n e . F u t u r e r e s e a r c h m a y l e a d t o r e d u c t i o n s o f t h e s e h i g h l o ss e s a n d p e r h a p st o t h e i n t r o d u c t i o n o f f u r t h e r v a r i a b l e s w h i c h a t t h e p r e s e n t t i m e h a v e b e e n o v e r l o o k e d o ri g n o r e d .

3 . G e n e ra l R e m a r k s C o m e r n i ~ g t h e P r e s s u re L o ss e s i n a B l a d e R o w . - - T h e o v e r a l l p r e s s u r e l o s so c c u rr i ng i n a b h d e r o w m a y b e c o n v e n i e n t l y s u b d i v i d e d i n t o a n u m b e r o f c o m p o n e n t l os s es ,e a c h c o m p o n e n t l o s s b e i n g i n f lu e n c e d b y s o m e o f t h e v a r i a b l e s d e f i n i n g t h e a e r o d y n a m i c f o r m o ft h e g a s fl o w a n d b y s o m e o f t h e v a r i a b l e s d e f i n i n g t h e g e o m e t r i c f o rm o f t h e b l a d e r ow . T h e

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

(a ) Pr o f i l e lo s s , b e i n g t h a t l o s s d u e to s k i n f r i c ti o n o r s e p a r a t i o n w h i c h w i l l t a k e p l a c e w i t ha u n i f o r m t w o - d i m e n s i o n a l f l o w a cr o s s a c a s c a d e o f b l a d e s

(b ) Secondar y lo s s , w h i c h r e s u l t s f r om n o n - u n i f o r m i t y o f t h e t h r e e - d i m e n s i o n a l f lo w t h r o u g ha r o w o f b l a d e s ( in p a r t i c u l a r , l o s s es d u e t o i n t e r a c t i o n b e t w e e n t h e b l a d e e n d s a n d t h eb o u n d a r y l a y e r o n t h e a n n u l u s w a l l s )

( c) T @ c lear ance lo s s , o r l o s s e s d u e t o l e a k a g e o f g a s r o u n d s h r o u d b a n d s

(d) A ~ u l u s lo ss , b e i n g t h e s k i n - f r i c t i o n l o s s o n t h e e n d w a l l s o f a r o w o f b l a d e s .

C a r t e r 1 p o i n t s o u t t h a t (b) a n d (c) a re c l o s e l y r e l a t e d t h e o r e t i c a l l y b u t f o r a n a l y s i s p u r p o s e si t i s c o n v e n i e n t t o k e e p t h e m s e p a r a t e d . O n t h e o t h e r h a n d , s i n c e b o t h (b) a n d (d) a r e p r i n c i p a l l ya s s o ci a te d w i t h t h e b o u n d a r y l a y e r s o n t h e a n n u l u s w a l l s t h e a u t h o r s h a v e a d o p t e d t h e p r a c t i c eo f c o n s i d e r i n g t h e a n n u l u s lo s s a s p a r t o f t h e s e c o n d a r y l o ss . A n a d d i t i o n a l a n n u l u s l o s s w o u l do n l y b e a d d e d i f t h e l e n g t h o f a n n u l u s w a l l b e t w e e n a d j a c e n t b l a d e r o w s w a s s u f f i c ie n t l y l a r g et o m a k e t h e e x t r a s k i n - f r i c t io n lo s s a p p r e c i ab l e .

Wh e r e v e r c o n v e n i e n t , p r e s s u r e l o s s e s a r e r e f e r r e d t o i n t e r m s o f a l o s s c o e f f i c i e n t , Y , d e f i n e da s :

y ~ Loss of total- head pressure

Tota l pressure a t blade out le t - - sta t ic pressure a t blade out le t "

2



H o w e v e r , i t is f o u n d t h a t s o m e o f t h e ' c o m p o n e n t l o ss e s m a y b e c o r r e l a t e d b e t t e r o v e r a w i d ee o f b l a d i n g b y d e f i n i n g l o s s i n t e r m s o f a d r a g c o e f f ic i e n t, C ~, b a s e d o n v e c t o r m e a n v e l o c i t y .

e e n CD a n d Y i s q u o t e d i n A p p e n d i x I .

T h i s s y s t e m f o r e x p r e s s i n g l o ss se e m s b e t t e r s u i t e d t o a n a l y s i s t h a n t h e b l a d e v e l o c i t y c o-i c ie n ts a d o p t e d i n t h e p a s t b y s t e a m - t u r b i n e e n g i ne e r s. I t a ls o l e n d s i t se l f m o r e r e a d i l y t o t h e

a m i c r e s e a r c h d a t a a c q u i r e d f r o m o t h e r f ie l ds o f i n v e s t i g a t i o n , a n d viceF u r t h e r m o r e , i t m a y m o r e e a s i ly e n a b l e t h e c h a r a c t e r i s t i c p r o b l e m s a s s o c i a t e d w i t h t h e

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

3.1. N o m e n c l a t u r e . - - A l i s t o f s y m b o l s i s g i v e n i n A p p e n d i x t . F i g s . 1 a n d 2 i l l u s t r a t e t ti em a d o p t e d f o r d e f i n in g t h e g e o m e t r y o f a b l a d e r o w a n d t h e g a s a n g le s r e l a t i v e t o a b l a d e

I t i s t o b e n o t e d t h a t t h e s y s t e m f o r d e f in i n g g a s a n g le s is a rt e x t e n s i o n o f t h e s y s t e ms l y e s t a b l i sh e d f o r a x i a l c om p r e s s or s . A c o n s e q u e n c e o f t h i s is t h a t t h e v a l u e s o f g a s

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

e d i n t h e t e x t t h e n e g a t i v e s i g n h a s b e e n i g n o re d . T h u s ; t h e p h r a s e ' h i g h o u t l e t a n g l e s '

t o a n g l e s h a v i n g a h i g h n u m e r i c a l v a l u e a n d a n ' i n c r e a s i n g o u t l e t a n g l e ' i s a n a n g l e w h o s e

4 . T w o - D i m e n s i o n a l F l o w th r ou g h R o w s o f T u r b i n e B l a d e s . - - C a s c a d e te st s ~'a'4, 5,,,7, s h a v e be end e o n a v a r i e t y o f b l a d e s e c t i o n s to d e t e r m i n e p r o fi le lo s se s a n d g a s o u t l e t a n g l e s o v e r a f a i r l y

r a n g e o f i n c id e n c e , M a c h n u m b e r , a n d R e y n o l d s n u m b e r . T h e b l a d e se c t io n s w h i c h h a v e

(a) R A F 2 7 a n d C . 7 a e ro fo iP 4 '6 '7 s e c t io n s o n c i r c u l a r - a r c (C .5 0 ) a n d p a ra b o l i c - a r c (P .4 0 )

c a m b e r - l i n e s h a v i n g t /c = 1 0 p e r c e n t a n d 2 0 p e r c e n t

(b) ' C o n v e n t i o n a l ' s e c t i o n s 5' 8 h a v i n g t/c -"- 1 5 p e r c e n t t o 2 5 p e r c e n t .

' C o n v e n t i o n a l ' w a s i n t r o d u c e d i n R e f . 9 a n d i s s o m e w h a t v a g u e . I t e m b r a c e s a l a r g e

r t i o n o f b l a d e s e c t io n s a t p r e s e n t i n u s e w h i c h , fo r e a s e o f m a n u f a c t u r e , a r e c o m p o s e d o f am b e r ( o f t e n t h r e e ~7) o f c i r c u l a r - a r c s a n d s t r a i g h t l i ne s . B r o a d l y s p e a k i n g i t d e f i n e s t u r b i n e

TM o n a p a r a b o l i c c a m b e r - l i n e , t h e p o i n t o fa x i m u m c a m b e r b e i n g a b o u t 4 0 p e r c e n t t o 43 p e r c e n t 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 dg e .

F o r t w o - d i m e n s i o n a l f l ow t h e v a r i a b l e s i n t h e g a s s t r e a m l i k e l y t o e f f ec t p e r f o r m a n c e a r ed e n c e , M a c h n u m b e r , R e y n o l d s n u m b e r , a n d tu r b u l e n c e . T h e v a r i a b l e s d e f i n in g t h e g eo -

r d ra t i o. T h e a m o u n t o~ i n f o r m a t i o n r e l a t i n g t o b a s e p r o fi l e s h a p e

4 . 1 . Pr o f i le Los s es a t Lo w M ach Nu mb er ( le ss t han O . 5), H i g h R e y n o l d s N u m b e r ( a p p r o x i m a t e l y

and sm al l Inc~de nee . - - (a) N ozz le b lades (~1 = 0 d e g ) . - - F i g . 3 a ( r e p r o d u c e d f r o m R e f . 9 )

A F 2 7 s e c t i o n s o n c i r c u l a r - a r c a n d p a r a b o l i c - a r c c a m b e r - l i n e s . L o s s V a r ie s w i t h s/c a n d c~2 b u tt o b e l i t t l e a f f e ct e d b y t h e v a r i a t i o n s i n b a s e p r o f il e s h a p e a n d t h i c k n e s s / c h o r d r a t i o .

m e a n a c c e l e r a t io n i m p a r t e d t o t h e g a s f lo w t h r o u g h n o z z le r o w s i s l a r g e a n d H a r g e s t 1° (1 95 0)a t o n c o n v e n t i o n a l n o z z l e b l a d e p r o fi le s t h e r e g io n s o f r e t a r d e d f lo w a re s m a l l , s o t h a t

i s l i t t l e d a n g e r o f m a r k e d s e p a r a t i o n o f t h e f lo w fr o m t h e u p p e r s u r f ac e o f t h i s t y p e o f b l a d e .e v e r , c u r v a t u r e o n t h e u p p e r s u r f a ce o f t h e p r o fi le b e t w e e n t h e b l a d e t h r o a t a n d t r a i l i n g

y l e a d t o la r g e r lo s se s a t h i g h o u t l e t M a c h n u m b e r . T h i s p o i n t w i l l b e d i sc u s s e d i n s e c t i o n5 . F r o m t e s t d a t a o n h i g h r e a c t i o n b l a d e s a f a m i l y o f c u r v e s o f n o z z l e b l a d e p r o f il e l o s s h a s

n u p a s s h o w n i n F ig . 4 a. T h e s e lo s s v a l u e s a re t y p i c a l o f t h e t y p e s o f b l a d e e n u m e r a t e d

3

( ~ s a G s ) a 2



( b ) B l a d e s h a v i ~ g fi~ > 0 d e g . - - A s t h e m e a n a c c e l e r a t i o n o f t h e f lo w t h r o u g h a h i g h - d e fl e c t i o nb l a d e r o w i s r e d u c e d ( i . e . , a s t h e r a t i o o f ~ t o - - ~2 i n c r e a s e s o r t h e s t a g g e r a n g l e is r e d u c e d ) i tm a y b e e x p e c t e d t h a t p r of il e fo r m a n d t h i c k n e s s / c h o r d r a t i o m a y b e c o m e m o r e c r i ti c a l s in c el o c a l p r e s s u r e g r a d i e n t s o n t h e b l a d e u p p e r s u r f a c e s o p p o s i n g t h e m o t i o n o f t h e g a s w i l l b e c o m em o r e p r o n o u n c e d . T h e i n c r e a s i n g s e v e r i t y o f o p p o s i n g p re s s u r e g r a d i e n t s i s i l l u s t r a t e d i n F i g . 5i n w h i c h t h e p r e s s u r e d i s t r i b u t i o n s o n c o n v e n t i o n a l b l a d e s o f 15 d e g a n d 5 5 d e g i n l e t a n g l e a n d

6 0 d e g o u t l e t a n g l e a r e c o m p a r e d .

V e r y l i t t le s y s t e m a t i c w o r k t o d e t e r m i n e o p t i m u m p ro f il e s h a p e s h a s y e t b e e n a c c o m p l i sh e d .O p t i m u m s h a p e w i l l b e l a r g e l y r e l a t e d t o t h e f o r m o f t h e p r e s s u r e d i s t r i b u t i o n r o u n d t h e b l a d e ,p a r t i c u l a r l y o n t h e c o n v e x u p p e r s u r fa c e , s i nc e t h i s w i l l g o v e r n t h e b e h a v i o u r o f t h e b o u n d a r yl a y e r .

O p i n i o n a s t o t h e b e s t f o r m o f p r e s s u r e d i s t r i b u t i o n t o a c h i e v e d i f fe r s w i d e l y . A . W . G o l d s t e i n ~1(1 94 9) s u g g e s t s t h a t t h e s u c t i o n p r e s s u r e o v e r t h e u p p e r s u r f a c e o f t h e b l a d e s h o u l d b e c o n s t a n to v e r a s la r g e a n a r c o f t h e s u r f a c e a s p o ss i b l e w i t h a f i n a l o p p o s i n g g r a d i e n t n e a r t h e t r a i l i n g e d ge ,t h i s f i n a l p r e s s u r e g r a d i e n t b e i n g a s s h a r p a s p o s s ib l e w i t h o u t c a u s i n g s e p a r a t i o n . O t h e r o p i n i o nf a v o u r s a p e a k s u c t i o n p o i n t a s f a r f o r w a r d t o w a r d s t h e l e a d i n g e d g e a s p o s s ib l e w i t h a l i n e a ro p p o s i n g p r e s s u r e g r a d i e n t o v e r t h e l a r g e r p a r t o f t h e b l a d e u p p e r s u r f a ce . T h i s l a t t e r f o r m i so n e w h i c h f r e q u e n t l y o c c u r s o n c o m p r e s s o r b la d e s . U n f o r t u n a t e l y t h e r e i s l i t t l e e x p e r i m e n t a le v i d e n c e t o s u p p o r t e i t h e r t h e o r y , a l t h o u g h a c a s c a d e t e s t e d b y E c k e r t TM (1949) in an in te r fe ro -m e t e r t u n n e l h a d a d i s t r i b u t io n o f t h e f i rs t t y p e a n d a t a s m a l l p i t c h /c h o r d r a t io s h o w e d v e r yl i t tl e s e p a ra t i o n ( th e g as in l e t a n d o u t l e t a n g le s b ei n g a p p r o x i m a t e l y 5 6 d e g a n d - - 7 5 d e gr e s p e c t i v e ly ) . H o w e v e r , n o l o ss m e a s u r e m e n t s w e r e m a d e o n t h i s c a s c a d e so t h a t n o r e li a b l ec o n cl u si o n m a y b e d r a w n . T h e w h o l e p r o b l e m o f o p t i m u m s h a p e w il l b e f u r th e r c o m p l i c a t e da t h i g h M a c h n u m b e r s w h e n lo c a l s h o c k -w a v e s a p p e a r i n t h e p a s sa g e . I t m a y b e t h a t o p t i m u ms h a p e s f o r h i g h a n d l o w M a c h n u m b e r w i l l e v e n t u a l l y b e f o u n d t o d if fe r.

R e t u r n i n g t o e x i s t i n g t e s t r e s u l t s F ig . 3 b c o m p a r e s t h e l o ss e s i n ro w s o p e r a t i n g u n d e r i m p u l s ec o n d i t io n s o f t h i c k c o n v e n t i o n a l b la d e s ( h a v i n g n e a r l y c o n s t a n t p a s s ag e a r e a t h r o u g h t h e r o w )a n d 1 0 p e r c e n t t h i c k b l a d e s c o m p o s e d o f R A F 2 7 a e ro f o il se c t i o n s o n c ir c u l a r - a rc c a m b e r - l i n e s.

T h e l o s s e s o n t h e c o n v e n t i o n a l b l a d e s a r e v e r y m u c h h i g h e r t h a n t h o s e o f t h e a e r o f o i l s e c t i o n s .T h i s m i g h t p o s s i b l y b e a t t r i b u t a b l e t o d i f fe r e n ce s i n t / c a l t h o u g h o t h e r d i f f e r e n c e s i n s e c t i o np r o f il e , c a m b e r - l i n e s h a p e , s c a l e , a n d t u r b u l e n c e m u s t a l s o i n f l u e n c e t h e r e s u l t s .

S o m e d e f i n i t e e v i d e n c e o n t h e e f f e c t o f t / c ( o t h e r fa c t o r s b e i n g c o n s t a n t ) i s p u b l i s h e d i n R e f s . 6a n d 7 . B l a d e s c o m p o s e d o f a C .7 a e r o f o i l s e c t i o n o n a p a r a b o l i c ( P .4 0 ) c a m b e r - l i n e w i t h[ /1 = 30 deg, c os - 1 o / s = 60 deg , s / c = 0 . 6 2 5 , a n d t / c = 1 0 p e r c e n t a n d 2 0 p e r c e n t w e r e t e s t e di n t h e s a m e t u n n e l . M i n i m u m l o s s es o f 0 . 0 2 8 a n d 0 . 0 4 w e r e o b t a i n e d o n t h e 1 0 p e r c e n t t h i c ka n d 2 0 p e r c e n t t h i c k b l a d e s r e s p e c ti v e l y . O n n o z z le b l a d e s , h o w e v e r , t h e e f fe c t o f t / c a p p e a r st o b e v e r y s m a l l . T h e a v a i l a b l e e v i d e n c e s u g g e s t s, t h e r e f o r e , t h a t t / c h a s a n i n c r e a s i n g e f f e c t a st h e r e a c t i o n o f a b l a d e r o w i s d e c r e a s e d ( o r a s t h e r a t io /~1 /~2 i n c r e a s e s ). T e n t a t i v e l y i t is s u g g e s t e dt h a t p r o fi le l o s s r o u g h l y v a ri e s p r o p o r t i o n a l l y t o ( t / c ) - ~ ' ~ ' ~ , f o r c o n v e n t i o n a l b la d e s . A f a m i l yo f c u r v e s o f pr o fi l e l o ss e s t y p i c a l o f i m p u l s e b l a d e s o f c o n v e n t i o n a l f o r m a n d h a v i n g t / c = 2 0 p e r

c e n t i s s h o w n i n F i g . 4 b . t / c = 2 0 p e r c e n t h a s b e e n c h o s e n s i n c e i t i s r e p r e s e n t a t i v e o f v a l u e sf r e q u e n t l y e n c o u n t e r e d i n p r a c t i c e o n i m p u l s e b l a d e s e c t i o n s a n d i s a l s o c o m p a r a b l e w i t h t h ev a l u e s o f t / c o n b l a d e s f o r w h i c h t e s t r e s u l t s a r e a v a i l a b l e .

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

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

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

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

h i g h d e f l e c t i o n ( 1 2 0 d e g o r m o r e ) a n o p t i m u m b l a d e s h a p e m a y h a v e a f a i r l y t h i c k s e c t i o n ( e . g . ,

b l a d e t e s t e d i n R e f . 1 2 ) . F o r t h i s r e a s o n i t i s n o t a d v i s a b l e t o a p p l y t h e s u g g e s t e d c o r r e c t i o n f o r

t / c o v e r a w i d e r r a n g e t h a n 1 5 p e r c e n t < t / c < 2 5 p e r c e n t o n h i g h - d e f l e c t i o n n e a r - i m p u l s e b l a d e s .

4



T y p i c a l p r o f i l e l o s s e s o n c o n v e n t i o n a l b l a d e s i n t e r m e d i a t e b e t w e e n n o z z l e a n d i m p u l s e b l a d e sy b e i n t e r p o l a t e d i n t h e f o l lo w i n g m a n n e r : - -

(a) D e t e r m i n e t h e v a l u e o f ~/o~ 2, o:2, s/c a n d t ic f o r t h e b l a d e c o n s i d e r e d

(b ) F r o m F ig . 4 a f i n d Ypla~=01 fo r a 2 0 p e r c e n t t h i c k b l a d e h a v i n g s a m e v a l u e o f ~ a n d s /c

(c) F r o m F i g . 4 b f i n d Y p/~, . . . / f o r a 2 0 p e r c e n t t h i c k b l a d e h a v i n g s a m e v a l u e o f ~2 a n d s /c

(d ) T h e n r e q u i r e d v a l u e o f Y p i s : - -

c~2 \0 " 2 / . . . . . . .

e c u rv e s i n F ig . 4 fo r Y pla,= 0/ a n d Y pf,~ . . . 1 d i f f e r s l i g h t l y f ro m a n d su p e r se d e e a r l i e r c u rv e sn b y t h e a u t h o r i n R e / . 1 3 (1 94 9).

4 . 2 . V a r i a ti o ~ , o f P r o f il e L o s s w i t h I ~z cid e ~c e : a n d V a l u e s o f S t a l l in g I m i d e m e . - - S p e a k i n gb l a d e s i n w h i c h t h e m e a n a c c e l e r a t i o n o f t h e g a s fl ow i s l a r g e h a v e a w i d e r a n g e o f i n-

w h i c h t h e p r o f i le l o ss e s a r e lo w w h e r e a s l o w - r e a c t i o n b l a d e s h a v e a s m a l l e r i n c i d e n c eM a n y b l a d e s, s u c h a s t h e i m p u l s e b l a d e r e p r e s e n t e d i n F i g . 6 , s h o w a n a r r o w i n c i d e n c el os s. T h e s e v e r y l o w lo s se s p r o b a b l y i n d i c a t e a l a rg e d e g r e e of l a m i n a r o r

p a r a t e d f l o w o n t h e b l a d e . I n a t u r b i n e s t a g e , h o w e v e r , w h e r e t u r b u l e n c e w i l l b e v e r y l a r g ea k e s f r o m p r e c e d i n g b l a d e r o w s i t is i m p r o b a b l e t h a t s u c h l o w lo s s es w i l l b e a c h i e v e d

t h e p o s s ib l e e x c e p t i o n o f a fi r s t -s t a g e n oz z l e r ow ) . F o r t h i s r e a s o n t h e s e n a r r o w r a n g e s o fn e r a l l y i g n o r e d .

T h e s t a l l i n g i n c i d e n c e ( is ) i s d e f i n e d a s t h e i n c i d e n c e a t w h i c h t h e p r o f il e l o s s i s e q u a l t o t w i c ei m u m l o ss . I t h a s b e e n f o u n d t h a t t h e p o s i t i v e s t a l l i n g i n c i d e n c e o n t u r b i n e b l a d e s c a n

w i t h ~ , s ic a nd /3 1/ ~2 . T h e m e t h o d a d o p t e d w a s to d e t e r m i n e f ir s t t h en o f i , a n d ~ w i t h s ic f o r a w i d e v a r i e t y o f b l a d es . T h i s v a r i a t i o n ( u s in g s ic = 0 . 7 5 as

i s i l l u s t r a t e d i n F i g . 7 a . B y t h i s m e a n s t h e s t a l l i n g i n c i d e n c e s o f b l a d e s o f a l l p i t c h / c h o r d

e d t o s ic = 0 . 7 5 a n d th e r e su l t i n g v a lu e s o f i,(,f~=0.~s a r e p lo t t e d in F ig . 7 b ,a n d ~ a/~ 2 a s p a r a m e t e r s . T h e f a m i l y o f c u r v e s i n F i g . 7 w i l l e n a b l e t h e p o s i t i v e s t a l l i n g

o f a n a r b i t r a r y c o n v e n t i o n a l t u r b i n e b l a d e t o b e d e t e r m i n e d t o w i t h i n a b o u t ~ : 3 d e g,

I t i s o b s e r v e d t h a t b l a d e s h a v i n g a h i g h p o s i t i v e s ta l l i n g i n c i d e n c e g e n e r a l l y h a v e a h i g hs t a l l i n g in c i d e n ce , a n d vice versa. I t i s p o s si b le , t h e re f o r e , t o r e p r e s e n t a p p r o x i m a t e l y

e re l a t i ve prof i le loss o f a n y tu rb in e b l ad e ( p~o~loao,~~o~o~. . . ho~ ~= 0dog) a s a u n i q u e f u n c t i o n o f r e l a t i v e(i/ i ,) . T h i s is s h o w n i n F ig . 8a . T h e s c a t t e r o f t h e p o i n t s i s l a r g e b u t f o r t h e p u r p o s e s

p e r f o r m a n c e c a l c u l a t i o n t o i n c i d e n ce s d o w n t o i / i , = - - 2 . 0 a s i n g l e m e a n c u r v e is s u f f i c i e n t l y

4.3. G a s E f /g u x A n g l e s a t L o w M a c h N u m b e r a n d H i g h R e y ~ o l d s N u m b e r . - - ( a ) Z e ro I n c i d e m e . - -- t u r b i n e i n v e s t i g a t o r s f o u n d t h a t t h e g a s o u t l e t a n g l e c o u l d b e c l o s e ly r e l a t e d t o c o s -1 (o/s) .

b l a d e s f o r w h i c h t h i s r e l a t i o n e x i s t e d g e n e r a l l y h a d a s t r a i g h t u p p e r s u r f a c e t o t h e b l a d el e b e t w e e n t h e t h r o a t a n d t h e t r a i l i n g e d g e. R e c e n t e x p e r i m e n t a l e v i d e n c e c o n f i rm s t h i s

o n s u c h b l a d i n g b u t a l s o i n d i c a t e s t h a t c u r v a t u r e o f t h e u p p e r s u r f a c e b e t w e e n t h e t h r o a tt r a i l i n g e d g e t e n d s t o i n c r e a s e ( n u m e r i c a l l y ) t h e g a s o u t l e t a n g l e .

T h e r e l a t i o n sh i p b e tw e e n c~2 a n d c o s -1 (o / s ) f or ' s t r a i g h t - b a c k e d ' b l a d e s d e d u c e d f r o m r e s u lt sb y B r i d l e 5 (1 94 9) i s s h o w n i n F i g . 9 a. T h i s i s s u p p o r t e d b y i n d e p e n d e n t e v i d e n c e

t e d b y E m m e r t ~5 ( 19 50 ), s h o w n b y d o t t e d l i n e s i n F i g . 9 a .

A v a i l a b l e d a t a s u g g e s t s t h a t t h e i n c r e a s e i n g as o u t l e t a n g le d u e t o c u r v a t u r e o f t h e b l a d es u r fa c e b e t w e e n t h e t h r o a t a n d t h e t r a i l in g e d g e m a y b e a p p r o x i m a t e l y r e la te ~t t o t h e

5



r a t i o s /e w h e r e s = b l a d e p i t c h a n d e = m e a n r a d i u s o f c u r v a t u r e o f t h e u p p e r s u r f a c e o f t h eb l a d e s e c t i o n b e t w e e n t h e b l a d e t h r o a t a n d b l a d e t r a i l i n g ed g e (see F i g . 1 ). G a s o u t l e t a n g l e i sf o u n d t o f i t t h e r e l a t i o n s h i p : - -

c~ - - o~* - - 4 ( s / e ) : . . . . . . . . . (2)

w h e r e ~ * i s t h e o u t l e t a n g l e c o r r e s p o n d i n g t o a ' s t r a i g h t - b a c k e d ' b l a d e ( F ig . 9a ).

(b ) V a r i a t i o n o f O u t le t A n g l e w i t h I n c i d e n c e . - - T h e v a r i a t i o n o f g a s o u t l e t a n g l e w i t h i n c i d e n c ei s o n l y s l i g h t. A t p o s i t i v e in c i d e n c e s t h e o u t l e t a n g l e t e n d s t o d e c r e as e s l i g h t l y a s t h e l o s s i n -c r ea s es . T h i s s l i g h t d e c r e a se o f a n g l e p r e s u m a b l y r e s u l t s f r o m a t h i c k e n i n g o f t h e b o u n d a r yl a y e r o n t h e b l a d e u p p e r s u r f a c e w h i c h w i l l a c c o m p a n y t h e i n c r e a s e o f l os s. T h i s t r e n d i sd e m o n s t r a t e d i n F ig . 8 b w h e r e c h a n g e o f o u t l e t a n g l e ( u s i n g t h e o u t l e t a n g l e a t t h e i n c i d e n c e

• ( l o s s a t a n y i n c i d e n c eg i v i n g m i n i m u m l o s s a s a d a t u m ) i s p l o t t e d a g a i n s t r e l a t i v e p r o f i le l o s s v i z . , ~ ) .

T h e g a s o u t l e t a n g l e f r o m a r o w o f b l a d e s t e n d s t o d e c r e as e b y a b o u t 2 d e g b e t w e e n z e ro i n c i d e n c ea n d p o s i t i v e s t a l l i n g i n c i d e n c e •

A t n e g a t i v e i n c i d e n c e s t h e r e i s n o d e a r l y d e f i n e d t r e n d i n t h e c h a n g e o f o u t l e t a n g l e ; f o rp e r f o rm a n c e p r e d i c t io n i t m a y b e a s s u m e d t o r e m a i n c o n s t a n t w i t h o u t i n t r o d u c i n g e x c es s iv ee r ro r .

4 .4 . E f fe c t o f R e y n o l d s N u m b e r o n P r o fi le L o ss a n d G a s E f f tu x A n g l e . - - V e r y l i t tl e d e t a i l e d s t u d yo f t h e e f f e c t o f R e o n lo s s i n t u r b i n e b l a d e r o w s h a s y e t b e e n m a d e . I f d i s c u s s io n is co n f i n e d t ot w o - d i m e n s i o n a l f l ow t h e n t h e r e p r e s e n t a t i v e s c a l a r l e n g t h s e l e ct e d t o d e f i n e t h e R e y n o l d sn u m b e r i s t h e b l a d e c h o r d a n d t h e r e p r e s e n t a t i v e v e l o c i t y , d e n s i t y , a n d v i s c o s i t y i s c h o s e n a st h e b l a d e - o u t l e t m e a n v a l u e . A s m a y b e a n t i c i p a t e d f r o m w o r k i n o t h e r fi el ds , e.g . , G o l d s t e i n! Ed . ) 1° (1 93 8), c a s c a d e t e s t s ( F i g . 1 0) s h o w t h a t t h e p r o f i le lo s s e s i n c r e a s e a s t h e R e y n o l d s n u m b e ri s r e d uc e d . T h e l o s se s f r e q u e n t l y i n cr e a se m o r e r a p i d l y w i t h d e c r e as i n g R e y n o l d s n u m b e r w h e nR e i s l e s s t h a n a b o u t 1 × 105 t h a n a t h i g h e r v a l u e s o f R e . B e l o w R e = 1 × 105 th e lo ss inc rea sea p p e a r s t o b e m o r e s e v e r e o n lo w - r e a c t i o n b l a d e s h a v i n g h i g h t h i c k n e s s / c h o r d r a t i o s t h a n o nh i g h - r e a c t i o n n o z z l e b l a d e s, a l t h o u g h e x p e r i m e n t a l r e s u l t s d o n o t e x t e n d t o s u f f i c i e n t ly l o wv a l u e s o f R e t o b e s u r e o n t h i s p o i n t . Th e g e n e r a l ef f e ct o f R e m a y b e i l l u s t r a t e d b y p l o t t i n g

]oss

re la t iv e lo ss (de f ined as ~a tR~ = 2× ,0~) ag a in s t R e ( F ig . l l a ) . F o r p e r f o r m a n c e p r e d i c t i o n t h ee f f e c t o f R e y n o l d s n u m b e r d o w n t o R e = 5 × 1 0 ¢ f o r a l l t y p e s o f b l a d e , i n c l u d i n g c o m p r e s s o rb l a d i ng , m a y v e r y a p p r o x i m a t e l y b e r e p r e s e n t e d i n t h i s w a y b y a si n g le cu r ve .

T h e i n c r e a s e o f l o ss w i t h d e c r e a s i n g R e w i l l b e a c c o m p a n i e d b y a n i n c r e a s e in t h e t h i c k n e s so f t h e b o u n d a r y l a y e r o r s e p a r a t e d f lo w r e g i o n o n t h e u p p e r s u r f a c e of t h e b l a d e a t t h e t r a i l i n ge d ge . T h i s i n t u r n m a y l e a d t o a s l i g h t r e d u c t i o n i n m e a n g a s e f ft u x a n g i e f r o m t h e c a s ca d e .T h i s t r e n d i s i n d i c a t e d b y t h e e x p e r i m e n t a l r e s u l t s p l o t t e d i n F ig . l l b . T h e d e c r e a s e of a n g l ew i t h d e c r e a s i n g R e a p p e a r s l e s s o n h i g h r e a c t i o n o r n o z z l e b l a d e s t h a n o n l o w r e a c t i o n h i g hd e f le c t io n b la d e s . T h e v a r i a t i o n o f a n g le a s R e i s r e d u c e d m a y c o r r e l a te b e t t e r w i t h t h e i n c r e a s eo f l o s s a s s o c i a t e d w i t h d e c r e a s i n g R e . T h u s , b l a d e s i n w h i c h t h e i n c r e a s e o f l o s s w i t h r e d u c t i o nin R e i s o n l y s l i g h t m a y b e e x p e c t e d t o s h o w o n l y a s m a l l c o r r e s p o n d i n g d e c r e a s e i n o u t l e t a n g l e ,a n d v i ce ver s a .

Th e e f f e c t o f R e o n o v e r a l l t u r b i n e p e r f o r m a n c e i s d is c u s s ed b r i e f l y in s e c t i o n 8 .

4 .5 . E f fe c t o f M a c h N u m b e r o n P ro f il e L os s a n d O u tl et A n g l e . - - O n n o zz le r o w s h a v i n g c o n v e r g e n tf lo w p a s s a g e s a n d h i g h g a s e f fl u x an g l e s o u t l e t M a c h n u m b e r s c o n s i d e r a b l y i n e x c e s s of u n i t ym a y b e a c h i e v e d w i t h o u t a n y v e r y s e r i o u s in c r e a s e i n l o ss or s e v e re d e v i a t i o n s i n o u t l e t a n g l e .T h i s i s i l l u s t r a t e d b y m a n y s t e a m - t u r b i n e n o z z l e t e s t s (e .g . , Refs . 17 to 23 ) and i s con f i rm ed toa l i m i t e d e x t e n t b y c a s c a d e t e s t s o n g a s - t u r b i n e n o z z l e r o w s , p u b l i s h e d b y B r i d l e 5 (1 94 9). U pt o t h e p r e s e n t t i m e g a s - t u r b i n e d e s i g ne r s h a v e n o t e m p l o y e d n o zz le M a c h n u m b e r s a p p r e c i a b l yi n e x c es s of u n i t y f o r t h e f o l lo w i n g r e a s o n s : (a) t h e n o z z l e o u t l e t M a c h n u m b e r o f t u r b i n e so p e r a t i n g a t h i g h t e m p e r a t u r e a n d d e s i g n e d f o r s t a g e v e l o c i t y r a t i o s o f a b o u t 0 . 5 o r m o r e ( toa c h i e v e g o o d e ff ic ie n cy ) ar e l i m i t e d b y t h e m a x i m u m p e r i p h e r a l s p e e d s a t w h i c h i t is s a f e t o r u n

6



rotor rows, this lim itati on generally restricting the nozzle Mach numbe r to about 1.0 or less,) fear of loss of efficiency due t o intera ction b etween the nozzle shock-waves and the following

. On the other han d turbines emp loying high supersonic velocities at outlet from the

lX{ach numbers are achieved with rela tive ly low absolute gas velocities.

An influence of Mach nu mber on loss (at consta nt incidence) is first noticeable when the localat the peak suc tion point on the blade exceed sonic velocity, as shown by Harges t 1°

950) ; the loss the n increasing slightly due to thick ening of the boun dary layer thr ough the smallth at arise in the blade passage. The ' critical ' outlet Mach num ber at which thesefirst appear in the passage is in t he region of 0.6 on 20 per cent th ick impulse blades

about 0 .9 on nozzle blades. As the outle t Mach numb er is increased ab ov e the criticalty the profile loss ma y either continue to rise or it may fall. The processes under lying

ation in loss above the critical Mach numbe r are not yet fully comp rehe nded but it ma ynd largely upon the blade profile shape and to a limited exten t upon the turbulence.

Statistical analysis of many cascade tests suggests that when M~ approaches unity the profile

hroat and the trailing edge (defined by the ratio s / e ; s e e Fig. 1). The nature of the tren dillustr ated by some test results plotted in Fig. 12a which show tha t for large curvatures of the

( v i z . , high values of s / e ) the profile-loss coefficient as measured in a cascade tunnel atlet Mach num ber ma y be as muc h as four times the loss at low Mach number. Somehed work at the N.G.T.E. has s ho wn tha t this high loss is associated with lamin ar

of the blade ; the separat ion being initially triggered by shock-waves inassage when the outiet Mach numb er exceeds its critical value. If the bound ary

( e . g . , by a transition wire oll the leading portion of thee upper surface) the separation can be avoide d and norm al profile-loss coefficients at M~ = 1.0

Curvature of the tail tends to move the point of peak suction on the upper surfaceds the trailing edge in comparison to a straight-backed blade. Thus with an inlet gas

on a curved than on a straight-b acked blade. Furthe rmore , since a shock-wave is mo reto lead to flow separat ion if the bou ndar y layer is lamina r than if it Js turb ulen t (Liepm ann2~

It is conceivable th at the t ren d illustrated in Fig. 12a may be partially co unter acted by in-

ce. Thus, it is possible tha t a blade operating in the hi ghly turb ulen t gas strea m within a

The gas out let angle is also influenced by Mach number. If the pressure loss when 21/_/, = 1.0

er downs trea m of the row is unity the flow angle is given closely by cos -1 o / s . It isent tha t this must be appro ximat ely true since when M2 = 1.0 the flow area downs trea m

to the blade thro at area. It is worth noting at this poi nt tha t if a blade( i . e . , 'flare ') or converge between the throat section and the

trea m reference flow plane th en whe n M, = 1.0 the gas outlet angle will be givenoxima tely by cos -1 (throat area/outl et annulus area). However, if appreciable pressure

ses occur do wnstr eam of the blade th roa t (due, for example, to separat ion of the flow from the

low area downst ream of the blade when M~ = 1.0 gr eater than the t hroa t area,henc e an outl et angle less than cos --1 o / s .

7



i ll b e a u n i f o r m l os s a lo n g t h e b l a d e ( a ss u m i n g a h u b r a t i o o f n e a r l y 1 . 0 ) c o r r e s p o n d i n go d i m e n s i o n a l p r o f i le l o ss , ~p . A l s o t h e r e w i l l b e c o n c e n t r a t i o n s of s e c o n d a r y l os s

t o l e n g t h s A h a t t h e b l a d e e x t r e m i t i e s a n d t h e a v e r a g e v a l u e o f t h i s l o ss o v e r th e s h o r th i s r e p r e s e n t e d b y ~ ,. T h e m e a n t o t a l - h e a d l os s o v e r th e w h o l e b l a d e w i ll t h e n b e g i v e n

y @ + 2c5 , A h / h . T h e t e r m 2 ~ s A h / h c o n s t i t u t e s t h e s e c o n d a r y lo s s t o b e a d d e d t o t h e p r o fi les t o g i v e t h e m e a n t o t a l lo s s a c ro s s t h e b l a d e . N o w t h e l e n g t h Ah i n w h i c h t h e e n d l o ss e s a r e

d w i ll d e p e n d l a r g e ly u p o n t h e t h i c k n e s s , Oh, o f t h e w a l l b o u n d a r y l a y e r s a t t h e o u t l e tr ow . T h i s th i c k n e s s m a y b e i n fl u e n c e d b y t h e i n l e t v e l o c i t y d i s t r i b u t i o n , t h e a n g l et u r n e d t h r o u g h , a r id t h e a c c e l e r a t io n i m p a r t e d t o t h e g a s i n p a s s in g t h r o u g h t h e r o w .

l a d e (o f c o n s t a n t s e c t io n ) t h e w a l l b o u n d a r y l a y e r s r e m a i n f i x e d i n s iz e w h i l e t h e b l a d eh is v a r i e d t h e n t h e m e a n s e c o n d a r y lo s s (2rS~A / h ) w i l l v a r y i n v e r s e l y as t h e s p a n , o r , i f t h e

s m a i n t a i n e d c o n s t a n t , i t w i ll v a r y i n v e r s e l y a s t h e a s p e c t ra t i o . O n t h e o t h e r h a n d i f t h eb o u n d a r y l a y e r s a n d b l a d e s p a n r e m a i n f i xe d i n s iz e w h i le th e c h o r d d i m e n s i o n i s v a r i e d

e m a g n i t u d e o f t h e s e c o n d a r y lo s s w i ll n o t b e i n f l u e n c e d b y t h e a s p e c t r a t io . T h i s iso n s t r a t e d i n F ig . 1 5b w h i c h h a s b e e n d e r i v e d f r o m t h e r e s u l ts o f a s e ri es o f r e a c t i o n t e s ts

n s o m e s t e a m t u r b i n e n o z z l e b l a d e s p u b l i s h e d b y K r a f t a° (1 94 9). M a n y o f t h e s e n o z z l e b l a d e sr o u g h l y s i m i l a r p r o f il e f o rm , O u t le t a n g le , a n d p i t c h / c h o r d r a t i o b u t d i ff e re d w i d e l y i na n d c h o r d . A l t h o u g h l i t tl e i n f o r m a t i o n i s a v a i l a b l e o f t h e a c t u a l t h ic k n e s s e s o f t h e w a l l

u n d a r y l a y e r s it is v e r y p r o b a b l e , s i n ce a ll t h e t e s ts w e r e m a d e o n t h e s a m e a p p a r a t u s , t h a ts s e s w e r e n e a r l y i d e n t i c a l o n a l l t e s t s . T h e t e s t s s h o w d e a r l y a r a p i d i n c r e a s e o f l o ss

s t h e b l a d e h e i g h t i s r e d u c e d ( c h o rd r e m a i n i n g c o n s t a n t ) p a r t i c u l a r l y w h e n t h e h e i g h t i s l es sh a n a b o u t 1 i n . I t i s n o t e w o r t h y t h a t t h e r a p i d i n c re a s e o f l os s w h e n t h e b l a d e h e i g h t is r e d u c e do l es s t h a n 1 i n . a c c o rd s w i t h t h e f i n d i n g of G u y ~ ( 19 39 ). O n t h e o t h e r h a n d , w h e n t h e h e i g h ts fi x e d t h e l os s is s c a r c e l y a f fe c t ed * b y l a r g e c h a n g e s i n b l a d e c h o r d .

T h u s i t is a p p a r e n t t h a t t o c o r r e la t e s e c o n d a r y l os se s o n d i f f er e n t b la d e s i t i s n e c e s s a r y t ok n o w t h e f o r m o f t h e w a l l b 0 n n d a r y - l a y e r a n d i t s s i z e r e l a t i v e t o t h e b l a d e h e i g h t .

T o t h e t i m e o f w r i t i n g o n l y a v e r y s i m p l if i ed s t u d y h a s b e e n m a d e o n t h e t h e o r e t i c a l e v a l u a t i o no f s e c o n d a r y l o ss e s. C a r t e r 1 (1 94 8) s h o w s t h a t f o r c a s c a d e s o f b l a d e s o f s m a l l d e f l e c t i o n a n ds m a l l v a l u e s o f b l a d e p i t c h / b l a d e h e i g h t t h e d r a g c o e f f ic i e nt , C v s , e q u i v a l e n t t o s e c o n d a r y lo ss i s

C~, = I C 2 [ 1 - - ( h ' / h ) ] / ( s / c ) . . . . . . . . . . ( 3 )

w h e r e CL is li f t c o e ff ic ie n t b a s e d o n v e c t o r m e a n v e l o c i t y

h i s N a d e s p a n

h ' i s d i s t a n c e b e tw e e n t h e v o r t i c e s c re a t e d a t t h e b l a d e e n d s d o w n s t r e a m o f t h e b l a d e s

N o w t h e t e r m E1 - ( h ' / h ) ] i s p r o b a b l y p r o p o r t i o n a l t o t h e b o u n d a r y - l a y e r t h i c k n e s s , t h e t h i c k n e s so f t i le b o u n d a r y l a y e r a t t h e b l a d e o u t l e t p o s s i b l y b e i n g m o r e s i g n i f ic a n t i n th i s r e s p e c t t h a n t h et h i c k n e s s a t t h e b l a d e i n le t . I n p a r t i c u l a r i f t h e r e l a t i v e b o u n d a r y - l a y e r t h i c k n e s s , , ~ h / h , r e m a i n sc o n s t a n t t h e n so al so m a y E1 - ( h ' / h ) ] . F u r t h e r m o r e , . a l t h o u g h th e t h e o r y is o n l y s t r ic t l ya p p l i c a b l e t o b l a d e r o w s o f s m a l l c a m b e r i t p r o v i d e s a p o s s i b le t h e o r e t i c a l b a s i s f o r a n e m p i r i c a l

l a w i n w h i c h s e c o n d a r y l o s s i s e x p r e s s e d a s= . . . . . . . . . . . . . . ( 4 )

w h e r e ~ i s a f a c to r , t o b e d e t e r m i n e d b y e x p e r i m e n t , w h i c h m a y d e p e n d , t o l a r g e o r s m a l l de g re e ,o n t il e i n l e t a n d o u t l e t v e l o c i t y d i s t r i b u t i o n , a n g le t h r o u g h w h i c h t h e g a s i s t u r n e d , w a l l b o u n d a r y -l a y e r t h i c k n e s s , a n d p o s s i b l y h u b r a ti o ~ .

* The slight increase of loss shown on Fig. 5b as aspect ratio is reduced (height-fixed) is probably accountable to theincrease in frictional loss on the end walls as the length of the blade passage is increased.

The system heretofore adopted (Ainley9'13 (1948, 1949)) of defining seco nda ry loss as Y, = 0.04{1 - - ( .~ / c % ) } C ~ , .2 2has now been discarded. This system does not compare well with recent data. The system now adopted has a firmertheoretical basis and further more resembles tile system adopted in axial-compressor theory. It is hoped that eventuallysecondar y losses in axial compressors and turbines may be related on a truly common basis.

9



a g a i n s t ( A d A 1 f l , a s d r a w n i n F i g . 1 6a . S u c h a c u r v e s h o u l d g iv e a r e a s o n a b l e e s t i m a t e o f3 h / h i s a b o u t 0 . 1 t o 0 . 1 5 . R o w s i n w h i c h t h e b l a d e

t i s v e r y s m a l l ( s a y l e ss t h a n 1 . 0 i n .) o r in w h i c h i n l e t v e l o c i t y d i s t r i b u t i o n i s c o m p a r a t i v e l y

h t o r v e r y u n i f o r m i n l e t v e l o c i t y d i s t r i b u t i o n s m a y b e e x p e c t e d t o g i v e s m a l l e r lo s se s .

B y a d d i n g v a l u e s o f s e c o n d a r y l o s s p r e d i c t e d f r o m F i g . 1 6 a t o v a l u e s o f p ro f il e lo s s p r e d i c t e d, a n e s t i m a t e o f t o t a l l o ss m a y b e m a d e f o r a n oz z l e ro w . A c o m p a r i s o n o f t h e p r e d i c t e dm e a s u r e d v a l u e s f o r t h e n o z z l es q u o t e d i n T a b l e 1 i s m a d e i n t h e f o l lo w i n g t a b l e .

T A B L E 2

Ro w

Measured Y~o~ . . . . . . . .Predicted Yto~ . . . .Nozzle veloc ity coefficient ida/2 =' 0" 8) ..

0.061O" 057O" 978

0.0560.0540.980

0.0690.0670.975

0.0580.05200.979

t h a t t o t a l l o ss i n a t y p i c a l n oz z l e r o w o f a p r e s e n t - d a y t u r b i n e m a y b ea t e d w i t h a n e r r o r w i t h i n a b o u t + 1 0 p e r c e n t . A n e r r o r o t _+_ 1 0 p e r c e n t i n t h e m e a n

o f a b o u t : ]: 1 p e r c e n t t o :~- 1½ p e r c e n t ; w h i c h m a y b e r e g a r d e d a s s a t i s f a c t o r ym o s t p u r p o se s . E x p e r i m e n t a l e r r o r i n m e a s u r i n g t u r b i n e p e r f o r m a n c e i s f r e q u e n t l y o f t h e

T h e f o u r n o z z l e s d e t a i l e d i n T a b l e s 1 a n d 2 g i v e v e l o c i t y c o e f fi c ie n t s o f b e t w e e n 0 " 9 7 5 a n d 0 . 9 8 ,a r e w e l l w i t h v a l u e s m e a s u r e d o n m o d e r n s t e a m - t u r b i n e n o z zl es ( e . g . , D ol lin 89 (1940),

u y 4~ (19 39 )) h a v i n g th e s a m e e f f lu x a n g le .

A c o m p a r i s o n h a s b e e n m a d e b e t w e e n t h e l o ss e s m e a s u r e d o n v a r i o u s t y p e s o f n o z z le b l a d et l y b e n t s h e e t m e t a l n o z z le b l a d es ) b y t h e S t e a m N o z z l e R e s e a r c h C o m m i t t e e ( R ef s. 1 8 t o 2 3)

e s . T h i s is p r e s e n t e d i n T a b l e 3 b e lo w , a n o u t l e t M a c h n u m b e r o f 0 . 8 b e i n ge d i n a l l i n s t a n c e s .

T A B L E 3

tional section nozzle blade) ..sheet metal nozzle .. . .

edge chamfered ..

edge chamfered . . . . . .sheet metal nozzle . .. .

edge chamfered .. . .hick sheet metal nozzle, trailingedge chamfered . . . . . .

Gaseffluxangle

777279*

79

79*78-578-5

82" 5

82"5*

Cos-1 ;

77"37378- 7

78" 7

78" 779" 783"2

83"2

83'2

0"750"320"45

0 " 4 5

0"330"450"57

0" 57

0"45

0"20o.6150.064

0.064

0"0480.0130.052

0.052

0-041

te fj~

s s

0.020.05 1.080 ' 1 5 0 "8 4

0 0-84

i : 0 0 , 4 7-4 80-53

0 0.53

0 0.88

Y~

0-1350.1480.260

0.166

0.141

0.1560.186

0.165

0'135

PredictedY, for

conventionalnozzle+

0.1060.1050.120

0.120

0-126

0.1160.113

O. 147

O . 1 4 8

* Gas angle is conjectural.t f is radius of curvature of bent sheet.

All predicted values of Y, correspond to td s = 0.025

For full details of the blading tested Refs, 18 to 23 should be consulted.

11



In comparing these values of loss coefficient it mu st be rem embe red tha t the possible error ofthe predictions for conve ntion al blades at these high values of gas outlet angle (being anextrap olatio n of existing data) will be about ± 15 per cent and the possible exper ime nta l errorin d eter minin g the loss coefficient in the stea m nozzle tests will be about ± 10 per cent (equivalentto an error of ± 0.5 per cent in velocity coefficient).

Thus the predicted and measured values oi loss for the profiled nozzle having a gas outletangle of 77 deg seem to be in fair agreement*. The losses on the thin and th ick sheet met al bladesare greater than would be exp ect ed from convent ional nozzle blades. This applies particul arlyto the thick sheet metal blades, much of the high loss on these blades being associated with thever y large trailing-edge thickness. On the other ha nd if the trailing edge of the thic k sheetmetal blades is chamfered the losses compare well with those expected from profiled blades,particula rly when the gas efflux angle is very high (about 80 dog). However, it is not antici pate dtha t this will apply to nozzles having efflux angles less th an about 70 deg.

5.3. E f fe c t o f R a d i a l T i p C l e a r a m e . - - A s the radial tip clearance in a blade row of a turbine isincreased the pressure losses in the row increase,~ resulting in a decrease of turbine efficiency.The gas mass flow arid the power output corresponding to a fixed turbine speed and pressure

ratio also change. Publishe d quanti tat ive data on the effect of tip clearance is very incomplet eand in most instances the details of the turbines to which experimental results refer are notquoted, so that a reliable collective analysis is difficult.

Stodola 17 quotes a value (attr ibuted to Anderhub) for the loss associated with the tip clearanceas

w h e r e : - -

~ o l . . . . . e o = 6 . 2 6 k l ' 4 / h . . . . . . . .

~ = ~j-2 __ 1

a c tu a l o u t l e t v e lo c i ty~ is ve loci ty coefficient --- ~ .... t~ outletvelocity

k is radial clearance

. . ( 5 )

h is blade heig ht corresponding to zero clearance.This formula is empirical, it is not non-dimensional, and canno t be regar ded as satisfactory.In a later paper St0dola 3~ (1925) quotes t ha t on a Brown Boveri reaction st eam- turbi ne the dropin efficiency due to tip clearance (clearance on Both rotor a nd sta tor rows) could be expressedapproximately by A~ -----3.1 (k/h). MeldahP ~, (1941) f ound on a single-stage reacti on tu rbi ne th atA ~ ~ 3 . 5 ( k / h ) . Other unpub lishe d data gives A~ ~ 2.6(k/h) on a 50 per cent reaction turbine.

Fro m a theor etica l stand poin t Carter 1 (1948) points out t he similarity of the induce d effectsof tip clearance and s econdary flow, and a simple theoretical expression may be de riv ed for thedrag coefficient on a row due solely to radial clearance at one end as

c a , , = ½ C L ~ ( k / l ~ ) / ( s / c ) , . . . . . . . . . . . . ( 6 )

if s /h and gas turning angle is small.

It is interes ting to d eter mine what effect this drag w ould have or~ the efficiency of a 50 per centreactio n turbine. An expression for the efficiency of a 50 per cent reaction turbi ne is

1 / ~ = 1 + 2 c o s e c 2 ~ , , , ( C ~ / C L ) . . . . . . . . . . . ( 7 )

* It is of interest to not e t hat the series of nozzles tested by Kra ft 3° (1949} (results shown in Fig. 15b) gave a losscoefficient of 0.075 for a nozzle comparable to th e S.N.R.C. profiled blade. This is rath er lower than t he predict edvalue. However, t he pr edicted value gives a good indication of the average loss measured on high efflux angle nozzlerows, and unt il s uch time as the fact ors leading to ver y low losses are compl etely underst ood a generM predictioncannot go any further t han this. Furt hermor e, nozzles of such high outlet angle as 77 deg are at present only ofacademic interest to gas turbines.

12



Cv =C~0+C~,

CD 0 is d rag coefficient with zero clearance

C~ k is drag coefficient due to clea rance

= ½ C ? ( k / h ) / ( ~ / c ) .

[ 1 / ( ~ ) ~ [ a ~ / ~ ( k / h ) l = c o s e c 2 o : , ,F ~ /( s /c ) . . . . . . . . . ( 8 )

A r l / ( k / h ) given by this expression of reaction turbines having gas outlet angleslade rows of 50 dog, 60 deg and 70 dog are app roxim ately 2.0, 2.3, and 2 .9 respectively.

iment al meas urem ents of the effect of change in clearance, the use of the simple theore tical

So far it has been assumed tha t clearance is varied e qually on bot h rotor and st ator of a 50 pertion turbine. It m ay be demonst rated that in a turbine of any degree of reaction the

tion in stage efficiency due to s mall radial clearance on a s tator row alone is

~ . } s e c 3 ~ o ,~ E C L l ( s / c ) ? ?A ~ -"- ( K • . A T / U , , ~ ) ( U , ~ I V ~ ) 2 ( k / h ) ~ . . . . . . . . . (9)

educti on in stage efficiency due to a small radial clearance on a rotor row alone is :

~ . } s e c 3 ~ , ,, ~ [ C L / ( s / c ) ~ ~( k / h ) , . . . . . . . .

T = turb ine work te mper atu re drop per stage ; suffix s refers t o stato r row ; suffix r refersow. These expressions show tha t on low-reaction stages a clearance on the st ator-row

as a slig htly greater effect tha n t he same clearance on the rotor row, particula rly if the nozzle

as outlet angle is high.

Shroud bands round the blade tips are often used since a smaller flow leakage round the bladetips ma y sometimes be achieved with an end-ti ghtened shroud band tha n with a radial tipclearance. The flow leakage round a shrou d band will depe nd largely upon the mi ni mum clearance

etween the band and the stator casing. The simplest form of shroud band is shown diagram-matically in Fig. 2, in which the minimum clearance is represented by k ' . If this is comparedwith a simple radial clearance in which k = k ' then it is probable that the shrouded arrangement

will incur less loss ; part ly due to-less interference betw een the leakage flow and th e main str eamflow, and partly due to the fact tha t the more tortuous p ath which the flow must take rou nd theshroud will reduce the actual qua nti ty Of leakage flow. For this reason it is suggested tha t forsuch a shr ouded row the losses migh t be about haK of the losses corresponding to an uns hro udedrow in which k--=- k'. Thus, for a simple shroude d blade row it will be ass umed tha t

c ~ - - - . K c L ~ / i s / c ) ] k ' / h . . . . . . . . . . . . . ( 1 1 )

On more complex shrouds ( e . g . , shrouds incorporating a labyrinth seal) which, for a givenmin imu m clearance, r~duce the flow to a f raction of th e =value corresponding to' th e simple formconsidered above it may be anticipated that the losses will be even smaller.

13



In addition to creating pressure losses a radial clearance also affects the momentum meangas efflux angle from a row since the clearance space will allow a portion of the gas flow to passthrough the row with little or no deflection. Suppose that with zero clearance a row passes amass flow, W, with a mo me nt um mean efflux angle of ~2. When clearance is intr oduc ed supposethat a fraction of the flow, X( k / h ) ( cos a~/cos ~)W, passes thro ugh undeflected whilst therema inder , [1 -- X( k/ h) (c os ~/c os cq, W , issues from the row at an angle ~2. The me an outl et

angle is then given approximately by

c~' -= t an -1 {[1 - - X( k / h ) ( cos ~l/cos a,)] tan so + X( k / h ) ( cos ~/ cos ~,) ta n a~}. (12)

The fraction passing throu gh unde flected is defined in terms of (k/h)(cos ~l/cos e~) since thister m repre sents the ratio of the flow area of the unde flected flow in the clearance space to thethr oat area of the blade. Some unpubl ished nozzle cascade tests and tur bine tests suggest avalue for X of 1.35. This value for X appears large and it may be th at reduct ion in outlet gasangle not only results from the simple mixing process assumed above but also from inducedflows created by the vortices and possibly by the vorticity set up by the motion of the blade tipsrelative to the stationary wall.

It may be expected that the reduction in mean outlet angle will be less with shrouded blades

due to the reduction in leakage flow for a given clearance. In such instances it is suggested thatthe expression derived in the last paragraph might be used for simple shrouding if k is replacedby k ' and if it is assumed tha t X = 0.7. Alternat ively, for complex shrouds, the expression(k/h)(cos ~l/cos ~) may be replaced by (w./W) where zv is the estimated leakage flow round theband and W is the total mass flow.

Combining the expressions derived above for increase in loss and reduction in mean gas outletangle it is possible to calculate the change in power outp ut and mass flow thr ough a stage opera tedat fixed speed and pressure ratio resulting from an increase in clearance. Calculations showth at on a typical 50 per cent reaction stage the mass flow increases slightly and the power outp utdecreases; on a typical impulse stage the power output and mass flow both decrease. The testsby MeldahP2 (1941) on a reaction stage par tia lly confirm this.

5.4. The Pressure Losses i x Rotor Rows. - -Typical tot al pressure losses in rotor rows have beenderived for a wide variety of blade rows from routine performance tests on turbine stages inwhich measurements were made of overall pressure ratio, total-head isentropic efficiency, massflow, and rotat ional speed. The me tho d of deriving the rotor losses was as follows. First anestim ate of the me an to tal- head loss coefficient in tile nozzle row was made from the data derivedin the prece ding sections. Then b y trial a nd error a value fer total loss coefficient in the rotorwas de ter mine d such tha t the calculated overall efficiency of the t urbin e at a selected value ofoverall pressure ratio and speed equalled the e xperim ental efficiency. Havi ng derived a valueof tot al loss coefficient in thi s way an est ima te was ma de of (a) profile loss (as in sect ion 4.1) and(b) the blade tip clearance or shroud loss (section 5.3). The rem ain ing secondary loss in the rotorrow was the n derived as :-

Derived total Es tim ate d profile Est ima ted tip .. (13)Secondary loss = loss -- loss -- clearance loss " ""

Now the absolute error in this estimated secondary loss is likely to be considerable since it willcomprise the separate errors involved in estimating the total loss, the profile loss, and the tipclearance loss. However, providing the secondary losses dete rmi ned in this way are alwaysused in conjunction with the profile losses and clearance losses specified ill sections 4.1 and 5.3the n th e final estimate of total loss in a bla de row should not be excessive.

The results of an analysis of the performance of a number of turbine stages which was carriedout in the mann er described is tabulated in the following table t ogether with some relevantdetails of the rotor blades in each instance.

14



T A B L E 4

Turbine i l l (re~d) ~ s /c(m/d) Hub rat io, m A 2 / A ~

123456

789

10

52394031434414

534

18

--62--54--63

--50--54

--68--46--69--53--46

0"450"460"63

0"680"610"430"770"710"67

0 '77

0"850"780"880"65

0"850"800"690"64

0"790"71

0"940"890"73

0"750"92

0"66O" 670"38

0"810"78

0.0250.022

0.0110.0210.0290.008

0.0110.0050.0100.012

N o t e . - - A 1 = (ann ulus area at inlet to blade row) × cos fit

A~ = (ann ulus area at outlet from bla de row) × cos 7~2

A2 / A I , t h e s e c o n d a r y l o s s e s b e i n g p a r t i c u l a r l y l a r g e o n t h e b l a d e s o f t u r b i n e s1 a n d 5 w h i c h h a d l o w - r e a c t i o n b l a d e s o f h i g h d e f l e c t io n .

F o l l o w i n g t h e s a m e p r o c e d u r e a s w i t h t h e n o z z l e b l a d e s t h e v a l u e s i n T a b l e 4 a r e p l o t t e d i n(A~ /A1)2. T h i s f i g u r e c l e a r l y d e m o n s t r a t e s t h e t e n d e n c y f o r s e c o n d a r y l o s s e s

a c c e l e r a t io n o f t h e g a s f lo w i n t h e b l a d e r o w is s m a l l . I t s e e m s a l so t h a t t h ee c t of a r e a r a t i o i s m o r e i m p o r t a n t t h a n t h e m a g n i t u d e o f t h e g a s d e f le c t io n ( cf . t u r b i n e s N o s .

R e e m a n ~ (1 94 6) a l so i o u n d o n c a s c a d e t e s t s t h a t s e c o n d a r y l o s s es w e r e l i t t l e i n f l u e n c e dt h e m a g n i t u d e o f t h e d e f l e c ti o n ; i m p u l s e b l a d e s o I l o w d e f le c t i o n h a v i n g s e c o n d a r y l o s se s

T h e f ig u r es i n T a b l e 4 s u g g e s t t h a t , i n a d d i t i o n t o A~/AI , t h e h u b r a t i o i n f l u e n c e s t h e s e c o n d a r ys s. F o r e x a m p l e , t u r b i n e s N o s . 3 a n d 4 h a v e r o u g h l y s i m i l a r v a l u e s fo r A~ /A~ b u t t h e s e c o n d a r y

s of t h e r o w h a v i n g .t he s m a l l e r h u b r a t i o i s v e r y m u c h g r e a t e r t h a n t h e O t h er . T h i s e f f ec t i sa b l y a s s o c i a t e d w i t h t h e l o w s t a g e r e a c ti o n s ( as c o m p a r e d w i t h t h e m i d - b l a d e h e i g h t ) a k t h e

r o w s h a v i n g a s m a l l h u b r a t io , a l t h o u g h t h e p r e ci s e n a t u r e o f t h e f lo w a t t h e r o o t s o f

O n a c c o u n t o f t h e a p p a r e n t e f fe c t o f h u b r a t i o i t h a s b e e n p r e f e r r e d t o p l o t ,~ a g a i n s t a p a r a m e t e r( A 2 / A1 ) 2 / [ 1 4 - ( I .D . / O . D . ) J. T h i s i s s h o w n i n F i g . 1 7 i n w h i c h a l l a v a i l a b l e r e s u l t s , i n c l u d i n g t h e

d i s cu s s e d i n s e c t i o n 5 .2 a n d s o m e c a s c a d e l os se s p u b l i s h e d b y R e e m a n ~ ( 19 46 ), h a v eI n s e l e c t in g c a s c a d e r e s u l t s f r o m R e f . 4 o n l y b l a d e a r r a n g e m e n t s o f s i g n i fi c a n t

t o t u r b i n e d e s i g n h a v e b e e n c h o s en . F u r t h e r m o r e , t h e a c c u r a c y w i t h w h i c h t h e s eo s se s w e r e m e a s u r e d m a y h a v e b e e n p o o r, p a r t i c u l a r l y o n ro w s w h i c h g a v e t h e f lo w

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

T r a v e r s e s a t t h e t u r b i n e o u t l e t h a v e o n l y b e e n m a d e i n a fe w i n s t a n c e s s o t h a t c o r r e l a t io ndh/h h a s n o t b e e n p o ss ib l e . O n t h e n o z z le b l a d e s w h i c h w e re t r a v e r s e d

Oh / h w e r e b e t w e e n 0 . 1 0 a n d 0 . 1 5 w h e r e a s i n t h e f e w in s t a n c e s w h e n t h e o u t l e tOh / h ( a b o u t 0 - 1 5

) w e r e r e c o rd e d . I t is t h u s p r o b a b l e t h a t t h e h i g h e r s e c o n d a r y l o ss e s o n t h e s e b l a d e s a r er t l y a c c o u n t a b l e t o t h i c k e r b o u n d a r y l a y e r s o n t h e e n d w a ll s. N e v e r t h e l e s s , i t i s a l so v e r y

a t c o m p a r a t i v e l y t h i c k b o u n d a r y l a y e r s ar e u n a v o i d a b l e i n t h e l o w - re a c t io n bl a d es .

15



A t y p i c a l o u t l e t d i s t r i b u t i o n o f v e l o c i t y f ro m a l o w - r e a c t io n t u r b i n e s t a g e i s s h o w n i n F i g . 19.T h e m a j o r t h i c k e n i n g of t h e b o u n d a r y l a y e r oc c ur s a t th e b l a d e r o o t ; a t t h e t i p t h e f lo w i sa c c e l e r a t e d t h r o u g h t h e r a d i a l t i p c le a r a n c e sp a c e. A m a j o r f r a c t i o n o f t h e s e c o n d a r y lo s s o ns u c h b l a d e r o w s t h e r e f o r e a p p e a r s t o o c c u r i n t h e v i c i n i t y of t h e b l a d e r o o t , w h e r e t h e l o c a l g a sa c c e l e r a t i o n s t h r o u g h t h e r o w a r e l e a s t .

O n h i g h - r e a c t i o n t u r b i n e s t h e v e l o c i t y d i s t r i b u t i o n s a r e m o r e U n i f o rm a n d t h e s e c o n d a r y l o s se sa r e n o t s o g r e a t .

T h e t r e n d o f t h e s e s e c o n d a r y l o ss re s u l t s is s i g n i f ic a n t i n t h a t i t d e m o n s t r a t e s t h e d e s i r a b i l i t yo f p r o v i d i n g a m a r k e d d e g r e e o f g a s f l o w a c c e l e r a t i o n i n a b l a d e r o w , p a r t i c u l a r l y w h e n i t i sw i s h e d t o n e g o t i a t e h i g h d e fl e ct i on s . T h i s a c c o rd s w i t h o b s e r v a t i o n s m a d e i n t h e p a s t b y s t e a m -t u r b i n e i n v e s t i g a t o r s w h o f o u n d t h a t t h e i n t r o d u c t i o n o f a s m a l l d e g r e e o f r e a c t i o n i n t o a t u r b i n es t a g e w h i c h h a d i n i t i a l l y b e e n d e s i g n e d a s a n i m p u l s e s t a g e a l l ow e d a s u b s t a n t i a l i m p r o v e m e n tin e f f ic iency .

T h e f o l l o w i n g t a b l e i l l u s t r a t e s t h e c o m p a r a t i v e m a g n i t u d e s o f t h e v a r i o u s c o m p o n e n t l o s se s i ns o m e t y p i c a l i m p u l s e a n d n o z z l e b l a d e s e ct i o n s.

T A B L E 5

Blade type . . . . . . . . Nozzle Impulse

Outlet angle . . . . . . 60 70 50 60

Deflection . . . . . . 60 70 100 120

s / c . . . . . . . . 0"8 0-7 0-7 0-6

Profile-loss coefficient, Y j , . . 0.024 0-038 0.074 0.101

Secondary-loss coefficient, Y, . . 0.0266 0.0314 0.289 0. 328

Clearance-loss coefficient, Y,,:

(t~/~ = o. 02)

• . 50

.. 50

. . 0 '9

•. 0"021

0" 0242

•. 0' 0273

0"0715

0"974

0' 0452

0 . 0 3 9 6 0.0603 0-094 0.119

Total-loss coefficient, Y, . . . . 0.0902 0-1 297 0-427 0.548

Blad e vel oci ty coefficient (M 2 = 0' 8) 0.96 7 0" 955 0.87 7 0" 852

0.05 06 0" 0694 0. 333 0' 429

0.983 0-975

Total-loss coefficient, Y , . . . .

Blade velocity coefficient (M2 = 0" 8~ 0 - 8 9 9.980 0"877

Zero tip

clearance.

O n n o z z l e b la d e s t h e p r o fi le lo s se s a re c o m p a r a b l e t o t h e l o ss e s w h i c h w o u l d b e a n t i c i p a t e dd u e t o s k i n f r i c t i o n a s s o c ia t e d w i t h a t u r b u l e n t b o u n d a r y l a y e r o n t h e e n t i r e b l a d e s u rf a c e t o g e t h e rw i t h t h e l o s s d u e t o t h e f i n i t e t r a i l i n g - e d g e t h i c k n e s s ( o f . A ndr ew s an d Scho f ie ld 71 (1950)) . Th e

. s e c o n d a r y l o s s es c o m p a r e w i t h t h e t h e o r e t i c a l e s t i m a t e ( e q u a t i o n ( 3) , s e c t i o n 8 .2 ) i f [1 - - ( h ' / h ) ]is a p p r o x i m a t e l y e q u a l to 0 . 0 3 . N o w i f t h e r a t i o of t h e b o u n d a r y - l a y e r th i c k n e s s t o t h e b l a d eh e i g h t i s a p p r o x i m a t e l y 0 . 1 5 ( s e e T a b l e 1) t h e n a v a l u e o f E1 - ( h ' /h ) ] o f 0 . 0 3 i s a p p r o x i m a t e l ye q u a l t o t h e r a t i o o f t h e d i s p l a c e m e n t t h i c k n e s s o f t h e w a l l b o u n d a r y l a y e r t o h a l f t h e b l a d eh e i g h t , a s s u m i n g a t u r b u ] e n t w a l l b o u n d a r y l a y e r . I n o t h e r w o r d s , f ol l o w i n g C a r t e r ' s a n a l o g y 1( C a r t e r 1 ( 19 48 )) b e t w e e n s e c o n d a r y l o s s a n d t i p c l e a r a n c e l o s s, t h e s e c o n d a r y l o s s i s r o u g h l ye q u i v a l e n t t o t h e t h e o r e t i c a l l o s s d u e t o a t i p c l e a r a n c e a t e a c h e n d o f t h e b l a d e e q u a l t o t h e w a l lb o u n d a r y - l a y e r d i s p l a c e m e n t t h ic k n e ss . I t s e em s p la u s ib l e t o c o n je c t u re f r o m t h i s t h a t t h em e a s u r e d s e c o n d a r y l o ss e s a r e a s l o w a s m a y b e e x p e c t e d f o r t h e t y p e o f v e l o c i t y d i s t r i b u t i o nn o r m a l l y e n c o u n t e r e d i n a n oz z l e r o w ; a n d f u t u r e d e v e l o p m e n t i s u n l i k e l y t o r e s u l t in a s u b -s t a n t i a l d e c r e a s e in n o zz l e l o s s, e x c e p t p e r h a p s b y s u c h a m e t h o d a s w a l l b o u n d a r y - l a y e r s u c t i o n

16



h o t t u r b i n e s d o e s n o t a p p e a r p r a c t i c a b le . O n lo w - r e a c t i o n b l a d e s, h o w e v e r , t h ea g n i t u d e o f t h e p r o fi le lo s se s i m p l i e s t h a t t h e r e i s a s u b s t a n t i a l a m o u n t o f l o ss d u e t o f lo w

r a t i o n ; t h i s m a y e v e n t u a l l y b e r e d u c e d b y u s e of b e t t e r s e c t i o n p r of il es . T h e s e c o n d a r ys e s a r e a ls o v e r y m u c h l a r g e r ( i n t e r m s o f e q u i v a l e n t t i p c l e ar a n ce ) o n im p u l s e b l a d e s t h a n o n

b l a d e s a n d t h i s m a y i n d i c a t e t h a t l o s se s a r e t a k i n g p l a c e d u e t o s e p a r a t i o n r e s u l t i n g f ro md a r y f lo w s. W h e t h e r s u c h l os s es m a y b e r e d u c e d b y u s e o f d i f fe r e n t b l a d e p r of i le s o r w h e t h e r

e y a r e i n e s c a p a b l e o n h i g h - d e f l e c ti o n b l a d e s h a v i n g l o w r e a c t i o n is n o t k n o w n . H o w e v e r , ita y b e s i g n i fi c a n t t h a t a n o r m a l v a l u e f o r 1 o n a n a x i a l c o m p r e s s o r b l a d e r o w i n w h i c h t h e g a sd i ff u s ed , i s a b o u t 0 . 0 2 ; t h i s v a l u e i s m u c h l e s s t h a n t h a t d e d u c e d f o r a n i m p u l s e t u r b i n e b l a d e

0 2 8 ) . T h u s i t m a y b e c o n j e c t u r e d t h a t e i t h e r t u r b i n e i m p u l s e - b l a d e s e c o n d a r y l o ss e se n t u a l l y b e r e d u c e d t o g i v e a v a l u e o f 1 a t l e a s t c o m p a r a b l e t o t h e a x i a l c o m p r e s s o r v a l u e

a t i v e l y t h e h i g h e r v a l u e o f 1 m e a s u r e d o n i m p u l s e t u r b i n e b l a d e s i s i n h e r e n t l y a s s o c i a t e dh t h e h i g h g a s de f l e ct i o n i n t h e l a t t e r a n d t h a t t h e e a r li e r d e d u c t i o n t h a t s e c o n d a r y lo s s i s

g r e a t l y i n f l u e n c e d b y d e f le c ti o n i s e rr o n eo u s .

S i n c e t h e u s e o f h i g h - d e f l e c ti o n b la d e s w i t h l o w r e a c t i o n i s h i g h l y a d v a n t a g e o u s i n g a s t u r b i n e sz e , w e i g h t , c o s t a n d t h e u s e o f b l a d e c o o li n g ) a f u t u r e d e t a i l s t u d y o f t h e s e p r o b l e m s

5.5. V a r i a t i o n o ~ S e c o n d a r y a n d P r o fi le L o s se s w i t h I n c i d e n ce i n a T u r b i n e . - - T h e p r e v i o u ss e c o n d a r y l o s s r e l a t e s s t r i c t l y o n l y t o b l a d e s o p e r a t i n g a t i n c i d e n c e s i n t h e v i c i n i t y

z e ro . I f i t is a s s u m e d t h a t 1 r e m a i n s c o n s t a n t f o r a l l i n c i d e n c e s a n d t h e p r o f i le l o s s i s v a r i e di t h t h e m e a n c u r v e s h o w n i n F ig . 8 a t h e n i t i s f o u n d t h a t e s t i m a t e s o f t o t a l l o ss

n e g a t i v e i n c id e n c e a re g e n e r a l l y l o w e r r a t h e r t h a n t h o s e m e a s u r e d . C o r r e l a t i o n m a y b er o v e d e i t h e r b y a d j u s t i n g t h e v a r i a t i o n o f p r o fi le l o ss w i t h i n c i d e n c e o r b y a d j u s t i n g t h e v a l u e

t a t in c i d e n c e s o t h e r t h a n z e ro . A n a d j u s t m e n t o f t h e f o r m e r t y p e r e s u l t s i n a v a r i a t i o n o fi l e l o ss w i t h i n c i d e n c e f o r t u r b i n e b l a d e r o w s a s s h o w n i n F ig . 18 . T h u s , b y a d j u s t i n g p r o fi le

s s w i t h i n c id e n c e in a c c o rd a n c e w i t h t h e m e a n c u r v e m a r k e d ' t u r b i n e ' a n d a s s u m i n g t h a t ii n s c o n s t a n t a s t h e i n c i d e n c e is v a r i e d t h e t o t a l l o ss a t i n c i d e n c e s d o w n t o i /G a u = - - 2 . 0

a y b e p r e d i ct e d w i t h f a ir a c c u r a c y ( ± 15 p e r c e n t) .

I t i s w o r t h y o f n o t e t h a t t h e d i ff e re n c e s b e t w e e n t h e ' t u r b i n e ' a n d ' c a s c a d e ' v a r i a t i o n s o fi le l o ss w i t h i n c i d e n c e a r e q u a l i t a t i v e l y s i m i l a r t o t h o s e t h a t m i g h t b e a n t i c i p a t e d a s a

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

6 . 0 1 b t $ m u m B l a d e P i t c h i n g . - - S e c o n d a r y a n d t i p c l e a r a n c e l o s s e s i n a b l a d e r o w m a y b e e x -

Y, + :G = (Gs + G )(cos dcos

= [ i + 0 . 5 ( k / h ) l E c o s ' d co s 3 o J F C L / ( s / c ) y

- -- - 4 1 i - I - 0 " 5 ( k / h ) ] [ c o s ~ ~ d c o s ~ , . ] [ t a n ~ , - - t a n ~ ] ~ . . . . . . . ( 1 4 )

u a t i o n ( 1 4) s h o w s t h a t s e c o n d a r y a n d t i p c l e a r a n c e l o ss e s i n a b l a d e r o w h a v i n g f i x e d in l e t

u t l e t g a s a n g l e s a r e in d e p e n d e n t o f s / c . T h i s le a d s t o t h e s i m p l e c o n c lu s i o n t h a t t h e o p t i m u mb l a d e s i s e q u a l t o t h e p i t c h g i v i n g t h e m i n i m u m p r o fi le l os s. T h i s c o n c l u s i o n

t h t h a t r e a c h e d b y J o h n s t o n 27 ( 19 51 ).

T h u s , t h e o p t i m u m p i t c h / c h o r d r a t i o s f o r n o z z l e a n d r o t o r b l a d e s m a y b e d e t e r m i n e d d i r e c t l y4 . T h e s e v a l u e s a r e p l o t t e d i n F i g . 2 0 a g a i n s t g a s o u t l e t a n g l e . I t i s o f i n t e r e s t t o

T h e e a r l ie s t r u l e f o r o p t i m u m s p a c i n g o f i m p u l s e b l a d e s w a s f o r m u l a t e d b y B r i l l i n g (see Ret . 17)h a t t h e m e a n r a d i u s o f c u r v a t u r e o f t h e b l a d e p a s s ag e s h o u l d b e t w i c e t h e p a s s a g e

T h i s r e s u l t s i n a n o p t i m u m p i t c h / c h o r d r a t i o f o r i m p u l s e b l a d e s ( d e s i g ne d f o r c o n s t a n ta r e a ) o f 1 / ( 2 . 5 s i n 2 c ~ ) . Z w e i f e P 5 ( 19 4 5) , b y a t h e o r e t i c a l a p p r o a c h , e x t e n d e d t h i s r u l e

e s o f b l a d i n g a n d d e d u c e d t h a t t h e o p t i m u m s p a c i n g w a s sp e c if ie d b y a ' l o a d i n g

17B

(6.3a68)



c o e f fi c ie n t ' ( e q u i v a l e n t t o t h e l i f t c o e ff i c ie n t b a s e d o n o u t l e t v e l o c i t y , CL °2) o f 0 . 8 . I n d e p e n d e n t l y ;b u t b y a s im i l a r t h e o r e t i c a l a p p r o a c h , H o w e l l a n d C a r t e r 3° (1 94 6) d e d u c e d t h a t o p t i m u m s p a c i n go c c u r r e d w h e n C Lo 3 = 1 .12516(s / c ) - - 1 ] /5 (s / c ) . T h e v a l u e s o f o p t i m u m s /c d e r i v e d b y t h e s er u l e s a r e c o m p a r e d w i t h t h o s e d e r i v e d b y t h e p r e s e n t a n a l y s i s i n F i g . 2 0 . T h e r e is a p p r e c i a b l ed i ff e re n c e b e t w e e n t h e v a l u e s g i v e n b y e a c h o f t h e r u l e s ; n o t a b l y t h e p r e s e n t a n a l y s i s d o e s n o ti n d i ca t e a t e n d e n c y f o r o p t i m u m s /c t o i n c r e a s e a t h i g h g as o u t l e t a n g l e s . S o m e t e s t s b y D o w s o n 3s

(1 93 8) o n t h e e ff e ct o f c i r c u m f e r e n t i a l p i t c h i n g o n a r e a c t i o n s t e a m t u r b i n e e q u i p p e d w i t h b l a d e sh a v i n g 6 5 d e g o u t l e t a n g l e a n d s m a l l i n l e t b l a d e a n g l e (i.e., n e a r l y e q u i v a l e n t t o n o z z l e bl a de s )g a v e a n o p t i m u m p i t c h / c h o r d r a t i o of r o u g h l y 0 - 6 . T h i s is s m a l l e r t h a n w o u l d b e p r e d ic t e d b yt h e p r e s e n t a n a l y si s a n d c e r t a i n l y l e nd s n o s u p p o r t t o t h e t h e o r y t h a t o p t i m u m v a lu e s o f s ici n c r e a s e a t h i g h o u t l e t a n g l e s .

T h e p r e s e n t a n a l y s i s g i ve s v e r y h i g h v a l u e s o f s /c f o r lo w - d e f l e c t i o n i m p u l s e b l a d e s w h e n c o m -p a r e d w i t h t h e p r e v i o u s t h e o ri e s . I n a p p l y i n g t h i s d a t a i t s h o u l d b e n o t e d t h a t l a r g e v a l u e s o fs /c l e a d t o s m a l l s t a l l i n g i n c id e n c e s • T h u s v a l u e s o f s /c w h i c h a re l es s t h a n t h e o p t i m u m m a yg i v e s l i g h t ly h i g h e r l os se s t h a n t h e m i n i m u m b u t a t t h e s a m e t i m e w i l l g i ve a b e t t e r w o r k i n gr a n g e of i n c id e n c e . F u r t h e r m o r e , i t m a y b e s e en f r o m F i g . 4 t h a t c o n s i d e r a b le v a r i a t i o n o f s /ci s p o s s i b le w i t h o u t a p p r e c i a b l y a f f e c t i n g t h e l o s s.

7 . E f f e c t, o f A ~ n ~ t l ~ s F l a r e . - - S m a l l a n g l e s o f d i v e r g e n c e b e t w e e n t h e w a l l s a t t h e e n d s o f b l a d e sr e d u c e t h e m e a n a c c e l e r a t i o n o f t h e g a s i n t h e b l a d e p a s s ag e s . T h i s p r o b a b l y r e s u lt s i n at h i c k e n i n g o f t h e w a l l b o u n d a r y l a y e r s a t t h e o u t l e t f r o m t h e b l a d e a n d a n i n c re a s e i n s e c o n d a r yl os s i n a c c o r d a n c e w i t h t h e i n c re a s e i n t h e p a r a m e t e r (A2/AI)~/[1 - [ - ( I .D . /O .D. ) ] as showni n F i g . 1 7 . L a r g e a n g l e s o f f la r e, h o w e v e r , m a y r e s u l t i n a c o m p l e t e s e p a r a t i o n o f t h e f l o wf r o m t h e i n n e r w a l l, a c c o m p a n i e d b y h i g h p r e ss u r e l o ss es a n d l a r g e a n g u l a r d e v i a t i o n s o ft h e f lo w f ro m t h e d e s ig n b l a d e e f f lu x a n gl e s in t h e v i c i n i t y o f t h e i n n e r h a l f o f t h e b l a d e h e i g h t .O n n o z z l e r o w s h a v i n g o u t l e t a n g l e s i n t h e r e g i o n o f 6 0 d e g t o 7 0 d e g a d i v e r g e n c e b e t w e e n t h ew a l ls o f a b o u t 2 5 d eg c a n p r o b a b l y b e e m p l o y e d w i t h o u t r is k o f t h i s s e p a r a t io n . O n lo w - r e a c t i o nb l a d e r o w s o r r o w s h a v i n g s m a l l h u b r a t io s , h o w e v e r , t h e f la r e a n g le s h o u l d b e l es s t h a n t h i si f p o s s ib l e .

8 . E f fe c t o f R e y n o l d s N u m b e r o n T ~ r b i ~ e E f f i c i e ~ c y . - - T h e i n f l u e n c e o f R e o n p ro f i l e l o s sh a s b e e n b r i e f l y d i s c u s s ed i n s e c t i o n 4 .4 . I n a d d i t i o n t o p r o f i l e l o s s i t is p o ss i b l e t h a t R e w i l la l so i n f lu e n c e t h e m a g n i t u d e o f t h e b o u n d a r y q a y e r t h i c k n e s s o n t h e a n n u l a r w a l ls . a n d c o n -s e q u e n t l y a f f e ct t h e s e c o n d a r y lo s s. T h u s , i f s e c o n d a r y l os s i s r o u g h l y p r o p o r t i o n a l to t h eb o u n d a r y - l a y e r t h i c k n e s s a n d t h e b o u n d a r y l a y e r o n t h e a n n u l u s w a ll s i s t u r b u l e n t (a s i t m a y b ee x p e c t e d t o b e) t h e n i t m i g h t b e a n t i c i p a t e d t h a t s e c o n d a r y l os s w i l l v a r y a p p r o x i m a t e l y a sR e - W E A b o v e R e = 1 . 0 x 1 05 F i g . 1 0 s h o w s t h a t p r o f i l e l o ss a l so v a r i e s r o u g h l y to t h e s a m ep o w e r o f R e s o t h a t i s i s p r o b a b l e t h a t f o r a c o m p l e t e t u r b i n e s t a g e (1 - - ~ ) o c R e - l ~ 5 w h e nR e > 1 .0 × 105 . When R e < 1 . 0 × 1 05 c a s c a d e p r o f il e l o ss e s t e n d t o i n c r e a s e m o r e s t e e p l yw i t h d e c r e as i n g R e , i n m a n y i n s t a n c e s t h e l o s s b e i n g m o r e n e a r l y p r o p o r t i o n t o R e -~ /2, p a r t i c u l a r l yw i t h l o w - r e a c t io n b l ad e s . H o w e v e r , t h e h i g h d e g re e o f t u r b u l e n c e t h a t m u s t e x i s t Jn a t u r b i n es t a g e m a y h a v e t h e e f f e c t o f r e d u c i n g t h e ' c r i t i c a l ' R e , b e l o w w h i c h t h e p r o f i l e l o s s b e g i n s t o

r i s e s t e e p l y , t o v a l u e s s u b s t a n t i a l l y l es s t h a n t h e v a l u e o f a b o u t 1 . 0 × 1 0 5 i r / d i c a t e d b y c a s c a d ete s t s .

E v i d e n c e e x i s t s o f r e a c t i o n t u r b i n e s g i v i n g r e l a t i v e l y h i g h e f f ic i en c i es ( o v e r 8 5 p e r c e n t ) a tR e y n o l d s n u m b e r s a s lo w a s 2 x 1 0 4, w h i c h i m p l i e s t h a t t h e f a l l o f e f f ic i e n c y w i t h d e c r e a s i n gR e y n o l d s n u m b e r b e l o w R e = 1 × 105 m a y n o t b e a s s e v e r e a s c a s c a d e te s t s m i g h t s u g g e s t.M o r e e x p e r i m e n t a l e v i d e n c e i s r e q u i r e d b e f o re t h i s m a y b e p r o v e d o r re f u t e d .

H o w e v e r , i n t h e a b s e n c e o f m o r e e x p l i c i t d a t a t h e a s s u m p t i o n t h a t t u r b i n e a e r o d y n a m i c• " " - - 1 / 5e f f ic i e n c y v a r i e s w i t h R e a c c o r d i n g t o t h e l a w ( 1 - - ~ ) o c R e s h o u l d p r o v e t o b e r e a s o n a b l y

r e l ia b l e d o w n t o R e y n o l d s n u m b e r s o f a b o u t 3 . 0 × 10 4.

18



I t s h o n l d b e e m p h a s i s e d t h a t t h i s la w a p p l ie s o n l y to a e r o d y n a m i c e ff ic ie n c y. I f t h e r e d u c t i o nR e o c c u r s a s a c o n s e q u e n c e o f a r e d u c t i o n i n r o t a t i o n a l s p e e d o r , f o r a i r c r a f t u n i t s , a s a c o n -

n c e o f a n i n c r e a s e i n a l t i t u d e t h e n t h e r a t i o o f m e c h a n i c a l lo s s e s i n b e a r i n g s , g e a r s , e t c. , t ot p u t w i l l i n c r e a s e ; t h u s t h e m e c h a n i c a l e f fi c ie n c y w i l l d r o p . F o r e x a m p l e ,o p e r a t i n g a t c o n s t a n t s p e e d a t d i f f e r e n t a l ti t u d e s t h e m e c h a n i c a l e f fi c ie n c y

v a r y r o u g h l y a c c o r d i n g t o t h e l a w (1 - - ~ ,~)oc R e -~ . T h i s m a y h a v e a n a p p r e c i a b l e e f f e c t

(i.e., ~ ... dynamic × ~ o ~ o ~ ) at lOW va lu es of R e .

9 . D i s c W i n d a g e L o s s e s . - - A n u m b e r o f e x p e r i m e n te r s 16' ~7, 87 h a v e m e a su re d th e p o w e r r e q u i r e dt a t e d i sc s i n s ti l l g a s o r f l u id a n d h a v e a t t e m p t e d t o c o r r e l a t e t h e p o w e r w i t h t h e o r e t i c a la t e s b a s e d o n s k i n - f r i c t i o n l a w s f o r f l o w o n f l a t s u r f a c e s . A r6 s u m 6 o f t h e t h e o r e t i c a l w o r k

d s o m e r e l i a b l e e x p e r i m e n t a l r e s u l t s a r e q u o t e d b y G o l d s t e i n ( E d . ) 16 (1 93 8) f o r d i s c s r o t a t i n gs t a t i o n a r y f lu i d w h i c h e x t e n d s t o i n f i n i t y . T h e r e s u l ts m a y b e e x p re s s ed a p p r o x i m a t e l y

H . P . = 0 . 0 9 v ° 2 p (D )" ~ (N / lO 0 0 ) 28 . . . . . . . . . . . . (15)

i f N D 2 / v > 107

s c d i a m e t e r , I t ; N = r . p . m . ; v i s k i n e m a t i c v i s c o s i t y , s q f t / s e c ; p i s g a s d e n s i t y , l b / c u f t ).

T h i s e x p r e s s i o n c a n o n l y b e e x p e c t e d t o g i v e a v e r y a p p r o x i m a t e i d e a o f t h e d i sc f r ic t io n s i n c es k n o w n o n t h e o n e h a n d t h a t i t c a n b e s u b s t a n t i a l l y r e d u ce d b y t h e p r e s e n ce o f a d j a c e n tt i o n a r y s u r f a c e s ( S t o d o l a 17 (1 94 5)) a n d o n t h e o t h e r h a n d i t c a n b e i n c r e a s e d b y t h e p r e s e n c e

H o w e v e r , a s a p r o p o r t i o n o f t h e t u r b i n e o u t p u t p o w e r t h e d i sc f r i c t i o n i s n o r m a l l y s u f fi c i e n tl yt o b e n e g l e ct e d e x c e p t o n v e r y s m a l l tu r b i n e s o r t u r b i n e s o p e r a t i n g a t v e r y l o w R e y n o l d s

10 . N o t e o n In f l u e n c e o f O ut le t F l o w C o n d i ti o n s f r o m t he L . P . S t a ge o n O v e r al l E x p a n s i o nl o w - r e a c t i o n t u r b i n e s t h e a x i a l v e l o c i t y a n d s w i r l o f t e n h a s a f o r m s i m i l a r to

s h o w n i n F i g . 1 9. N o t a b l y t h e r e i s f r e q u e n t l y a m a r k e d r e d u c t i o n i n v e l o c i t y n e a r t h e i n n e r

o f t h e t u r b i n e a n n u l u s w h i c h m a y l e a d t o e a r l y fl ow se p a r a t i o n o n t h e i n n e r s u rf a ce o fa n n u l a r d i f fu s i n g d u c t p l a c e d d o w n s t r e a m o f t h e t u r b i n e . N o w t h e o u t l e t v e lo c i ti e s a r e( a n d c o n s e q u e n t l y t h e d e s i r a b i l i t y fo r d if f u si o n i n t h e e x h a u s t d u c t i s a l so g r e a te s t ) o n

c t io n t u r b i n e s h a v i n g h i g h o u t p u t p e r s t ag e a n d o n s u c h t u rb i n e s t h e r e d u c t io n i n o v e ra l ln s i o n e f fi c ie n c y a s a re su lL o f e x h a u s t d u c t l o ss e s m a y b e c o n s i d e r a b le . T h u s , w h e n s p e c u l a t i n g

t h e n u m b e r o f s t a ge s t o b e e m p l o y e d i n a tu r b i n e t o a c h i e v e a r e q u i re d w o r k o u t p u t t h i su s t l o ss s h o u l d b e g iv e n c a r e fu l c o n s id e r a t i o n . T a b l e 6 b e l o w c o m p a r e s t h e o v e r a l l e x p a n s i o n

f ic ie n ci es of a si n g le a n d t w o - s t a g e t u r b i n e f o r a h y p o t h e t i c a l j e t e n g i n e i n w h i c h i t i s a s s u m e da t t h e e x h a u s t a n d j e t - p i p e l os s es a re 2 0 p e r c e n t o f t h e k i n e t i c e n e r g y a t t h e t u r b i n e o u t l et .

T A B L E 6

S i n g le s t a g e T w o s t a g et u r b i n e t u r b i n e

K~AT/½U 2 ( p e r s t a g e ) . .

U/Vo ( o u t l e t ) . . . .~7 ( tu r b in e a lo ne ) . . . .

(overall) . . . . . .

4 . 0

1 . 0

0 . 8 6

0 . 8 2 5

2 . 0

1 . 8

0 . 9 0

0 " 8 8 5

o r t h y t h a t t h e t w o - s t a g e t u r b i n e n o t o n l y h a s a s m a l l e r e x h a u s t l os s t h a n t l~ e s i n g l e -s t a g eb u t a ls o ( if b l a d e p e r i p h e r a l s p e e d s a r e t h e s a m e i n b o t h c as es ) t h e a e r o d y n a m i c e f f ic i en c y

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

19

2



A u t h o r

A . S t o d o la . . . . . . . .

H . W . L i e p m a n n . . . . . .

C . H . H a u s e r , H . W . P l o h r a n dG . S o n d e r .

J . R e e m a n a n d E . A . S i m o n i s . .

I . H . J o h n s t o n . . . . . .

A . D . S . C a r t e r . . . . . .

M . C . H u p p e r t a n d C . M a c G r e g o r

H a n s K r a f t . . . .

J . H . K e e n a n . .

M e l d a h l . . . .

A . S t o d o l a . . . .

A . R . H o w e l l . .

O . Z w e i f el . . . .

A . R . H o w e l l a n d A . D . S . C a r t e r

K e a r t o n . . . . . . . .

R . D o w s o n . . . . . .

F . D o l lin . . . . . . . .

D . G . A i n l e y , S . E . P e t e r s e n a n dR . A . J e f f s .

S . J . A n d r e w s a n d N . W . S c h o f i e l d

K . B a m m e r t a n d G . K o r b a c h e r . .

H . L . G u y . . . . . .

REFERENCES --continued

Title, etc.

S t eam and Gas Turb ines . V ol . I (6 th Ed i t ion ) .S m i t h , N e w Y o r k . 1 94 5.

1 s t R e p o r t o f t h e S t e a m N o z z l es R e s e a r c h C o m m i t t e e .1923, pp . 1 to 22 .

2 n d R e p o r t o f t h e S t e a m N o z z l es R e s e a r c h C o m m i t t e e .1923, pp . 311 to 395.

3 r d R e p o r t o f t h e S t e a m N o z z l es R e s e a r c h C o m m i t t e e.1924 , pp . 453 to 525 .

4 t h R e p o r t o f t h e S t e a m N o z z l es R e s e a r c h C o m m i t t e e .1925, pp . 474 to 843.

5 t h R e p o r t o f t h e S t e a m N o z z l e s R e s e a r c h C o m m i t t ee .1928, pp . 31 to 121.

6 t h R e p o r t o f t h e S t e a m N o z z le s R e s e a r c h C o m m i t t e e .1930 , pp . 215 to 315 .

T i l e i n t e r a c t i o n b e t w e e n b o u n d a r y l a y e r a n d s h o c k - w a v e s i n t r a n s o n icf low . J . A e . S c i . , Vol. 13 , No . 12 . 1946.

S t u d y o f t h e f l o w c o n d i t i o n s a n d t h e d e f l e c t i o n a n g l e a t e x i t o f t w o -d i m e n s i o n a l c a s c a d e o f t u r b i n e r o t o r b l a d e s a t c r i t i c a l a n d s u p e r c r i t i c a lp r e s s u r e r a t i o s . N . A . C . A . R M E g K 2 5 . 1 95 0.

T h e e f f e ct o f t r a i l i n g - e d g e t h i c k n e s s o n b l a d e l o ss . R . A . E . T e c h . N o t eEng .116 . 1943 .

A n a l y s i s o f t h e a i r f l ow t h r o u g h t h e n o z z l e b l a d e s o f a s i n g l e - s ta g e t u r b i n e .C .P . 131. Fe b r ua ry , 1951 .

V o r t e x w i n d - t u n n e l t e s t s o n v a r io u s v o r t e x f lo w s. P o w e r J e t s R e p o r tN o . R .1063 . 1945 .

C o m p a r i s o n b e t w e e n p r e d i c t e d a n d o b s e r v e d p e r f o r m a n c e o f a g a s t u r b i n es t a t o r r o w d e s i g n e d f o r f r e e v o r t e x f lo w . N . A . C . A . T e c h . N o t e 1 8 10 .

R e a c t i o n t e s t s o f t u r b i n e n o z z l e s f o r su b s o n i c v e l o c i t i es . T r a n s . A . S . M . E . ,

V ol . 71 . O c to be r , 1949 .R e a c t i o n t e s t s o f t u r b i n e n o z z l e s f o r s u p e r s o n i c v e l o c i t ie s . Trans .

A . S . M . E . , V ol . 71 , N o . 7 . O c to be r , 1949 .

T h e e n d l o s s e s o f t u r b i n e b l a d e s . T h e B r o w n B o v e r i R e v i e w , Vol. 28 ,N o . 1 1. N o v e m b e r , 1 94 1.

T r i a l s of a B r o w n B o v e r i b a c k p r e s s u re t u r b i n e . Engineer ing , Vol. 120O c tobe r , 1925 .

T h e p r e s e n t b a s i s o f a x i a l c o m p r e s s o r d e s ig n . R . & M . 2 0 9 5. J u n e , 1 94 2.

T h e s p a c i n g o f t u r b o - m a c h i n e b l a d i n g e s p e c i a ll y w i t h l a r g e a n g u l a rde f l e c t ion . T h e B r o w n B o v e r i R e v i e w , Vol. 32 , No. 12 . 1945.

F l u i d f l o w t h r o u g h c a s c a d e s o f a e r o fo i l s. P u b l i s h e d i n P r o c . o f C o n g r e sso f A p p l i e d M e c h a n i c s . 1 94 6.

Steam turbine theory and pract ice . P i t m a n , 5 t h E d i t i o n . 1 94 8.

T h e e f f ec t of c i r c u m f e r e n ti a l p i t c h o f s t e a m t u r b i n e b l a d e s o n t o r q u e .P r o c . I . M e c h . E . , Vol. 1 . Ap ri l , 1938.

I n v e s t i g a t i o n o f s t e a m t u r b i n e n o z z l e a n d b l a d i n g e f f ic i en c y . Prec . I .M e c h . E . , Vol. 114, No . 4 . 1940.

O v e r a l l p e r f o r m a n c e c h a r a c t e r i s ti c s o f a f o u r - s t a g e r e a c t i o n t u r b i n e .R . & M . 2 4 1 6 . S e p t e m b e r , 1 94 6.

A n 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 o f a t h i c k a e r o f o i l n o z z l e c a s c a d e . R . & M .2883 . M a y , 1950 .

T h e c h a r a c t e r i s t i c d i a g r a m o f s i n g l e - s t a g e r e a c t i o n g a s t u r b i n e s , l VI .0 .S .( A ) V o l k e n r o d e R e p o r t & T r a n s l a t i o n N o . 6 39 .

S o m e r e s e a r c h e s o n s t e a m t u r b i u e n o z z l e e ff i ci e n cy . J o u r n a l o f the Ins t .of Civi l Engineers , Vo l. 13. 1939.

P u b l i s h e d b y P e t e r

Proc . I . Mech .E .

P r o c . I . M e c h . E .



P r o c . I . M e c h . E .

Proc . f . Mech .E .

21



N o m e ~ . c l a t ~ r e

CA

c~2

L

y

p

yJ

2

a .

b

C

g

h

i

k

k'

kp

0

M2

S

t

t~

A1

A2

X

Ca

C a I~

C L

CL v2

P I

P ~

APPENDIX I

Gas inlet angle

Gas outlet angle

Vector mean gas angle

Blade inlet angle

Blade outlet angle

Ratio of specific heats

Gas density

Blade velocity coefficient

A factor defining secondar y loss , - C D , ( s / c ) / C c 2

Loss of total pressure between blade inlet and outlet

Stage efficiency

Distance of point of maxim um camber from leading edge

Maximum camber

Blade chord

Mean radius of curvature of upper surface betwe en the t hroa t and the trai lingedge

Blade height

Incidence

Radial tip clearance -

Minimum shroud clearance

Specific heat at constant pressure

Blade opening

Mach number at outlet from a blade row

Blade pitch

Blade thickness

Trailing-edge thickness

Inle t flow area = (annulus area at blade inlet) × cos 81

Out let flow area = (annulus area at bla de outlet) × cos c~2

Factor defining amo unt of gas undeflected by r otor row due to end clearance

Drag coefficient based on vector mean velocity

Drag coefficient due to tip clearance, based on vector me an veloc ity

Lift coefficient based on vector m ean velocity

Lift coefficient based on outle t velocity

Total pressure Of gas ente ring blade row

Total pressure of gas leaving blade row

22



P 2 star

U ,.

V ~

V ~

V w i

Y w

V J J ~

Y ,

Y ,

Y ~

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

M e a n t u r b i n e r o t o r b l a d e s p e e d

I n l e t v e l o c i t y

O u t l e t v e l o c i t yI n l e t a x i a l v e l o c i t y

O u t l e t a x i a l v e l o c i t y

I n l e t w h i r l v e l o c i t y

O u t l e t w h i f f v e lo c i t y

V e c t o r m e a n v e l o c i ty

P r o f i l e - lo s s c o e f f i c i e n t

S e c o n d a r y - l o s s c o e f f i c i e n t

T i p - c l e a r a n c e - l o s s c o e f fi c ie n t

T o t a l - l o s s c o e f f i c i e n t

d a m e n t a l r e la t io n s h ip s : - -

(a) V e c t o r m e a n a n g l e : -

t a n c~,~ ---- ½ [ta n ~1 + t a n ~-2]

( b ) L i f t c o e f f i c i e n t :

C L - 2 ( s i c ) [ t a n ~, - - ta n c~2) co s g , ,

CL- = 2 ( s / c ) [ t a n cq - - t a n ~2] co s 3 c~,n/cos" a2

(c) D r a g c o e f f i c i e n t : - -

c ~ , = c o ( s / c ) c o s o : , , , / ( ~ / 2 ) p . v o ?

C , = (s/c). Y c o s ~ ~ , , , / c o s ~ ~

2 3



F

U

U

u9

LT_

El

O ]

O , O E

O'OZ

I . . . . .

F T r ,

C O N V E N T I O N A L 5 E C T I O N , P . /C = I ~ / ~X C O N V E N T I O N A L 5 E C T I O N I , L / C = 1 6 %

s i c = ~ . ~ . . - j - ~ - . - L _ . .~ - - C J -s / c " e '~ s J !~ , s / c = 0 - 7 5 I

5, 'C = 0 ' 94

_ 3 0 o - 4 0 ° - 5 0 ° - 6 0 ° - TD ° - 6 0 °

O U T L E T A N G L E , ~ z

B A S E P R O F I L E = R A F ~ 7 ; C ~ R C U L A R - A R C C . A M B E R ; o / / c = 5 0 %

C Q N V E N T t O N A L ~ S L A D I N G ; " B A 5 E P R O F I L E A P P R O X T 6 ;

A P P R O X . P A R A B O L I C - A R C C A M B E R ; g / i: : - -~ 4 5 ~ a

~/'c = ~5 - 3 1 %

R e = 2 x 1 0 5 ; M < 0 " 6

G

u

u31,9o

0~a.

0 . 1 £

0 . 0 8

0 . 0 4

. I M P U L 5 E B L A D E 5 ( ~ _, ~ - ~ 2 ° ) . : _

0 . O °

FIG. 3.

t /

I

- 3 0 - 4 0 ° - 5 0 ° - 6 0 ° - 7 0 °O U T L E T A N G L E , o ( a

P r o f i l e - l o s s c o e f f i c i e n t s f o r c a s c a d e s o f t u r b k l e b l a d e s ,

Incid ence -"- 0 deg.

( b )

-8 0

z

bJo

o_J

c,O~fo_

O 40

0 ' 0 5

D < 9 6

O , 0 4

0 ' 0 £

00 0 .~

N O Z Z L E

0,4-

_ - : -

0 ' 6 0 "8

BLAOC~ ( / 3 , = 0 )

V A L U E 5 O FO U T L E T ~ 5 A N G L E~ ? .

• - 7 5 ' / L 7 °

~ / " / .-55

. ~ _ _ _ _ ~ - / " ~ - ~ - 6 0

~ - . _ 50 °~ - " - -~ 'L _q42 /r

I. o t,E

Pt TCH / CH O RD

( ° )

v- -

zIdO

u

tO#3

s

lJ_Jff

o

o.

0 'L '0

0 . 1 8

0 ' 1 6

0 ' 1 4

0 . i 8

0 q 0

0 ' 0 8

0 . 0 6

0 , 0 4

00

I0 '~

I M P U L S E

\k

\\

B L A D E S ( # , = - ~ 3i' - 7 0/"

/

//

/

/

/

"~ ~ -40

I0 " 4 0 ' 6

P I T C H / C H O R D

0' 8 I.O I-~

( b )

FtG. 4. Profile-loss coefficients for conve ntion al section blades at zero

incidence. t/c----2Opercent; Re=2 × 105; M <0 .6.



-? 0

-t0'-6i

if:

I

. 2 0 o

fl

+10

Lo ~ : : . = - - 5 5 ° T O - 6 5 0

z .. ' ~ z : - 4 " 5 ° T O - 5 5 0

: ,=cz = - 3 5 ° T O - 4 5

/- - - F0' 5, 4 0 , 6 0 ' 9

1 I IV A R I A T I O N O F S T A LL I N G

I N C I D E N C E W I T H

P I T C H CH O R D R A T I O

D A T U M ~~0 ,NB>K "/

0 " 7 0 " 8

PITCH / CHORD

IVALUE5OF o< z

o L 6 °

1'0

(o )

V A R I A T I O N O F 0 < W I T H $ / C

1,0

i ~ 0 ' 9 0[ ' O ' ' P I T C H / C H O R D 0 " 7 0 " 8 0 . 9 ! . 0,, 4

Oii

z

W

3n

Oz

O2

. . . }J

+4-0

+ 3 0

+ ~ 0

+ I O

I l lX(x= = - ~ 5 ° T O - 3 5 ° I

. . ~ - e <

= - 3 5 ~ T O -4 5~ 11 " " ~ " . . . B L A D E S E C T I O N 5

- 4 5 " T O - .5 5 ~ , . . - . " . . W H E N s l c = 0 . 7 5

-5 7 ~ "7"0 -6/'d.B o )o x.

- 6 Z ° T O - / 6 7 " ~ 5 ~ o ( - 6 , ",

c Z- "~ : ~ -~- ....

, ¢ - " -4 C-Z

. .- ,E j ~ - ~ _ "

I I ISTALLING INCDENCE

• OF TURBINE

' ~ " ~ ~ ~ ~ < " ' ~ V A LU E 5 10Fo ~

z~

o- I - ~ - O . B - 0 . 4 0 - K ) , 4 t - O' B

~ , / , % , ( w H E . s / c - o . 7 ~ )

I } 1• .+1.£

F I G . 7 . ~ P o s i t i v e s t a l l i n g i n c i d e n c e s o f c a s c a d e s o f t u r b i n e b l a d e s .R e = 2 x 1 0 5 ; M < 0 . 6 .

I- -

(J

h_

8

o,

M

I1_

I--.4:g

5" 0

4 ' 0 - -

3' 0

Z' O

t' 0

0 -4- ' 0

F I G. 8a .

V A R I A T I O N O F R E ! . .A T I V E P R O F I L E

( . .0 , ~ 5 . W I T H R E L A T I V E I N C I D E N C E

M z < 0 . 5

R¢ = ~ x IQ 5

X X

.y.x

x

X •Xz

i 2

y,

o ~ . o

I N C I D E N C E c / L s

x ̧ ,.~ x

x~ ~x

x ; { x

- ~ ' 0 - ~ 0 - f ' O

R E L A T IV E

V a r i a t i o n o f lo s s a n d o u t l e t a n g l e w i t h i n c i d e n c e .

~0

"Z)-

2

o -%.._>tD

- t .C

{Jz

- ~ ' 0

!

-5 "CI' 0

F I G. 8b .

I- Z

i

A

1. 4 1,6,

M Z < O . B

R e . = 2 x l O s

+

l

1 . 8 z . o

V a r i a t i o n o f % w i t h r e l a t i v e p r o fi l e l o ss a t p o s i t i v einc idences •



-50'

LOp

I |

-50 O o

0-0~

IRELATIONSHIP 6ETWEEN (~a AND /

h05-' 0/ $ FOR .STI~AIGHT SACKED BLADE5 / /

M 2 < 0 '5 / /

Re. = ~ x tO ?

./Y/

/400 ° , 53 70

C 0 5 - ' ( o / s )

FOR 6LADEO IN WHICH THE UPPER 5URFAC E OF THE ~SLADEPROFILE 15 CURV ED BETWEEN THE THRO AT AND TH ETRAILING ED GE THE OUTLET ANGLE 15 APPROXIMATELYEQUAL TO ~ -4 (5 / e ) , WHEN M < 0 . 5 AND Re = ~ x t O 5

/

DEVIATION -BETWEEN °ca AND C0 5- t o/5

WHEN M R = I ' D ( R e = Z ' x l O s )

I I 1 IWHEN MB = 1"0 i -

o (~ = --C 05- ' 0 /~ , " ,~ OlN I"0/5

/

J

/

I-SEE ALSO FIG. ~(b]]

/

//

J1 1

_ _ I0

0 0-I 0"~ 0"5 0'4 O55/e

( .b)

IO:6

P_>-

v--zi, iu_

ht~

0u

O303o,._i

u._iixoIx"n

0"343

0 ' ? 0

O qO

O.OB

0 ' 0 6

0 , 0 3

( > O Z

o-oi0. I

%\

\

"\<' k " *

%

0 . ? 0 - 3 . 0 -4 0.5 (~6 0 " 8 I - 0

R E Y N O L . D 5 N U M B E R x I 0 ~

B L A D E D E T A I L . 5

BLAD E SECTI ON I : / c 5 / C / 5~ ~

! T . 6 3 1 . $ % 0 . 6 2 5 5 5 . 4 5 8

P T . 6 ~ . 1"7 % 0 , 6?. 5 45"5 +5

5 T. 6 Z4,6 % 0 . 6 ~ 5 4 9 . O 5 0

4 T. 6 Z3" 6 % 0.584- 35-5 5 7

5 C . 7 ?0,0 % 0 . 6 2 5 - 5 0 6 2

6 T , 6 . 15"0 % 0"584 I 6 " 9 4 . 6

7 T , 6 . 1 8 . 1 % 0 . 5 . 51 1 8 " 8 5 7

B C.7. 1 0 - 0 % 0 , 6 2 5 I 3 0 5 8

~ '0

FIG. 9 . Gas o u t l e t an g l e f ro m cascad es o f t u rb i n e b l ad es . F IO . 1 0 . V ar i a t i o n o f 'p ro f i le l o ss w i t h R ey n o l d s n u m b er ( ( -~- 0 ) .



t O¢43

5 " 0 :

S U G G E S T E D

\

0 j~ Ga_ i,0

0

0 '~

F I G . l l a .

M E A N C U R V E F O R

T U R B I N E B L A D E 5

• T Y P I C A L

.~.I COMPRE550R

0 - 3 0 " 4 0 ' 6 0 " 8 I ' O

R E Y N O L D S N L I M I N Z ~ n 1 0 - s

V a r i a t i o n o f p r o n e l o s s w i t h R e y n o l d s n u m b e r .

~ '0

X

t~tl

@

Z1,3a:

I

¥I

÷1 °

0 °

_j o

- 3 ' 0 " ~ 0 ' 3

F m . l l b .

f

0 " 4 0 " 6 ~ 0 '8 I ' 0

R E Y N O L D S N U M B E R x ; O - 5

V a r i a t i o n o f % w i t h R e y n o l d s n u m b e r .

Z-O

,o

F i g . 1 2 a .

I 1

R e = £ x IO s

C

o

" " " ' ~ f o

/f j ,.,o / ~ "

j - x J

~ i 7 ~ - - - f f " --~- - f t . - +

o - 0 .2 0 ,4 0 .6

5 /e

// • VALUE5OF Ma

~ × / O " g /

0 .8

0 '8 I -0

V a r i a t i o n o f p r o fi l e lo s s w i t h M a c h n u m b e r a n d s / e .

3

7

8u

+

0'£

0";

0 J I

- 0 " I0

F i g . 1 2 b .

X x / Xx /

x

x /

o-£ o.4 0.6 o .8

s / e

G a s o u t l e t ' a n g l e w h e n M ~ = 1 . 0 .

(%0 -~- - - cos -1 o / s + • s i n - 1 o /s w h e n M 2 = 1 - 0 . )

I'0



! J14 . . . .

INLET

VELOCIT Y DIS" i 'R iB U T I O N 5

1 / / / ,

/ / / / .

. . . . I L I M I T O F ~ - ~ F - ~ s - ~LO ~I 150LINDAR ~'/ / / '~

_ _ _ ] L A I R 5 "~' ~K- '2/ / / / ," / / / ,

f ~ h , . . . ; . . . , a h

i

L 0 5 5 ~ -U T L E T

P R E 5 5 U I ~ E L 0 5 5

Fro. 15a. Idealised thre e-dime nsiona l flow throu gh a row of blades.

O-~(3

,n 0,16od

d

P-0 ' 1 2

I-z ,

,l~j,

tAhLLLJO C ~ 0 8(J

dNN0Z

0 " 0 4

00

1.0'~ \

- - VALUE 5 OF

BLADE HEIGHT.

0"5 1.0

A$1=F...CT

FIG. 15b.

CONSTANT CHORD AND

VARYING HEIGHT.

CONST ANT HEIGHT AND

VARYING CHORD.

~ BLADE CHORD

4 ' 0 ' ~ ~ . .

1 - 5 ~ , 0 2 " 5

RATIO ( B L A D E H E I G H T / B L A D E C H O R D )

5 '0

Variation of nozzle-loss coefficient with blade aspect ratio.

s / c - ' - O . 77 ; cos -~ o / s - " - 78 deg ; M 2 = 0.8.

0.0,

0.02

OO2

0'01

0 L,

O'0"

0'0~

X

0.0I

00

T U R B I N EI i

NOZZLE I~OW5

I

/

/

i/

//

/J

J

X NOZZLE "rEST5

0 REACTION InJRglNI~3

O ' a 0 ' 4 , 0. 6 0 ' 8 I ' 0 t.a

ITURBINE

. . @ . -

0.£

IR O T O R BLADE

/

® ~.,,@

i

I0 - 4 0 ' 6

IROW5

//

//

/

®

I/

l®p

e

iIi

O'B l'O 1'2

FIG. 16. Seconda ry losses in turbine blade rows.

( b )



II

.K

0-0~

0 ~ 2

0 . 0 1

00

T U R B IN E R O T O R R O W 5 .

T U R B I N E N O Z Z L E R O W S .

C A S C A D E T E S T 5 .

._0._ I

®

x

/

: ) j / ®/ v

/

//

/

Y ~®

/

O ' l 0 ' ~ 0 " 3 0 " 4

D * 0 alO.D.)]

S e c o n d a r y l o s se s i n t u r b i n e b l a d e r o w s .IG. 17.

/

//

o r

/

I l l0 '5

6 " 0

o 5 . 0 ] /

11 M E A N V A R I A T IO N.J

X F R O M C A S C A D E

t a T E ~ ' r $ ( F I G . 8 ( 4 ) ) ~ ! ~ M E A N V A R IA T IO Ni ~ / I N T U R B I N E

i i ! /.0 I / (A~SUMING

CO.STANT)

3' 0O O

Z'O o

b - O O L J

. ~ o ~o / /

1 .0 ' ~ e ( ~ ° ' ~o o O

0

-5.0 -2.0 -i'O 0 I'O 2'0 3'0

R E L A T I V E I N C I D F ' N r _ ~ i ,/ L ~ ;

F IG. 18 . Va r i a t i o n o f p ro f i l e l os s w i t h i nc i dence i n t u rb i ne rows ,( d e d u c e d f r o m t u r b i n e * e s t s, a s s u m i n g t h a t Z i s c o n s t a n t f o r a b l a d e r o w ) .

a 2



p-F~

o~

.D .

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Aeronaut ica l Research

R . & M . N o . 2 8 91

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A N N U A L T E C H N I C A L R E P O R T S O F T H E A E R O N A U T I C A LR E S E A R C H C O U N C I L ( B O U N D V O L U M E S )

I9 3 6 Vo l . I . Ae ro d y n am ics Ge n e ra l , Pe r fo rm an ce , A i r screws , F lu t t e r an d Spin n in g . 4 a s . (4 1 s td .1Vo l . I1 . S tab i l i ty an d Co n t ro l , S t ru c tu re s , Seap lan es , En g in es , e tc . 5 0 5 . (5 In i a ,. )

1 9 3 7 Vo l . I . A e ro d y n a mics Ge n e ra l , Pe r fo rm an ce , A i r screws , F lu t t e r an d Sp in n in g . 4 a s . (4 1 s. I t . )Vo l . ] [ I . S tab i l i ty an d Co n t ro l , S t ru c tu re s , Seap lan es , En g in es , e tc . 6 a s . (6 i s . rd . )

I 9 3 8 V o l . I . A e r o d y n a m i c s G e n e r a l , P e r f o r m a n c e , A i n c r e w s . 5 a s. ( S i s . l d . )Vo l . I I . S tab i l i ty an d Co n t ro l , F lu t t e r , S t ru c tu re s , Seap lan es, Win d Tu n n e ls , M a te r ia l s . 3 o J

( 3 I s . I d . ) i

I 9 3 9 V o l . L A e r o d y n a m i c s G e n e r a l , P e r t o r m a n c e , A i rs e re w s , E n g in e s . 5 a s. ( S i s . ! d . )Vo l . I I . S tab i l i ty an d Co n t ro l , F lu t t e r an d Vib ra t io n , In s t ru m en ts , S t ruc ture s, Seap lan es, e tc

63s. (64.s. 2d.)

I9 4 o Ae ro an d Hy d ro d y n am ics , Ae ro foi l s, A i r se rews , En g in es , F lu t t e r , I c in g , S tab i l ity an d Co n t ro l .S t ru c tu re s , an d a misce l lan eo u s sec tio n . ~ ;o s . (5 I s . rd . )

1 9 4 1 Ae ro an d H y d ro d y n am ics , Ae ro fo il s , A i r screws , En g ines , F lu t t e r , S tab i lk y an d Co n t ro l .Structu res . 63s . (64s. 2d .)

1 9 4 2 Vo l . I . Ae ro an d Hy d ro d y n am ics , Ae ro fo i ls , A i r screws , En g in es . 75s. (76s. 3d.)Vo l . I I . No ise, Pa rach u te s , S tab i l i ty an d Co n t ro l , S t ru c tu re s , V ib ra t io n , W in d Tu n n e ls .

47 s. 6d. (48s. 7 d.)L

t9 4 3 Vo l . I . Ae ro d y n am ics , Ae ro fo i ls , A i r screws . 8 a s . ( 8 i s ; 4 d . )

Vo l . I I . En g in es , F lu t t e r , M a te r ia l s , Pa rach u te s , Pe r fo rma n ce , S tab i l ity an d Co n t ro l , S t ru c tu re s9 as . (9 IS . 6 d . )

I9 4 4 V o l . I . Ae ro an d Hy d ro d y n am ics , Ae ro fo i ls , A i rc ra f t , A i r sc rews, Co n tro ls . 8 4 s . (8 5 s . 8 d .)V o l . I I . F l u t t e r a n d V i b r a t i o n , M a t e r i al s , M i s c e ll a n e ou s , N a v i g a t i o n , P a r a c h u te s , P e r f o r m a n c e ,

Pla te s an d Pan e l s , S tab i l i ty , S t ru c tu re s , Tes t Eq u ip men t , Win d Tu n n e ls .84s. (85s. 8d.)

A n n u a ~ F ~ e p o r t s o f t h e A e r o n a ut ic a l R e s e a r ch C o u n c i l -1933-34 IS. 6d. (IS. 8d.) 1937 2s. (2s. eat.)19 34 -35 xs . 6d . ( IS. 8d .) 1938 xs . 6d . ( Is . 8d . )

Ap r i l i , ~ 9 3 5 to Dec . 3 ~ , I9 3 6 4 s . (4 s . 4d . ) I9 39 -4 8 • 3s . (3 y . 2d .)

~ n d e x ~ e all!t R e p o r t s a n d M e m o r a n d a p u b l i s h e d i n 'th e A n n u a lT e c h n i c a l R e p o r t s , a n d s e p a r a t e l y - - ,

Ap r i l , 1 9 5 o R . & M . No . 2 6 0 0 . 2 s . 6 d . (2 s. 7 ½4 . )

A ¢ l th o r ] In d e x ~ o a ll R e p o r t s a n d M e m o r a n d a o f t h e A e r o n a u t i c a l~ e s e a r e h C o u n c i l - -

I 9 o 9 - J a n u a r y , r 9 5 4 . R . & M . N o . 2 ~ 7 o . i ~ s . ( i ~ s . 4 at .)

~ r ~ d e x e ~ ~ o t h e T e c h n i c a l R e p o r t s o f t h e A e r o n a u t i c a l R e s e a r c hC o u n e f i t - -

D e c e m b e r I , I 9 3 6 - - J u n e 3 0, I 9 39 .J u ly I , I 9 3 9 - - J u n e 3 0, i 9 4 5 .J u l y x , I 9 4 5 - - J u n e 3 0, I 9 4 6 .J u ly r , i 9 4 6 - - D e c e m b e r 3 1, I 9 46 .J a n u a r y x , 1 9 4 7 - - J u n e 3 o , i9 4 7 .h l y , t 9 5 1 .

J a n u a r y , I 9 5 4 .J u l y , 1 9 5 4 .

R . & M . N o . i 8 5 o .R . & M . N o . 1 9 5o .R . & M . N o . 2 0 5 0 .R . & M . N o . 2 1 5 o .R . & M . N o . 2 2 5 0 .R . & M . N o . 2 ~ o .

R . & M . N o . 2 4 5 0 .R . & M . N o . 2 5 5 0

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an examination of the flow and pressure losses in blade rows of axial-flow turbines

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