NASA Technical Memoranhm a 9 3 1

e

b Computation of Full-Coverage Film-Cooled Airfoil Temperatures by Two Methods and Comparison With High Heat Flux Data

{&ASA-TB-8893 1) COBPGTATICI CF N87-23934 F CLL-COVEBIGB PILE-CCCLEC AILICJIL I E E P E E A T U B E S EP ?BO BIE'IHOCS BEL CCLIEABISCI L I T 8 ElGH BEA'1 € 1 U X DA'IA ( & & $ A ) 18 p Uoclas Avai l : l ! iIS EC A O 2 / L I € A01 CSCL 20D H1/34 00797C7

H.J. Gladden, F.C. Yeh, and P.J. Austin, Lewis Research Center Cleveland, Ohio

Prepared for the 32nd International Gas Turbine Conference Exhibition sponsored by the American Society of Mechanical Engineers Anaheim, California, May 31-June 4, 1987

https://ntrs.nasa.gov/search.jsp?R=19870014501 2018-09-06T08:00:30+00:00Z

COMPUTATION OF FULL-COVERAGE FILM-COOLED AIRFOIL TEMPERATURES

BY TWO METHODS AND COMPARISON WITH HIGH HEAT FLlJX DATA

H. J. Gladden, F. C . Yeh,

and P. J. A u s t i n Jr .

N a t i o n a l Aeronaut ics and Space A d m i n i s t r a t i o n Lewis Research Center Cleveland, Ohio 44135

Y

ABSTRACT

Two methods were used t o c a l c u l a t e t h e h e a t f l u x t o f u l l - c o v e r a g e f i l m c o o l e d a i r f o i l s and, subsequent ly, t h e a i r f o i l w a l l tempera tures . The c a l c u l a t e d w a l l t empera tu res were compared t o measured tempera tures o b t a i n e d i n t h e Hot S e c t i o n F a c i l i t y o p e r a t i n q a t r e a l eng ine c o n d i t i o n s . t o 1900 K and 18 atm w i t h a Reynolds number up t o 1.9 m i l l i o n were i n v e s t i g a t e d . 1 a t e d b y t h e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t adia- b a t i c w a l l method and b y t h e s u p e r p o s i t i o n method which i n c o r p o r a t e s t h e f i l m i n j e c t i o n e f f e c t s i n t h e heat t r a n s f e r c o e f f i c i e n t . The r e s u l t s o f t h e comparison i n d i c a t e t h e f i r s t method can p r e d i c t t h e exper imenta l d a t a r e a s o n a b l y w e l l . However, s u p e r p o s i t i o n overpre- d i c t e d t h e h e a t f l u x t o t h e a i r f o i l w i t h o u t a s i g n i f i - c a n t m o d i f i c a t i o n o f t h e t u r b u l e n t P r a n d t l number. The r e s u l t s o f t h i s r e s e a r c h suggests t h a t a d d i t i o n a l r e s e a r c h i s r e q u i r e d t o model t h e p h y s i c s o f f u l l - coverage f i l m c o o l i n g where t h e r e i s s i g n i f i c a n t tem- p e r a t u r e l d e n s i t y d i f f e r e n c e s between t h e qas and c o o l an t .

Gas tempera tures and p ressu res up

Heat f l u x was c a l c u -

NOMENCLATURE

h9 h e a t t r a n s f e r c o e f f i c i e n t d e f i n e d b y Eq. (1)

h g ( e ) h e a t t r a n s f e r c o e f f i c i e n t d e f i n e d b y Eq. ( 5 )

K c o n s t a n t

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

P p r e s s u r e

* q h e a t f 1 ux

Re Reyno lds number

4

S e q u i v a l e n t s l o t h e i g h t

T tempera tu re

V/Vcr c r i t i c a l v e l o c i t y r a t i o ,

X

X 1

Y s p e c i f i c h e a t r a t i o

s u r f a c e d i s t a n c e f r o m st-agnat ion p o i n t

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

n f i l m c o o l i n g e f f e c t i v e n e s s

e t e m p e r a t u r e d i f f e r e n c e r a t i o , Eq. ( 6 )

11 v i s c o s i t y

P d e n s i t y

S u b s c r i p t s

aw a d i a b a t i c w a l l

C c o o l a n t o u t

9 gas

9e e f f e c t i v e gas

meas measured

W w a l l o u t e r s u r f a c e

1 , 2 , 3 ,

INTRODUCTION

rows o f f i l m c o o l i n g h o l e s

Improved per fo rmance o f t u r b o j e t and t u r b o f a n eng ines i s t y p i c a l l y accompanied b y i nc reased c y c l e

p r e s s u r e r a t i o and combustor e x i t qas tempera ture . Gas p r e s s u r e l e v e l s o f 25 t o 30 atm and qas tempera tures o f 1600 K e x i s t i n some c u r r e n t o p e r a t i o n a l eng ines w h i l e p ressu re l e v e l s up t o 40 atm w i t h gas tempera tures o f 1800 K a r e a n t i c i p a t e d i n advanced commercial enq ines . These c o n t i n u i n g i nc reases i n t h e t u r b i n e e n t r y gas p r e s s u r e and tempera tu re o f t h e modern qas t u r b i n e eng ine and t h e h i g h development c o s t p u t s a premium on an accu ra te i n i t i a l aerothermal des iqn o f t h e t u r b i n e h o t s e c t i o n hardware.

The des ign g o a l s f o r commercial j e t eng ines i n c l u d e h i g h c y c l e e f f i c i e n c y , i nc reased d u r a b i l i t y o f t h e h o t s e c t i o n components ( l ower maintenance c o s t s ) , and lower o p e r a t i n g cos ts . These qoa ls a r e c o n t r a d i c - t o r y i n t h a t h i g h c y c l e e f f i c i e n c y r e q u i r e s m i n i m i z i n g t h e c o o l i n g a i r requ i rements w h i l e i nc reased d u r a b i l i t y r e q u i r e s me ta l tempera tures and tempera tu re q r a d i e n t s t o be min imized. An optimum des iqn can o n l y be r e a l - i z e d th rough an improved unders tand ing o f t h e f l o w f i e l d and t h e h e a t t r a n s f e r p rocess i n t h e t u r b i n e gas pa th .

S o p h i s t i c a t e d computer des ign codes a r e b e i n g developed wh ich have t h e p o t e n t i a l o f p r o v i d i n q t h e des igne r w i t h s i g n i f i c a n t l y b e t t e r i n i t i a l e s t i m a t e s o f t h e f l o w f i e l d and hea t l oad on t h e h o t s e c t i o n com- ponents. These codes a r e be ing eva lua ted and v e r i f i e d th rough low tempera tu re and p r e s s u r e research i n cas- cades and t u n n e l s . However, b y design, t h e s e f a c i l i - t i e s do n o t model a l l o f t he processes t h a t e x i s t i n a r e a l eng ine environment, and t h e r e f o r e , t h e a b i l i t y o f t h e des ign codes t o p r e d i c t t h e i n t e r a c t i o n o f t h e v a r i o u s parameters cannot be f u l l y eva lua ted .

Research Cen te r p r o v i d e s a " rea l -enq ine " env i ronment w i th e s t a b l i s h e d boundary c o n d i t i o n s and conven ien t access f o r advanced i n s t r u m e n t a t i o n t o s t u d y t h e aero- the rma l per fo rmance o f t u r b i c e h o t s e c t i o n components. The the rma l per fo rmance and, u l t i m a t e l y , t h e l i f e o f t h e s e components i n a r e a l i s t i c a p p l i c a t i o n i s depen- d e n t on t h e d e s i q n e r ' s a b i l i t y t o p r e d i c t t h e l o c a l h e a t l o a d d i s t r i b u t i o n .

The h e a t f l u x t o a s t a t o r a i r f o i l , wh ich has f u l l coverage f i l m c o o l i n g , p resents a p a r t i c u l a r l y c h a l - l e n g i n g s i t u a t i o n f o r t h e des igner because o f t h e com- p l e x f l o w f i e l d and t h e i n t e r a c t i o n between t h e h o t and c o l d a i r streams. Even though f i l m c o o l i n g has been s t u d i e d f o r s e v e r a l years , t h e r e i s a l i m i t e d amount o f r e a l i s t i c eng ine d a t a a v a i l a b l e t o v e r i f y t h e ana- l y t i c a l models.

f l u x t o f i l m c o o l e d su r faces and have been d i scussed and compared i n t h e l i t e r a t u r e ( 1 ) . method d e f i n e s t h e hea t f l u x basFd on s tandard convec- t i v e h e a t t r a n s f e r c o e f f i c i e n t and an a d i a b a t i c w a l l tempera ture . The i n f l u e n c e o f f i l m c o o l i n q i s t h e n d e s c r i b e d i n an e f fec t i veness parameter. i s d i scussed i n Ref . 2. i ng , another approach i s t o r e d e f i n e t h e hea t t r a n s f e r c o e f f i c i e n t b y i n c o r p o r a t i n g t h e e f f e c t s o f c o o l a n t i n j e c t i o n i n t h e c o e f f i c i e n t and t h e n comput ing h e a t f l u x u s i n g t h e r e c o v e r y tempera ture o f t h e qas s t ream ( 3 ) . I n a lmost a l l v e r i f i c a t i o n l e v a l u t a t i o n e x p e r i - ments used t o d e f i n e t h e c o r r e l a t i o n c o e f f i c i e n t s f o r t h e s e methods, l o w temperature, c o n s t a n t p r o p e r t y , hea ted s u r f a c e models a r e cons idered. I n r e a l enq ine a p p l i c a t i o n s , t h e s e d e v i a t i o n s can have a s i g n i f i c a n t e f f e c t on t h e d e s i q n e r ' s a b i l i t y t o p r e d i c t t h e temper- a t u r e and l i f e o f t h e s t r u c t u r e .

approaches t o c a l c u l a t i n g heat f l u x a t h i g h tempera tu re and compare p r e d i c t e d w a l l tempera tures o f a t u r b i n e a i r f o i l w i t h measurements taken i n t h e Ho t S e c t i o n F a c i l i t y . These exper imenta l d a t a were taken a t

The Hot S e c t i o n F a c i l i t y a t t h e NASA Lewis

Two models have been developed t o p r e d i c t t h e h e a t

A w i d e l y used

T h i s approach For f u l l - c o v e r a g e f i l m coo l -

The purpose o f t h i s paper i s t o examine these two

Reynolds numbers o f 1.25 and 1.90 m i l l i o n , qas tempera- t u r e s and p ressu res o f 1350 t o 1900 K and 9 t o 18 atm, and c o o l a n t b l o w i n g r a t i o s f r o m 0.5 t o 1.5.

The r e s u l t s a r e p resen ted as a comparison o f ana- l y t i c a l and exper imen ta l a i r f o i l t empera tu re d i s t r i b u - t i o n s . f u l l coveraqe f i l m c o o l e d s u r f a c e i s compared t o t h e exper imen ta l d a t a f o r each Reynolds number c o n d i t i o n s .

FACILITY

Each method o f c a l c u l a t i n g t h e h e a t f l u x t o a

General d e s c r i p t i o n A p h y s i c a l l a y o u t o f t h e Ho t S e c t i o n F a c i l i t y

(HSF) i s shown i n t h e p e r s p e c t i v e v iew ( F i g . l ( a ) ) . The HSF f a c i l i t y l o c a t e d a t NASA Lewis Research Cen te r i s a un ique f a c i l i t y h a v i n q f u l l y - a u t o m a t e d c o n t r o l of t h e research r i g t h r o u q h an i n t e g r a t e d system o f m i n i - computers and programmable c o n t r o l l e r s . The m a j o r components o f t h i s f a c i l i t y and how t h e y i n t e r f a c e t o g e t h e r t o p r o v i d e a r e a l enq ine env i ronment a r e shown i n t h e f l o w d iagram ( F i q . l ( b ) ) . T h i s f a c i l i t y i s d i s - cussed i n more d e t a i l i n Refs. 4. and 5.

t o a n o n v i t i a t e d p rehea te r . t h e a i r t empera tu re between ambient and 560 K. Through a s e t o f r o u t i n g va lves , two modes o f o p e r a t i o n can be s e l e c t e d . U t i l i l z i n q t h e compressor bypass system, a i r can be p r o v i d e d t o t h e t e s t r i g a t 10 atm and up t o 560 K. The second mode, compressor-mode, can p r o v i d e a i r t o t h e research r i q a t p r e s s u r e up t o 20 atm and a tempera tu re up t o 730 K when u t i l i z i n q t h e h e a t o f compression.

The research t e s t r i q s ( F i q . l ( a ) ) c o n s i s t o f two independent t e s t s tands : ( f u l l annu la r cascade r i q ) and a combustor t e s t r i q . The combustor t e s t r i q was used t o deve lop and document t h e e x i t t empera tu re p r o f i l e and e f f i c i e n c y o f t h e h e a t sou rce f o r t h e f u l l annu la r cascade. U t i l i z i n q t h r e e p a i r s o f i n s t r u m e n t a t i o n rakes ( tempera tu re , p ressure , and exhaust p r o d u c t s ) l o c a t e d a t t h e e x i t o f t h e com- b u s t o r , t h e c i r c u m f e r e n t i a l and r a d i a l p r o f i l e s were documented p r o v i d i n g a known i n p u t p r o f i l e f o r t h e cascade vane row.

The main a i r s u p p l y system p r o v i d e s a i r a t 10 atm The p r e h e a t e r modu la tes

a m o d i f i e d t u r b i n e t e s t r i q

Cascade c o n f i g u r a t i o n A c r o s s - s e c t i o n of t h e Ho t S e c t i o n Cascade R i q i s

shown i n F ig . 2. The m a j o r components c o n s i s t o f a h e a t sou rce (combustor ) , t h e f u l l annu la r vane row ( c o n t a i n i n g f u l l - c o v e r a g e f i l m c o o l e d vanes), an exhaust d u c t l i n e , a quench system ( t o l ower t h e tem- p e r a t u r e o f t h e exhaust qas) , and t h e exhaust system.

The vane row c o n s i s t s o f 36 f u l l - c o v e r a g e f i l m - c o o l e d (FCFC) s t a t o r vanes. The 36 vanes a r e separa ted i n t o two groups: 10 t e s t s vanes and 26 s l a v e vanes. The t e s t vane and s l a v e vane c o o l i n q a i r i s s u p p l i e d f r o m two separa te m a n i f o l d s w i t h t h e f l o w r a t e s t o each m a n i f o l d i ndependen t l y computer c o n t r o l l e d .

FCFC vane The s t a t o r vane c o n f i g u r a t i o n used f o r t h e s e t e s t s

was a f u l l - c o v e r a g e f i l m c o o l e d d e s i g n w i t h an impinge- ment i n s e r t t o p r o v i d e auqmented c o o l a n t - s i d e h e a t t r a n s f e r . The vane row hub and t i p d iamete rs were 0.432 and 0.508 m y r e s p e c t i v e l y . Bo th t h e vane h e i g h t and c h o r d were 3.81 cm. More d e t a i l e d qeomet r i c d a t a a r e q i v e n i n Tab le I and Ref. 6.

F i g . 3 ( a ) . The c o o l i n g a i r s u p p l y t u b e on t h e t i p o f t h e t e s t vane a l l o w s c o o l i n g a i r t o be s u p p l i e d f r o m a m a n i f o l d separa te f r o m t h e s l a v e vane supp ly . The t e s t vane shown i n F i g . 3 ( a ) i s i n i t s f i n i s h e d f o r m w h i l e t h e s l a v e vane i s shown i n a p a r t i a l l y f i n i s h e d fo rm.

A t y p i c a l s l a v e vane and t e s t vane a r e shown i n

U

2

A d e t a i l e d a i r f l o w c a l i b r a t i o n o f each t e s t vane was per fo rmed be fo re i n s t a l l a t i o n i n t h e s t a t o r case. T h i s i n f o r m a t i o n was used t o s e l e c t t h e t e n t e s t vanes w i t h s i m i l a r f l o w c h a r a c t e r i s t i c s and t o p r o v i d e "p ressu re l o s s " c o e f f i c i e n t s f o r t h e computer code.

F i g . 3 ( b ) . l eads a r e c l e a r l y shown. The c a v i t y d i r e c t l y over t h e vane rnw feeds c o o l i n g a i r t o t h e s l a v e vanes w h i l e a separa te m a n i f o l d (downstream o f t h e s t a t o r row) feeds c o o l i n g a i r t o t h e t e s t vanes. The t o p dead c e n t e r

c i r c u m f e r e n t i a l l o c a t i o n s a r c measured i n a c o u n t e r c l o c k w i s e ( C C W ) d i r e c t i o n f rom t h i s p o s i t i o n l o o k i n q downstream.

I n s t r u m e n t a t i o n

s i s t s p r i m a r i l y o f t h e c o n v e n t i o n a l s teady -s ta te tempera tu re and p r e s s u r e measurements. f o i l s c a r r y thermocoup les and p r e s s u r e sens inq tubes t o sense t h e gas s i d e me ta l tempera tures , gas-stream s t a t i c p ressures , and c o o l i n g a i r s i d e tempera tures and p ressu res . C o o l i n g a i r f l o w i s c o n t r o l l e d and measured a t t h e v e n t u r i i n each o f t h e supp ly l i n e s . Coo l i ng - a i r t empera tu res and p ressu res a r e a l s o measured i n the i n t e r n a l m a n i f o l d s o f each c o o l i n q a i r system.

row i n l e t and e x i t . Each l o c a t i o n has t h r e e f i x e d p robe p o r t s f o r mount ing r a d i a l l y - a c t u a t e d water-cooled probes. R a d i a l gas-path su rveys o f b o t h tempera tu re and p r e s s u r e a r e reco rded f r o m vane hub t o t i p .

shown i n F i g . 4 w i t h a compos i te summary o f i n s t r u m e n t l o c a t i o n s on t h e a i r f o i l . The l o c a t i o n s shown i n F i g . 4 r e p r e s e n t s e i t h e r me ta l t empera tu re o r s t a t i c p ressu re measurements. Because each a i r f o i l c o u l d accommodate o n l y a l i m i t e d number o f i n s t r u m e n t a t i o n grooves, t h e tempera tu re o r p r e s s u r e d i s t r i b u t i o n s r e p o r t e d a r e composed o f measurements f r o m seve ra l a i r f o i l s i n t h e t e s t vane s e c t o r o f t h e annulus.

EXPERIMENTAL PROCEDURE

The s t a t o r case i s shown p a r t i a l l y assembled i n The t e n t e s t vanes and some i n s t r u m e n t a t i o n

p o s i t o n ( z e r o degree) i s a l s o n o t e d i n t h e f i q u r e . A l l

Research i n s t r u m e n t a t i o n i n t h e Cascade R i g con-

The vane a i r -

Gas p a t h c o n d i t i o n s a r e m o n i t o r e d a t t h e s t a t o r

A c r o s s - s e c t i o n a l schematic o f t h e vane a i r f o i l i s

The re were two b a s i c modes o f f a c i l i t y o p e r a t i o n : 10- and 20-atm. W i t h i n each mode t h e research r i q was opera ted w i t h t h e combustor o p e r a t i n q ( b u r n i n q ) o r w i t h o u t combustor o p e r a t i o n ( i s o t h e r m a l ) . The research o b j e c t i v e s were t o i n v e s t i g a t e t h e aero thermal perform- ance o f t h i s cascade o v e r a ranqe o f Reynolds numbers, and a t a c o n s t a n t Reynolds number, o v e r a range of com- b u s t o r e x i t t empera tu res and pressures . The va r ious o p e r a t i n g modes o f t h i s f a c i l i t y i s shown i n F i g . 5 and Tab le 11. The d a t a r e p o r t e d h e r e i n a r e taken from cases 10 and 12.

The gas c o n d i t i o n s were e s t a b l i s h e d b y s e t t i n g the combustor i n l e t t o t a l p ressu re , t h e vane e x i t o u t e r r a d i u s s t a t i c p ressu re , and t h e combustor f u e l / a i r r a t i o t h r o u g h p rede te rm ined i n p u t va lues s t o r e d i n t h e o p e r a t i o n s computer. a t u r e were v a r i e d s y s t e m a t i c a l l y a t f i x e d gas cond i - t i o n s e i t h e r t h r o u g h p rede te rm ined i n p u t values t o t h e computer o r b y m a n u a l l y i n p u t t i n g values t o t h e c ompu t e r . ANALYTICAL PROCEDURE

The c o o l a n t f l o w r a t e and temper- ,

The two methods t h a t were used t o de termine h e a t f l u x t o t h e t u r b i n e a i r f o i l w i l l be p resen ted f i r s t . Then t h e method o f c a l c u l a t i n g t h e a i r f o i l w a l l temper- a t u r e s w i l l be d iscussed.

Gas-side h e a t f l u x Method I . T h i s method d e f i n e s t h e hea t f l u x u s i n s

a c o n v e n t i o n a l c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t a n i an a d i a b a t i c w a l l tempera ture .

where t h e a d i a b a t i c w a l l t empera tu re i s d e f i n e d b y a f i l m e f f e c t i v e n e s s equa t ion .

" =( 1 '") (2

where Tge i s t h e e f f e c t i v e gas tempera tu re based on r e c o v e r y o f t h e v e l o c i t y .

A l t h o u g h i t i s recogn ized t h a t i n j e c t i o n i n t o t h e boundary l a y e r w i l l a f f e c t t h e h e a t t r a n s f e r c o e f f i - c i e n t , p a r t i c u l a r l y nea r t h e i n j e c t i o n s i t e , t h e va lue o f t h i s c o e f f i c i e n t i s t y p i c a l l y equated t o t h e "unblown" value. The e f f e c t s o f i n j e c t i o n , geometry, e t c . a r e i n c o r p o r a t e d i n t h e f i l m e f f e c t i v e n e s s term. The STAN5 (1) boundary l a y e r code was used h e r e i n t o compute t h e "unblown" hea t t r a n s f e r c o e f f i c i e n t on t h e a i r f o i l . t o a t u r b u l e n t s t a t e a t t h e f i r s t row o f ho les .

c o r r e l a t i o n f o r m a t found i n t h e l i t e r a t u r e . One f o r m o f c o r r e l a t i o n t h a t was deve loped f o r convex-curved s u r f a c e s i s ( 2 )

The boundary l a y e r was assumed t o be " t r i p p e d "

The f i l m e f f e c t i v e n e s s was based on a " t y p i c a l "

L Even though t h i s f o r m was o r i g i n a l l y deve looed f o r

s l o t s i t i s a l s o used f o r rows o f ho les . The c o n s t a n t K was found t o be 1.50 i n Ref. 8 wh ich i n v e s t i g a t e d two rows o f f i l m c o o l a n t i n j e c t i o n o n t o a convex-curved s u r f a c e w i t h t e s t c o n d i t i o n s t h a t s i m u l a t e d eng ine o p e r a t i o n .

F o r a f u l l - c o v e r a q e f i l m c o o l e d su r face , t h e f i l m e f f e c t i v e n e s s r e l a t e d t o each succed inq row o f h o l e s i n t h e downsteam d i r e c t i o n i s i n f l u e n c e d b y t h e f i l m f r o m ups t ream rows. f u r t h e s t downstream row can be c a l c u l a t e d b y t h e f o l l o w i n g summation (2).

The f i l m e f f e c t i v e n e s s f o r t h e

where "film i s t h e compos i te e f f e c t i v e n e s s down s t ream o f t h e l a s t row o f ho les .

Method 2 - The e f f e c t o f f i l m c o o l i n g i s i n c o r p o - r a t e d i n t h e h e a t t r a n s f e r c o e f f i c i e n t f o r t h i s method and t h e h e a t f l u x i s d e f i n e d b y t h e f o l l o w i n g e q u a t i o n d e r i v e d i n Ref . 3.

where a d imens ion less tempera tu re parameter i s de f i ned as

Through l i n e a r superpos o f t h e h e a t t r a n s f e r c o e f f i c

3

( 5 )

t i o n arguments t h e va lue e n t a t any va lue o f e

~~

Eq. 3. T h i s approach r e s u l t e d i n w a l l tempera tures c a l c u l a t e d f o r t h e s u c t i o n s u r f a c e wh ich have a s l o p e s i m i l a r t o t h e exper imen ta l tempera tures b u t w i t h a magn i tude 100 t o 200 K h i q h e r .

f i l m e f f e c t i v e n e s s o n T h e p r e s s u r e s u r f a c e t o be lower t h a n t h a t o f t h e s u c t i o n s u r f a c e f o r a g i v e n "b low ing" r a t i o . s u r f a c e were made w i t h t h e c o n s t a n t o f Eq. ( 3 ) s e t a t 1.20. The c a l c u l a t e d w a l l tempera tures show qood agreement w i t h t h e exper iment b o t h i n s l o p e and magnitude.

The r e s u l t s o f method 2 c a l c u l a t i o n a r e a l s o shown i n F i g . 9. S i m i l a r t r e n d s as method 1 a r e noted. The p r e s s u r e s u r f a c e c a l c u l a t i o n s compare w i t h t h e e x p e r i - ment r e a s o n a b l y w e l l on t h e f o r w a r d p o r t i o n o f t h e a i r - f o i l b u t d e v i a t e up t o 100 K h i g h e r on t h e a f t p o r t i o n . The c a l c u l a t i o n s on t h e s u c t i o n s u r f a c e f o l l o w t h e sane p a t t e r n as method 1. I n o r d e r t o o b t a i n t h i s compari- son i t was necessary t o i n c r e a s e t h e t u r b u l e n t P r a n d t l number b y a f a c t o r o f 3.5 above t h e f r e e s t r e a m va lue o f 0.86 as t h e boundary l a y e r c a l c u l a t i o n approached t h e w a l l . A f a c t o r o f 2.0 i s recommended i n Ref. 7, however, a v e r y poo r comparison between a n a l y s i s and exper imen t was o b t a i n e d u s i n g 2.0. V a r i a t i o n s i n DELMR and ALAM o f 2 : l f r o m t h e recommended va lues were unable t o improve t h e comparison. The two e m p i r i c a l param- e t e r s , DELMAR and ALAM, wh ich a r e i n c o r p o r a t e d i n t o the STANCOOL model t o account f o r f i l m i n j e c t i o n were n o t s u f f i c i e n t t o model t h e r e a l enq ine s i t u a t i o n .

There i s no c l e a r - c u t reason why t h e t u r b u l e n t P r a n d l t number shou ld i n c r e a s e b y t h i s much as i t approaches t h e w a l l . However, t h e exper imen ta l d a t a i n t h e l i t e r a t u r e used t o de te rm ine i t s f u n c t i o n a l r e l a t i o n a r e g e n e r a l l y measured w i th a " h o t " w a l l and " c o l d " a i r s t ream wh ich tends t o d e s t a b i l i z e t h e boun- d a r y l a y e r . The d a t a o f t h e exper iment r e p o r t e d h e r e i n were t a k e n on a " c o l d " w a l l w i t h a " h o t " gas stream. T h i s h i g h r a t e o f c o o l i n g o f t h e qas s t ream i s u s u a l l y a s s o c i a t e d w i t h a s t a b i l i z i n q e f f e c t on t h e boundary l a y e r . T h i s i s c o n s i s t a n t w i t h t h e l ower h e a t t r a n s f e r c o e f f i c i e n t s c a l c u l a t e d w i t h t h e h i g h e r t u r b u l e n t P r a n d t l number nea r t h e w a l l . T h i s phenomena does not a p p l y t o t h e method 1 c a l c u l a t i o n s i n c e t h e c o r r e l a t i o n (Eq. ( 3 ) ) i s based on exper iment w i t h a " c o l d w a l l " and a "gas h o t " s t ream.

There has been some a r b i t r a r i n e s s i n s e l e c t i n q e m p i r i c a l c o e f f i c i e n t s f o r t h e c a l c u l a t i o n procedures. The p r i m a r y g u i d e f o r t h e s e l e c t i o n has been t h e exper- i m e n t a l da ta . However, t h e r e i s a b a s i s f o r t h e se lec- t i o n . The p o i n t t o b e made i s t h a t n e i t h e r c a l c u l a t i o n method has modeled t h e phys i cs w e l l enouqh t o p e r m i t an a c c u r a t e p r e d i c t i o n o f a i r f o i l tempera tures w i t h o u t some p r i o r knowledge. Method 1 does model t h e s u c t i o n su r face d a t a r e a s o n a b l y w e l l e s p e c a l l y i n t r e n d wh ich i s n o t s u r p r i s i n g s i n c e t h e c o r r e l a t i o n i s based on convex c u r v a t u r e da ta . Method 2, wh ich i s more r i g o r - ous i n a c c o u n t i n g f o r t h e phys i cs o f t h e problem, does as w e l l as method 1 on t h e s u c t i o n s u r f a c e once t h e t u r b u l e n t P r a n d t l number i s mod i f i ed . However, method 2 does n o t p r e d i c t w i th any degree of accuracy t h e phenomena on t h e a i r f o i l a f t p ressu re surface.

There a r e many a d d i t i o n a l parameters i n t h e STANCOOL model wh ich c o u l d a f f e c t t h e c a l c u l a t e d h e a t f l u x t o t h e a i r f o i l su r face . Even t h e assumption of 1 i n e a r i t y o f t h e energy e q u a t i o n c o u l d b e i n v e s t i g a t e d .

Kasag i e t . a l . (13 ) p r e s e n t s r e s u l t s t h a t show the

Consequent ly, t h e c a l c u l a t i o n s f o r t h e pressure

b

SUMMARY OF RESULTS

Two methods were used t o c a l c u l a t e t h e h e a t f l u x t o f u l l - c o v e r a q e f i l m coo led a i r f o i l s and, subse- q u e n t l y , t h e a i r f o i l w a l l temoera tures . The c a l c u l a t e d tempera tu res were compared t o measured tempera tu res o b t a i n e d i n t h e H iqh P ressu re F a c i l i t y . The f o l l o w i n q r e s u l t s were ob ta ined .

b a t i c w a l l t empera tu re approach p r e d i c t e d t h e s loDe o f t h e exper imen ta l a i r f o i l tempera tures r e a s o n a b l y w e l l on t h e s u c t i o n s u r f a c e . However, t h e maqn i tude o f t h e p r e d i c t i o n was u p t o 200 K h i g h e r t h a n t h e exper imen ta l da ta . d i c t e d reasonab ly w e l l b y dec reas inq t h e e m p i r i c a l c o e f f i c i e n t o f t h e f i l m e f f e c t i v e n e s s c o r r e l a t i o n b y 2 0 pe rcen t .

The m o d i f i e d s u p e r p o s i t i o n approach d i d as w e l l as t h e f i r s t method on t h e s u c t i o n s u r f a c e f o r b o t h s l o p e and magnitude. However, t h e r e was a r e l a t i v e l y poo r comparison w i t h t h e exper imen ta l d a t a on t h e a f t p o r t i o n o f t h e p r e s s u r e su r face .

The s u p e r p o s i t i o n method r e q u i r e d a m o d i f i c a t i o n o f t h e t u r b u l e n t P r a n d t l number nea r t h e w a l l i n o r d e r t o o b t a i n t h e r e l a t i v e l y good comparison w i t h t h e exper imen ta l d a t a and w i t h method 1. The r e s u l t s o f t h i s r e s e a r c h sugqests t h a t a d d i t i o n a l r e s e a r c h i s r e q u i r e d t o model t h e p h y s i c s o f f u l l - c o v e r a g e f i l m - c o o l i n g w i t h s i q n i f i c a n t t e m p e r a t u r e / d e n s i t y d i f f e r - ences between t h e gas and c o o l a n t as found i n a gas t u r b i n e en v i ronment .

The c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t , ad ia -

The p r e s s u r e s u r f a c e tempera tu re d a t a was p re -

REFERENCES

1. Ecker t , E.R.G., " A n a l y s i s of F i l m C o o l i n q and Fu l l -Coveraqe F i l m C o o l i n q o f Gas Tu rb ine Blades, J o u r n a l o f E n q i n e e r i n q f o r Gas Tu rb ines and Power, Vo l . 106, No. 1, Jan. 1984, pp. 206-213.

T r a n s f e r , Vo l . 7, J.P. H a r t n e t t and T.F. I r v i n e , Jr., eds., Academic Press, New York, 1971, pp. 321-379.

2. G o l d s t e i n , R.J., " F i l m Coo l inq , " Advances i n Heat

3. Choe, H., Kays, W.M., and M o f f a t , R.J., "The Super -Pos i t i on Approach t o F i l m Coo l ing , " ASME Paper 74-WA/HT-27, Nov. 1974.

4. Gladden, H.J., Yeh, F.C., and Fronek, D.L., "Heat T r a n s f e r R e s u l t s and Opera t i ona l C h a r a c t e r i s t i c s o f t h e NASA-Lewis Research Center Hot S e c t i o n Casecade T e s t F a c i l i t y , "ASME Paper 85-GT-82, Mar. 1985.

5. Cochran, R.P., N o r r i s , J.W., and Jones, R.E., " A H igh-pressure , High-Temperature Combustor and Tu rb ine -Coo l i ng T e s t F a c i l i t y , " ASME Paper 76-WA/GT-4, Dec. 1976.

6. M o f f i t t , T.P., and Whitney, W.J., "Aerodynamic E f f e c t o f a Honeycomb Ro to r T i p Shroud on a 50.8 Cent imeter -T ip -D iameter Core Turb ine , " NASA TP-2112, 1983.

7. Crawford, M.E., and Kay, W.M., "STAN5 - A Proqram f o r Numer ica l Computat ion o f Two-nimensional I n t e r n a l and E x t e r n a l Boundary Layer Flow," NASA CR-2742 , 1976. 4 However, t h e purpose o f t h i s paper i s t o p o i n t o u t the

s t a t e o f p r e d i c t i n g tempera tures on a f u l l - c o v e r a q e f i l m - c o o l e d a i r f o i l i n a r e a l i s t i c , h o s t i l e environment. 8. R icha rd , B.E., ApDels, C., V i l l e , J.P., and I n a d d i t i o n , t o p i c s f o r a d d i t i o n a l r e s e a r c h w i t h Salemi, C., " F i l m C o o l i n q on Heated T u r b i n e p r o p e r l y s c a l e d t e m p e r a t u r e l d e n s i t y r a t i o s have become Sur faces a t S imu la ted Cond i t ions , " A I A A Paper apparent . 77-947, J u l y 1977.

9. Co l laday , R.S., "Ana lys is and Comparison o f Wal l C o o l i n g Schemes f o r Advanced Gas Tu rb ine A p p l i c a t i o n s , " NASA TN D-6633, 1972.

10. Crawford , M.E., Kays, W.M., and M o f f a t , R.J., "Fu l l -Coverage F i l m Coo l ing on F l a t I so the rma l Sur faces : 1980.

Data and Pred ic t i ons , " NASA CR-3219,

11. M e i t n e r , P.L., "FORTRAN Program f o r C a l c u l a t i n g Coo lan t F low and Me ta l Temperatures o f a Fu l l -Coverage-F i lm-Cooled Vane o r 61 ade," NASA TP-1259, 1978.

12. F l o r s c h u e t z , L.W., Metzger, D.E. and Truman, C.R., " J e t A r r a y Impinqement w i t h C r o s s f l o w - C o r r e l a t i o n o f Streamwise Reso lved Flow and Heat T r a n s f e r D i s t r i b u t i o n s , 'I NASA CR-3373, 1981.

13. Kasaqi , N . H i r a t a M., Ikeyama, M., Makino, M., and Kurnada, M., " E f f e c t s o f t h e Wal l C u r v a t u r e on t h e Fu l l -Coveraqe Cool i n q E f fec t i veness , " P resen ted a t t h e Symposium on T r a n s p o r t Phenomena i n R o t a t i n q Machinery, Hono lu lu , H I , Apr. 28-May 3, 1985.

0

6

TABLE I . - STATOR VANE GEOMETRY

Mean diameter, cm . . . . . . . . . . . . . . . 46.99 Vane h e i g h t , cm . . . . , . . . . . . . . . . . 3.81 A x i a l chord, cm . . . . . . . . . . . . . . . . 3.81 A x i a l s o l i d i t y . . . . . . . . . . . . . . . . 0.929 Aspect r a t i o . . . . . . . . . . . . . . . . . 1.000 Number of vanes . . . . , . . . . . . . . . . . 36 Leading edge r a d i u s , cm . . . . . . . . . . . . 0.508 T r a i l i n g edge r a d i u s , cm . . . . . . . . . . . 0.089

Case Combuster e x i t Coolant E x i t temperature,

Temperature, Pressure, V / V c r K V/Vcr, Re.ynolds K atm mean number

r a d i u s

4.9 7.4

700 9.5

7 8 9

1 0 11 12

320

1300 1535

945 1165 1500 1500

Mode o f o p e r a t i o n ,

atm

0.775 1 0

Burning mode

10.8 .71-.83 9.0 .72-.80

11.7 .775 17.7 .775

0 . 5 ~ 1 0 6 0 . 5 ~ 1 0 ~

1. 2 5 ~ 1 0 ~ 1 . 2 5 ~ 1 0 ~

1.9ox106

1.9ox106

1 0 1 0 20

1

I

-\:‘-DRIVERS

M A I N AIR SUPPLY

1 PREHEATER ._

C OMPRE S - S OR - BYPASS

I SYSTEM

P R E -HEATER - C OMPRES -

NO. 1

20 atm/730 K I I

CD 1 1 0 1 I 1

(a) Perspective view.

COMPRES-

BYPASS SYSTEM

(FUTURE) COMPRES-

NO. 2 40 at m /890 K

I

I I I I I I I I I I

ANNULAR CASCADE

COOLING

SYSTEMS

330- 730 K I

I I I

I -MAIN AIR SYSTEM a- HIGH PRESSURE AIR SYSTEM TEST RIG -

(b) HSF f low schematic.

F igu re 1. - Hot section test faci l i ty.

EXHAUST SYSTEM

C f X HAU ST -

CD-Y.1518)

Figure 2. - Cascade schematic cross-section of the combustor and the cascade vane row.

&%

COOLING AIR SUPPLY TUBE ---,

TRAILING EDGE% a

V A I Y L

PRESSURE SURFACE

SUCTION SURFACE C-84-5548

(a) The slave vane i s shown in a partially machined fo rm wh i l e t h e

Figure 3. - Fu l l coverage f i l m cooled vanes for t h e Hot Section Facil- test vane i s shown in f in ished form.

ity cascade rig.

(b) Part ia l assembly of FCFC stator case showing test vane sector. Figure 3. - Concluded.

J

s 3 I

SUCTION SURFACE

SENSOR XlL

SP 0.0 s1 .067 s2 ,188 s 3 .346 s4 .612 s5 .836 S6 ,972

P3 P 4

p5 '\\, FCFC STATOR AlRFOlL

Y

p2 P1' SP \

P6

\

PRESSURE SURFACE

SENSOR x / L

P1 0.083 P2 .174 P3 .314 P4 .587 P5 .826 P6 .973

s1

-

\

'- TYPICAL SENSOR LOCATIONS

P

40 F- 35 t 25

COMBUSTOR EXIT

PRESSURE, atm

10 ir DESIGN OPERATING ENVELOPE 7,

_ ~ _ _ _ _ _ _ ~ ~ /7 -- - - ;

I n 10 ATM NON-BURNING 20 ATM NON-BURNING

10 6 20 ATM BURNING

500 1500 2000 2500

: 2500

COMBUSTOR EXIT TEMPERATURE, K

REYNOLDS NO. IS BASED ON VANE EXIT CONDITIONS AND THE VANE CHORD. OIAconr IS THE BOUNDARY LAYER COOLING RATE

Figure 5. - Cascade r i g simulation of real engine operating conditions.

0 "\, 0 / -

A T

PRESSURE S UR FACE / I

J 0 EXPERIMENTAL DATA INVISCID DESIGN DISTRIBUTION Y

1.0 0 . 2 . 4 .6 .8

Figure 6. - Crit ical velocity rat io design conditions for the

0

DIMENSIONLESS SURFACE DISTANCE, xlL

stator air fo i l tested.

2600

+ I 2 2600

2200

1800

1400

1000

-

SUCTION SURFACE

0 . 2 . 4 . 6 . a 1.0 2ooo

3500 I 3000

0 . 2 . 4 . 6 . 8 1.0

4500

4000

3500

3000

2500

C

50OO I 8 = 0

16OO 1 0 . 2 . 4 .6 .8 1.0

DIMENSIONLESS SURFACE DISTANCE X I 1

(a) Suction surface. (b) Pressure surface.

Figure 8. - Film-cooled heat transfer coefficients for method 2 calcu- lated by the Stancool boundary layer code,

#

8oor - METHOD 1 CALC --- METHOD 2 CALC 0 EXPERIMENTAL DATA

600

500

400

I SUCTION SURFACE

900

800

700

600

500

400

9oc

800

700

600

500

400

\ - \

PRESSURE SURFACE

/

-

SUCTION SURFACE

0 .2 . 4 .6 . a 1.0 300 1

0 . 2 . 4 . 6 . 8 1.0 DIMENSIONLESS DISTANCE XIL

(a) Reynolds number - 1250 Ooo. (b) Reynolds number = 1 9 0 0 OOO. Figure 9. - Comparison of airfoil temperatures calculated by method 1 and method 2 with experimental data,

1. Report No.

NASA TM-88931

Computation of Full-Coverage Film-Cooled Airfoil Temperatures by Two Methods and Comparison With High Heat Flux Data

H. J . Gladden, F . C. Yeh, and P. 3 . Austin, Jr.

7. Author@)

2. Government Accession No.

9. Performing Organization Name and Address

7. Key Words (Suggested by Author@))

National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135

18. Distribution Statement

2. Sponsoring Agency Name and Address

9. Security Classif. (of this report)

Unclassif led

National Aeronautics and Space Administration Washington, D . C . 20546

20. Security Classif. (of this page) 21. No. of pages 22. Price'

Unclassified

3. Recipient's Catalog No.

5. Report Date

6. Performing Organization Code

505-62-22 8. Performing Organization Report No.

E-3372 10. Work Unit No.

11. Contract or Grant No.

13. Type of Report and Period Covered

Tec hni cal Memorandum 14. Sponsoring Agency Code

5. Supplementary Notes

Prepared for the 32nd International Gas Turbine Conference and Exhibition, sponsored by the American Society of Mechanical Engineers, Anaheim, California, May 31 - June 4, 1987.

6. Abstract

Two methods were used to calculate the heat flux to full-coverage film cooled airfoils and, subsequently, the airfoil wall temperatures. The calculated wall tempergtures were compared to measured temperatures obtained in the Hot Section Facility operating at real engine conditions. Gas temperatures and pressures up to 1900 K and 18 atm with a Reynolds number up to 1.9 million were Investigated. Heat flux was calculated by the convective heat transfer coefficient adiabatic wall method and by the superposition method which incorporates the film injection effects in the heat transfer coefficient. The results of the comparison indicate the first method can predict the experimental data reasonably well. superposition overpredicted the heat flux to the airfoil without a significant modification o f the turbulent Prandtl number. The results of this research sug- gests that additional research i s required to model the physics of full-coverage film cooling where there i s significant temperature/density differences between the gas and coolant.

However,

Film cooling; Heat transfer; Gas turbine

Unclassified - unlimited STAR Category 34

b