AlAA 89-1867 Prediction of TL,bulent Mixing and Film- Cooling Effectiveness for Hypersonic Flows J. Wang Rockwell International Corp. Los Angeles, CA

AlAA 20th Fluid Dynamics, Plasma Dynamics and Lasers Conference

Buffalo, New York / June 12-14, 1989

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 370 L’Enfant Promenade, S.W., Washington, D.C. 20024

P R E D I C T I O N OF TURBUI.ENT MIXING AND FIIM~COOLING E F F E C T I W N E S S F O R I3YPERSONIC FLOWS

* Jong 11. Wnng

North American A i r c r a f t Rockwell Intel-national

AIAA-89-1867

w $ w

"

0 stagnation c o n d i t i o n t i m e averaged value

f l u c t u a t i n g component

1

1.0 Introduction

'The cooling of an 1R sensor window on board n hypersonic vehicle is an important design issue. The wi.ndow must be configured to withstand the hi.gh pressure, shear, thermal, and shock loads to which thc vehicle will be subjected during the course of its mission. Flow-field and heating e f f e c t s on optical. signal propagation must also bo accuraLc ly predicted to evaluate boresight e r ro r and image blur s o the window thermal protcction systems can be adequately desi.gned. Therefore, the ability to accurately predicr the acrothermal load., and environment is critical to a successful overall vehicle design.

-'

i;i.gure 1 shows a configurations Chat is called the "Chisel Body". A differenr configuration. for which there are four l l a r cuts on the forebody, is called the "Tetracone Body". One of the objectives of the current hypersonic vehicle program '" is to provide an analytical tool for predicting the window temperature response as well as the mixing layer mean and turbulent fluctuating flow-field properties ahove the window region. Thr mixing layer is generated by the interface between the vehiclk outer boundary-layer flow and the coolant fl.ow injected over the window.

To solve the mixing-layer flow in the region of the optical sensor window, there err three possible approaches: 1) Navier-Stokes; 2) PNS; and 3 ) Inviscid-viscous coupling. A bxief discussion of each method follows.

1.) Navier-Stokes Approach

The Navier-Stokes approach, in which solutions to the full Navior-Stokes equations are

accurate results. However, due to the complexity of the problem, the solution cost is relatively high. I n addition. longer lead time6 are required for computer-code development. Therefore, this approach was not chosen for the present program.

2 ) PNS Amroach

-' obtained, will, in principle, give tho most

The PNS approach (e.g., Ref. 3) neglects the axial diffusion terms in the Navier-Stokes equati.onS. Solutions to the resulting equation subset can be obtnined by marching from the nose of the body to downstream locations wi.thout iteration in the streamwise direction. Therefore, compared to the full Navier-Stokes equations, the saving of computational cost is significant, but the CPU time is still high compared with the inviscid-viscous coupling approach.

3 ) Inviscid-viscous Couolinp. Amroach

This approach assumes that viscous effects are limited to the mixing-layer region and the immediate vicinity of the wall. mixing layer, the flow may be treated as inviscid and the flow phenomena are governed by the Euler equations. The outer inviscid and mixing-layer (viscous) regions are solved separately with different solution algorithms and coupled together by proper boundary-condition mntchi.ng at the outer-edge of the viscous region. This approach has been found to give good results for many flow problems (Reference 4 ) . In t h i s study the CM3DS (Conformal Mapping 3-Dimensional Supersonic) code was utilized for the inviscid flow-fields. The solutions provide outer-edge boundary conditions for the mixing-layer code.

Outside the

5 V'

For the mixing layer, the Axisyrnmetric Lateral Momcntum Analyzer (ALMA) computer program 6 ' 7 ' 8 was chosen a s a tool for predicting the two-dimensional (2D) mixing-layer properties subject to various coolant flow rates. Although the actual flowfields in the window region may not be two-dimensional, the 20 approach w a s selected for the following reasons:

1) For ze ro yaw angles, the flow over the window centerline region may be treated as t w o dimensional;

2) The use of turbulence models for predicting the spreading rate of mixing jets can be vcrified for 2D flow rather than going to a more extensive 30 calculation ; 9

3) Many design parameters such a s injection slot height, coolant stagnation conditions. and various flight conditions can be effectively studi.ed by using the 2D scheme.

The ALMA code is a modified version of the CENMIX code", which has been applied to 8 wide variety of boundary-layer flow problems. The main features of the ALMA code is that it has an option for solving the lateral momentum equation. A K - e two-equation turhul.ence model is also implcmcnted in thc program.

have applied the ALMA code to several flow problems including subs0ni.c developing pipe flow, plane mixing jets and two coaxial supersonic jets in an enclosure. The predicted profiles for velocity, temperature, density, turbulent kinetic energy and turbulent shear stress are in agreement with data. In the same study, the code was also applied to investigate the front-slot film-cooling problem far a simple wind tunnel model. The predicted mean flaw property profiles w e r e shown to agree qualitatively with data. However, the turbulent fluctuating profiles for velocity and density did not match well with the data. The authors attributed the disagreement to the turbulence model.

7 Wassel and Elghobashi

The objective of this program is to predict the turbulenr flow field, heat transfer rate and film-cooling effectiveness for a hypersonic vehicle. This study continues the work reported in Ref. 7 . The ALMA code was tested extensively against wind tunnel data for two vehicle configurations. Some of the results related to optical applications were presented in Ref. 2 . The present method can also be applied to a wide variety of flow problems with and without chemical reaction. One particural application is for the study of NASP (National Aero-Space Plane) combustor reacting flows and exit nozzle wall film-cooling problems.

2.0 Formulation of the ALMA Model

For a turbulent flow, the two- dimensional/axisymmetric mean-flow conservation equations are as follows:

Continuitv:

2

The t u r b u l e n t (eddy) v i s c o s i t y a t each poirri~ in t.he f low is o b t a i n e d from:

2 C pk / e (9) & P

,where C is c o n s t a n t . The q u a n t i t i e s k and c

( t u r b u l e n c e k i n e t i c ene rey and i t s d i n s i p o r i o n rate) are governed by c o n s e r v a t i o n e q u a t i o n s of the form:

P

The l c n g t ~ h scale a t each p o i n t i n the f low ir: d r r i v c d fi-om:

The c o n s e r v a t i o n of ene rgy and inass specic.s e q u a t i o n s can o n l y be s o l v e d i f c e r t a i n assu inpt ions a r e inade r e g a r d i n g t h e turbulrnt Prandt:l nnr! Schmidt nuinbers. A l s o , t h e k ~ r modri contains empir ical c o n s t a n t s t h a t are assumed u n i v e r s a l , and t h e values o f which were i n f e r r e d by comparisons w i t h expe r imen ta l d a t a o f s imple f low c o n f i g u r a t i o n s . Table 1 p r e s e n t s t h e v a l u e s d of t h e c o n s t a n t s used i n t h e p r e s e n t computations.

3") (5 )

J

where. 11 0 for t w o ~ d i m e n s i o n ~ l f low, and n-1 f o r nxisymmecric f low The govern ing s e t of d i f f e r e n t i a l e q u a t i o n s The t empcrn ru r r and d e n s i t y are g iven by t h e i s so lved n u m e r i c a l l y u s i n g an i i n p l i c i t f i n i t e r e l a t i o n s ( f o r an i d e a l g a s ) : d i f f e r e n c e t e c h n i q u e . Thc e q u a t i o n s are f i r s t

t r ans fo rmed i n t o a stream f u n c t i o n p l ane ( x , w ) ,

i n t o f i n i t e - d i f f e r e n c e forin. The r e s u l t i n g t i i d i a g o n n l instrices are sol.ved hy e l i m i n n t i o n a i i d backward s u b s t i t u t i o n .

( 6 ) u s i n g a yon Mises-type trnns€ormntion, then cast

p ~ p/RT ~ pEI/RoT ( 7 )

where c o m p r e s s i b i l i t y e f f e c t s a r e a r ~ o u n t e t l f o r v i a b o t h p and T .

In t h e p r e s e n t s t u d y f o r b e t t e r accu racy i n coinputing c q u i l i b i - i u s a i r p ropeL- t ies , the r e a l gas s u b r o u t i n e of Ref . I 1 is adopted i n A l S l A . The s u b r o u t i n e LISPS R i n b l e l o c k ~ u p t echn ique t o detrrmine the thrrmodynnrnic p r o p e r r i r s . These p r o p e r t i e s i n c l u d e temperacur- , pressure , e n t h a l p y . and cntropy. The i n p u t c m be m y two of t h e f o u r p r o p e r t i r s . and the o t h e r two are o u t p u t . I n a d d i t i o n , t h e s u h r o u t i n e C a l c u l a t e s the s p e c i f i c ~ h c n c ra t i 0 and t hc coinpress i b i l i t y f n c r o r .

o f t u r b u l e n c e t o rhc d i f f u s i o n of inoineiitiiln,

e n e r g y . o r mass is r e p r e s e n t e d by an eddy v i s c o s i t y , p t , which i s superimposed on a l amina r

one i n the f o l l o w i n g f a s h i o n :

I n t h e rurbulcnce model12, the c o n t r i b u t i o n

T a h l r 1 C o n s t a n t s f o r the turhulencc modicl

.~ Nominal Value Equa t ion cons tan t

H m.

3 k

P t P

0 111.

J "k

cP CP

0.9

0.9

1 . 0

1 . 3

1.h3 1 . 0 2

0 . 0 9

0 . 1 6 4

pef f - !Jt + "lam ( 8 )

3

The boundary condition at tho E surface requires special treatment if the flow is supersonic. Consider a wave of angle 8 , striking the boundary which is ut an anele a as shown in Figure 2 . The velocity u is obtained from Eiilrr's equation

- 1

Also, from the lareral momentum equation along a stream line

one can write

From Figure 2 , and 6r - (rn - rn-l)U ;

d - xu 6x = x

E - tan (a + 8 ) - tan el, and al s a2

where 8 = sin M

(16) 2

(17) -1 -1

tot,l

(18)

From (15) through (le), the velocity v is given by

2 2 2 and M:ot,l- (ul + vl)/ cl

1

where u is the velocity at distance y from the wall, ue is the boundary-layer edge velocity given by the inviscid code, and 6 is the boundary- layer thickness calculated by the following equation:

6 - 0.37 x R e y ( 2 1 ) b) Temoerature:

where Tw is thc wall temperature at the

inlet, Taw is the adiabatic wall temperature, r (taken as 0.9 for turbulent flow calculations) is the recovery factor. and C is the specific heat et constant pressure.

P

c ) Turbulence Iintensitv (Tu1 - 1/2

Tu - (u") /u

Tu is assumed to vary linearly from the boundary layer edge to the near-wall point. (This profile approximates that for fully developed flow over a flat plate.)

2) For coolant flow:

a) Velocity u - constant b) Temperature T - constant c ) Turbulence intensity Tup ~ 3% (from wind

tunnel measurement)

The edge, near-wake, and coolant values of Tu depend on individual wind tunnel and coolant test conditions.

4 . 0 RESULTS AND DISCUSSIONS 2 2 + sin-'( c,/~ - tan al

Before the film-cooling problem, the ALMA The quantity p at the edge is set equal to code was applied to the flow over a flat plate for - testing the accuracy of the turbulence model. The the value at the near-boundary point (p, -

P,.~,~. p1 - P ~ , ~ - P,.~,~). corr-ction term at the edge, p,. is set equal to zero, thickness Reynolds number, Red equals 6 5 9 0 , the

n , d first case considered is Coles' experiment for a Mach 4 . 5 4 flow over a flat plate13. selected streamwise location, where the momentum

The pressure For a

3.0 Initial and Boundary Conditions

For the present window cooling problem (see Figure 3 ) , the numerical solutions are sensitive to the prescription of initial profiles for velocity, temperature and turbulence intensity. These values should be given by experimental measurements or from other calculations. However, for most problems, the data for the initial conditions are not available. Furthermore, the calculations for obtaining initial profiles are not straightforward. Based on experience, we found that the following profiles give reasonable results :

predicted velocity profile is compared with data in Figure 4 . This figure shows that the prediction agrees reasonably well with data except for the near-wall region where y/S < 0 . 1 .

It is seen that the model under-predicts the data by about 2% for 30 < y+ < 60. prediction does not match the data in the near wall region where y+ < 30. deviates from data in the wake region where y > 300. The maximum difference between predictions and data are 3% and 7.6% for the near-wall and wake regions, respectively.

Figure 5 depicts the profile for u+ vs y+ .

In addition, the

The prediction also +

1) For Outer Flow:

a) Velocity: 4

The predicted wall friction factor is compared with data in Figure 6. that ALNA under-predicts the data with a maximum difference of 12% for low Reg. FOK a high value

of Reg the prediction agrees well with data.

This figure shows

(20)

4

F i g u r e 7 compares t h e p r e d i c t e d f r i c t i o n f a c t o r

p l a t p . The inodel seems to do b e t t e r f o r subson ic f low than f o r h y p e r s o n i c f low.

w i t h d a t a l 4 f o r an incompress ib l e f l o w Over d flat

'The Code was a l s o a p p l i e d to a s i m i l a r f low 1 5

c o n f i g u r a t i o n i n v c s t i p q t e d by Winkler and Cha The i ree-s t ream Mach number i s 5 . 1 1 . Temperature

comparcd wi th d a t a i n F i g u r e 8 . T h i s f i e u i e a l s o shows tha t Al.MA unde.r-prrdict .s t.he d a t a , hy R S

much a s 1 3 % . f o r y/6 < 0 . 1 , The model i s i n good agreement w i t h da ta i n t,he Outer p a r t o f t he boundary l a y e r

f o r three d i f f e i e n t t es t cases are

'This s t u d y conc ludes Lhat f o r t h e hypc r son ic f low over a f l a t p l a t e , t h e AINA cod? w i t h t h e K~ c t u r h u l c n c e model can p r e d i c t t h e g e n e r a l !man f low p r o p e r t i e s such as w a l l s h e a r stress, h e a t t r a n s f e r rate, and t h e boundary l a y e r p r o f i l e s foi- v e l o c i t y and t e m p e r a t u r e . The numer ica l model is a c c e p t a b l e f o r engineer1,ng purposes . HoweYfr, one must be c a r e f u l i n s e l e c t i n g t h e l o c a t i o n of t he n e a r - w a l l po i t ic .

The l o c a t i o n of t h e n e a r - w a l l p o i n t is impor tnn t because t h e I ~ i ~ h - R e y n o l d s numhe~- v e r s i o n o f the r u r b u l p n c r model i s o n l y v a l i d f o r f u l l y t u r b u l e n t f l o w s . I n rhc v i c i n i t y o f the w n l l , the local f low Reynolds nmhrr is low and the. o v x h l i s no t accurate. This scridy also suggests that t h e

should lbe n o t e d t h a t rhc conservation rqunt . ions fot- inurnenturn, e n e r g y , and t u r b u l e n t p r o p e r t i c s ~ 1 - e n o t s o l v e d f o r t h e n e a r - w a l l p i n t . I n s t e a d , t h e w a l l f u n c t i o n s are used f o r p r o v i d i n g proper w a l l houndary c o n d i t i o n s . The o t h e r a l t e r n a t i v e is t o so lve the problem w i t h o u t using t h c w a l l Cuiictions by a p p l y i n g B low-Reynolds nuinher v e r s i o n of t l i ~

t u r b u l e n c e rnodel16. However, 8orc g r i d p o i n t s are r e q u i r e d i n t h i s approach a n d the coinputntioiial

n e a r - w a l l poin t . shou ld be 1oC;rLrd at y + > 30. l i

C U S t is ,nore e x p e n s i v e .

4.1 The F i l m - c o o l i n F . P r g j h

A s i inp lc schemat i c diagram o f t h e two- d imcos iona l f low f i e l d c o n s i d e r e d i n t h i s s t u d y is shown i n F igu re 3 . T h i s paper presents on ly t i t r e su l t s f o r t h r t e t r a c o n e r o n f i g u r a c i n n . For the t c s t cases c o n s i d e r e d , tile wind tuin,el f r e e - s t r e a m Mach number is 8 . t o t a l p r e s s u r e is 832 p s i n , and

t o t a l temperature i s 1350'R. te tnpernrure i s 14s0n. and t iw pi-cssiire dcpenr~s on the mass f low rate

The c o o l a n t e x i t

'The p r o h l m i s solvcd by u s i n g t h e in viscid^ v i s c o u s t w o ~ l n y e r approach . FiL-st , R t h r e e - d i ~ n t n s i o n a l i n v i s c i d c o d e , CM3DS, is used t o s o l v e f o r t h e i n v i s c i d f low f i e l d . In thc CM3DS c a l c u l a t i o n , t h e i n d e n t a t i o n O F tlic o p t i c a l widow w a s n o t c o n s i d e r e d and t h e window was nssumcd t o he " f l u s h " w i t h t h e v e h i c l e body sur face . Thr e f f e c t of t h e coolant f lo i r was a l s o n r g l e c t c d . The p r e d i c t e d surface pressures f o r four d i f f e r e n t a n g l e s o f a t t a c k RL-c compared wi th d a t a i n F igu re 9 . For t h e s e tes t runs t h e c o o l a n t mass f low >-a te i s 0 .06 lbm/sec and t h e c o o l a n t e s i c pressiire is k e p t at a c o n s t a n t value t h a t i s l o u e r than t h e o u t e r - s t r e a m s h o c k - l a y e r p r e s s u r e . The wind t u n n e l c o n d i t i o n s a r e also kep t constant. The o n l y v a r y i n g pa rame te r i s the a n g l e of a t t a c k . The windward-s ide shock l a y e r pressure i n c r e a s e s w i t h t h e a n g l e o f a t t a c k in rhe n e g a t i v e d i r e c t i o n . T h i s f i g u r e shows t h a t , w i thou t considering t h e coolant f l o w , t h e i n v i s c i d code

u n d e r - p r e d i c t s t h e window s u r f a c e p r e s s u r e ~ X C E Q ~

i n t h e area next to t h e coolant e x i t p l a n e . pressure t h e r e i s a f f e c t e d by t h e c o o l a n t csit c o n d i t i o n s , which are not modeled i n the i ~ w i i i r i d code.

T h p

With t h e window c e n t e r - l i n e pressure .LJ

p r e d i c t e d by t h e i n v i s c i d code as edge houndary c o n d i t i o n s , t h e ALMA code was used t o p r e d i c t t h e f i l m - c o o l i n g e f f e c t i v e n e s s . The d i s t r i b u t i o n of window surface t empera tu re is g i v e n by rhe wind t u n n e l measurements . A c l a s s i c a l i n v i s c i d ~ v i s c o u s c o u p l i n g approach r e q u i r e s t h e feedback of boundary l a y e r d i sp lncemout t h i c k n e s s i n t o t h e i n v i s c i d c o d e . Ilowevcr, c h i s p r a c t i c e WAS n o t used i n t h e p r e s e n t s t u d y . T h i s i s due t o t h e complex i ty o f t h e d i sp lacemen t t h i c k n e s s d i s t r i b u t i o n i n b o t h t h e strerlmwise and spanwisc d i r e c t i o n s . Although t h e d i sp lacemen t th i ck r l e i s can be o b t a i n e d e a s i l y from t h e boundary l a y e r code, i t is not a t r i v i a l j o b f o r t h e i ~ ~ v i s c i d code t o c o n s i d e r such a compl i ca t ed geometry . j u s t i f i c a t i o n f o r t h i s approach i s by comparing

next s e c t i o n .

'The

w i t h d a t a as w i l l he p r e s e n t e d i n the

F i g u r e 10 comparcs t h e AlSlA p r e d i c t e d %ill s u r f a c e pressure w i t h darn f o r d i f f e r e n t nng1i.s of a t t a c k . The c o o l a n t mass f low r a t e i s 0 . 0 6 lbm/sec. The compar isons show t h a t t he !model agrees reasonab1.e w e l l wich da ta FAeC.pt at thr' very end o f the window. The pressure there ii: h i g h duc to thc presence of t ho Tamp a t the r r ld O L t h e window. However, t h e p r e s e n t n p p r o n c h doi.5 n o t c o n s i d e r the e f f e c t o f t h e ramp. I t i s a l s o i n t e r e s t i n g t o n o t e t h a t , a s t h e a n g l e of a t t r i ck i n c r e a s e s , t h e pressure t e n d s t o ovc r shoo t a t about f o u r s l o t h e i g h t s downstream o f the c001iint e x i f plane .

Figure 11 d i s p l a y s t h e comparison of surF,acr pressure w i t h d a t a f o r c o o l a n t mass f low r a t e L' e q u a l t o 0 . 1 lhrn/src. A@in t h e ALMA rode can reproduce the d a t a r easonab ly w e l l .

F i g u r e s 1 2 and 13 compare the p r e d i c t e d tic,?: t r a n s f e r r a t e w i t h d a t a f o r c o o l a n t mi is$ f l o w i rn t r equal t w 0 . 0 6 and 0 . 1 l l m / s e c , r e s p e c t i v e l y . Tlrr agreemcnt o f t h e model p r e d i c t i o n s w i t h e x p e r i m e n t a l d a t a i s v e r y good. As a matte,- o f f a c t , the ALMA code has been used e x t e n s i v e l y To>- p r c - t c s c p r e d i c t i o n and p o s t - t e s c d a t a a n a l y s i s . A t one Lime i t was found chat t h e code disngrr-cd w i t h t h e d a t a . F u r t h r r i n v e s t i g a t i o n c o n c l i ~ i c d t h a t t he wind t u n n e l c o o l a n t s t a g n a t i o n t empera tu re was n o t c o r r e c t l y measured. r e s u l t e d i n r e v i s i o n of t h e wind t u n n e l t e s t darn. I t a l s o showed t h a t t h e numer ica l code i s a w r y u s e f u l t o o l f o r d e s i g n i n g a wind t u n n e l t e s t and a n a l y z i n g exper imenta l . r e s u l t s . As a comparison f o r 60 g r i d p o i n t s In t h e houndary l a y e r , t y p i c a l CPU t ime f o r t h e ALMA code is about 5 minutes on a VAX 11/750 computer . Typ ica l CPU t ime f o r t h e t h r e e - d i m e n s i o n a l PNS code is abou t 10 hours fo r a 19 x 75 g r i d sys tem and 400 inarching s t e p s i n t h e s t r eamwise d i r e c t i o n .

T h i s

F i g u r e s 16 and 15 compare AI& p r e d i c t e d f i l m - c o o l i n g e f f e c t i v e n e s s . 0 , wi th d a t a , W I I P ~ C 'I

~ ( T ~ ~ - T ~ ) / ( T : - T:), T ~ ~ , T:, and TO rPprPsc t~r

a d i a b a t i c wall, mixing l a y e r e d g e , and coo lan t s t a g n a t i o n t e m p e r a t u r e s , r e s p e c t i v e l y . The

a b s c i s s a , F i n F i g u r e s 14 and 1 5 is a d i m e n s i o n l e s s group i n v o l v i n g t h e axial d i s t a n c e , x . from t h e i n j e c t i o n l o c a t i o n , rhe i n j e c t i o n s l o t h e i g h t , s , t h e i n j e c t i o n Reynolds number based on s l o t h e i g h t . R e s , t h e r a t i o of c o o l a n t t o outer

edge flow v i s c o s i t y , p / p e , t h e r a t i o of c o o l a n t

d

t o Outer edge flow mass flux, A , and edge to coolant temperature ratio, Te/Tc. This

dimensionless parameter was found to provide good correlation for a wide range of test data'.

cooling effecti.veness is well predicted. This is the point that the hot shock-layer stream touches the wall and q deviates from the fully cooled value. Some discrepancy bctween data and predictions i.n the front end of the window are shown in thcse figures. This is because the adiabatic wall temperature was not measured in the test. The shock layer adiabatic wall temperature without cool.ant flow was used in the data reduction. Therefore the data show that the efficiency is higher than one. In the A I M calculation, howover, the local adiabatic wall temperature was used in reducing the film-cooling effectiveness.

It is v seen that the break away point for the film-

After validating the ALMA code against experimental d a m , the computer program w a s used to study several design parameters including the effects of varying slot height, coolant. and tunnel conditions. The effects o f using different coolant species were a l s o studied. Then the code was used to predict cooling effectiveness f o r different flight conditions. In addition, the output from the ALE& codc for mean and fluctuating density profiles, and the integral length scale IVCZP used to calculate the boresight er rors and i.mage blur circle f o r an optical sensor. Some of the rosults are presented in Rcf. 2 . The code has also been coupled with a transient two-dimensional heat conduction code for computing the response of the window surface subject to transient flow conditions

5.0 Conc1,usions

In conclus ion . this paper &scribes a

- iiunicrical model. and computer code for predicting two-dimensional or avisyminetric lanninar o r turbulent mixing-layer flows. The colnputer program has been applied to a variety of flows including subsonic and hypersonic flows over a flit plate, and the p r o h l e m of film-cooling over the optical window of a hypersonic vehicle. For the test CRSCS considered, code results compare v c r y well with ~xpczimenfal d a t a for wall h e a t flux. pressure. and film-cooling effec.tiveness. However, for the present turbulence model one m u s t be careful1 in selecting the location of the ~ P R I : -

wall point in the computational domain.

This study has demonstrated that the ALMA code is a very powerful and efficient design tool foe film-cooling problems with lateral pressure variation. A series of parameters, such as coolant slot height, coolant exit conditions, tunnel or flight conditions can he effcctively studied numerically. with a transient heat conducti.on code f o r predicting temperature response due to varying flow conditions.

The codc can a l s o he coupled

The present study, which does not iterate between the boundary layer and the inviscid codes, works reasonably well for the prosent problems. However, a fully inviscid-viscous coupled approach should be implemented to see the effect on t h e accuracy of the present approach.

d Finally it is acknowledged that the present K - r two-equation turbulence model is not perfect for modeling hypersonic flows. More research is

required in improving the accuracy of the turbulence model.

6.0 References

1. Weatherford, R.H., and Majeski, J.A., "Test Report: MDAC Window Cooling Wind Tunnel. Test-Model 4A, 'I McDonnell Douglas Astronautics Company (MDAC) Report No. MDC H3094, November, 1986.

2. Swigart, R.J., Shih, W . C . I . . , Wmg, J.H., Snow. R., Trolier, J . W . , Leone, S . A . , Martellucci, A.. and Lnganelli, A.L., "Hypersonic Film. Cooling Effectiveness and Aero-Optical Effects,", A I M preprint 8 8 - 2 4 , 1st Nati.onn1 Fluid Dynninics congress, JU1.y. 1.988.

3 . Kaul, 0. K . , and Chaussee, D. S . , "AFWAL Psrabolized Nuvier-Stokes Code," AFWAL-TR-83-3118, May, 1984.

4 . Anderson, D. A., Tnnnehill, J. C., Pletchrr, K. H., "Computational Fluid Mechanics and Heat Transfor", Chapter 7, McCraw-Hill Book Company, 1 9 8 4

5 . Hall, D. W. and Sontowski, J . , "Maneuvering Aerothermal Technology (MAT) Program: A Thrre- Dimensional Inviscid Flow Field Code for Maneuvering Reentry Vehicles with Non-Circular Cross-Sections and Flap Control S u r f a c e s , " RMO TR- 8 6 - 0 6 , February 19014.

6 . Elghoheshi, S . and Spnldi.ng, D.B., "Equilihrium Chemical Reaction o f Supersonic Hydrogen-Air Jets (The ALMA Computer Program) , " NASA CR-2725, January 1977

7. Wassel, A.T. and Elghobashi, S . , "Turbulent Analysis of a Cooled Boundary Layer." Vol. 11: Analytical Model, SAI-060-81R-006-lA. Final Technical Report, 1979. Also in "The Effect of Turhrilcnt Heat Transfer on the Propagation of an Optical. Beam Across Supersonic Roundary/Shear Layers,", Int. J . Heat Mass Transfer, Vol 2 3 , p 1229-1241, 1980.

8 . Wang, J.H., "ALMA Computer Code User's Manual." Physical Research, Inc. Report No. PRi-W-86, RO 1 1 , February, 1987.

9. Lee, K . R . and Wnng. J.H., "3DBL Computer Code User's Manual," NO. PRi-PV-86, RO 2 5 , December, 1986.

Physical Research, inc. Report

10. Spaulding, D. B., "GENMIX: Program for Two-dimensional Parabolic Phcnomcna," Imperial Coll.ege of Science and Technology, HTS/77/9, February 1977.

A General Computer

11. Daywitt, J., Brant, D., and Rosworth, F., "Computational Technique f o r Three-Di.mensiona1 Inviscid Flow Fields about Reentry Vehicles, Volume I , Numerical Analysis," SAMSO-TR-79-5, April 1978.

12. 30ne3, W. P. and Launder, B. E., "The Predictions of Larninarization with a Two-equation Model of Turbulence," International Journal of Heat and Mass Transfer, Volume 15, p . 310, 1972.

13. Coles, Donald, "Measurements in the Boundary Layer on a Smooth Flat Plate in Supersonic Flow," ORDCIT project. Contract No. DA-04-495-0rd 18, June, 1 9 5 3 .

6

14. Wieghardt, K . and Tillmann. W . , Zur I . _

Z . W . B . , K . W . I . , U & M 6611, 1944. 0 . - Turbulenten Reibungsschicht bei Druckansteig.

o,aQ 1 /. LF 15. Winkler and Cha, 1959, s e e "Compressible Turbulent Boundary Layer," edited by Fernholz, H.H., Von K a r r n a n Institute for Fluid Dynamics

0.10

, , , , , , , , Lecture Series 86, March, 1976. UlU*

0.-

16. W a n g . J . H . , Hen. H . F . , and tiartel, E.O., "Airfoil Heat Transfer Calculation Using a Low Reynolds Number Version of a Two-Equation 0.10

Turbulence Model," ASME Paper 84-GT-261, 1984, 0.m

Also in J . of Engineering f o r Gas Turbine and - xu -1/11_ . _*I.*,.

o.,o Power, January, 1985. O.m o.,o e.20 D X I Q . ' a 0.- 0.10 0 . 1 0 0 . m 0 - 0.-

Y/&

Figure 1. Chisel Body Configuration

il Figure 2. Definition of Notations far a Supersonic

Boundary Condition.

. . Figure 3. Schematic Of Uindow Cooling Problem.

Flgure 4. Comparlranr o f ALH4 Piedictions w i t h Coles' Oat& Velocity P m f l l e f o r a Supersonic Flow Over a F l a t P la te n. . 4 .54 . neg ~ 6590. ne(. - 70800. c t . 1.22~ 10-1

20

- 18

' . 10

10 100 I J

Figure 5 . Cmparlrmr of ALMA Predlctioni w l t h Coles' data, u+ VI y+ f o r a Superronlc rlar Over a F l a t Plate. H. = 4.54. R% - 6590. Rea. - 70800. Ct - 1 . 2 2 ~ 10.'

10-4 I , . . . , , , ,

IC IO] Re

J

7

..m ,

2 3.2

2 8

Figure 8. Cmparilml of ALW P r e d i c t i o n s with Data . Temperature Prof i le for Supersonic Flow Over a Flat P l a t e . H-5.11 Oafa are from Winkle? & CHA (1959)

: ;

CE.5' (L - 00

3 1.6

F igure 9 . Colnpariron of CM30S P r e d i c t e d Window Surface Pressure w i t h AEOC Tunnel 8 D a t a . T e t r a c o n e Geometry. fi = 0.06 lbrnls 1

8

6

i

. .. . - . - I 2.

I M O L I v l v a v S M O n v ~ v a 0

00 = n V W l V

01

a = 00

-4.0

a = - 1 4 O s o , - - - --

Figure 12. ComParironr of ALMA Predictions with REDC Tunnel B Data, Tetracone Geometry, n. = 0.06 lbmlr. Tu Varier Linearly frm I to 10%. Tu.=3%? 117th Power L a w elnitial Velocity Profile J

a = -100

10 0

a=-14'

Figure 13. Comparlronr Of RLHA Predictions with AEDC Tunnel 8 Data, Tetracone Geometry. m . = 0.1 lbmlr. Tu Varier Linearly fmm 1 t o 10%. Tu.=3%? 117th Power Law elnitidl velocity P r a f i l c J

0

10

> . O

Figure 14. Comparison o f ALMA Pred ic ted F i lm-Cool ing Ef fec t i veness w i t h AEDC Tunnel B Data, Tetracone Geometry, i. = 0.08 lbm/s

J

Figure 15. Comparison of ALMA Predic ted Film-Cool i n g Effect iveness w i t h AEDC Tunnel B Data, Tetracone, h. = 0.1 I b m l s J