3 Numerical and Experimental Studies of 3D Hyper Sonic Inlet

8/9/2019 3 Numerical and Experimental Studies of 3D Hyper Sonic Inlet

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N o m e n c l a t u r e hM Mach number lP pressure R0R e Reynolds numb er Fx, y, z Cartesian coordinates v = Ptth/Pt~A area x = x / l , y = y / lb, H0 width and height of the intake- h = h l H o relative height of the strut in the channel oo- fi = P I P ~ relative static pressure tOk angle of compression surface decline ent, exO1 starting angle of the wall decline th

height o f the flat intakelength of the compression surfacecompression surface radius at x=0flow rate coefficienttotal pressure recovery coefficientrelative coordinatesSubscr ipt snonperturbed mainstreamtotal parametersparameters in the channel entrance and exitparameters in the throat

Fig.1 The integrated vehicle configurationd e s i g n a n d o f f - d e s i g n re g i m e s , a s w e l l a s t h e k n o w l e d g eo f t h e b o u n d ary l a y er s t a t e i n t h ese co n d i t i o n s , a r e v eryl im i t ed . Th e q u es t i o n ab o u t t h e t h eo re t i ca ld e t e r m i n a t io n o f f l o w p a r a m e t e r s i n f l i g h t r e g i m e s w i t ht h e M a c h n u m b e r s m a l l e r o r l a r g e r t h a n t h e d e s i g n v a l u ei s s t i l l o p en . In t h i s case , a co m p lex sp a t i a l f l o w i sf o r m e d o n t h e c o m p r e s s i o n s u r f a c e u n d e r t h e c o n d i ti o n so f in t e rac t i o n wi th t h e b o u n d ary l ay er .

T h e o b j e c t i v e s o f t h e c o n d u c t e d n u m e r i c a l a n dex p er im en ta l s t u d i es were : ( a ) t o d e t e rm in e t h e i n v i sc idf lo w p aram ete r s i n a 3 D in l e t ; (b ) t o d e t e rm in e t h e i n l e ts t a r t i n g co n d i t i o n s an d t h e f l o w s t ru c tu re a t t h ec o m b u s t i o n c h a m b e r e n t r a n c e ; ( c ) t o d e v e l o p a n d v e r i f yt h e m e t h o d f o r c a l c u la t i n g t he 3 D f l o w a r o u n d a C A I i nd es ig n an d o f f -d es ig n r eg im es ; (d ) t o d e t e rm in e t h e i n l e tch arac t e r i s t i c s , i n c lu d in g t h e t h ro t t l i n g ch arac t e r i s t i c s ;( e ) t o m easu re t h e ch arac t e r i s t i cs o f a t h ree -d im en s io n a lb o u n d a r y l a y e r o n t h e s u r f a c e o f e x t e r n a l c o m p r e s s i o nan d to d e t e rm in e i t s e f f ec t o n t h e i n l e t s t a r t i n g ; ( f ) t ov e r i f y th e c a l c u l a t io n m e t h o d a n d t o c o m p a r e t h e r e s u lt sfo r t h e CAI an d 2 D in l e ts , i n c lu d in g t h e b o u n d a ry l ay er .

F o r r e a l c o n f i g u r a t i o n s , 7 0 o r 9 0 s e c t o r o f a ni n t er n a l a x i s y m m e t r i c f lo w i s u s u a l l y u s e d . T h e s c h e m eo f t h e ex t e rn a l co m p res s io n su r f ace i s sh o wn in F ig .2 (a ) .A sp ec i f i c f ea tu re o f b u i ld in g a CA I i s t h a t t h e l ead in ge d g e o f t h e c o w l l i p i s l o c a t e d s l i g h t l y l o w e r ( b yap p ro x im ate ly 0 .1 R ) t h an t h e cen t e r l i n e . In t h e d es ig n

r e g i m e , t he b o w s h o c k w a v e a n d c o m p r e s s i o n w a v e s a r ef o c u s e d o n t h e l e a d i n g e d g e o f t h e c o w l l i p . T h i s a l l o w so n e t o a v o i d t h e a p p e a r a n c e o f a s i n g u l a r i t y n e a r t h ecen t e r l i n e , wh ich i s t y p i ca l o f i n te rn a l ax i sy m m e t r i cf l o w s . T h e c o n d u c t e d e x p e r i m e n t a l s t u d i e s c o n f i r m e dth e e f f i c i en cy o f t h i s i d ea .

Y l~ ,

~ (a) Convergent nlet, Ox- syroxnetryaxis

I -r,L. - \ A,x l b0o) 2D inletFig.2 Convergent and 2D inlets

T h e s u r f a c e o f e x t e r n a l c o m p r e s s i o n c o n s i s t s o f a nin i t i a l i n t e rn a l co n e (AC) an d a co n to u r wi th ana d d i ti o n a l c u r v a t u r e f o r i n c r e a s i n g t h e f l o w c o m p r e s s i o n( C D ) . T h e c o n t o u r w a s c a l c u l a t e d b y t h e m e t h o d o fch ara cte risti cs [91.

A n e q u i v a l e n t 2 D i n l e t w a s d e v e l o p e d t o c o m p a r et h e p e r f o r m a n c e o f C A I a n d 2 D i n le t s i n th e d e s i g nr e g i m e ( F i g . 2 ( b ) ) . B o t h i n l e t s h a d a d e s i g n M a c hn u m b e r e q u a l t o 8 a n d t h e s a m e t o t a l a n g l e o f f l o wtu rn in g 0 k=2 0 fo r an eq u a l en t r an ce a rea A o . S u c h a ni n l e t i s e q u i v a l e n t i n t h e s e n s e o f g e o m e t r y . T o e n s u r ea n e q u i v a l e n t f l o w c o m p r e s s i o n a n d M a c h n u m b e r a tt h e d u c t , t h e 2 D in l e t sh o u ld h a v e t h e t o t a l an g l e o f f l o wtu rn in g eq u a l t o 2 9 .2 In t h i s case , b o th i n l e t s h av e ane q u a l l e v e l o f g e o m e t r i c c o m p r e s s i o n A = Ao]Fth=1 6 .

T h e a d v a n t a g e o f th e C A I in f l o w c o m p r e s s i o n f o ra n e q u a l a n g l e o f f lo w t u r n i n g o n t h e e x t e r n a lco m p ress io n su r f ace i s i l l u s t r a t ed i n F ig .3 . Th i sa d v a n t a g e b e c o m e s m u c h m o r e p r o n o u n c e d a s t he M a c hn u m b e r i n c r e a se s .


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200 Journal of Therm al Science, Vol.11, No.3, 2002

P / P ~80-

60 -

40 -

20 - (

0 2

, , / .I 3D convergent, 0k=20// /

2D , 2 o o j1

4 6 8 10 M* *Fig.3 C ompression pressure ratio of inlets

A n i m p o r t a n t c h a r a c t e r i s ti c o f h y p e r s o n i c i n l e t ist h e c o m p a c t n e s s o f th e d u c t e n t r a n c e s u r f a c e s . Ad e c r e a s e o f t h e s e a r e a s i s a s s o c i a te d w i t h t h e p r o b l e m o fc o o l i n g o f t h e m o s t h e a t - l o a d e d w a l l s o f t h e e n g i ne . T h em e a s u r e o f c o m p a c t n e s s i s a c o e f f i c i e n t t h a t s h o w s b yh o w m a n y t i m e s t h e d u c t c r o s s - s e c t i o n p e r i m e t e r i sg r e a t e r t h a n t h e p e r i m e t e r o f a c i r c l e w i t h e q u a l a r e a . Ac o m p a r i s o n o f t h e c o m p a c t n e s s c o e f f i c i e n t f o r i n l e t su n d er co n s id e ra t i o n d emo n s t r a t es a su b s t an t i a la d v a n t a g e o f C A I ( F i g . 4 ) . I t s h o u l d b e a l s o n o t e d t h a tt h e v a lu e o f A2D/AaD ch an g es o n ly s l i g h tl y w h en t h eg e o m e t r i c c o n f i g u r a t i o n o f t h e i n l e t c r o s s - s e c t i o n i sc h a n g e d . T h e s e a d v a n t a g e s c a n b e d e t e r m i n i n g i nc h o o s i n g t h e i n l e t f o r h y p e r s o n i c p r o p u l s io n .

3.0

2.0

1.0f

0 40 80

f

i i i f l l l l r l l l l l l l l l ,

Fig.4 R elative are a of surface throat of 3D inletsF o r a n e q u a l l e v e l o f p r e s s u r e i n c r e a s e , a

co n v erg en t i n l e t h as a smal l e r i n c l i n a t i o n an g l e o f t h ee x t e r n a l c o m p r e s s i o n s u r f a c e . A d e c r e a s e o f t h is a n g l ef o r C A I w i t h d i f f e re n t i n it ia l a n g l e o f t h e c o m p r e s s i o nsu r f ace can b e q u i t e s i g n i f i can t (5 fo r M ~=2 u p t o 1 6 ofo r M .o =10 ). F o r t h e ca se u n d e r s t u d y , t h i s an g l e wa s9 .2 E x p e r i m e n t a l S t u d i es

T o o b t a i n r e l i a b I e e x p e r i m e n t a l d a t a , t w o i n l e t

m o d e l s w e r e d e v e l o p e d . T h e m o d e l o f c o n v e r g e n t i n l e th a d a c o n v e r g e n t s e c t i o n o f e x t e r n a l c o m p r e s s i o n ( s e eF ig .2 (a ) ) , an i n t e rn a l co mp ress io n sec t i o n , an d anin t e rn a l d u c t wi th t ap ered c ro ss - sec t i o n (F ig .5 ) .

A-A

665

Fig.5 Convergent intake1-central bod y 2-static pressure probes 3-cowl4, 5-sidewall 6-sting 7-metal m esh

8-nozzle 9-total pressure rakeT h e m o d e l o f e q u i v a l e n t 2D i n l e t h a d a t h r e e - s h o c k

s e c t i o n o f e x t e r n a l c o m p r e s s i o n , a m o d e r a t e l e v e l o fi n t e rn a l co mp ress io n , an d a r ec t an g u l a r d u c t (F ig .6 ) .Th e m o d e l t h ro a t wa s a s l o t w i th t h e s i d es r a t i o o f 1 :15 .

A-___~A~ 1 ^ 3 4 5 6 7 8

2094 F~h=ll'2 S - - ~/ 7 .........

9'

Fig.6 Two-dimensional intake1,2-sidewaU 3-centralbody 4-cowl

5-sting 6-metal me sh 7-nozzle8-total pressure rake 9-static pressure probes

Bo th mo d e l s h ad a d i sc r e t e ly co n t ro l l ed t h ro a t , af l o w m e t e r d u c t, a n d a t h r o tt l in g d e v i c e f o r m e a s u r i n gth e a i r f l o w r a t e an d t h e t h ro t t l i n g ch arac t e r i s t i c . I t wasp o ss ib l e t o t e s t t h e mo d e l s wi th t h e s i d e wa l l s an dw i t h o u t t h e m . T h e s i d e w a l l s o f th e C A I h a dlo n g i t u d in a l s l o t s t o en su re t h e i n l e t s t a r t i n g i n o f f -d e s i g n r e g i m e s . T h e m o d e l s w e r e m o u n t e d i n t h e w i n dtu n n e l o n a t a i l s t i n g . S imu l t an eo u s ly , i t was p o ss ib l e t op l ace t h em o n t h e win d t u n n e l wa l l t o s imu la t e a t h i ckb o u n d a r y l a y e r u p s t r e a m o f t h e i n l e t i f i t i s l o c a t e du n d er t h e a i r c r a f t f u se l ag e .


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Marat A. Goldfeld et al. Num erical and Experimen tal Studies of 3D Hypersonic Inle t 201

T h e q u a n t it i es m e a s u r e d i n t h e c o u r s e o f t h e t e s t swere (1 ) t h e s t a t i c p r es su re d i s t r i b u t i o n s o n t h eco mp ress io n su r f aces , ( 2 ) t h e t o t a l an d s t a t i c p r es su resb eh in d t h e t h ro a t , ( 3 ) t h e t o ta l an d s t a t i c p r es su res a t t h ee x i t o f t h e s o n i c f l o w m e t e r n o z z l e , a n d ( 4 ) t he a i r f l o wra t e .

F r o m t h e r e s u lt s o f m e a s u r e d t o t a l p r e s s u re b e h i n dth e t h ro a t ( i n th e su b s o n i c d i f fu se r ) an d t h e a i r f l o w r a t e ,t h e t h ro t t l i n g ch arac t e r i s t i c s were d e t e rmin ed , i . e . , t h efu n c t i o n v ( t ) an d t h e d ep en d en c e o f t h e t o ta l p r es su rer e c o v e r y a n d f l o w r a t e c o e f f i c i e n ts o n t h e M a c h n u m b e r .Us in g t h e l a t te r d ep en d en ce , an ad d i t i o n a l d r ag o f t h ein l e t was ca l cu l a t ed , wh ich a ro se d u e t o t h e d ecrease i na i r f l o w r a t e i n o f f - d e s i g n r e g i m e s o f i n le t o p e r a t i o n .

I n a l l e x p e r i m e n t s t h e f l o w a r o u n d t h e m o d e len t r an ce was v i su a l i zed . F o r t h e 2 D mo d e l , t h e sch l i e r enp i c tu res o f t h e f l o w in t h e t h ro a t an d d i f fu se r were a l sot ak en t h ro u g h t h e g l as ses i n t h e s i d e wa l l s . Th e o i l - f i lmv i su a l i za t i o n o f t h e l imi t i n g s t r eaml in es o n ex t e rn a l an di n t e rn a l s u r f a c e s o f t he m o d e l w a s a l s o p e r f o r m e d .

T o d e t e r m i n e t h e b o u n d a r y l a y e r c h a r a c t e r i s t i c s o nc o m p r e s s i o n s u r f a c e s o f t h e in l e ts w e u s e d am i c r o t r a v e r s i n g g e a r w i t h a s t e p o f 0 .0 5 n u n i n t he Yd i r ec t i o n an d 0 .5 mm in t h e X d i r ec t i o n . Th e b o u n d aryl ay er v e lo c i t y p ro f i l e s , t h e i n t eg ra l ch arac t e r i s t i c s an dth e sk in f r i c t i o n co ef f i c i en t were d e t e rmin ed f ro m th em e a s u r e d P i t o t p r e s s u r e p r o f i l e s.

T h e t e s t s w e r e p e r f o r m e d i n a b l o w d o w n w i n dt u nn e l fo r M a c h n u m b e r s 2 ~ 6 a n d a ng l e s o f at ta c k -4 ~ 5 an d i n a h o t - sh o t win d t u n n e l ( ru n n in g t im e 1 2 0ms ) fo r M a ch n u mb er s 5 ~ 1 0.7. Th e t es t co n d i t i o n sa r e s h o w n i n T a b l e 1 .

Table 1

Mach

1.752

2.534566

6*8

10.7"

ParametersP**xl0 1, T t , ](Pa) (K)

Wind tunnel T-3133040 2832365 2821545 2821120 285690 286128 39547 445

R e 1 xl 0 "6,( I / m )1 9 . 925.928.434.559.614.38.6

Hot-shot wind tunnel IT-302M2490 1295 732400 1372 60379 1860 15.560 1900 0.7

* - runs with pressure multiplicatorA s t a n d a r d m e a s u r e m e n t c o m p l e x o f w i n d t u nn e l s

w a s u s e d i n t h e t e s t s . T h e m e a s u r e d p a r a m e t e r s w e r ed i r ec t l y t r an s fe r r ed t o a co mp u te r i n a r ea l - t ime sca l ewi th t h e i r su b seq u en t p ro cess in g an d an a ly s i s .

M e t h o d o f C a l c u l a t i o n

T h e a l g o r i t h m o f 3 D f l o w c a l c u l a t i o n i s b a s e d o nt h e s o l u t i o n o f 3 D u n s t e a d y E u l e r e q u a t i o n s b y t h ef i n i t e - v o l u m e m e t h o d I al] . T h e f l o w i n t h e c o m p u t a t i o n a ld o m a i n w a s a s s u m e d t o b e s u p e r s o n i c . T h e b o d ys u r f a c e w a s d e f i n e d a s a s e t o f c r o s s - s e c t i o n s w i t hX = c o n s t . T h e c a l c u l a ti o n s i n c r o s s - s e c t i o n s X = c o n s tw e r e p e r f o r m e d o n a s t r u c tu r e d g r i d o f d im e n s i o n N x L ,w h e r e N i s t h e n u m b e r o f p o i n ts o n t h e b o d y s u r f a c e a n dL i s t he n u m b e r o f c o m p u t a t i o n a l la y e r s b e t w e e n t h eb o d y s u r f a c e a n d t h e e x t e r n a l b o u n d a r y o f t h ec o m p u t a t i o n a l d o m a i n .

In ca l cu l a t i n g t h e i n l e t , an accu ra t e ca l cu l a t i o n o ft h e b o w s h o c k w a v e p o s i t i o n i s v e r y i m p o r t a n t . T h eer ro r s i n d e t e rm in in g t h e p o s i t i o n an d sh ap e o f t h e b o ws h o c k w a v e i n o f f - d e s i g n r e g i m e s l e a d t o t h e e r r o r i nca l cu l a t i n g t h e f l o w r a t e co ef f i c i en t o f t h e i n l e t . Wh enth e march in g sch eme i s u sed fo r ca l cu l a t i o n s , t h e i n i t i a ld a t a o n t h e l e f t b o u n d a r y a t X - -0 , th e f l o w p a r a m e t e r s o nt h e b o d y s u r f a c e c o r r e s p o n d t o t h e f r e e s t r e a mp a r a m e t e r s , a n d o n l y a f t e r s e v e r a l m a r c h i n g c r o s s -sec t i o n s ex ac t v a lu es a r e o b t a in ed . B eca u se o f t h a t , t h eb o w s h o c k w a v e d o e s n o t o r i g i n a t e a t t h e l e a d i n g e d g eo f t h e b o d y , b u t a r i ses a t a ce r t a i n d i s t an ce d o w n s t r ea mo f t h e l e a d i n g e d g e .

T o p r e v e n t t h e s h i f t o f t h e i n i t i a l p o i n t o f t h e b o wsh o ck wav e , i t i s su g g es t ed i n t h i s p ap er t h a t t h e i n i t i a ld a t a o n l e a d i n g e d g e s o f t h e b o d y s h o u l d b e t h e f l o wp a r a m e t e r s b e h i nd a p l a n e s h o c k w a v e ( o r e x p a n s i o n f a n )b a s e d o n t h e l o c a l n o r m a l t o t h e b o d y a n d t h e d i r e c ti o no f t h e f r e e s t r e a m v e l o c i t y v e c t o r . T o e l i m i n a t e t h ed i sco n t i n u i t y i n i n i t i a l d a t a n ear t h e co rn er p o in t o f t h el e a d in g e d g e , t h e f l o w p a r a m e t e r s w e r e d e t e r m i n e d f r o mt h e c o n d i t i o n s b e h i n d a n o b l i q u e s h o c k w a v e o r b e h i n dan ex p an s io n f an wi th a ce r t a i n an g l e f t . Th ec o r r e s p o n d i n g a n g l e s w e r e c a l c u l a t e d b y m e a n s o fi n t e rp o l a t io n o f t h e a n g l e s o f t h e o b l i q u e s h o c k w a v e o re x p a n s i o n f a n o n t h e l e e w a r d a n d w i n d w a r d b o d ysu r f aces i n t h e v i c in i t y o f t h e co rn er p o in t . Th e f l o wc o n i c i ty w a s a s s u m e d n e a r t h e c o r n e r p o i n t o f th el ead in g ed g e i n t h e co u r se o f s t ab i l i za t i o n o f t h eso lu t i o n wi th t ime . F o r t h u s p resc r i b ed i n i t i a l d a t a , t h eb o w s h o c k w a v e i n t h e d e s i g n r e g i m e w a s f o c u s e d o nt h e i n l e t c o w l , w h i c h c o r r e s p o n d s t o t h e p h y s i c a l f l o wp a t t e rn .

I t is k n o w n t h a t t h e c h o i c e o f t h e c o m p u t a t i o n a l g r i ds ig n i f i can t l y a f f ec t s t h e ca l cu l a t i o n accu racy . On e o f th em e t h o d s o f i n c r e a s i n g t h e a c c u r a c y a n d e f f i c i e n c y o fn u m e r i c a l s t u d ie s i s th e a d a p t a t i o n o f t h e c o m p u t a t i o n a lg r i d t o t h e so lu t i o n . In o rd er t o r ev ea l t h e sp ec i f i cf ea tu res o f th e so lu t i o n , t h e ca l cu l a t i o n s were p e r fo rm edo n a n a d a p t e d g r id . T h e f o l l o w i n g a l g o r i th m o f g r i dad ap t a t i o n t o t h e so lu t i o n was u sed . A t t h e f i r s t s t ag e ,


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202 Journal of Thermal Science, Vol. 11, No.3, 2002

the problem o f the f low around the body was solved onan almost uniform grid until the solution becamecompletely stable . In constructing the computationalgrid, the external bounda ry of the computational domainwas foun d on the basis of approximate determination ofthe bow shock wave shape. Based on the solutionobtained at the first stage, the grid was reconstructed ineach cross-section X=const b y mov ing the grid layersusing the m etho d de scribed in [~21 which allows one totrack the gradients of the controlling function. After that,the previously obtained solution was re- interpolated tothe new grid. Then the computation was repeated. Thestatic pressure was used in the computations as acontrolling function.

The proposed algorithm and numerical gr id areverif ied using a f inite-width wedg e as an examp le. Thisconfiguration is used as an external compression surfacein 2D inlets. Extensive experimental data available forthe f low around a f inite-width wedge allow anappropriate verif ication of numerical a lgorithms. As anexample, the calculation of a wedge with an angle of15 , half-width b=0.35 and length /--1 for the Machnumber 2.5 is presented. Such an example is chosen asthe most complicated case from the viewpoint of 3Deffect. A great number of test calculations wereperformed, and a good agreement of numerical andexperimental data was obtained, including a correctdetermination of shock wav e shapes and positions. Thismakes it possible to state that this algorithm isapplicable to the calculation of 3D compression f lows.This numerical a lgorithm was used to calculate the f lowparameters and the character istics of the convergentinlet. T he specif ic features of the external com pressionsurface of such an inlet is its essential three-dimensionality, the presence of an exten ded contractingsection of external compression, and the symm etry axisposition outside the f low f ield.

The convergent inlet whose sketch is shown inFig. l(a) was calculated in the design and off-designregimes within the Mach range from 2 to 8.Results and Discuss ion

A typical structure of a 3D f low around the externalcompression surface of a convergent inlet is shown inFig. 7.

I t is seen that, downstream from the leading edge,the shock wave changes the shape: i t is concave in thebeginning of the f low and becomes convex at the end.This is a cons equence of a combination o f the processesof shock wave formation by the leading edge, intensestreamwise compression, and lateral spillage. The shapeof the shock wave near the leading edge remainsconcave within the entire range of Mach numbers. At

the end of the compression surface the shock waveshape changes , and for M>__6 the con cave shape of thewave remains along the entire compression surface.This is caused b y a signif icant decrease of f low spillageas the Mach nu mber increases.

M.=6

Fig.7 Static pressure field in crosssections of convergent inlet

The effectiveness of convergent compression isil lustrated by the pressure distr ibution along the modelfor various Mach numb ers (Fig.8) . As the Mach nu mberincreases, the com pression also increases, especially forX >0.7. The data for Mach number 2 show that theeffect of 3D compression is insignif icant, and theexternal compression of a con vergent inlet is c lose to a2D flow. This occurs because of intensive spillagethrough the lateral faces as the pressure increasesdownstream and the width of the compression surfacesimultaneously decreases. Obviously, this decrease inpressure is favorable from the viewpoint of dragreduction at transonic and low supersonic f l ight speeds.

mP

1 5

1 0

5

experiment- - caiculatlons M..-~6

I I B B B N

I I I I I I I I I0 , 0 0 . 2 0 , 4 0 . 6 0 . 8 X

Fig.8 Static pressure distributions on the convergentinlet surface in the symmetry plane


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Marat A. Goldfeld et al . Num erical and Experimental Studies of 3D Hypersonic Inlet 203

The l a t e r a l s p i l l a ge de t e r m i ne d a de c r e a s e o f s t a t i cp r e s s u r e t o w a r d t h e s i d e e d g e s ( F i g . 9 ) . T h i s d e c r e a s eb e c o m e s m o r e s u b s t a n t i a l a s t h e M a c h n u m b e rd e c r e a s e s . T h i s M a c h n u m b e r e f f e c t i s c a u s e d b y ad e c r e a s e o f t h e c o n v e r g e n t c o m p r e s s i o n s u r f a c e w i d t ha nd t he c o r r e s pond i ng i nc r e a s e o f l a t e r a l s p i l l a ge . Ani m p o r t a n t f e a t u r e o f c o n v e r g e n t c o m p r e s s i o n f l o w i s as u b s t a n ti a l n o n - u n i f o r m i t y o f t h e f l o w f i e l d a l o n g t h eno r m a l t o t he s u r f a c e ( F i g . 10 ) , a nd i t i nc r e a s e s a s t heM a c h n u m b e r i n c r e as e s . T h i s f e a t u r e o f t h e f l o w i se x p l a i n e d b y t h e p r o p e r t i e s o f c o n v e r g e n t f l o w , s i n c et h e m a x i m u m c o m p r e s s i o n i s a c h i e v e d n e a r t h es u p p o s e d a x i s o f s y m m e t r y o f in t e rn a l c o m p r e s s i o nf l o w .

T h e d a t a p r e s en t e d i n F i g s . 8 ~ 1 0 d em o n s t r at e ag o o d a g r e e m e n t b e t w e e n n u m e r i c a l a n d e x p e r i m e n t a lr e s u lt s a n d c o n f i r m a p o s s i b i l i ty o f u s i n g t h e p r o p o s e dn u m e r i c a l m e t h o d w i t h i n th e f r a m e w o r k o f E u l e re q u a t i o n s f o r d e t e r m i n i n g t h e i n l e t p e r f o r m a n c e i n o f f -d e s i g n r e g i m e s .

P e x p e r i m e n t

- - c a l c u l a d on s

6 ~ " ~ ' i ~ X = I

X = 0 . 8 l4

X = 0 . 5 82 ~ - - - - - - - - - - t ~

X = 0 . 4 1M _ = 4

0 J t i t I t0.05 0.05 0.10 Z

Fig.9 Static pressure distributions on the surface

i " "x p e% 7 2

i M = 4 iiL=~ I i I 1 I I0 2 4 6 p

Fig.10 Static pressure distributionin the convergent inlet

Boundary LayerA s p e c i f ic f e a tu r e o f c o n v e r g e n t c o m p r e s s i o n f l o w

i s t h a t t h e b o u n d a r y l a y e r o n t h e c o m p r e s s i o n s u r f a c ec o n v e r g e s t o w a r d t h e s y m m e t r y p l a n e . T h i s i n c r e a s e st h e b o u n d a r y l a y e r t h i c k n e s s a h e a d o f t h e i n l e t d u c te n t r a n c e a n d c a n c h a n g e t h e e f f e c t i v e c o n t o u r o f t h eb o d y . T h u s , s y s t e m a t i c m e a s u r e m e n t s o f t h e b o u n d a r yl a y e r o n t h e e x t e r n a l c o m p r e s s i o n s u r f a c e w e r ep e r f o r m e d f o r M a c h n u m b e r s f r o m 2 t o 6 .

A d e t a il e d m e a s u r e m e n t o f v e l o c i t y p r o f i le sa l l ow e d u s t o ob t a i n t he i n t e g r a l c ha r a c t e r i s ti c s o f t heb o u n d a r y l a y e r a n d d e t e r m i n e i t s s t r u c t u r e a n d s p e c i f i cf e a t u r e s o f i ts e vo l u t i on . I t wa s s h ow n , i n pa r t ic u l a r , t ha ta f l o w w i t h o u t t u r b u l e n t b o u n d a r y l a y e r s e p a r a t i o n i sa l w a y s f o r m e d . A t t h e s a m e t i m e , a d o w n s t r e a mi n c r e a s e i n t h e b o u n d a r y l a y e r v e l o c i t y p r o f i l e f u l l n e s sw a s n o t e d . T h e v e l o c i t y p r o f i l e t h a t d e v e l o p s u n d e r t h ec o n d i t io n s o f a l a rg e a d v e r s e p r e s s u r e g r a d ie n t c a n b ed e s c r i b e d w i t h i n t h e f r a m e w o r k o f th e c l a s s i c a l " w a l l -w a k e " l a w o v e r t h e e n t i r e b o u n d a r y l a y e r t h i c k n e s s :U+=(l/k)lny++B+H/k. H o w e v e r , t h e c h o i c e o f t h epa r a m e t e r s o f t h i s f o r m u l a ( / 7 , k ) s ign i f i c a n t l y de p e ndson t he c ond i t i ons o f bou nda r y l a ye r e vo l u t i on [12'14] a ndo n t h e d e g r e e o f i ts k i n e m a t i c n o n - u n i f o r m i t y .

An i m po r t a n t f e a t u r e f o r i n le t s i s t he va r i a t i on o f t hebounda r y l a ye r c ha r a c t e r i s t i c s a l ong t he i n l e t up t o t heduc t e n t r a nc e p l a ne . I t wa s e s t a b l i s he d t ha t t he bounda r yl a y e r t h i c k n e ss a n d m o m e n t u m t h i c k n e ss i n c r e a se sd o w n s t r e a m m o r e t h a n t w i c e o v e r t h e l e n g t h X = 0 . 3 -1 .0 (Fig .1 l (a ) , (b) ) .

A c o m p a r i s o n w i t h t h e d a t a f o r 2 D i s e n t r o p i cc o m p r e s s i o n r e v e a l s t h a t t h e b o u n d a r y l a y e r b e c o m e st h i c k e r b e c a u s e o f it s c o n v e r g e n c e t o w a r d t h e s y m m e t r yp l a n e o f t h e m o d e l . T h e b o u n d a r y l a y e r c h a r a c t e ri s ti c swe r e c a l c u l a t e d b y t he K u t a t e l a dz e - Le o n t i e v m e t hod [15].T h i s i n t e g r a l m e t h o d h a s b e e n v e r i f i e d o n a w i d e c l a s so f p r ob l e m s , i nc l ud i ng h i gh p r e s s u r e g r a d i e n t s , he a tt r a ns f e r , i n j e c t i on , r oughne s s , e t c . The c onduc t e dc a l c u l a t i o n s s h o w ( F i g . l l ( b ) ) t h a t t h e t h e o r e t i c a l v a l u eo f m o m e n t u m t h i c k n e ss i s i n g o o d a g r e e m e n t w i t he xpe r i m e n t a l da t a . The r e s u l t s ob t a i ne d a l l ow one toc o r r e c t t h e e x t e r n a l c o m p r e s s i o n s u r f a c e t o e n s u r e t h er e qu i r e d f l ow r a t e a nd i n l e t s t a r t i ng . Be s i de s , t hem e t h o d u s e d a l l o w s t h e p r e d i c ti o n o f b o u n d a r y l a y e rs e p a r a t i o n b a s e d o n t h e c h a n g e s i n t h e v e l o c i t y p r o f i l ea nd s k i n f r i c t i on unde r t he a c t i on o f a dve r s e p r e s s u r eg r a d i e n t . The s k i n f r i c t i on m e a s u r e m e n t s a l ongc o m p r e s s i o n s u r f a c e s h o w s ( F i g . 1 2 ) t h a t f r i c t i o nc o e f fi c ie n t sl o w l y in c r e as e s a n d f o r X ~ . 6 b e c o m e sa pp r ox i m a t e l y c ons t a n t up t o i n l e t e n t r a nc e .

R e c e i v e d d a t a s h o w s t h a t s k in f r ic t io n i n c r e a s e s n o tm o r e t h a n 4 0 % a n d h i g h f a v o r a b l e p r e s s u r e g r a d i e n td o n ' t l e a d t o s t r o n g s k i n f r i c t i o n d e c r e a s e ( w h i c h i s


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:204 Journal of Therm al Science, Vol.11, No.3, 2002

2

00.2

/

fI I I I I I I0.4 0.6 0.8

(a )

e x p e r i m e n t ]- - i n t e g r a l m e t h o d t a l c .

2 D i n l e tI I I I I I I I

0.2 0.4 0.6 0.8Co)

Fi g.U Integral characterist ics of boundary layer forconvergent inlet (Mz= 4, Re1=50X 106 l/m )

1.2

1.0

0.8 I I I I I I I I0.2 0.4 0.6 0.8 X

Fig.12 Skin friction coefficient(M~-=4,Re1=50X 106 l/m )inhe ren t fo r sepa ra t i on r eady f l ows) . The r e l a t i veboun da ry l aye r t h i ckness and t he d i sp l acement t h i cknessa t t he duc t en t rance i nc rea se a s t he Mach numberinc rea se s whi l e t he momentum th i ckness dec rea se s(Fig.13(a) , (b)) . I t i s seen tha t the boundary layerth i ckness can r each 40% of t he duc t he igh t, whe reas t hed i sp l acement t h i ckness i s no more t han 10%. Th i sd i f f e rence is c aused b y a l a rge fu l l ne ss o f t he nea r -wa l lpor t i on o f t he b ound a ry l aye r ve loc i t y p ro f i l e.

rhe ,

0.08

0.04

8 " *

h ~

0.02

I I I I I I, 0 1 t2 4 6 M . M ,

I I I I I

2 4 6

( a ) ( b )Fig.13 B oundary layer characteristics

in the convergen t inlet entranceThe co mpara t i ve t e s ts o f t he conv e rgen t i n l e t mod e l

i n t h e b l o w d o w n w i n d t u n n e l s h o w e d t h a t t h e b o u n d a r yl aye r sepa ra t ion f rom the ex t e rna l compress ion su r faceo c c u r re d a t l o w R e y n o l d s n u m b e r s a n d M a t h n u m b e r s 5and 6 . Wi th h ighe r Reyno lds numbers ach i eved i n t heho t - sho t wind t unne l , a non-sepa ra t ed f l ow i s fo rmedand the inle t s ta r t ing i s ensured.In te gr a l C h ar ac te r i s t i c s

One o f t he ma in advan tages o f conve rgen t i n le t s i s aposs ib i l it y o f ob t a in ing a h igh e r degree o f co mpress ionin compar i son w i th t rad i t i ona l 2D in l e ts . As an example ,F ig .14 shows the conve rgen t i n l e t compress ion a scond i t i ons a t t he sc ramje t combus to r .

| - - - 4 1 - 2 D i n l e t / M . . = 6

I I I

0 20 40 60 X , m m

Fig.14 Static pressure distribution in the inlet channelI t i s seen t ha t r a the r h igh degrees o f compress ion

can be ob t a ined , e spec i a l ly fo r the M ach n umb er 6 . Thecor re spond ing Ma th number a t t he i n l e t en t rance i sshow n in F ig .15 .

Obv ious ly , a supe r son i c f l ow in t he i n l e t en t rancecan be r ea l i zed fo r Mach numbers l a rge r t han 3 , i fspec i al measure s a re no t t aken t o en sure a subson ic f l owin t he combus to r . The ve loc i t y (Mach number ) p ro f i l e smeasured a t t he combus to r en t rance demons t ra t e a l a rgenon-un i fo rm i ty which i nc rea ses a s t he M ach nu mbe rdec rea se s . Th i s i s exp l a ined by bounda ry l aye r


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Marat A. Goldfeld et al. Numerical and Experimental Studies of 3D Hypersonic Inlet 205

separ a t ion ahead of the en t r ance and in the in le t duc t .T h e e q u a l i z a t i o n o f p r e s s u r e a n d v e l o c i t y f i e l d s w a sa c h i e v e d b y t h e b o u n d a r y l a y e r b l e e d i n g t h r o u g h t h es lo t s in the s ide w a l l s . This appr oach to boundar y layerc o n t r o l w a s f o u n d t o b e e f f e c t iv e f o r a c o n v e r g e n t i n l et ,in cont r as t to a 2D in le t .

M on

I I I I I I I I

2 3 4 5 M .

Fig. 15 M ach number in the inlet entranceA la r ge inc r eas ing of the pr es sur e in the in le t

c h a n n e l c a n b e e x p l a i n e d b y t h e d e c e l e r a t i o n t osubsonic ve loc i ty . I t i s conf i r med by the in le t channe le x i t M a c h n u m b e r s n e a r c o w l a n d c e n t r al b o d y( F i g . 1 6 ) . T h e s e M a c h n u m b e r r e m a i n s s u b s o n i c i n t h ew h o l e r a n g e o f m a i n s t r e a m v e l o c i t y , a n d o n l y a t f r e es t r e a m M a c h n u m b e r M = 6 t h e v e l o c i t y a p p r o a c h e s t h esonic speed .

M0 . 9 -0 . 8 -0 . 7 -0 . 6 -0 . 5 I I I I I I 1 I I I I I

2 3 4 5 6 M .Fig. 16 Mach number in the exit of inlet channel

T h e l e v e l o f t o t a l p r e s s u r e r e c o v e r y a n d f l o w r a t ecoef f ic ien ts f or a conver gent in le t a r e pr esen ted inF i g .1 7 ( a ), ( b ) . T h e y a r e c o m p a r e d h e r e w i t h t h e d a t a f o r2D in le t s . I t i s s een tha t the to ta l p r es sur e r ecover ycoef f ic ien t w as smal le r than in the MI L - 500 s tandar d ,b u t a h i g h l e v e l o f p re s s u r e r e c o v e r y w a s a c h i e v e d f o rh igh Ma ch num ber s M. ,2>4. The f low r a te co ef f ic ien tsf o r c o n v e r g e n t a n d 2 D i n l e ts a l m o s t c o i n c i d e w i t h i n t h ee n t i re M a c h n u m b e r r a n g e .

V

0.80 . 6 -

0 . 4 -0 . 2 -

0

0.8"0 . 6 -

0 . 4 -0 . 2 -

l i I i l I I 02 4 6 M ,

fI l l l l l l2 4 6 M .

Fig.17 Total pressure recove ry andmass flow rate coefficients

0 conv. inlet without sidewalls (Mdesign=6)[] 2D inlet with side walls (Md~i~=6)A convergen t inlet with side walls (M~ig~=6) converge nt inlet with side walls (Mdesign=8)

W e m e n t i o n e d a b o v e a p o s s i b i l i t y o f w a v e d r a gr e d u c t i o n i n o f f - d e s i g n r e g i m e s a t l o w f l o w r a t ecoef f ic ien ts , bu t w i th equa l l eve l s o f ex te r na lc o m p r e s s io n , m a i n l y d u e t o t h e d e c r e a s e o f t h e e x t e rn a lcompr ess ion sur f ace a r ea in the h igh- pr es sur e r eg ion . Ac o m p a r i s o n o f t h e w a v e d r a g o f c o n v e r g e n t a n d 2 Dinle t s w i th an equa l angle of f low tur n ing ( 0~=20) andequa l comp r ess ion lev e l ( 0~=29.2 ) show tha t mo r e thana t w o - f o l d r e d u c t i o n o f w a v e d r a g c a n b e a c h i e v e dw i th in the en t i r e r ange of Mach number s ( F ig .18) . As igni f ican t decr ease of the hea t f lux leve l in ac o n v e r g e n t c o m p r e s s i o n f l o w c a n a l s o b e ex p e c t e d .

Cx

0.15

0.10

0.05

c o n v e r g e n t i n i e ~2 D i n l e t , 0 ~ = 2 0 I2 D i n l e t , e k = 2 9 ~

I I I I I I2 4 6 M, ,

Fig.18 Inlets wave dragI n l e t S t a r t i n g

For h igh pr es sur e gr ad ien ts , a spec i f ic cont r ac t ingshape of the ex te r na l compr ess ion sur f ace g ives r i s e tot h e p r o b l e m o f i n le t s t ar t in g f o r M a c h n u m b e r s s m a l l e rt h a n t h e d e s i g n v a l u e e v e n i n t h e a b s e n c e o f i n t e r n a lcom press i on. I t w as f ou nd th at fo r Mac h n um bers M**_~


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206 Journal of Thermal Science, Vol.11, No.3, 2002

The normal shock wave could be observed on theexternal compression surface upstream of the ductentrance (Fig.19) . I t was caused by the non-star ting of asemi-bounded contracting duct. The stand-off distanceof the normal shock wave from the duct entranceincreases as the Mach number decreases. An effectivemethod of inlet star ting is the remov al of the side walls.However, this leads to a smaller level of externalcompression, and the convergent inlet character isticsbecom e closer to the 2D inlet performance. I t was foundthat the reason for inlet non-star ting is the boundarylayer thickening and its separation. Thus, the boundarylayer bleeding was p erformed through longitudinal slotsin the side wails upstream of the duct entrance (X'__._0.7).Their effectiveness is caused by a moderate width of theexternal compression surface. As a result of thismodification, the inlet was started within the entirerange of Mach numbers without substantial reduction ofcompression level. The conducted studies confirmed thepossibili ty o f effective control of the con vergent inlet bymeans of moving the side walls or changing the shapeand size of the slots made in these walls. This type ofcontrol is impossible for traditional 2D inlets.Simultaneously, this control a llows one to reduce thepressure non-uniformity in the inlet duct and at thecombustor entrance.

Fig.19 Schlieren visualization forconvergent inlet for M. =4

ConclusionThe conducted complex study of a 3D inlet a llows

the following conclusions to be made.1. A signif icantly higher level of compression is

achieved in a con vergent inlet , as compared with a2D inlet.

2. The use of convergent inlet a llows one to reducethe inlet drag at transonic speeds.

3. A decrease of the area of the duct surfaces ensuresthe heat protection of the inlet and combustor .

4. An effective control of converge nt inlet is achievedby changing the shape and size of slots in the sidewalls or by mov ing the side walls.

5. Based on the solution of 3D Euler and boundarylayer equations, it is possible to obtain a reliableprediction of the inlet performance in off-designregimes and determine the f low structure.

6. The hot-shot wind tunnel is an effective facili ty forinlet testing at high Reynolds numbers within theMach num ber range from 5 to 16.

References

[ 1 ] B e c ke r , J V . Ne w Appr oa c he s to Hype r son icAircraft. JCA S Paper, 1970, (16)[2] Weinder , S P. Propulsion Air Frame Integration

Considerations for High Altitude Hypersonic Vehicles.AIAA Paper 1980 - 0111 , 1980

[3] Goldfeld, M A. Experimental Study of 3-D Inletsfor High Supersonic Flight Vehicles. The ICMAR ITAM,5-94, 1994

[4] Molder , S, Szpiro, E J. The Busemann Inlet forHypersonic Speeds. J. Spacecraft Rockets, 1303-1, 1966

[5] Gutov, B I, Zatoloka, V V. Convergent Inlet Diffuserswith the Initial Shock and Additional ExtemalCompression. Aerophis. Issledovania, ITAM SD USSRAS Novosibirsk, 1973 , (2)

[6] Trexel, C A. Iniet Performance of the Integrated LangleyScramjet Module (Mach 2.3 to 7.6). AIAA Paper, 75-1212, 1975

[7] Billig, F S, Kothari, A P. Streamline Tracing Techniquefor Designing Hypersonic Vehicle. In: Proc. of the 13~International Symposium on Air Breathing Engines.Chatanooga, Tennessee, USA, 1997, 2

[8] Gutov, B I, Zatoloka, V V. Design and ExperimentalInvestigations o f the Convergent Inlet Configuration with3D Flow Combinations. Preprint ITAM SD USSR AS,1983, 30-- 83[9] Schepanovsky, A V, Gutov, B I. Gasdynamical Designof Supersonic Inlets. Novosibirsk: Nauka, 1993

[10]Goldfe ld , M A, Lisenkov, I G. Inves t iga t ion ofCompressible Turbulent Boundary Layer at LargeAdverse Pressure Gra dien t. Separated Flows and JetsIUTAM Symposium, Novosibirsk, USSR, Springer-Verlag, 1990

[11] Shashkin, A P, Volkov, V F. The One N umerical Schemefor Inviscous Flows. Zadachi Obtecania TelProstranstvermoi Configuratsii, Novosibirsk, 1978

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