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\ ^\ > GAR Dograph-79

AGARDograph

JET SIMULATION IN GROUND TEST

FACILITIES

PINDZOLA fr\ .

NORTH ATLANTIC TREATY ORGANIZATIONADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT

ru e de Varenne . Paris VII

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A G A R D o g r a p h 79

NORTH ATLANTIC TREATY ORGANIZATION

ADVISO RY GROUP FOR AERONA UTIC AL RESEARCH AND D EVELOPMENT

(ORGANISATION DU TRAITE DE L 'ATLANTIQUE NORD)

JE T S I M U L AT I O N I N G R O U N D TEST FA C I L I T I E S

b y

M. Pindzola

November 1963

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Th is is one of a series of publications by the A G A R D - N AT O FluidDynamics Panel.

Professor Wi lbur C . Nelson of The University of Michigan is the Editor.

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S U M M A R Y

This paper presents a review of various techniques employed in thesimulation of a jet exhaust in ground test facilities. A brief summaryof the characteristics of a jet exhausting into both q uiescent andm o v i n g media is presented. The importance of duplicating t he initialinclination angle o f t h e j e t , 8 . , when conducting simulation studiesi s pointed out. Various scaling parameters are enumerated. A requ ire-ment for the duplication of the jet pressure ratio, j et momentum, and t heparameters 7jMj//3j and (RT)j is indicated. Experimental data are alsopresented which verify the importance of t hese parameters in simulationstudies. One method of s electing the geometry and test conditions for asimulation m odel in order t o account for a difference in betweenm o d e l and f u l l scale and s till duplicate the important similarity para-meters, is presented.

S O M M A I R E

Ce papier pre'sente une revue de diverses tec hniques employees dansl a simulation de 1' echappement du j e t , en essais a terre. Un bre fsommaire des caracteristiques de 1'echappement du jet en m i l i e u calmee t agite est presente. L' importance de doubler 1'inclinaison initialed u j et S . dans 1'etude de la simulation es t ponctue e. Differentsparametres d' 'chelle sont enume'res. Une condition pour la duplicationd u rapport de pression du j e t , de son moment, et des parametres7jMj2//3. et (RT)j es t i n d i q u e e . Des resultats experimentaux qu ive ' r i f ien t 1' importance de ces parametres e n etudes simu lees sont aussipresentes. Aussi est presentee une met hode qui p e r m e t de choisir lag e o m e t r i c et les conditions du test pour une simulation afin de tenirc o m p t e d'une difference dans y * entre m o d e l e e t pleine e c h e l l e , toute n cependant doublant les parametres similaires importants.

533.6.072:533.697.43 b l c

3b2e2

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C O N T E N T S

P a g e

S U M M A R Y i i i

S O M M A I R E i i i

L I S T O F TA B L E S v i

L I S T O F F I G U R E S v i

N O T A T I O N v i i i

I . I N T R O D U C T I O N 1

I I . J E T F L O W C H A R A C T E R I S T I C S 1

1 . J E T S E X H A U S T I N G I N T O A M E D I U M A T R E S T 21 . 1 I n i t i a l I n c l i n a t i o n o f t h e J e t B o u n d a r y 31 . 2 J e t B o u n d a r y S h a p e s 51 . 3 I n t e r c e p t i n g S h o c k B o u n d a r y 61 . 4 P r i m a r y W a v e l e n g t h o f t h e J e t 71 . 5 D i s t a n c e t o t h e F i r s t M a c h D i s c 71 . 6 J e t M i x i n g R e g i o n 71 . 7 J e t N o i s e 8

2 . J E T S E X H A U S T I N G I N T O A M O V I N G S T R E A M 92 . 1 I n i t i a l I n c l i n a t i o n o f t h e J e t B o u n d a r y 1 02 . 2 J e t B o u n d a r y S h a p e s 1 12 . 3 J e t M i x i n g R e g i o n 1 22 . 4 J e t S h o c k R e f l e c t i o n 1 2

I I I . S C A L I N G P A R A M E T E R S 1 3

3 . J E T B O U N D A R Y S I M U L A T I O N 1 3

4 . J E T S H O C K S I M U L AT I O N 1 4

5 . S I M U L AT I O N O F J E T F LO W P A R A M E T E R S 1 55. 1 Je t M a s s F l o w 155 . 2 J e t K i n e t i c E n e r g y 1 55 . 3 J e t I n t e r n a l E n e r g y 1 65 . 4 J e t E n t h a l p y 1 65 .5 Je t M o m e n t u m 165 . 6 J e t T h r u s t 1 7

6 . B A S E H E AT I N G S I M U L AT I O N P A R A M E T E R S 1 7

7 . J E T M I X I N G S I M U L A T I O N 1 7

8 . J E T N O I S E S I M U L AT I O N 1 8

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Page

IV . METHODS OF JET S IMULATION 19

9. COLD GAS JETS 199 .1 Air 199. 2 H e l i u m 199. 3 C a r b o n D i o x i d e 19

10. COLD GAS M I X T U R E S 19

11. HOT GAS JETS 2 011.1 Ho t A i r ZO11 . 2 H y d r o g e n a n d A i r 2 011. 3 H y d r o g e n P e r o x i d e 2 011. 4 T u r b o j e t S i m u l a t o r 2 0

12 . R O C K E T M O TO R S I M U L ATO R S 2 1

V. E X P E R I M E N TA L RESULTS 2 1

13. JE T EXIT EFFECTS 2 113. 1 I n i t i a l I n c l i n a t i o n o f t h e J e t B o u n d a r y 2 213. 2 B as e P r e s s u r e 2 213.3 Ex i t Shock P o s i t i o n 2 2

14. D O W N S T R E A M EFFECTS 2 314.1 T r a n s m i t t e d S ho c k P o s i t i o n 2 314.2 T r a n s m i t t e d Sh oc k S t r e n g t h 2 314. 3 Tr a n s m i t t e d S ho c k A n g l e 2 314.4 Je t B o u n d a r y S h a p e 2 414.5 Je t M o m e n t u m E f f e c t s 2 4

VI. DISCUSSION 24

15. JE T EXIT EFFECTS 2 4

16. D O W N S T R E A M EFFECTS 2 5

17. A D D I T I O N A L R E M A R K S 2 5

VII . REFERENCES AND B I B L I O G R A P H Y 2 6

TABLES 32

FIGURES 34

DISTRIBUTION

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L I S T O F T A B L E S

Page

TABLE I S u m m a r y of S c a l i n g Parameters 32

TABLE II P r o p e r t i e s of Gaseous M e d i a 33

L I S T O F F I G U R E S

Fig.1 E f f e c t of jet M a c h n u m b e r on the i n i t i a l i n c l i n a t i o n a n g l e of a jete x h a u s t in g i n t o a m e d i u m a t r es t(a) 7j = 1.667 34(b) 7j = 1.38 35(c ) 7j = 1.25 36(d) 7j = 1.133 37

Fig.2 E f f e c t of the r a t i o of s p e c i f i c h e a t s of the jet on the i n i t i a li n c l i n a t i o n a n g l e of a jet e x h a u s t i n g i n t o a m e d i u m at r e s t 38

Fig.3 E f f e c t of the r a t i o of s p e c i f i c h e a t s of the jet on the i n i t i a li n c l i n a t i o n a n g l e of a jet e x h a u s t i n g i n t o a v a c u u m 39

Fig.4 C o m p a r i s o n of i n i t i a l i n c l i n a t i o n a n g l e of a jet e x h a u s t i n g i n t oa m e d i u m a t r e st c a l c u l a t e d b y a n e x a ct a n d a n a p p r o x i m a t e s e r ie ss o l u t i o n 40

Fig.5 E f f e ct o f t h e r a ti o o f s p e c if i c h e a ts o f t h e j e t o n t h e b o u n d a r yof a jet e x h a u s t i n g i n t o a m e d i u m at r e s t 41

Fig.6 E f f e c t of the jet p r e s s u r e r a t io on the b o u n d a r y of a jete x h a u s t i n g i n t o a m e d i u m at r e s t 42

Fig.7 E f f e c t of jet M a c h n u m b e r on the b o u n d a r y of a jet e x h a u s t i n g i n t oa m e d i u m at r e s t 43

Fig.8 E f f e c t of jet M a c h n u m b e r on the s p r e a d i n g r a t e p a r a m e t e r of a jete x h a u s t i n g i n t o a m e d i u m at r e s t 44

Fig.9 Effects on jet n o i s e of a s u b s o n i c je t e x h a u s t i n g i n t o a m e d i u mat r e s t 45

Fig.10 E f f e c t of jet M a c h n u m b e r on the i n i t i a l i n c l i n a t i o n a n g l e of a jete x h a u s t i n g i n t o a m o v i n g s t re a m 46

Fig.11 Effect of the r a t i o of s p e c i f ic h e a t s of the jet on the i n i t i a la n g l e of a jet e x h a u s t i n g i n t o a m o v i n g s t r ea m 47

Fig.12 E f fe c t o f f r e e s t re a m M a c h n u m b e r o f t h e i n i t i a l i n c l in a t i ona n g l e of a jet e x h a u s t i n g i n t o a m o v i n g s t r ea m 48

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Fig.13 Effect of f r e e s t r e a m M a c h n u m b e r on the b o u n d a r y of a jete x h a u s t i n g i n t o a m o v i n g s t re a m 49

Fig.14 Ty p i c a l Schlieren p h o t o g r a p h of a jet e x h a u s t i n g i n t o a m o v i n gs t r eam 50

Fig.15 C o m p a r i s o n of an e x p e r i m e n t a l and c a l c u l a t e d je t shock in a jete x h a u s t i n g i n t o a m o v i n g s t re a m 51

Fig.16 Va l u e s of the i n i t i a l i n c l i n a t io n a n g l e of a jet e x h a u s t i n g i n t oa m e d i u m at r e s t u s i n g a cons t an t je t M a c h n u m b e r s i m i l a ri t yp a r a m e t e r

(a) (Pj/Pa, - 1) = 2.4 527j

(b) (Pj/Pa, - 1) = 31.2 537J

Fig. 17 Va l u e s of the i n i t i a l i n c l i n a t i o n a n g l e of a jet e x h a u s t i n g i n t oa m e d i u m at re s t u s i n g a cons t an t jet p r e s s u r e r a t i o s i m i l a r i t yp a r a m e t e r , 7jMj//8j =3.98 54

Fig . 18 I n i t i a l i n c l i n a t io n a n g l e of a son ic je t e x h a u s t i n g i n t o a m o v i n gs t r eam 55

Fig.19 E f f e c t of a son ic je t exhaus t on b a s e p r e s s u r e 55

Fig.20 E f f e c t of the e x i t s ho c k f ro m a s o n i c j e t on the p r e s su rec o e f f i c i e n t a t a p o i n t i n a m o v i n g s t re a m 5 6

Fig.21 E f f e c t of the t r a n s m i t t e d s h o c k f r o m a son ic jet on the p r e s s u r ec o e f f i c i e n t a t a p o i n t i n a m o v i n g s t re a m 5 6

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N O T A T I O N

Symbol

a speed of sound

A area

c s p e c if i c h e a t

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

d d i a m e t e r

F th rus t or force

k shock r e f l e c t i o n p a r a m e t e r

L length

m m a s s

Mach number

p s t at i c p r e s s u r e

q d y n a m i c pressure

R g a s c o n s t a n t o r r a d i u s

t t i m e

T t e m p e r a t u r e

u v e l o c i t y i n t h e x d i r e c t i o n

V v e l o c i t y

w s o u nd p o w e r

x , r c o o r d i n a t e s i n t h e a x i a l a n d r a d i a l d i r e c t i o n s

/3 (M 2 -

k K a w a m u r a p a r a m e t e r

7 r a t i o of s p e c i f i c heats

8 f l o w i n c l i n a t i o n a n g l e

Dimensions

L/t

L 2

L 2 /t 2 T

N o n e

L

F

N o n e

L

m

N o n e

F/L 2

F/L 2

L2/ t 2T or L

t

T

L/t

L/t

mL2/ t 3

L

N o n e

N o n e

N o n e

N o n e

V l l l

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Symbol

M

v

P

Subscripts

b

B

f

P

j

m

m d

P

geometric angle

M a c h angle

t u r n in g an g l e f ro m M = 1 t o M > 1

d e n s i t y

experimental constant

je t boundaryboat-tail or base

f u l l s c a l e

t h r u s t

c o n d i t i o n s a t t h e j et nozzle e x i t

m o d e l

M a c h d i s c

nozzle

at constant p r e s s u r e

i n t e r c e p t i n g s h o c k b o u n d a r y

t o t a l o r s t a g n a t i o n

a t constant v o l u m e

f r e e s t r e a m

c o n d i t i o n s b e f o r e e x p a n s i o n o r c o m p r e ss i o n

c o n d i t i o n s a f t e r e x p a n s i o n o r c o m p r e s s i o n

c o n d i t i o n s a t t h e nozzle t h r o a t

D i m e n s i o n s

N o n e

N o n e

N o n e

m/L3

N o n e

i x

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J E T S I M U L T I O N I N G R O U N D T E ST F A C I L I T I E S

M . Pindzola*

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

S h o rt l y a f t e r t h e i n c e p t i o n of t h e u s e o f j e t p r o p u l s i o n f o r a i r v e h i c l e s , i t w a so b s e r v e d t h a t s i g n i f i c a n t c h a ng e s w e r e r e a li ze d b e t w e e n the j e t - o n and j e t - o f f caseso n t h e a e r o d y n a m i c a n d t h e r m o d y n am i c c h ar a c t er i s t ic s o f t h e v e h i c l e . E a r ly s u m m a r i eso f t h e s e e f f e c t s a r e p r e s e n t e d i n R e f er e n c e s 1 a n d 2 f o r a i r c r a f t a n d m i s s i l e c o n -f i g u r a t io n s r e s p e c t i v e l y. S i n ce t h e s e s u m m a r ie s w e r e p u b l i s h e d , m a n y a d d i t i o na li n v e s t i ga t i o n s h a v e b e e n c o n d u c te d i n o r d e r t o m o r e a c c u ra t e l y d e f i n e t h e j e t i n t e r -actions. S o me o f t h e m o r e r e c e n t s t u d ie s a r e l i s t e d a s R e fe r e n c e s 3 t o 1 0 i n t h i sR e p o r t . E a c h o f t h e s e r e f e r e n c e s i n t u r n l i s t s t h e m o s t r e c e n t w o r k i n th e r e s p e c t i v ef i e l d s of s t u d y.

T h e p u r p o s e o f t h i s R e p o r t i s t o s u mm a r i ze t h e v a r i o u s t e c h n i q u e s w h i c h a r e u s e dt o o b t a i n t h e j e t - o n c h a r a ct e r i s ti c s . R e s u l t s o f s u c h i n v e s t i g a t i o n s w i l l b e q u o t e do n l y t o s h ow t h e m e r i t o f t h e t e c h n i q u e s e m p l o y e d .

T h e d i s c u s s i o n w i l l b e l i m i t e d p r i ma r i l y t o a n a x i s ym m e t r i c , u n d e r - e x p a n d e d j e t .A s h o r t r e v i e w o f t h e c h a r a c t e r i s t i c s o f such a j e t a r e p r e s e n t e d i n Section I I . Thisr e v i e w i s s e p a r a t e d i n t o t h e c a t e g o r i es o f a j e t e x h a u s t i n g i n t o a m e d i u m a t r es t a n di n t o a m o v i n g stream. I t s h o u l d b e r e a li ze d t h a t e v e n w it h a v e h i c l e i n m o t i o n ,p o r t i o n s o f t h e j e t e x h a u s t f o r c e r ta i n b a s e c o n f i g u r a t i o n s c a n b e t y p i f i e d a s t h o u g he x h a u s t i n g i n t o a m e d i u m a t r es t.

I n S e c t i on I I I , s o m e o f t h e s c a l i n g l a w s o f p a r t i c u l a r c o n c e r n t o t h e s u b j e c tm a t t e r a r e p re s e n te d . N o d i s cu s s i on o f t h e m o r e u s u a l f l u i d d y n am i c a n d t h e r m o d y n a m i cs i m i l a r i t y p a r a m e t e r s s u ch a s t h e R e y n o l d s a n d Prandtl n u m b e r s i s p r e se n t ed .

M e t h o d s o f j e t s i m u l a t i o n u s e d i n g r o u n d t e s t f a c i l i t i e s a r e n e x t p r e s e n t e d i nS e c t i o n I V f o l l o w e d b y a p r e s e n t a t i o n o f t y p i c a l t e s t r e s u l t s u s i n g t h e s e t e c h n i q u e si n S e ct i o n V. T h e m o r e i m p o r t a n t as p ec t s o f t h e se r e s u lt s a r e d i s cu s s e d i n S e ct i o n V I .

T h e b i b l i o g r a p h y a t t h e c o n c l u s io n o f t h e R e p o r t i s c a t e go r i ze d a c c o r di n g t o t h e

s u b j ec t m a t t e r o f t h e v a r i o u s s e c t i o n s o f t h e R e p o rt .

I I . J E T F L O W C H A R A C T E R I S T I C S

The s t u d y of the c h a r a c t e r i s t i c s of the f l o w of a jet of gas i n t o a s u r r o u n d i n gm e d i u m h a s r e c e i v e d m u c h a t t e n t i o n s i n c e t h e w o rk o f S t . Ve n a n t a n d Wantzel in 1839.A c o m p r e h e n s i v e s u m m ar y o f t h e s e s t u d i e s u p t o 1 954 i s g i v e n b y P ai i n R e f e r e nc e 1 1 .I n o r d e r t o k e e p t h e r e f e r e n c e s in t h i s R e p o r t w i t h i n b o u n d s , t h os e l i s t e d i n Pai'sp u b l i c a t i o n w i l l n o t b e r e p e a t e d h e r e .

* A P O , I n c . , USAF A rn o ld E n g in ee r i ng D e ve lop men t C e n t e r , Tu l l a h o m a T e n n e s s e e , U.S.A.

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T h e i n i t i a l s t r u c t u re o f a n a x i s y m m e t r i c j e t c o n s i s t s o f a c o r e s u r r o u n d e d b y ana n n u l a r m i x i n g r e gi o n. F a r t h e r d o w n s t re a m , t h e e n t i r e j e t i s a m i x i n g r e g i on .T h e or i e s t o p r e d i c t t h i s j e t s t r u ct u r e h a v e b e e n d e v e l o p e d u n d e r t h e a s su m p t io n o fe i t h e r i n v i s c i d o r v i s c o u s c o n s i d e r a t i o n s .

F o r j e t s i n w h i c h t h e r a t io o f t h e p r e s s u re a t t h e e x i t o f t h e j e t nozzle t o t h ea m b i e n t pressure o f t h e s u r r o u n di n g m e d i u m i s low, i n v i s c i d t h e o r i e s b a se d o n t h el i n e a r i z e d e q u a t i o n s o f f l u i d f l o w (Refs.12 t o 1 9 ) a re u s e d t o d e s c r i b e t h e j e tc h ar a c te r i st i cs . S i n ce t h e s e d e r i v a t i o n s ar e n o t a p p l i c a b l e a t h i g h e x i t t o a m b i e n tp r e s s u r e r a t i o s , r e s o r t i s m a d e t o t h e m e t h o d o f characteristics (Refs.20 t o 2 3 ) o rto a p p r o x i m a t e s o l u t i o n s b a s e d o n v a r i o u s a s s u m p t i o n s (Refs.24 t o 29).

\

A l t h o u g h t h e i n v i s c i d t h eo r i e s h a v e b e e n f a ir l y successful i n p r e d i c t i n g t h e j ets t r uc t u r e i m m e d i a t e l y do w n st r e a m o f t h e j e t e x i t , r e s o rt m u s t b e m a d e t o v i s c o u st h e o r i e s (Refs.30 t o 3 7 ) t o o b t a i n j e t c h a r a c t e r i s t ic s f u r t h e r d o w n s t r e a m . I n t h e s ecases, t h e f l u i d f l o w e q u a t i on s b a s e d o n t h e b o u n da r y l a ye r a p p r o x i m a t i o n s a r e u s e da s s u m in g e i t h e r l a m i n a r o r t u r b u l e n t m i x i n g .

Va r i o u s e x p e r i m e n t a l s t u d i e s (Refs.38 t o 4 5 ) h a v e a l so b e e n m a d e t o d e t e r m i n e t h es t r u c t u r e o f jets a n d t o s e r v e a s a c h e c k o n t h e v a l i d i t y o f t h e t h e o r e t i c a l analyses.F r om b o t h t h e a n a l y t i c a l a n d e x p e r i m e n t a l s t u d i e s o f g a s j e ts , t h e f o l l o w i ng i n f o rm a -t i o n i s d e r i v e d .

1 . J E T S E X H A U S T I N G I N T O A M E D I U M A T R E S T

A s k e t c h o f t h e g e n e r a l i z e d f l ow p a t t er n o f a n u n d e r - e x p a n d e d ( o v e r - p r e s s u r e d )a x i s y m m e t r i c j e t e x h a u s t i n g i n t o a m e d i u m a t r e s t i s s h o wn b e l o w :

J e t S h o c kJet Bounda ry R e f l e c t e d J e t Shock

eBPoo

M a c h D i s c

A s t h e j e t e m e r g e s f r om t h e nozzle, i t e x pa n d s t o t h e p r e s s u re o f t h e s u r r o un d i n gm e d i u m a t t he j e t b o u nd a ry. T h e c o n d i t i on o f c o n st a n t p r e s s u r e a t t h e b ou n d a r y causes

t h e c u r v a t u r e o f th e b o u n da r y t o t e n d b a c k t o wa r d t h e a x i s o f t he f l o w. T h e j e t s ho cki s f o r m e d b y t h e c o a l e s c e n s e o f t h e c o m pr e s s io n w a v e s r e q u i r e d t o t u r n t h e f l o w a t t h eb o un d ar y. F o r a s l i g h t l y u n d e r - e x p a n d e d j e t , t h e j e t s h oc k s m e e t t o f o rm a s h oc k

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diamond. However, as the nozzle pressure ratio is increased, a Mach ref lectionoccurs in the jet forming a Mach or shock disc. A reflection of the jet shock occursi n eit her case, and the pattern is repeated at the intersection of the reflect ed shockand the jet boundary.

The study of the jet structure thus involves the prediction of the above patternas influenced by the various variables such as the nozzle pressure ratio, jet Machnumber, ratio of specific heats of the jet, and so forth. Near the e x i t of thenozzle, t he effects of viscosity are small and inviscid theories describe the flowreasonably well. However, further downstream from the exit the mixing region betw eent h e jet and free stream predominates and viscous theories are required.

1.1 Initial Inclination of the Jet Boundary

I n exhausting from the pressure at the exit of the nozzle, p. , to a lower ambientpressure, p^ , the jet will initially undergo a tw o-dimensional expansion at thenozzle lip. This expansion is governed by the Prandtl-Meye r equations. In ex pandingfrom a Mach numb er of 1.0 to a higher Mach number, M , the relationship between t heturning angle v and M is given by

v - arctan I B - arctan/3 . (H-l)

The angle requ ired f or expansion from some initial supersonic Mach number, M t , tosome higher Mach number, M 2 , is simply the difference in the values of v at thetwo Mach numbers, i.e.

The ratio of the final t o initial static pressures is given by

P 2

P,

2 + (y-l)MJ

2 + (7-1 )M|

y - i(II-3)

For a jet exhaus ting into a mediu m at rest, the jet exit conditions (denoted by the

subscript j) b ecom e the conditions before the expansion (subscript 1) and the free-stream pressure p^ is the pressure after the expansion, p 2 . For values of 7jequal to 1.667, 1.38, 1.25 and 1.133, an e xplic it relationship for Av in terms of/3. and P J / P Q , can be det ermined. For these values of 7j , Equations (II-l) and(II-3) reduce to the following:

For 7 = 5/3 = 1.667

B3(II-4)

(II-5) II (/3 2 + 4)-4 .

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I n terms o f /3 j and Equations (II-4) and (II-5) can be combined to give

+ 4) - 4t a n A i =

3/2 O . U

(3/3] + 4) - Sfll < / 3 * + 4) /3j + S B

3 2 \ . 4

(/32 + 4)(3/3] + 4) - 8 3/3| + 4)

II-6)

For 7 = 29/21 =1.38

tanv =(/33 - 1.250) 6. 25 + / 32)* + 3.125/3 + 6.S/33

(6.25 ' + 4 /32) (6 .25 11.25/S2 + 15.625 -

. 276

32 + 6.25) - 6.25 II-8)

For 7 = 5/4 = 1.25

tanv =8B3

27 + 18/32 - II-9)

/3 = f^i 9 ) -9 . 11-10)

For 7 = 17/15 = 1.133

tanv =/93 80 - f i 2 )

256 + 160/32 - 15/3(11-11)

0 . 1 1 7 7(/32 + 16) - 16 (H-12)

Curves showing the effects of jet Mach n u m b e r , M j , and pressure ratio, Pj/Pm .on the tu rning angle of the jet flow, A i^ , for the above values of 7j are presentedi n Figures 1 and 2.

The limiting values of Av which represent the turning angles when exhausting intoa vacuum are shown in Figure 3. These values of k v are approached when consideringproblems associated with the exploration of space (see Ref.45 for example).

I n addition t o t h e parameters ment ioned above (i.e., P J / P O J , y , a n d M,), t h e initialinclination angle o f t h e jet, 8j , also depends o n t h e nozzle ex it angle a n d i sg i v e n b y :

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5

Sj = 0N + A v II-13)

Thus a fourth parameter is available and often used to obtain matched condit ionsof the initial inclination angle of a j e t .

For small values of the angle, Av , the ratio of the free stream static pressureand the jet exit static pressure can be expressed by the following series:

pj

- 27

2D M - 2 M + ( Av )3 + 11-14)

T h e p r e s s u r e r a t i o r a n g e f o r w h i c h E q u a t i o n (11-14) i s a p p l i c a b l e c a n b e d e d u c e d f ro mt he c u r v e s o f F i g u r e 4 . T h e c u r v e s l a b e l e d 1 s t, 2 n d a n d 3 r d ar e ob t a i ne d b y r e t ai n i n gt h e c o r r e sp o n d i n g t e r m s o f t h e e q u a t i o n .

1.2 Jet Boundary Shapes

T h e s h a p e o f t h e j e t b ou n d a ry f o r th e f i rs t f e w d i a m e t e r s d ow n s tr e a m o f t h e nozzlee x i t c a n b e as s u m e d t o b e a f f e c t ed o n l y s l i g h t l y b y v i s co u s e f f e c ts a n d t h e r e f o r e c a nb e d e t e r m i n e d b y i n v i s c i d solutions. T h e m e t h o d o f ch a ra c t er i st i c s i s t h u s g e n e ra l l yu s e d a s a n 'exact' s o l u t i o n f o r th e j et b o u n d a r y a n d v a r i o u s a p p r o x i m a t e t e c h n i q u e sa r e e m p l o y e d t o d u p l i c a t e t h e c h a r a c t e r i s t i c s o l u t i o n .

A p p r o x i m a t e l y 3000 b o u n d a r i e s d e t e r m i n e d b y t h e m e t h o d o f c h a r a ct e ri s ti c s o v e r t h er a ng e o f t h e p a r a m e t e rs u s e d i n t h e p r e v i o u s discussion o f i n i t i a l a n g l e s a r ep r e s e n t e d i n R e f e r e n c e 2 0 . A f ew o f t h e s e a r e r e p r o d u c e d i n F i g u r e s 5 , 6 a n d 7 i no r d e r t o s h o w t h e e f f e c t s o f t h e p a r a m e t e r s .

I t w a s s h o wn i n R e f e re n c e 2 0 t h a t a c i r c u l a r a r c o f constant r a d i u s , R b , p r o v i d e sa n a d e q u a t e a p p r o x i m a t i o n t o t h e j e t b o u n d ar y u p t o t h e p o i n t o f m a x i m u m d i a m e t e rp r o v i d e d t h i s p o i n t c a n b e d e t e r m i n e d i n a d v a n ce . H o w e v e r , n o s u i t a bl e m e t h o d f o ra c c ur a te l y p r e d i c t i n g t h e m a x i m u m j e t d i a m e t e r a n d i t s l o c a t io n h a s a s y e t b e e nd e t e r m i n e d .

T h e r e s u lt s o f a s p r e a d in g s tu d y o f a n a i r je t a t h i g h a l t i t u d e s r e p or t e d i nR e f e re n c e 2 7 i n d i c a t e t h a t a n a p p r o x i m a t e l o c a ti o n o f t h e j e t b o un d ar y c a n b e o b t a in e db y t h e f o l l o w i n g t e c h n i q u e . Wi t h r e f e re n c e t o t h e s k e tc h o v e r l ea f , a f t er d e t e r m i n i n gt h e i n i t i a l i n c l i n a t i o n a n g l e o f t h e je t f r o m E q u a t i o n (11-13), a l i n e i s c o n s t r u c t e dp e r p e n d i c u l a r t o t h i s t a n g e n t t o t h e j et b o u n d a r y. T h e bo u n d a r y r a d i u s , R b , f o r

7j = 1.4 is d e t e r m i n e d f ro m the f o l l o wi n g e q u a t i o n :

(II-15)

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Jet Boundary

Intercepting ShockBoundary

This radius is located along th e pe rpendicu la r and the jet boundary is drawn as acircular a rc . A s su m in g that the radius ratio is proportional to a /Uj for yother than 1.4, Rb fo r other 7, can be obtained by using th e 7 1 =1 .4 r ad iu sr a t io as a r e f e r e n c e v a l u e at a p a r t i c u l a re q u a t i o n (see Eqn.(19) in Ref.27):

a n d s u b st i t u t i n g i n t o t h e f o l l o w i n g

R_ b _r j

(11-16)

O t h e r a p p r o x i m a t e t e c h n i q u e s f o r c a l cu l a ti n g t h e j e t b o u nd a r y e x h a us t i ng i n t o a m e d i u ma t r e s t a re s u m m a r i z e d i n R e f e r e n c e 2 8 .

1.3 I n t e r c e p t i n g Shock B o u n d a r y

T h e j e t b ou n d a ry c a l c u la t i o n s i n R e f e r e n c e 2 0 b y t h e m e t h o d o f c h a ra c t e ri s t ic s a ls od e f i n e d t h e j e t o r i n t e r c e p t i n g sh oc k b o u n d a r y w i t h i n t h e j e t bo u n d ar y. T h i s b o u n d a r y( s e e p r e v i o u s sketch) i s i n i t i a l l y t a n g e n ti a l t o t h e f i n al M a c h l i n e o f t h e e x p a n s i o n f a na n d i s t h e n f o r m e d b y t h e r e f l e c t i o n o f t h e e x p an s i o n f a n w a v e s f r o m t h e j e t b o u nd a ry.

In R e f e r e n c e 28 a c i r c u l a r arc a p p r o x i m a t i o n for the i n t e r c e p t i n g s ho ck (see sketch)i s g i v e n w i t h t h e r a d i u s o f c u r v a t u r e g i v e n b y

= Rh c o s / L t H-17)

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1where u = arcs n .

M2

Thus, again if a method of determining R,, is available, an approximation to the jetshock boundary can be obtained readily.

1. 4 P r i m a r y W a v e l e n g t h o f t h e J e t

Many investigators have att empted to derive an analytical expression for the primarywavelength of a jet, Lj , that is, the length of t he first periodic jet structure.For values of p^/p,,, < 2 the equation given by Pack 16 which is based on linear theoryapplie s satisfact orily, i.e.

P \ - 2 9 1-i ) - 1.205 . (11-18)?o

For higher pressure ratios, purely analytical determinations of the wavelength havebeen unsuccessful. In Reference 20 an empirically det ermined equation for the primarywavelength is given by

L , _ > 0 . 4 3 7 _ -.

-i = 1.52M) + 1.55 (2M? - 1)* - 1d j L J J

- 0.55/Sj + 0 . 51.55

(11-19)

This equation was derive d from a large amount of experime ntal data obtained with highpressure air jets expanding into still air at atmospheric pressure or lower withP J / P O , > 2 It was shown in Reference 20 that the jet nozzle exit angle, $ N , hadl i t t le effect on the primary wavelength.

1 . 5 D i s t a n c e t o t h e F i r s t M a c h D i s c

A method for calculating the distance from the nozzle exit to the f irst Mach disc,Ljuj , has been given in Reference 25. The assumption is made that t he static pressure

immediately downstream of the Mach disc or normal shock is equal to the ambientpressure of the su rroundings, p^ . Thus i f the centerline Mach numb er and pressuredistribut ion, which are identical up to the shock for any fixed nozzle, are known, theshock position can be c omputed.

1 . 6 J e t M i x i n g R e g i o n

A qu alitative pictu re of t he mix ing regions of t he jet exhaust can be obtained byreferring to the sketch overleaf. Immediately downstream of the nozzle, an annularmixing region, I , surrounds a core o f potent ial flow. Region III consists of anentirely turbulent mixing zone in which t he velocity profiles across the jet are

similar. Region II in turn represents a transition zone between t he conditions at Iand III.

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F o r a s u p e r s o n i c j e t , a t t e mp t s h a v e b e e n m a d e t o c o r r e l a t e t h e so u n d p o w e r b ya d d i n g a s u i t a b l e f a ct o r t o t he L i g h t h i l l p a r am e t e r t o a c c o u n t f o r t h e n o i s e g e n e r a t e di n t h e s u p e r s o n i c p o r t i o n o f t h e jet. T h e s e c o r r e l a t i o n s a r e s t i l l n o t v e r y s a t i s-f ac to ry.

2 . J E T S E X H A U S T I N G I N T O A M O V I N G S T R E A M

T h e g e n e r a l i z e d f l o w p a t t e r n o f a n u n d e r - e x p a n d e d a x i s y m m e t r i c j e t w i t h a n e x itnozzle d i a m e t e r e q u al t o t h e b a s e d i a m e t e r e x h a u st i n g i n t o a st r e am m o v i n g f a st e rt h a n t h e s p e e d o f s o u n d (M^ > l ) i s s h o w n i n t he s k e t ch b e l o w :

ON-, 1J

J et Shockr

Je t Boundary

R e f l e c t e d Shock

x i t S h o c k T r a n s m i t t e d S h o c k

O n e m e r g i n g f r o m t h e n o z z l e , t h e e x p a n d i n g j e t s e t s u p a d i s t u r b a n c e i n th e e x t e r n a lf l o w p r o d u c i n g a n e x i t shock. T h e p r e s s u r e a t t h e j e t b o u n d a r y j u s t a f t o f t h e nozzlel i p , P 2 , i s a ba l an c e b e t w e e n t h e e x t e r n a l p r e s s u r e d o w n s t r e a m o f th e s h o c k w a v ec a u se d b y t h e d e f l e c t i o n a n g l e , S j , a n d t h e j e t p r e s su r e d o w n s t re a m o f t h e e x p an s i onf a n t h r o u g h the a n g l e , A v . The p r e s s u r e a l o n g the jet b o u n d a r y, p b , a l so v a r i e si n t h i s c as e b e c a u s e o f t h e c h a n g i n g s l o p e o f t h e b o u n d a r y a n d t h e t h r e e - d i m e n s i o n a lf l o w e f f e c t s . T h e j e t s h o c k r e m a i n s i n t h e f o r m o f a shock d i a m o n d a t p r e s s u r e r a t i o sh i g h e r t h an f o r th e case o f t h e a m b i e n t m e d i u m b e c a u se o f t h e i n c r e a s e i n p r e s s u r ea t t h e j e t b o u n da r y. D e p e n d i n g o n t h e co n d i t i o n s i n t he t w o s t re a m s t h e j e t s h oc k i sp a r t i a l l y r e f l e c t e d a t t h e b o u n d a r y. T h e p e r i o d i c s t ru c t ur e o f t h e j e t i s m u c h l es sd e f i n e d a n d i n m o s t cases n o t p r e s e n t a t all.

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10

As a first approximation, the flow pattern in the vicinity of a blunt-based bodyi n a moving s tream can be considered as a combination of a sharp base jet exhaustinginto a m e d i u m at rest and a moving stream. Up to a streamline separating the movingstream from t he quiescent m e d i u m in the base r e g i o n , the flow pattern is similar t othat of a jet exhausting into t he m e d i u m at rest. Beyond this streamline the externalflow experiences an exit shock resulting in a flow pattern as desc ribed above. Thepressure at the base of the model is of course dependent upon t he jet and free-streamconditions and should be det ermined by the methods out lined in Reference 5 when anaccurate representation of the flow pattern is desired.

2.1 Initial Inclination of the Jet Boundary

Conditions at the jet boundary immediately downstream of t he nozzle exit aredepicted in the following sketch:

M

Conditions in the jet or expansive flow are s t i l l governed by Equations (II-l), (II-2)and (II-3). For the external or compressive flow, conditions are governed by thefollowing equation:

t an

which for 7 = 7/5 = 1 . 4 reduces to

tan 8. =

/ P2 \fe- 1 00 /7ajM 2 _ /Pj _

\POO

27JW

7oo^

7 - 1) - (7o,

P2

+ 1) + (7oo -Poo

P2 1)

1) _ a

(11-23)

(11-24)

When # N = # B = 0 then Av and Sj must be equal and the conditions exist ing at thenozzle exit are obtained by equating, for e x a m p l e , Equations (II-6) and (11-24).Such solutions have been obtained for various jet conditions exhausting into a streama t Mach numbers greater than 1.0 with y ^ = 1.4 , and # N = 6 - 0 . The results

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1 1

showing t he effect s of the various jet and free stream conditions are shown inFigures 10, 11 and 12.

For small values of the angle, 8, , the ratio of the pressures across the shocki n the ex ternal flow is given by

Pooor

=

J

P (n . 26)

Po

To the first order (see Eqn. (11-14)), conditions in the expansive flow are relatedto Av by the expression

Av = P2

(11-27)

Equating the ex pressions for 8, and Avconditions exist ing at the nozzle exit.

gives the following relationship for the

- P 2 _

P 2 - P c

(11-28)

2.2 Jet B o u n d a r y Shapes

As in the case of a je t expanding into a quiescent medium, the method of character-

istics can be used to determine t he boundaries for a jet exhausting into a streammoving with M^ > 1 . For a jet expanding into a mov ing stream, conditions a t theboundary cannot be considered under a constant pressure but must be determined by theinteraction of the jet and external stream. If the stream flow is hypersonic, theNewtonian approximation can be used to determ ine the jet boundary pressure. Thiscondition is represented by

Po os in 28 + 1 (11-29)

The results of calculations of jet boundaries using the method of characteristics forthe jet flow and the ab ove boundary conditions are presented in Referenc e 21.

Representative boundaries obtained from this Report are reproduced in Figure 13.An approximate technique e mploying this s ame boundary condition is presented in

Reference 29. In this met hod, one-dimensional flow theory in conjunction withNewtonian theory is used to define the jet structure. A comparative boundary withthat obtained by the method of characteristics is shown as the dashed curve inFigure 13.

The jet boundaries calculated by each of the above methods represent the d i v i d i n gstreamlines between the jet and the exte rnal stream. Comparison with ex perimentalboundaries, which are wide mixing regions are shown by the schlieren photograph inFigure 14 obtained from Reference 29. is therefore rather difficult. In order to

obtain a more meaningful comparison, the jet shock boundary can be comput ed from thejet boundary by a method contained in Reference 28. The method consists of determ iningthe local Mach l i n e at each calculated boundary point for the jet flow. Thecoalescence of these Mach lines specifies the shock location. The results of such

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12

a n analysis as obt ained from Reference 29 are shown in Figure 15. The flow field isrepresented by the photograph and jet boundary shown in Figure 14. As is apparentfrom the plot, a close approximation betwe en the c alculated and experimental jetshock is obtained.

2.3 Jet Mix ing Region

For the case of a jet exhausting into a moving stream, t he velocity profile in them i x i n g zone corresponding to Equation (11-19) can be approximated by

u 1 + U.J u, - u,,, / ru = -J 1 + -2 e r f c r

2 [_ "j + a, \ x

where Uj = the je t free stream velocity

u^ = free stream velocity of the moving stream.

T h e value o f c r suggested b y Golik 37 i s g i v e n by

12

(11-30)

o - =

+ 2.758M 1 (II-31)

1-^UJ

where U j > .

2.4 Jet Shock Reflection

On the basis of linearized theory, the following paramete r was derived in Reference17 to indicate the st rength of the transmitt ed shock (see sketch on p. 9):

(11-32)

When k = l , the jet shock is not reflected at the jet boundary and no periodicbehavior of the jet is noticeable. When the ratio increases or decreases from unity areflected wave of increasing mag nitu de occurs. For k > i , the boundary exhib its a

periodic behavior.

A s imilar parameter i s derived in Reference 19 and is discussed in Reference 20 ast h e Kawamura parameter given by

\ = - sinM COSM = ; (11-33)

The difference in the value of this parameter betw een the jet and free stream flowsdetermines the c haracter of the jet shock reflection. If V, is larger than A^(where the values of the parameter are t he local value s at the interface) a compression

wave reflects as a compression wave, while if \ m is larger than k . a compressionw a v e reflects as an expansion wave.

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13

I I I . S C A L I N G P A R A M E T E R S

I n g r o u n d t e s t f a c i l i t i e s , i t i s m a n y t i m e s necessary o r m o r e c o n v e n i e n t t o per-fo rm j e t t e s t s w i t h t e s t f l u i d s o f d i f f e r e n t c o m p o s i t i o n a n d w i t h t e st m o d e l s o fd i f f e r e n t s i ze f r om t h o se o f t h e a c t u a l v e h i c l e . T h us , i t b e c o m e s necessary t o d e t e r m i n es c a l i n g p a r a m e t e r s f o r w h i c h t h e r e s u l ts o b t a i n e d w i t h t h e t e st m o d e l a r e s i m i l a r t ot h o s e o f t h e f u l l s c a l e v e h i c l e .

T h e e q u a t i o n s g o v e r n i n g t h e b e h a v i o r o f t h e i n t e r a c t i n g j e t a n d f re e s t r e a m f l o w sa r e a t b e s t v e r y a p p r o x i m a t e . T h us , t h e us e o f t h e s e e q u a t i o n s i n d e r i v i n g s i m i l a r i t yp a r a m et e r s i s l i m i t e d . A d i m e n s i o n a l analysis o f a l l o f t h e v a r i a b l e s i n v o l v e d (seeRef.2) l e a d s t o a h o s t o f p a r a m e t e r s o f w h i c h m a n y a r e r e l a t i v e l y u n i m p o r t a n t . I nw h a t f o l l o w s, t h e r e f o r e , o n l y t h o s e s c a l in g p a r am e t e r s , o r m o r e a c cu r a te l y e q u i v a l e n c er e la t i on s h ip s , a r e d i s c us s ed w h i c h h a v e b e e n s ho w n o r i n t u i t i v e l y a p p e a r t o b e i m p o r t a n tin t h e s i m u l a t i o n o f j e t e x ha u st s .

I n a n y g i v e n p r o b l e m , o n l y c e r ta i n s c a l i n g p a r a m e t e r s a r e i m p o r t a n t . F o r e x a m p l e ,w h e n d e t e r m i n i n g t h e e f f e c t s o f a je t e x h a u s t o n b a s e p r e s s u r e , t h e p a r a m e t e r sg o v e r n i n g t h e s h a p e o f t h e i n i t i a l p o r t i o n o f t h e j et a r e m o r e i m p o r t a n t t h a n t h o s eg o v e r n i n g t h e j et s h a p e f a r d o w n s t r e a m . T h u s , a n e v a l u a t i o n m u s t b e m a d e o f t h eo b j e c t i v e s o f e a c h s p e c i f i c t e s t i n o rd e r t o d e t e r m i n e t he e x t e n t o f s i m u l a t i o nr e q u i r e d .

3 . J E T B O U N D A R Y S I M U L A T I O N

I n R e f e r e n c e 2 0 i t w a s s h o w n t ha t , i n o r d e r t o o b t a i n j e t b o u n d a r y s i m u l a t i o n , t h ei n i t i a l i n c l i n a t i o n w a s t h e m o s t i m p o r t a n t p r o p e r t y t ha t m u st b e d u p l i ca t e d . S i m u l a -t i o n o f t h e i n i t i a l p o rt i o n o f t h e j e t b o un d a r y w o u l d b e i m p o r t a n t i n s t u d i e s t od e t e r m i n e ba s e p r e s s u r e , b a s e h e a t i n g , o r t h e e f f e c t s o f t h e e x i t s h o c k o n a d j a c e n tsurfaces or jets.

F o r s m a l l t u rn i n g a n g le s , s i m i l a ri t y p a r a m et e r s w h i c h p r o v i d e t h e s am e f l ow t u r n i n ga n g l e f o r t h e m o d e l a n d f u l l s ca l e t e s t s c a n b e o b t a i n e d s t a r t i n g w i t h E q u a t i on (11-14).I f a f r e e c h o i c e o f a n y o f t h e t h r e e v a r i a b l e s i s a l l o w e d , t h e n t h e f i r st o r d e r t e r mo f E q u at i o n (11-14) i n d i c at e s t h a t t h e f o l l o w in g r e l a t i o n s h i p b e t w e e n t h e m o d e l a n df u l l s c al e t e s t s m u s t be s a t i s f i e d to p r o v i d e i d e n t i c a l f l o w t u r n i n g a n g l es , A v :

I f i t is as s um e d a s i n R e f e r en c e 4 6 t h a t t h e je t M a c h n u m b e r o f t h e m o d e l , MJ mi s t h e s am e a s t h e j e t M a ch n u m b e r o f t h e f u l l s ca l e v e h i c l e , M J f , t h e n t h e f o l l ow i n gr e l a t i o n s h i p i s o b t a i n e d :

(IH-2)

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t h e j e t b o u n d a r y. Such s i m u l a t i on r e q u i r e s t h e d u p l i c a t i o n o f t h e p a ra m e t er g i v e n i nE q u a t i o n (11-32). The s i m u l a t i o n p a r a m e t er t h u s o b t a i n e d is g i v e n by :

U s i n g t h e as s u m p t i o n t h a t t h e f r e e s t re a m c o n d i t i o n s f o r y m a n dtests a re i d e n t i c a l t o t h o s e i n f l i g h t , t h e p a r a m e t e r r e d u c e s t o

P c o / 3 .

IH-7)

for the model

III-8)

I f t h e as s u m p ti o n i s a ls o m a d e t h a t t h e m o d e l a n d f u l l

scale s t at i c p r e s s u r e r a ti o i s

m a t c h e d , t h i s p a r a m e t e r a l s o r e d u c e s t o t h a t g i v e n b y E q u a t i o n (III-3) o r t h a t g i v e nby the K a w a m u r a p a r a m e t e r , E q u a t i o n (11-33).

5 . S I M U L A T I O N O F J E T F L O W P A R A M E T E R S

I n t h i s s e c t io n r e l a t i o n sh i p s a r e d e f i n e d w h i c h g o v e r n t h e s i m u l a t i o n o f t h e v a r i o u sjet f l o w p a r a m e t e r s (see Ref.48). The e x p r e s s i o n s are d e r i v e d by r e l a t i n g the jetf l o w p a r a m e t e r s t o s i m i l a r f r e e st r e am p a r a m e t e r s.

5.1 Jet Mass F l o wT h e s i m u l a t i o n p a r a m e t e r f o r t h e mass f l o w characteristics i s o b t a i n e d b y r e l a t i n g

t h e j e t mass f l o w t o a r e p r e s e n t a t i v e f r e e s t re a m mass f l o w. I n e q u a t i o n f o r m ,

(III-9)

T h e r e s u lt i n g s i m i l a r i t y p a r a m et e r i s t h e r e f o r e

~Aj2p]7JM|(RT)

J_ lm

(111-10)Uf

I n a d di t i o n t o t h e p a r a m e t e r s i n v o l v e d i n t h e s i m u l a t i o n o f t h e je t b o u n d a r y a n d j e ts h o c k , a r e q u i r e m e n t t h a t (RT)j o f th e m o d e l b e r e l a t e d t o t h a t o f t h e f u l l s c a l ee n g i n e i s o b t a i n e d .

5 .2 Je t K i n e t i c E n e rg y

D u p l i c a t i o n o f t h e k i n e t i c e n e r g y p e r u n i t mass i s o b t a i n e d b y s i m u l a t i o n o f t h ev e l o c i t y r a t i o o f t h e j e t a n d f r e e streams. I n e q u a t i o n f o r m ,

7 00 M2(RT) 00

(III-ll)

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The resulting similarity parameter becomes

(111-12)

For matched conditions of the free stream parameters, the parameter reduces to

5.3 Je t I n t e r n a l Energy

Duplication of t he internal energy per unit mass is obtained by simulating thefollowing relationship:

(c vT)j _ (7 CO-1)(RT) J

(CyT). (7 j -D(RT) OD

which gives the following simulation parameter:

(111-14)

(7oo-D(RT)

(7j-l)(RT) co

(7oo-D (RT)

(7 j -D(RT) 00(111-15)

5.4 Je t E n t h a l p y

Duplication of the enthalpy per unit mass is obtained by s imulating the followingrelationship:

(111-16)

which gives the following simulation parameter:

7 00 -l)7j RT) j 7

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5.6 Je t Thrus t

T h e r e l a t i on s h i p f o r t h e s i m u l a ti o n o f t h e j e t t h r u s t i s o b t a i n e d b y s t a r ti n g w i t ht h e j e t t h r u s t c o e f f i c ie n t d e f i n e d b y

w h e r e th e t h r u s t i s g i v e n b y

F, = (pi^A), + (p, - Pa,)A, .J J J J

T h e s i m u l at i o n p a r a me t e r t h u s o b t a in e d i s g i v e n b y

(1 + 7jMj) - 1P m

J J

(111-20)

(111-21)

(111-22)

6 . B A S E H E AT I N G S I M U L AT I O N P A R A M E T E R S

M u c h e x p e r i m e n t a l a n d s o m e t h e o r e t ic a l w o rk h a s b e e n d o n e r e c e nt l y o n t h e p r o b l e m sassociated w i t h t h e ba s e h e a t i n g o f r o c k e t - p o w er e d mode l s . A gene ra l discussion o ft h e i m p o r t a n t s i m u l a t i o n p a r a m e t e r s i s p r e s e n t e d in R e f e r e n c e 4 9 . I n a d d i t i o n tot h o s e p a r am e t e r s a l r e a d y d i s c u ss e d w e r e t h e j e t e m i s s i v it y, j e t - t o - b a s e f o r m f a c t o r,e n g i n e e f f i c i e n c y, nozzle w a l l c o o l i n g e f f e c t s , f u e l d i s t r i b u t i o n p a t t e r n , f l a m e s pe e da n d i g n i t i o n d e l a y characteristics o f t h e e n t r a i n e d f u e l a n d o t h e r associated p rope r t i e s .

S i m i l a r i t y p a r a m e t e r s c o n c e r n i n g t h e base f l o w p a t t e r n s a r e d e r i v e d i n R e f e r e n c e4 7 . T h e r e s u l t i n g r e l a t i o n s h i p s a r e r e fe r red t o a s a n e x ce s s p u m p i n g mass p a r a m e t e r

A v . _ (pu)j p u dr(111-23)

a n d a j e t b o u n d a r y s t r e a m l i n e to t a l p r es s u r e h e a d p a r a m e t e r

p t (rj) P(rj)[u(rj)]2

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v i s c o s i t i e s , m o m e n t u m s , a n d h e at transfer r a t e s o f t h e l oca l e l e m e n t s o f t h e f low a tt h e j e t boundary. I t w o u l d a p p e ar t h e r e f o r e t h a t s i m u l a t i o n o f t h e m i x i n g processesw o u l d b e g o v e r n e d b y t h e d e g r e e o f s i m u l a t i o n o f t h e j e t f l o w p a r a m e t e r s discus sedin S e c t i o n 111-5 .

8 . J E T N O I S E S I M U L AT I O N

The simulation parameter for the noise generated in the f ar field of a subs onicj e t a n d a p o r t i o n o f t h e s u p e r s o n i c j e t c a n b e d e r i v e d f rom E q u a t i o n (11-22). T h efollowing paramete r is obtained for the correlation of sound power:

(RT)

y l 12 (RT)] /2 111 -25 )

For matched conditions of the free stream conditions the parameter reduces to

m = [ Aj 7JMJ RT)j] f . (111-26)

Thus, under these conditions the jet sound power is proportional to the jet kineticenergy.

A summary of the scaling parameters discussed in the prec eding paragraphs ispresented in Table I. An examination of the general s imulation parameters for the

various j et characteristics reveals that t he pressure ratio function varies appreciablyamong the relationships. It would appear therefore that a matc hing of this parameterbetween model and full soale tests is ess ential for good s imulation. As pointed outpreviously, the free stream conditions of 7,,., and MO , for the full scale article canbe duplicated with relative ease f or a model in ground test facilities. If it isfurther assumed that the other free stream c onditions are matched, the simulationparameters redu ce to those shown in the second column of Table I. Under these condi-tions, besides matching the initial inclination angle of the jet exhaust, 8simulation of the parameterstests appears desirable.

and between model and f u l l scale

As mentioned in the introduction to t his section, a complete simulation of all ofthe parameters listed in Table I is not required for all jet tests. In the followingsect ions, the jet effec ts are separated into exit effects and downstream effects.Conditions at the base of the model wou ld appear to depend primarily upon t he initialshape of the jet at the nozzle exit. Thus duplication of the initial inclinationangle of the jet, 8. , would suffice for base pressure studies. In addition, forbase heating (temperature) studies, duplication of the jet temperature would berequired. In studies in which model surfaces are located within or near to the jetstream duplication of the jet flow properties would have t o be considered. Thus athorough examination of the test objectives is required in order t o specify whic hsimulation parameters mus t be duplicated.

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I V. M E T H O D S O F J E T S I M U L A T I O N

Various methods are in use for the ex perimental simulation of an exhaust jet inground test facilities. These vary in complexity from the us e of simple cold gas jetst o an almost exact duplication of the full scale jet. The degree of similitude used orr e q u i r e d depends on the particular problem under investigation. Some of the t echniquesw h i c h have been employed o r proposed a r e discussed i n t h e following paragraphs.

A p p r o x i m a t e values f or the properties of turbojet, ramjet, and.rocket exhausts arel i s t e d in Table II. The ramjet properties are also typical of an after-bu rning turbojet.As will be discussed in the f ollowing sect ions, the simulation of these properties ist h e goal o f t h e other m edia listed i n t h e Table.

9 . C O L D G A S J E T S

The use of a cold gas for the simulation of a jet exhaust has the primary advantageo f relative simplicity in set -up and operation. Cold gases are particularly appealingwhen t h e simulation o f j e t t emperature i s considered o f little importance.

9 . 1 A i r

Since high pressure air supplies are most commonly available, the use of cold airhas found wide application for jet studies. As seen in Table I I , only the value ofR is in the same range of the properties of the jet exhausts which must be duplicated.

9.2 H e l i u m

Cold helium has been used in many studies (see Refs.51 to 53) because the highvalue of its gas constant, R , allows for an almost exact simulation of the value of(RT)j f or a ramjet or afterburning turbojet. As shown in Section III-5, the simula-tion of (RT)j is important for the duplication of jet flow parameters. The h i g h valueof the ratio of specific heats for cold h e l i u m , however, is a prim e disadvantage.

9.3 C a r b o n D i o x i d e

The value of the ratio of specific heats of carbon dioxide makes its use attractive

for a simulation me dium. The low value of its gas constant is, h o w e v e r , a disadvantage.This medium was used in the studies reported in Reference 54 at a t emperature of580R so that it s value of 7 matched that of a hot jet of burning hydrogen and airat 2600R.

1 0 . C O L D G A S M I X T U R E S

I n the stu dies reported in Reference 53, a cold mixt ure of hydrogen and carbond i o x i d e was used as the jet fluid. The mixtu re used (.46 H 2 and .54 C0 2) provided aduplication of (RT)j f or the ramjet conditions as did the use of helium. The value

of the ratio of specific heats although lower than that of the helium j e t , was stillhowever above that required f o r exact simulation.

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The proportions of hydrogen and carbon dioxide requ ired t o simulate (RT). for aturbojet exhaust were computed and listed in Table II. For a rocket exhaust thevalue of (RT)j is almost identical to that of cold hydrogen. In each case, however,the valu e of 7j for the simulation f luid is higher than that of the engine exhaust.

I n the study reported in Reference 55, it was s hown that by t he addition of a thirdgas t o hydrogen and carbon dioxide bot h t he (RT), and y ^ of a turbojet exhaust couldb e simulated. For the case cited in Table II, ethane. C 2H6 , was used as the third gas.It was stated in Reference 55 that the u pper temperature l i m i t for which completesimulation is possible with a cold (T, = 530R) gas mixture is on the order of 1650R.By heating the mixture somewhat, simulation for higher temperatures could be achieved.

1 1 . H O T G A S J E T S

The properties of a jet exhaust can be simulated mu ch more closely with a hotrather than a cold gas stream. However, the complex ity in providing a hot gas jet isincreased considerably over that of a cold gas jet.

1 1 . 1 H o t A i r

The properties of a hot air jet at a temperature (3300R) corresponding to that ofa ramjet or after-burning tu rbojet exhaust a re shown in Table II. As a result o fheating t he air, the ratio of specific heats approaches that of the jet exhaust muchmore closely than does that of a cold air jet giving close s imulation of (RT), and

11.2 H y d r o g e n a n d A i r

The us e of a burning mixt ure of hydrogen and air was used in the studies reportedi n References 53 and 54 to duplicate t he properties of an after- burning turbojet.Since t he resulting jet properties at a temperature of 3300R are typical of those ofa ramjet or after-burning turbojet, they were chosen to represent the properties of aramjet exhaust in Table II.

11.3 H y d r o g e n P e r o x i d e

The development of a hydrogen peroxide simulator for jet exhaust tests is describedi n Reference 56. The characteristics of the simulator exhaust using hydrogen peroxideof 90 per cent concentration (10 er cent pure H 20) are shown in Table II. As pointedout in Reference 56, the system is mu ch simpler and easier to operate t han a burninggas. In addition, the product s of decomposition, steam and oxygen, are muc h safer tohandle in ground test facilities. ^

11.4 T u r b o j e t S i m u l a t o r

A simulation device described in Reference 57 uses a turbojet combustor for theduplication of a jet exhaust. Such a d e v i c e , frequently employed, burns a mixture of

a hydrocarbon fuel and air. The jet properties can be adjusted to closely simulatethose of a turbojet or ramjet exhaust.

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1 2 . R O C K E T M O T O R S I M U L A T O R S

In order to achieve the duplication of the h i g h temperature of a rocket exhaust(see Table II), resort is made to the use of scaled rocket motors for jet simulation.Both solid and liquid propellent engines are used. Results are presented in Reference58 wherein a liquid propellent rocket engine operating on gaseous oxygen and hydrogenwas used. A combination of l i q u i d oxygen and jet engine fuels has also be en usedsuccessfully.

I n References 48 and 59, turbojet exhaust simulators are described wherein solid-propellent rocket motors are used to simulate the exhaust jet. The characteristicsof one of these rocket motors, a JATO unit, are shown in Table II.

A number of m ethods are employed to introduce the s imulation fluids into the model.The most widely used method is to mount the model from a side strut and use the insideo f t h e strut t o duct t h e fluids. A second t echnique wherein h i g h pressure a i r i sducted through a sting support and discharged in such a way as to duplicate a jetexhaust is described in Reference 60. A similar technique developed for use for shortr u n t i m e a t hypervelocities i s described i n Reference 6 1 . A third met hod (seeRef.62) which can be used for jet studies utilizes a duct extended t hrough the windtunnel nozzle from the upstream stilling chamber. The use of a strut or a sting isthus entirely avoided. Such a method is appealing for transonic studies where strutinterference problems are especially troublesome. For missile studies, the duct canalso be used to simulate the ve hicle body.

The recent interest in space exploration has provided a requirement for a lowpressure environment for an emerging jet and stimulated the development of such testchambers. Test cells us ing cryopumping to provide near vacuum conditions are beingd e v e l o p e d at a rapid rate. Anothe r novel techniqu e (see Ref.63) using an existingw i n d tunnel utilizes t he low pressure environment e xist ing downstream of a blunt basem o d e l m p u n t e d in a supersonic w i n d tunnel as the simulated test chamber.

V . E X P E R I M E N T A L R E S U L T S

Numerous studies (Refs.3 to 10) have been made to determine the effects of a jetexhaust on base pressure, stability, drag, interference w i t h nearby wings and control

surfaces and other aerodynamic and thermodynamic phenomena using t he techniquesdescribed in the preceding section. However, very f ew systematic investigations haveb e e n undertaken to determine the reliability of these techniques for the particularp r o b l e m s under study. In the following sections, only those data are presented whichindicate t h e sensitivity o f t h e je t flow properties i n simulating actual flow condi-tions.

1 3 . J E T E X I T E F F E C T S

Jet exit effects are defined as those effects which should be affected little by

the mixing process and therefore should be amenable to prediction by inviscid theoriesa n d to simulation by parameters derived t herefrom.

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The relative location of t he shocks and boundaries were deduc ed from the pressuredata. A typical plot showing the effect of the exit shock on the pressure orificelocated 3.47 je t diameters downstream of the jet exit, as obtained from Reference 54.is shown in Figure 20. The dashed curve is obtained from the

7, = 1.66 resu lts

using the assumption that nozzle conditions whi'ch yield the same value of the initialinclination angle of the jet produce the same pressure coefficient.

1 4 . D O W N S T R E A M E F F E C T S

Jet characteristics which would appear to be affected by the mixing at the jetboundary are considered in the following paragraphs.

14.1 T r a n s m i t t e d Shock P o s i t i o n

I n a manner s imilar to that us ed to obtain the effects of the ex it shock (seesketch in Section V - 13.3), data w ere also obtained in References 52 and 53 to deter-mine the effects of the transmitted jet shock. A typical plot showing the effects ofthe transmitted shock on a pressure orifice located 7.63 je t diamete rs downstream oft h e je t e x i t is shown in Figure 21. As the pressure ratio is increased, the shockmoves from a position ups tream to a position downstream of the pressure orificebecause of the increase in the jet primary wavelength, L, , with a resu lting decreasei n t he pressure coefficient. As shown in Table II, the value of y , is identicalfor the air and H 2 + C0 2 mixt ure, while the value of (RT)j is essentially the same fo rt h e helium and H 2 + C0 2 mixtures. By c orrecting the helium results to a y , - 1.40to account for the diffe rence in the initial inclination angle of the jet gives goodagreement with t he H 2 + C0 2 results for shock position. Although the initial inclina-tion angles for the air and H 2 + C0 2 mixtu re should be identical, the difference inshock position is probably a result of t he differenc e in mix ing caused by the largedifference in the value of (RT)j bet ween these media.

14.2 Tr a n s m i t t e d Shock S t r eng th

The difference in the l e v e l of t he values of the pressure coefficient in Figure 21before and after the transmitted shock passes over the pressure orifice indicates adifference in the strength of this shock betw een the helium jet and the air andH2 + C0 2 mixture jets. The ratio of these differences for the case shown is approx-imately proportional to the ratio of t he values of the similarity parameter given byEquation (III-7). In the case of the helium jet the reflected shock (see sketch inSection V - 13.3) is of greater magnitu de than t hat of the H 2 + C0 2 and air jetswhich in turn reduces the strength of the transmitted shock.

14.3 T r a n s m i t t e d Shock A n g l e

The results of References 51 to 54 for free st ream Mach numb ers of 1.1 to 2.02indicate that the angle whic h the transmitted shock makes with the cente rline of thejet is very nearly equal to the Mach angle based on the free stream Mach number. Itshould be noted, however, that t hese investigations were limite d to jet pressure ratiosless than 10.

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14.4 Je t B o u n d a r y Shape

The relative locations of the jet boundaries for the Reference 53 results shownpreviously see sketch in Section V - 13.3) can be deduce d from the shock positions.The H 2 + C0 2 mixtu re boundary would be largest, followed by the air and heliumboundaries respectively. The fact that the positions of both the jet and the trans-mitted shock for the helium jet c an be made to agree with t he positions of theseshocks for the H 2 + C0 2 mixture by correcting for the difference in the initialinclination angle of the jets, indicates that these boundaries would be identical ifcompared using t he same e xit angle conditions. For these jets, the values of (RT) 1are approximately equal. Since 7j for the H 2 + C0 2 mixture and air are the same,the diff erence in the jet boundary shape is attributed to the difference in (RT),between the jets see Table II).

The results of other invest igations see Refs.68 and 69) also indicate a slight

increase in the rate of mix ing as the value of (RT), is increased.

14.5 J e t M o m e n t u m E f f e c t s

The importance of simulating the jet momentum is discussed in Reference 62 .Results obtained from subsonic tests are presented, which indicate that t he downwashangle and the drag of an airfoil in the wake of a jet exhaust are both independent oftemperature w hen the momentum is maintained constant.

VI. DISCUSSION

I n keeping with the previous Section, the discussion of the results will beseparated into the categories of jet exit effects and downstream effects. Thesecategories can also be thought of as those effects which are not affected by jetmixing and those which are affected by mixing.

15. JET EXIT EFFECTS

As pointed out in Reference 20 and discussed in Section II, matching of the initialinclination angle of the jet, 8, , is the most important requ irement in order to

duplicate jet ex it effects bet ween a model and full scale vehicle. The results of theprevious Section and of many investigations show that this angle can be predictedaccurately by the Prandtl-Mey er equ ations for a two- dimensional expansion seeSection II - 1.1).

The results shown previously also indicate that base pressure results and dataaffected by exit shock position can be correlated among tests conducted with variousje t media. These correlations are obtained by assuming that nozzle conditions whichg i v e the same initial inclination angle of t he jet produce identical results.

No satisfactory similarity paramet er has been deriv ed to provide an expression

relating all of the parameters which affect the initial inclination angle of a jet.A free choice of t hese parameters to obtain s imilarity is provided, however, by usingdata such as presented in Figures 1,2,10,11 and 12. Some measure of success in jetflow studies has been achieved b y duplicating the jet pressu re ratio, P/Pa, .

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nozzle b o a t- t a i l a n g l e , # N . and the f r ee s t r e a m f l u i d p r o p e r t i e s and u s i n g the s i m i -l a r i ty p a r a m e t e r 7jMj/& g i v e n b y E q u a t i o n (III-3) t o accoun t f o r t h e d i f f e r e n c e i ny, of the jet m e d i a .

From t h e f o r e g o i n g , t h e r e f o r e , i t d o es a p p e a r t h a t j e t e x i t e f f ec t s o b t a i n e d f r omm o d e l tests c a n b e u s ed w i t h s o m e m e a s u r e o f c o n f i d e n c e i n p r e d i c t i n g f u l l s c a leresults.

1 6 . D O W N S T R E A M E F F E C T S

T h e results p r e s e n t e d i n S e c t i o n V , a l t h o u g h l i m i t e d i n s c op e , i n d i c a t e t h a t i fthe j e t i n c l i n a ti o n a n g l e a n d (RT)j a r e m a t c h e d t h e j et b o u n d a r y s h ap e a n d t h e p o s i t i o no f t h e t r a n s m i t t e d shock w i l l b e d u p l i c a t e d , p r o v i d e d f r e e s tr ea m c o n d it i o n s a r em a t c h e d . T h e s t re n g t h o f t h e t r a n s m i t t ed s h oc k h a s b e e n shown t o b e a f u nc t io n o f t h eK a w a m u r a p a r a me t e r , A/7jMj 2 . Wi t h all o t h e r c o n d i t i o ns t he s a m e , an i nc rease in(RT), , w h i c h r e p r e s e n t s a n i nc rease i n j e t v e l o c i t y, p r o d u c e s a n i n c r e a s e i n t h e j e tboundary.

A l t h o u g h m a t c h i n g o f (RT), a p p e a r s t o p r o v i d e a m e a n s o f s i m u l a t i n g t h e m i x i n gb o u n d a r y, n o c o r r e l a t i o n p a r a m e t e r s a r e a v a i l a b l e f or u s e i n p r e d i c t i n g f u l l s c a l eresults f r o m d a t a o b t a i n e d a t u n m a t c he d c o n d i t i o n s o f (RT)j.

W h e n w i n g o r t a i l surfaces a r e i m m e r s e d i n o r p l a c e d n e a r t o t h e j e t e x h a u s t ,d u p l i c a t i o n o f t h e j et m o m e n t u m h a s b e e n s h o wn t o be a n i m p o r t a n t e q u i v a l e n c e p a r a me t e r.A l t h o u g h m o s t o f t h e j e t p r o p e r t i e s s u c h a s v e l o c i t y, t e m p e r a t u r e a n d m a s s f l o w va r y

d o w n s t r e a m o f t h e je t e x i t , t h e j e t m o m e n t u m r e m a i n s c o n s t a nt a n d t h e r e f o re a p p e a r st o b e t h e m o s t c r i t i c a l j e t f l o w p r o p e r t y f o r s i m u l a t i o n .

1 7 . A D D I T I O N A L R E M A R K S

From t he f o r e g o i n g i t i s a p p a r e n t t h a t a l t h o u g h m a n y t h e o r e ti c a l an d e x p e r i m e n t a ls t ud i es h a v e b e e n m a d e t o d e f i n e t h e j e t c h a r a c t e r i s t i c s , f e w s y s t em a t i c i n v e s t i g a t i o n sh a v e b e e n m a d e t o d e t e r m i n e s i m u l a t i on p a r a m e t e r s a n d t h e f e a s i b i l i t y o f v a r i o u se x p e r i m e n t a l t e c h ni q u e s . O n t h e b a s i s o f t h e e x i s t i n g d a t a , t h e j e t p r e s s u r e r a t i oIs shown t o h a v e t h e g r e a t e s t e f f e c t o n p e r f o r m a n c e characteristics. C e r t a i n c h a r a c -

t e r i s t i c s a r e a f f e c t e d b y c o n d i t i o n s i n t he i m m e d i a t e v i c i n it y o f t h e base. T h e s econditions i n t u r n a r e shown t o be a f f e c te d m o s t b y t h e i n i t i a l i n c l i n at i o n a n g l e o ft h e jet . Characteristics a ffec ted b y d o w n s t r e a m j e t c o n d i t i o n s a r e s een t o b ed e p e n d e n t u p o n t h e p a r a m e t e r s , 7jM?/A a n d (RT)j a n d t h e j et m o m e n t u m .

O f t h e c o l d g as m e d i a l i s t e d i n Ta b l e I I , s i m u lt a n e o u s d u p l i c a t i o n o f 7j an d(RT), is p o s s i b le o n l y w i t h a 3 - c o m p o n e n t m i x t u r e . Use of such a gas w o u l d of c o u r s ea l l o w e x a ct d u p l i c a t i o n o f a j e t e x h a u s t w i t h o u t t h e a d j u s t m e n t o f a n y o f t h e re m a i n -i ng v a r i a b l e s a c c or d i n g t o t h e s ca l in g p a r a m et e rs . H o w e v e r , tests w i t h s uc h m i x t u r e sa r e r e q u i r e d t o o bt a i n e x p e r i m e n t a l v er i f i c a t i on o f t h e i r u s e.

U s e o f t h e 1 - o r 2 - c o mp o n e n t c o l d g a s m e d i a d oe s r e q u i r e a n a dj u s t m en t o f o t h e rv a r i a b le s t o account f o r t he l a c k o f d u p l i c a t i o n o f b o t h 7j a n d (RT)j. O n e p o s s i bl ec o m b i n a t i o n w h i c h w o u l d satisfy t he m o s t c r i t i c a l s i m u l a t i o n p a r a m e te r s i s to u s e t h e

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f o l l owing procedure. In itia lly select a gas which duplicates (RT) , and f u r t he rmore, . , _ . . . . . . . . . . . . Assuming 7, isspecify model operation at matched jet pressure ratios,

not matched, an adjustment i s made in M, of the model to'satisfy the parameter7jMj 2//3j to account for duplicat ion of the jet shock properties. Since, as shown inFigure 17, this correction does not c omplet ely provide the necessary correction to theflow turning angle of the jet, Av , the nozzle exit angle can be adjusted accordingto Equation (11-13) to provide duplication of the initial inclination angle. 8. ,of the jet. Simulation of the remaining important scaling parameter, the jet momentu m,is obtained by an adjust ment of the mode l exit area acc ording to Equation (111-19).

V I I . R E F E R E N C E S A N D B I B L I O G R A P H Y

S e c t i o n I

1. Squire, H.B.

2. Li, T.Y.et alii

3. Krzyw oblocki, M.Z.

4. Beheim, M.A.et alii

5. Chow, W. .

6. Hinson, W.F.Falanga, R.A.

7. Hayman, L.O., Jr.

McDearmon, R.W.

8. Jackson, B.C.Crabill, N.L.

9. Hammi t t , A . G .

Jet Flow and Its Effects on Aircraft. Aircraft Eng . ,Vol .XXII , No .253 . March 1950, p.62.

The Design of Wind Tunnel Experiments for the Study ofJet On E f f e c t s . N AV O R D Repor t 3473. April 1953.

Jets - Review of Literature. Jet Propulsion, Vol.26;No.9 . September 1956, p.760.

Jet Effects on Annular Base Pressure and Temperature ina Supersonic Stream. N A S A T R R-125, 1962.

O n the Base Pressure Resulting from the Interaction ofa Supersonic External Stream with a Sonic or Subsonic Jet.Journal of the Aerospace Sciences, Vol .26 , No .3 , March1959. p. 176.

Effect of Jet Pluming on the Static Stability of Cone-Cylinder Flare Configurations at a Mach Number of 9.65..N A S A T N D-1352, September 1962.

Jet Effects on Cylindrical Afterbodies Housing Sonic andSupersonic Nozzles wh ich Exhaust Against a SupersonicStream at Angles of Attack from 90 to 18CP. N A S A , T ND-1016, March 1962.

Free Flight Investigation of Jet Effects at Low Supersonic Mach Numbers on a Fighter Type ConfigurationEmploying a Tail-Boom Assembly. N A C A R M L57F19, August1957.

The Oscillation and Noise of an Overpressure Sonic Jet.Journal of the Aerospace Sciences, Vol .28, No .9 ,September 1961. p.673.

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10. Howes, W.L. Simi lar i ty of Far N o i s e Fields of J e t s .1959.

NASA TR R-52.

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12. Ward, G.N.

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Fluid Dynamics o f Jets. D . van N ostrand Company, Inc.,1954.

Linearized Theory of Steady High-Speed Flow. CambridgeUniversity Press, 1955, Chap.8.

O p e r a t io n a l Method o f Determining Initial Contour of andPressure Field About a Supersonic Jet.. N A S A TN D -279,April I960.

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15. Pistolesi, E.M ar ini . M .

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17. Ehlers, F.E.Strand, T.

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19. Kawamura, R.

Linea r i zed S u p e r s o n i c Flow i n a n Axisymmetr ic J e tI s su ing in Air a t Res t . Institute of Aeronautics,University of Pisa, TR-1, March 1961.

Linear iz ed Supersonic Flow o f a n Axisymmetr ic J e t i n aSupersonic St ream. Institute o f Aeronautics, Universityof Pisa, TR-2, Marc h 1962.

T h e Osc i l l a t i ons o f a Supersonic G a s J e t Embedded i n aSupersonic St ream. Journal of the Aeronaut ical Sciences,Vol.23, No.8, August 1956, .747.

T h e Flow o f a Supersonic J e t i n a Supersonic St ream a ta n Angle of At tack. Journal of the Aerospace Sciences,Vol.25, No.8, August 1958. P.497.

T h e In terna l F low P r o b l e m i n Axi-Symmetr ic .SupersonicF l o w . Philosophica l Transact ions of the Royal Society,Series A, Vol.251. 1959, p.l.

Ref l ec t i on o f a W a v e a t a n In t e r f ace o f Supersonic Flowsa n d Wa v e Pa t te rns i n a Supersonic C ompound J e t . Journal

of the Physical Society of Japan, Vol.7, No.5, September-October 1952.

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21. Wang, .J.Peterson, J.B.

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Exper imenta l and Theore t ica l Studies of Axisymmetr icFree Je ts . NASA TR R-6, 1959. Supersedes NACA RM L54L31,RM L55J14. RM L56G18, and TN 4195.

Spreading of Supersonic J e t s f rom Axia l ly Symmetr icNozz l e s . Jet Propulsion, Vol.28, No.5, May 1958. p.321.

Resu l t s o f t h e Computa t ions o f Supersonic Flow Fie lds

A f t o f Ci rcu lar Cyl indr ica l Bodies o f Revolut ion b y t h eMethod of Cha rac t e r i s t i c s . ABMA Rep. No.DA-R-49,March 1958.

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23. M o e , M.Troesch, B.A.

24. Lo ve, E.S.

25. Adamson, T.C., Jr.Nicholls. J.A.

26. Lord, W.T.

27. Latvala, E.K.A n d e r s o n , T.P.

28. A d a m s o n , T.C., Jr.

29. Benson, J.R.Robertson, J.E.

30. Chrisman, C.C.

31. Pai , S.I .

32. K l e i n s t e i n , G.

33. Va s i l i u , J.

34. Szablewski, W.

35. Szablewski. W.

J e t F l o w w i t h S h o c k s . ARS Journal, Vol.30, May 1960,P.487.

A n A p p r o x i m a t i o n o f t h e B o u n d a r y o f a S u p e r s o n i c A x i -s y m m e t r i c J e t E x h a u s t i n g i n t o a S u p e r s o n i c S t r e a m . .Journal of the Aeronautical Sciences, Vol.25, No.2,February 1958, p.130.

O n t h e Structure o f J e t s f r o m H i g h l y U n d e r e x p a n d e dN o z z l e s i n t o S t i l l A i r . Journal o f t h e AerospaceSciences, Vol.26. No.l, January 1959, p.16.

O n A x i s y m m e t r i c a l G a s J e t s , w i t h A p p l i c a t i o n t o R o c k e tJ e t F l o w F i e l d s a t H i g h A l t i t u d e s . RAE Report No. A e r o2626, Ju l y 1959.

S t u d i e s o f t h e S p r e a d i n g o f R o c k e t E x h a u s t J e t s a t H i g hA l t i t u d e s . B a l l i s t i c M i s s i l e s and Space Technology,Vo l . 1 1 , Pergamon Press, 1961.

A p p r o x i m a t e M e t h o d s f o r C a l c u l a t i n g t h e S t r u c t u r e o fJ e t s f r o m H i g h l y U n d e r e x p a n d e d N o z z l e s . I n s t i t u te o fScience and Technology, U n i v e r s i t y of M i c h i g a n ,3768-26-T, June 1961.

M e t h o d s o f A p p r o x i m a t i n g I n v i s c i d J e t B o u n d a r i e s f o rH i g h l y U n d e r e x p a n d e d S u p e r s o n i c N o z z l e s . AEDC-TDR-62-7,May 1962.

Evaluation o f t h e F r e e J e t S p r e a d i n g R a t e P a r a m e t e r s f o rA x i - S y m m e t r i c F l o w o f A i r a t M a c h N u m b e r T h r e e .O k l a h o m a State U n i v e r s i ty Thesis, Au gus t 1962.

L a m i n a r J e t M i x i n g o f T w o C o m p r e s s i b l e F l u i d s w i t h H e a tR e l e a s e . Journal of the Aeronautical Sciences, Vol.23,No.11, N o v e m b e r 1 95 6, p.1012.

A n A p p r o x i m a t e S o l u t i o n f o r t h e A x i s y m m e t r i c J e t o f aL a m i n a r C o m p r e s s i b l e F l u i d . Quarterly o f A p p l i e dM a t h e m a t i c s , Vol.XX, No.l, A p r i l 1 96 2, p.49.

T u r b u l e n t M i x i n g o f a R o c k e t E x h a u s t J e t w i t h a S u p e r -s o n i c S t r e a m I n c l u d i n g C h e m i c a l R e a c t i o n s . Journal o ft h e Aerospace Sciences, Vol.29, N o . l , January 1962, p.19.

7 u r 6 u i e n t e Aus&reitung r u n d e n H e i s s l u f t s t r a h l e s i nB e w e g t e r L u f t . Ingenieur-Archiv, X X V I , Band 1958, p.358.

7 u r 6 u Z e n t e / I u s 6 ri e tu n g e i n e s r u n d e n H e i s s l u f t s t r a h l e s i nr u h e n d e r A u s s e n l u f t . I n g e n i e u r - A r c h i v, X XX , Band 1961,P. 96.

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36. Pozzi, A.

37. Chow, W.L.Korst. H.H.

38. Maczynski, J.F.J.

39. Ryhming, I.L.

40. Johannesen, N.H.

41. Rollin, V.G.

4 2 . Willis, D . R .Glassman, I.

43. R ousso, M .D.Baughman, L. E.

44. Seddon, J.Haver ty, L .

45. E a stma n , D .W .Radtke , L.P.

Efflusso di un Getto in un Ambiente in Moto . Missili,Vol.3, February 1961, p.21.

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Structure Within

a Constant Pressure Com-pressible Turbulent Jet Mixing Region. Engineer ing

Expe r imen t a l Station, University of Illinois, ME-TN-393-1,July 1962.

A Round Jet in an Ambien t Co-Axial Stream. Journal ofFluid M echanics , Vol .13, Part 4 , August 1962.

O n the M ixing Problem of an Axi Symmetric Free Je t intoAir Including Chemical Reactions. General DynamicsC o r p ., C o n v a i r D i v. , ZA-332, March 1961.

Fur ther Resul t s o n t h e Mix ing o f Free Axia l ly Symmetr ica l

J e t s of Mach Number l . W. ARC 20.981, FM 2817, N.88.May 1959.

Effec t o f J e t Tempera ture o n Je t -Noise Genera t ion .NACA TN 4217. March 1958.

T h e Mix ing o f Unbounded Coax ia l Compress ib le S t reams.Jet Propulsion, Vol.27, December 1957, p.1241.

Spreading Charac ter i s t ics o f a J e t Expanding f rom ChokedNozz l e s at Mac h 1 .91 . NACA TN 3836, December 1956.

Spread o f Ve loc i t y i n a Co ld J e t D i scha rg ing w i th Exces sP re s su re f rom a Sonic Ex i t i n t o Sti l l A i r . RAE TN Aero2400, November 1955.

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46. Covert, E.E.

47. Goethert, B.H.Barnes, L.T.

48. de Moraes, C.A.et alii

Je t Simulation in the W i n d Tunnel . MassachusettsInstitute of Technology, Naval Supersonic Laboratory,TR 252, July 1957.

Some S tudies o f t h e Flow Pat te rn a t t h e Base o f Mis s i l e swi th Rocke t Exhaus t J e t s . AEDC-TR-58-12, June I960.

Design a nd Evalua t ion o f a Tu rbo j e t Exhaus t S imu la to rUt i l iz ing a Sol id-Propel lent Rocket Motor for Use inFree-Fl ight Aerodynamic Researc h Models . NACA RML54I15, December 17, 1954.

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49. Beheim, M.A.Obery, L.J.

50. Ericsson, L.E.

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Scaling Pa rame te r s fo r Simula t ion o f Base F low Re-c i r c u l a t i o n on Mis s i l e s w i th M u l t i p le R o c k e t E x h a u s tJ e t s . Lockheed Aircraft Corp. M.&S. Div., LMSD 800239,October I960.

Sec t ion I V

51. Bressette, E.

52. Bressette, E.Leiss, A.

53. Bressett e, E.

54. Lee, G.

55. Tempelmeyer, K.E.

56. Runckel, J.F.Swihart, J.M.

57. Evans, A.J.

58. Herstine. G.L.et alii

59. Leiss, A.

60. Englert, G.W.Luidens, R. W.

Investigation of the Jet Effects on a Flat SurfaceDownstream of the Exit of a Simulated Turbojet Nacelleat a Free Stream Mach Number of 2.02. N A C A R M L54E05a,June 23. 1954.

Investigation of Jet Effects on a Flat Surface Down-stream of the Exit o f a Simulated Turbojet Nacelle at aFree Stream Mach Number of 1.39. N A C A R M L 55L13, April2, 1956.

Some Experiments Relating to the Problem o f Simulationof Hot Jet Engines in Studies of Jet Effects on AdjacentSurfaces at a Free Stream Mach Number of 1.80.N A C A RM L56E07, July 11 , 1956.

An Investigation of Transonic Flow Fields SurroundingHot and Cold Sonic Jets.. N A S A TN D-853, April 1961.

An Analytical Study of Ho t Jet Simulation with a ColdG as Mixture. AEDC-TN-58-54, September 1958.

A Hydrogen Peroxide Hot Jet Simulator fo r Wind-TunnelTests of Turbojet Exit Models . N A S A M em o 1-10-59L.February 1959.

The Simulation of th e Effects of Internal Flow in WindTunnel Model Tests of Turbojet Powered Aircraft.A G A R D A G 19/P9. Papers Presented at the Seventh M eetingof the Wind Tunnel an d Model Testing Panel, June 1955,P. 53.

Base Heating Experimental Programs for Saturn S IV Stage.S.M.F. Fund Paper N o. FF-31, Presented at the IAS 30thAnnual M ee ting , N ew York , January 22-24 , 1962.

Design an d Evaluation of a Turbojet Exhaust Simulatorwith a Solid Propellent Rocket Motor for Free FlightResearch. N A C A R M L57E10a, July 5, 1957.

Wind-Tunnel Technique fo r Simultaneous Simulation o fExternal Flow Field about Nacelle Inlet and Exit Airstreams at Supersonic Speeds. N A C A TN 3881. Jan. 1957.

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61. Stalmach. C.J.Cooksey, J.M.

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New Tes t Techn iques f o r a Hyperveloc i ty W i n d Tunnel .Aerospace Engineering. Vol.21. No.3, March 1962, p.62.

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In terac t ion of Highly Underexpanded Je ts wi th Simula ted

Luna r Su r f aces . NASA TN D-1095, December 1961.

Section V

64. Falanga, R.A.et alii

65. Baughman, L. E.Kochendorfer, F.D.

66. Cortright, E.M., Jr.Kochendorfer, F.D.

67. Goethert, B.H.

68. Tatro, R. E.

69. Rousso, M.D.Kochendorfer, F.D.

Exploratory Tests of the Effects of Jet Plumes on theFlow Over Cone Cylinder Flare Bodies. N A S A TN D -1000,February 1962.

Je t E ff ec t s on Base Pressures of Conica l Af terbodies a tM a c h 1 .91 and 3 .12 . NACA RM E57E06, August. 1957.

Je t E ff ec t s on Flow Over Af terbodies in SupersonicSt ream. NACA RM E53H25. November 1953.

Base F low Cha rac t e r i s t i c s o f Mis s i l e s w i th C lus t e r-Rocke t Exhaus t s . Aerospace Engineering, Vol.20, No.3,March 1961, .28.