NASA Technical Memorandum 898 12 AIAA-87-2 1 1 1

Two-Dimensional Nozzle Plume Characteristics

(kAS8-TB-89812) !IPO-f3!lEISICEAL hOZLLE N 87- 105 40 ELUEIE CHABACTEBISlICS (NASA) 23 C S C L 018

Unclas G3/02 4383d

Uwe H. von Glahn Lewis Research Center Cleveland, Ohio

Prepared for the

cosponsored by the AIAA, SAE, ASME, and ASEE San Diego, California, June 29-July 2, 1987

c 23rd Joint Propulsion Conference

' c

TWO-DIMENSIONAL NOZZLE PLUME CHARACTERISTICS

Uwe H. van Glahn N a t i o n a l Ae ronau t i cs and Space A d m i n i s t r a t i o n

Lewis Research Cen te r Cleveland, Ohio 44135

A b s t r a c t

F u t u r e h i g h performance a i r c r a f t w i l l l i k e l y f e a t u r e asymmetr ic o r two-dimensional nozz les w i t h o r w i t h o u t e j e c t o r s . d imens iona l n o z z l e l e j e c t o r systems o f minimum s i z e and we igh t , t h e plume decay and sp read inq charac- t e r i s t i c s o f b a s i c two-dimensional n o z z l e s must f i r s t be e s t a b l i s h e d . t h e exper imen ta l ana lyses of t hese plume charac- t e r i s t i c s and i n c l u d e s t h e e f f e c t s o f n o z z l e aspec t r a t i o and f l o w c o n d i t i o n s ( j e t Mach number and tempera tu re ) on t h e plume decay and spread ing o f two-d imens iona l nozz les . C a r r e l a t i ons i n c l u d i n q these v a r i a b l e s a r e deve loped i n a manner s i m i l a r t o t h o s e p r e v i o u s l y developed s u c c e s s f u l l y f o r c o n i c and d u a l - f l o w plumes.

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Nomenclature

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c o r r e l a t i o n parameters

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Reynolds number

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s t a t i c tempera ture

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a x i a l d i s t a n c e p l a n e

w i d t h d i s t a i c e and p l a n e

h e i g h t d i s t a n c e and p l a n e

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I n t r o d u c t i o n

C u r r e n t l y some h i g h per fo rmance a i r c r a f t , such as t h e F-111 and SR-71, a r e equ ipped w i t h ax i symmet r i c n o z z l e / e j e c t o r enq ine exhaust systems. The e j e c t o r s a r e used t o m ix t h e enq ine exhaust f l o w w i t h ambien t a i r i n o r d e r t o p r o v i d e t h r u s t augmenta t ion under some o p e r a t i n q c o n d i t i o n s . F u t u r e h i g h per fo rmance a i r c r a f t w i l l l i k e l y f e a - t u r e asymmetr ic o r two-dimensional n o z z l e s w i t h o r w i t h o u t e j e c t o r s . n o z z l e systems inc ludes , amonq o t h e r cons idera- t i o n s , enhanced a i r c r a f t maneuver ing c a p a b i l i t y .

e n t l y more r a p i d plume v e l o c i t y and tempera tu re decay w i t h a x i a l d i s t a n c e f r o m t h e n o z z l e e x i t p l a n e than do c o n i c nozz les . S i m i l a r l y , t h e plume sp read ing i s more r a p i d f o r a two-d imens iona l n o z z l e i n t h e n o z z l e h e i g h t d imens ion and l e s s i n t h e n o z z l e w i d t h d imens ion compared w i t h t h a t f o r a c o n i c n o z z l e o p e r a t i n g a t equa l f l o w and t h r u s t c o n d i t i o n s . Two-dimensional n o z z l e s when coup led w i t h two-d imens iona l e j e c t o r s have a q r e a t l y reduced shroud l e n g t h compared w i t h ax i symmet r i c n o z z l e / e j e c t o r systems due t o t h e b e n e f i t s r e s u l t - i n g f r o m t h e more r a p i d plume decay o f t h e two- d imens iona l p lume compared w i t h t h e c o n i c plume.

The f u t u r e use o f asymmetr ic

Two-dimensional n o z z l e systems p r o v i d e i n h e r -

F o r d e s i g n purposes, t h e v e l o c i t y l t e m p e r a t u r e decay and t h e r a d i a l sp read inq o f asymmetr ic exhaust plumes must be taken i n t o account i n o r d e r t o p r o v i d e a c c e p t a b l y smal l , e f f i c i e n t and l i g h t we igh t asymmetr ic e j e c t o r systems. By t a k i n q i n t o c o n s i d e r a t i o n t h e t r a n s i t i o n d u c t des ign f r o m t h e ax isymmet r ic geometry a t t h e enq ine t u r b i n e e x i t face t o t h e asymmetr ic geometry a t t h e n o z z l e e x i t p l a n e as w e l l as t h e a i r c r a f t e x t e r n a l f u s e l a q e

1

s i z e and shape c o n s t r a i n t s , s i n g l e eng ine two- d imens iona l n o z z l e aspect r a t i o s w i l l most l i k e l y be i n t h e range o f 3 t o 6. eng ine i n s t a l l a t i o n s t h e r e f o r e w i l l have e f f e c t i v e aspec t r a t i o s o f t w i c e those o f t h e s i n g l e eng ine aspec t r a t i o s , o r 6 t o 12.

two-dimensional n o z z l e l e j e c t o r systems, t h e plume decay and sp read ing c h a r a c t e r i s t i c s o f b a s i c two- d imens iona l n o z z l e s must f i r s t be e s t a b l i s h e d . Consequent ly, t h e p resen t work d e a l s w i t h t h e plume c h a r a c t e r i s t i c s o f two-dimensional n o z z l e s w i t h o u t e j e c t o r s . I nc luded i n t h e s t u d y a r e t h e e f f e c t s o f n o z z l e aspect r a t i o and f l o w c o n d i t i o n s i n c l u d i n g j e t Mach number and tempera tu re on t h e plume decay and spread ing o f two-d imens iona l nozz les . C o r r e l a t i o n procedures i n c l u d i n g these v a r i a b l e s a r e developed i n a manner s i m i l a r t o those deve lop d s u c c e s s f u l l y f o r c o n i c and dua l - f l o w nozz1es.f-3

Background

S ide-by-s ide dua l

I n o r d e r t o des ign e f f i c i e n t , r a p i d - m i x i n g

General ~-

S t u d i e s o f two-dimensional o r i f i c e l n o z z l e

The e a r l y work was plume c h a r a c t e r i x t i c s hsve been a v a i l a b l e i n t h e l i t e r a t u r e f o r o v e r 50 yr. g e n e r a l l y o f more academic i n t e r e s t t h a n o f p rac - t i c a l a p p l i c a t i o n t o a i r c r a f t . Consequent ly, much o f t h e e a r l y exper imenta l work was conducted w i t h o r i f i c e s r a t h e r t h a n nozz les . Sketches o f v a r i o u s o r i f i c e t y p e s used i n these s t u d i e s a r e summarized i n F i g . 1. As w i l l be shown l a t e r , t h e t y p e o f o r i f i c e used can s i g n i f i c a n t l y a f f e c t t h e plume v e l o c i t y and tempera ture c h a r a c t e r i s t i c s , p a r t i c u l a r l y when compared w i t h n o z z l e da ta .

The b a s i c o r i f i c e s used i n t h e l i t e r a t u r e includg-3quare-edge, sharp-edge and round-edge t ypes . I n some s tud ies , two-dimensionsal

r e used t h a t t e r m i n a t e d as a w a l l o r i - channg13-yti f i c e . I n o t h e r s tud ies , t h e f l o w was f u r t h e r channeled between two p a r a l l e l p l a t e s a t tached t o t h e l o n s i d e s o f t h e w a l l o r i f i c e o r w a l l n ~ z z l e . ? ~ - ~ ~ F i n a l l y , i n t h e f r e e - s t a n d i n g nozz les (used i n seve ra l s t u d i e s , o n l y two s i d e s ( l o n g d imens ion o f t h e n o z z l e ) were c o n t r a c t i n q w h i l e t h e o t h e r two s ides ( s h r t e i t h e r p a r a l l e l o r d i v e r g i n g . 7 6-2! imens ion) were

The l i t e r a t u r e i nc ludes c o n s i d e r a t i o n of n o z z l e aspec t r a t i o s as h i g h as 40 (b lown f l a p a p p l i c a t i o n s ) . ''owever, i n t e r e s t i n more r e c e n t y e a r s has c e n t e r e d more on n o z z l e aspec t r a t i o s o f 3 t o 10.

I n qenera l , t h e e a r l y d a t a were o b t a i n e d w i t h low . l e t Mach numbers and c o l d f l o w o r r e l a t i v e l y l ow s t ream temperatures. More r e c e n t l y , l i m i t e d d a t a f o r j e t exhaust v e l o c i t i e s up t o l ow super- s o n i c speeds and temperatures up t o shout 600 K have become ava i 1 ab le . These d a t a were usua l 1 y o b t a i n e d w i t h aspec t r a t i o s o f 6 o r l e s s . Fur thermore , much o f the r e c e n t d a t a have been o b t a i n e d w i t h nozz les r a t h e r t h a n o r i f i c e s , t h e r e b y b e i n g o f more p r a c t i c a l v a l u e t o t h e a i r c r a f t e n q i n e e r i n g community.

Plume Flow Regions

I t has been g e n e r a l l y accepted t h a t a two- d imens iona l n o z z l e ( o r o r i f i c e ) plume c o n s i s t s o f

t h r e e main r e g i o n s shown s c h e m a t i c a l l y i n F i g . 2 and d e s c r i b e d as f o l l o w s :

(1) An i n i t i a l m i x i n g r e g i o n d e f i n e d i n t h e l i t e r a t u r e as t h e p o t e n t i a l c o r e r e g i o n . r e g i o n , t h e n o z z l e c e n t e r l i n e v e l o c i t y i s essen- t i a l l y c o n s t a n t w i t h i n t h e i n n e r m i x i n g boundar ies and w i t h t h e a x i a l e x t e n t of t h e r e g i o n b e i n g de termined b y t h e n o z z l e ha l f -he igh t , b /2 , i n t h e Z - d i r e c t i o n .

I n t h i s

( 2 ) A t r a n s i t i o n r e q i o n a l s o d e f i n e d i n t h e l i t e r a t u r e as t h e c h a r a c t e r i s t i c decay r e g i o n . t h i s r e g i o n , t h e c e n t e r l i n e v e l o c i t y decays w i t h i n c r e a s i n g a x i a l d i s t a n c e b u t a t each a x i a l s t a t i o n , X, t h e l o c a l v e l o c i t y w i t h i n t h e i n n e r m i x i n g boundary i s c o n s t a n t i n t h e Y - d i r e c t i o n . The a x i a l e x t e n t o f t h e t r a n s i t i o n r e g i o n i s a f u n c t i o n o f t h e n o z z l e ( o r i f i c e ) h a l f - w i d t h , a / 2 . Note t h a t a square n o z z l e does n o t have a t r a n s i t i o n r e g i o n because t h e plume decay i s i d e n t i c a l i n b o t h t h e Y - and Z - d i r e c t i o n s .

I n

( 3 ) Tile f i n a l r e g i o n i s d e f i n e d as t h e f u l l y - m ixed o r ax isymmet r ic - type f l o w r e g i o n . I n t h i s r e g i o n , t h e plume peak v e l o c i t y always occu rs a t t h e n o z z l e c e n t e r l i n e ; i.e., t h e r e i s no c o n s t a n t v e l o c i t y component i n t h e Y - d i r e c t i o n .

The plume tempera tu re decay c h a r a c t e r i s t i c s a r e s i m i l a r t o t h o s e d e s c r i b e d i n t h e p r e c e d i n q d i s c u s s i o n o f t h e plume v e l o c i t y decay. The a x i a l t empera tu re decay, however, i s i n i t i a t e d e a r l i e r ( c l o s e r t o t h e n o z z l e e x i t p l a n e ) t h a n t h a t of t h e v e l o c i t y as shown s c h e m a t i c a l l y i n F i g . 3. As a consequence, t h e plume r a d i a l t empera tu re spreads more r a p i d l y t h a n t h e r a d i a l v e l o c i t y , a l s o shown i n F i g . 3.

O v e r a l l Plume Decay C h a r a c t e r i s t i c s

A schemat ic s k e t c h o f t h e t y p i c a l two- d imens iona l n o z z l e plume c e n t e r l i n e decay w i t h a x i a l d i s t a n c e i s shown i n F i g . 4 t o g e t h e r w i t h t h a t f o r a c o n i c ( o r square) n o z z l e plume. I t i s apparent t h a t t h e two-dimensional n o z z l e v e l o c i t y decays f a s t e r t h a n t h a t f o r t h e c i r c u l a r n o z z l e under equa l f l o w c o n d i t i o n s . I n t h e i n i t i a l m ix - i n g r e g i o n , t h e shapes o f t h e two curves , once t h e decay has begun, i s t h e same a l t h o u g h t h e a b s o l u t e va lues a r e d i f f e r e n t . reg ion , t h e s l o p e o f b o t h cu rves f o l l o w an X- decay r a t e . A l though n o t shown i n t h e f i q u r e , t h e plume c e n t e r l i n e tempera tu re decay c u r v e i s s i m i l a r t o t h a t f o r t h e v e l o c i t y decay c u r v e shown i n F i g . 4 excep t t h a t t h e tempera tu re decay c u r v e i s d i s p l a c e d t o t h e l e f t o f t h e v e l o c i t y decay c u r v e i n d i c a t i n g an e a r l i e r decay i n i t i a t i o n .

A lso , i n t h e f u l l y - m i x f d

I n F i g . 5 i s shown a schematic s k e t c h o f t h e e f f e c t o f two-dimensional n o z z l e aspec t r a t i o on t h e plume c e n t e r l i n e v e l o c i t y decay c h a r a c t e r i s t i c s . W i th i n c r e a s i n q aspec t r a t i o , t h e i n i t i a t i o n o f t h e decay c u r v e s s h i f t s t o i n c r e a s i n q l y s m a l l e r va lues o f a x i a l d i s t a n c e f r o m t h e n o z z l e e x i t p lane . a t i o n o f p lume tempera tu re decay c u r v e s w i t h n o z z l e aspec t r a t i o . a t u r e decay, f o r a g i v e n aspec t r a t i o , beg ins sooner a x i a l l y t h a n t h a t f o r t h e plume v e l o c i t y decay as n o t e d e a r l i e r . noted, t h e plume tempera tu re sp read ing r a t e i s g r e a t e r t h a n t h a t f o r t h e plume v e l o c i t y .

S i m i l a r t r e n d s a r e o b t a i n e d f o r t h e v a r i -

However, t h e plume temper-

A l so , as p r e v i o u s l y

2

O r i f i c e l N o z z l e Plume-y Comparisons

I n some o f t h e plume f l o w reg ions , t h e r a t e o f plume v e l o c i t y decay d i f f e r s between o r i f i c e t y p e s and between o r i f i c e s and nozz les . The d i f - f e rences a r e most apparent i n t h e i n i t i a l and t r a n s i t i o n m i x i n g r e g i o n s o f t h e plume. Three p r i m a r y f a c t o r s c o n t r i b u t e t o these plume m i x i n g d i f f e r e n c e s , two o f wh ich a r e shown i n F i g . 6. These f a c t o r s a re : ( 1 ) t h e f l o w c o e f f i c i e n t wh ich v a r i e s w i t h o r i f i c e - e d g e shape ( F i g . 1 ) and con- t r i b u t e s t o d i f f e r e n c e s i n t h e s i z e and shape o f t h e o r i f i c e vena c o n t r a c t a and wh ich i s n o t p r e s e n t w i t h nozz les , ( 2 ) t h e d i f f e r e n c e s i n t h e i n f l o w t o t h e j e t s t ream f r o m t h e su r round ing medium due t o t h e o r i f i c e "wa l l , " and ( 3 ) t h e f l o w p r o f i l e d i f f e r e n c e s ( n o n u n i f o r m i t y ) a t t h e o r i f i c e e x i t p l a n e when a t u b u l a r o r channe l o r i f i c e i s used w i t h o r w i t h o u t a w a l l a t t he e x i t p lane . A l l o f t h e s e f a c t o r s a f f e c t t h e o r i f i c e plume v e l o c i t y decay, p a r t i c u l a r l y i n t h e r e g i o n s n e a r e s t t h e o r i f i c e e x i t p lane .

Some examples o f t h e e f f e c t o f some o f t h e p reced ing f a c t o r s on t h e o r i f i c e plume c e n t e r l i n e v e l o c i t y decay a r e shown i n F i g . 7. I n F i g . 7 ( a ) , t h e c e n t e r l i n e v e l o c i t y decay f o r a t h i n square- edge o r i f i c e and a n o z z l e a r e shown, h o t h hav ing an aspec t r a t i o o f 6. v e l o c i t y decay d a t a t o t h e l e f t o f t h e nozz le v e l o c i t y decay d a t a i s q u i t e ev iden t . I n Fig. 7 ( b ) , o r i f i c e v e l o c i t y decay d a t a f o r a nomina l aspect r a t i o o f 12 a r e shown f o r square- and round-edge o r i f i c e s and a nozz le . I t i s apparent t h a t b o t h s e t s o f o r i f i c e d a t a a r e s h i f t e d t o t h e l e f t of t h e n o z z l e d a t a ( c l o s e r t o t h e e x i t p lane ) , w i t h t h e square-edge o r i f i c e d a t a showing a g r e a t e r s h i f t t h a n t h e round-edge o r i f i c e da ta .

p e r a t u r e decay d a t a t o t h e v e l o c i t y decay da ta a r e n o t a v a i l a b l e . However, because o f t h e genera l r e l a t i o n s h i p between plume v e l o c i t y and tempera- t u r e decay,as w i l l be shown l a t e r , s i m i l a r t r e n d s would be expected.

The s h i f t i n t h e o r i f i c e

S i m i l a r o r i f i c e l n o z z l e plume c e n t e r l i n e tem-

Nozz le Plume C e n t e r l i n e Decay Trends ___________I__- __-__

Ve 1 oc i t y

c e n t e r l i n e v e l o c i t v decav f o r two-dimensional noz- Co ld f l o w . Pub l i shed d a t a on t h e c o l d - f l o w

F i g . 10, t h e parameters used c o r r e l a t e t h e d a t a w e l l f o r a two-dimensional n o z z l e w i t h an aspec t r a t i o of 5 and Wi th a D e l t a n o z z l e (F ig . 11 ) i t i s e v i d e n t t h a t t h e t r a n s i t i o n r e g i o n w i t h a heated j e t can occu r f a r t h e r downstream t h a n t h a t w i t h c o l d f l o w . A lso , t h e f u l l y mixed r e g i o n w i t h heated f l o w i s d i s p l a c e d f a r t h e r f r o m t h e c o n i c n o z z l e decay c u r v e t h a n t h a t w i t h c o l d f l o w . I n t h e i n i t i a l m i x i n g reg ion , t h e r e i s no e f f e c t o f j e t tempera- t u r e on t h e plume c e n t e r l i n e v e l o c i t y decay when p l o t t e d i n te rms o f t h e c o r r e l a t i o n parameters shown i n F i g s . 10 and 11.

Temperature

6 = 0 o v e r t h e range o f d a t a shown.

The plume c e n t e r l i n e s t a t i c t empera tu re decay i s shown p l o t t e d i n F i g . 12 as a f u n c t i o n o f t h e same absc i ssa parameter as t h a t used f o r t h e v e l o c i t y decay i n F i g . 11. The d a t a shown i n F i g . 12 a r e f o r a D e l t a n o z z l e w i t h 6 = 5 . A l s o shown i n t h e f i g u r e i s t h e plume c e n t e r l i n e s t a t i c t empera tu re decay c u r v e f o r a c o n i c nozz1e. l genera l , t h e d a t a t r e n d i s s i m i l a r t o t h a t d i s - cussed i n t h e p r e v i o u s s e c t i o n f o r t h e v e l o c i t y decay.

I n

Plume C e n t e r l i n e Decay C o r r e l a t i o n

The plume c e n t e r l i n e decay c h a r a c t e r i s t i c s were c o r r e l a t e d s e p a r a t e l y f o r t h e t h r e e plume decay r e g i o n s shown p r e v i o u s l y i n F i g . 2.

Vel oc i t y

I n i t i a l m i x i n r e ion . F o r s i m p l e two- d imens iona l nozzle'&), t h e plume c e n t e r l i n e v e l o c i t y decay d a t a were c o r r e l a t e d b y a f o r m parameter g i v e n b y [l + 0.15 (AR - l ) ] a m u l t i p l i c a t i o n f a c t o r f o r t h e absc i ssa t e r m X ( t j / t a ) 0 * 2 5 / D e ~ ~ shown i n F i g . 12. When t h e s h o r t d imens ion o f t h e n o z z l e i s f l a r e d , as f o r t h e D e l t a nozz les , an a d d i t i o n a l t e r m accoun t ing f o r t h e f l a r e ang le was r e q u i r e d . T h i s parameter was de termined t o be expressed b y [ l + 5 .5 ( tan B ) O - ~ ~ ] . Consequent ly, t h e genera l c o r r e l a t i o n parameter f o r two-d imens iona l n o z z l e s i n t h e i n i t i a l m i x i n g r e g i o n i s g i v e n by t h e f o l l o w i n g equa t ion :

wh ich i s

' ( 1 ) z l e s a r e shown i n F i g . 8. i s p l o t t e d as a f u n c t i o n o f X ( t j / t a ) o * 2 5 / D e ~ ~ ,

The v e l o c i t y decay, U c / U

The c o r r e l a t e d c e n t e r l i n e v e l o c i t v decav d a t a J a parameter p r e v i o u s l y found success fu l i n cor - r e l a t i n c o n i c and d u a l - f l o w n o z z l e plume decay d a t a . l - j A l s o shown i n t h e f i g u r e i s t h e con ic n o z z l e c e n t e r l i n e v e l o c i t y decay c u r v e f rom Ref. 1 I t i s apparent f r o m these d a t a t h a t t h e nozz le plume c e n t e r l i n e v e l o c i t y decay i s i n i t i a t e d i n c r e a s i n g l y sooner w i t h i n c r e a s i n g n o z z l e aspec t r a t i o , as shown s c h e m a t i c a l l y i n F i g . 5.

I f t h e n o z z l e s h o r t s ides , b, a r e f l a r e d a t an ang le , 6 ( D e l t a n o z z l e s i n Refs. 18 and 19 ) t h e c e n t e r l i n e v e l o c i t y decay i s i n i t i a t e d even e a r l i e r t h a n t h a t f o r a s i m i l a r n o n f l a r e d nozzle, i n c r e a s i n g as a f u n c t i o n o f t h e f l a r e angle. R e p r e s e n t a t i v e D e l t a n o z z l e c e n t e r l i n e v e l o c i t y decay d a t a a r e shown i n F i g . 9.

Heated f l o w . The e f f e c t o f h e a t i n g a two- d imens iona l n o z r l e j e t on t h e plume c e n t e r l i n e v e l o c i t y decay i s shown i n f i g s . 10 and 11. I n

i n t h e i n i t i a l m i x i n g r e g i o n a r e shown- in F i g s . 13 and 14 f o r c o n v e n t i o n a l two-d imens iona l and D e l t a nozz les , r e s p e c t i v e l y . A l s o shown i n t h e f i g u r e s , f o r re fe rence , i s t h e c o n i c n o z z l e c e n t e r l i n e v e l o c i t y decay c u r v e f r o m Ref. 1. The qood c o r - r e l a t i o n o f t h e c o n v e n t i o n a l two-dimensional and D e l t a n o z z l e d a t a i n t h e i n i t i a l m i x i n g r e g i o n w i t h t h e c o n i c n o z z l e c u r v e b y means o f Eq. ( 1 ) i s apparent .

T r a n s i t i o n r e g i o n . The c o r r e l a t i o n o f b o t h t h e c o n v e n t i o n a l two-dimensional and f l a r e d n o z z l e v e l o c i t y decay d a t a i n t h e t r a n s i t i o n r e g i o n r e q u i r e s t h e p r e d i c t i o n o f t h e s t a r t o f t h i s r e g i o n , h e r e i n des igna ted as t h e d e p a r t u r e p o i n t , r e l a t i v e t o t h e c o n i c n o z z l e c e n t e r l i n e v e l o c i t y decay c u r v e and t h e e s t a b l i s h m e n t o f t h e decay c u r v e downstream o f t h e d e p a r t u r e p o i n t .

3

The t r a n s i t i o n r e g i o n d e p a r t u r e p o i n t f r o m c o n i c n o z z l e c u r v e i n t h e t r a n s i t i o n reg ion , as ment ioned i n t h e p r e v i o u s s e c t i o n . t h e r e a r e no h i g h - f l a r e ang le d a t a a v a i l a b l e i n t h e f u l l y - m i x e d r e g i o n t o s u p p o r t o r r e f u t e t h e assumpt ion t h a t t h i s r e g i o n i s independent o f f l a r e ang le .

t h e c o n i c n o z z l e curve was de termined t o be func- t i o n s o f t h e n o z z l e aspect r a t i o , t h e n o z z l e f l a r e ang le , 6, and t h e je t - to -ambien t t o t a l t empera tu re r a t i o . wh ich t o c a l c u l a t e the d e p a r t u r e p o i n t , XDP, i n te rms o f t h e absc i ssa v a r i a b l e s used i n F i g s . 12 and 13: ( 2 ) S t a t i c Temperature

Consequent ly,

The f o l l o w i n g e q u a t i o n was deve loped w i t h

= [x ( t Ita) '25( Fi ) I De 4 E ] DP.v 'DP,v

I n i t i a l m i x i n q r e g i o n . Two-dimensional n o z z l e plume c e n t e r l i n e tempera tu re decay d a t a a r e v e r y l i m i t e d . Wh i le some such d a t a a r e a v a i l a b l e f o r o r i f i c e s , t h e s e d a t a i n t h i s f l o w r e g i o n a r e n o t

e a r l i e r . C o r r e l a t e d a v a i l a b l e d a t a a r e shown i n F i g . 18 f o r two n o z z l e c o n f i g u r a t i o n s . A l s o shown

T . / T (AR-l) [1 + (o.331Mj)4]-1 c o m p a t i b l e w i t h t h o s e f o r n o z z l e s as d i scussed = 25[1 + 2 0 ( t a n d 3 I [ { 7 ]

1 3 \ i n t h e f i g u r e i s t h e c o n i c n o z z l e cu rve . The parameter , F i n i t , used t o c o r r e l a t e t h e s e d a t a i s t h e same as t h a t used t o c o r r e l a t e t h e plume c e n t e r l i n e v e l o c i t y decay d a t a and i s g i v e n b y Eq. (1). The d a t a a r e seen t o be reasonab ly w e l l c o r r e l a t e d by t h i s parameter.

\ L I

The s l o p e o f curves th rough t h e d a t a i n t h e t r a n s i t i o n r e g i o n i q e n e r a l l y accepted as b e i n g a f u n c t i o n o f X-O.?.. F o r t h e a v a i l a b l e two- d imens iona l d a t a i n the t r a n s i t i o n r e g i o n , t h i s r e s u l t s i n t h e f o l l o w i n g c o r r e l a t i o n equa t ion :

Equa t ion ( 3 ) i s v a l i d when two-d imens iona l d e p a r t u r e s occu r i n t h e r e g i o n where t h e c o n i c n o z z l e c e n t e r l i n e v e l o c i t y decay c u r v e s l o p e i s equa l t o o r >0.5. When t h e s l o p e o f t h e c o n i c n o z z l e v e l o c i t y decay c u r v e i s t0.5, t h e exponent o f X p ,/F(X) i n Eq. ( 3 ) must be reduced because t h e s foge o f t h e d a t a w i l l be t0.5. S i m i l a r t r e n d s were encountered i n Refs. 2 and 3 and modi- f i c a t i o n s t o t h e equa t ions were i nc luded . However, t h i s m o d i f i c a t i o n was no t i n c l u d e d h e r e i n because p r a c t i c a l a i r c r a f t a p p l i c a t i o n s o f two-dimensional nozz les wou ld most l i k e l y be t h e range where a s l o p e o r exponent o f 0.5 a p p l i e s . I t shou ld a l s o be n o t e d t h a t f o r n o n f l a r e d two-dimensional noz- z l e s , t h e 6-term drops o u t o f Eq. ( 2 ) .

T r a n s i t i o n r e g i o n . The plume c e n t e r l i n e tem- -___ p e r a t u r e decay i n t h e t r a n s i t i o n r e g i o n f o r t h e two s e t s o f d a t a used f o r F i g . 18 a r e shown i n F i g . 19. The d e p a r t u r e p o i n t s f r o m t h e c o n i c n o z z l e decay c u r v e were c a l c u l a t e d u s i n g essen- t i a l l y Eq. ( Z ) , b u t w i t h o u t t h e i n c l u s i o n o f t h e tempera tu re d e p a r t u r e p o i n t s i n t h e t r a n s i t i o n r e g i o n i s g i v e n by:

= 25(1 + 2 0 ( t a n ~)~]/@zi[l + (0.033/Mj)4] ( 5 )

The s l o p e o f t h e tempera tu re t r a n s i t i o n r e g i o n c u r v e i n t h e range o f t h e a v a i l a b l e d a t a aga in i s g i v e n by an exponent o f 0.5, as was t h e case f o r t h e v e l o c i t y c u r v e i n t h e t r a n s i t i o n r e g i o n . F o r t h e a v a i l a b l e d a t a i n t h e t r a n s i t i o n r e g i o n , t h i s r e s u l t s i n t h e f o l l o w i n q c o r r e l a t i o n equa t ion :

The c o r r e l a t e d two-dimensional n o z z l e c e n t e r - l i n e v e l o c i t y decay da ta i n t h e t r a n s i t i o n r e g i o n a r e shown i n F i g s . 15 and 1 6 f o r n o z z l e s w i t h and w i t h o u t f l a r e d s ides , r e s p e c t i v e l y . The s o l i d symbols i n t h e f i g u r e s i n d i c a t e t h e c a l c u l a t e d d e p a r t u r e p o i n t s ob ta ined by use o f Eq. ( 2 ) . I n

- t a ) / ( t j - t a ) l t r a n =

[ ( t c - t a ) / ( t j - ta) lDp, t [ q m ] (6) genera1,the c a l c u l a t e d depar tu re p o i n t s and cu rves based on Eqs. ( 2 ) and (3 ) , r e s p e c t i v e l y r e p r e s e n t t h e d a t a q u i t e w e l l . I t shou ld be no ted t h $ t t h e f l a r e d n o z z l e d a t a w i t h a f l a r e anq le o f 30

o v e r t h e range o f d a t a a v a i l a b l e .

where f ( x ) is given by [ X ( t j / t a ) ~ . 2 5 / o e q q ] F i n i t and i s equa l t o o r g r e a t e r t h a n XDp,t: A d d i t i o n a l d a t a a r e r e q u i r e d t o p r o v i d e v e r i f i c a t i o n i n t h e a p p l i c a t i o n o f Eq. ( 5 ) f o r d i d

not show any departure from the conic curve o t h e r n o z z l e aspec t r a t i o s and f l o w c o n d i t i o n s .

Fu l l y -m ixed reg ion . As i n t h e case of t h e plume c e n t e r l i n e v e l o c i t y decay, w h i l e t h e i n i t i a l

f o r o r i f i c e s and nozz les . t h e decav i n t h e f u l l v -

Fu l l y -m ixed r e g i o n . The plume c e n t e r l i n e v e l o c i t y decay d a t a i n t h e f u l l y mixed reg ion was and transition mixing region decay rates d i f fe red c o r r e l a t e d by a parameter g i v e n by:

mixed r e g i o n was s u b s t a n t i a l l y t h e same f o r t h e k e ( 4 ) c o n f i q u r a t i o n t ypes . Because o f t h i s f a c t and Fv,,,ix = 1 + [6 (1-1 /AR)6(T j /Ta) ] /AR

t h a t o n l y p lume-ce t e r l i n e tempera tu re decay d a t a f o r a D e l t a nozz le f8 was a v a i l a b l e i n t h i s f l o w r e g i o n , o r i f i c e d a t a a r e a l s o used h e r e i n t o p ro - ,,ide a o f confidence in the present cor- r e l a t i o n procedure .

The plume c e n t e r l i n e tempera tu re decay d a t a

as t h e v e l o c i t y decay da ta ; however, an exponent o f o . 5 on the temperature ratio was used in place

I n F i g . 17, t h e c o r r e l a t e d d a t a a r e shown t o g e t h e r w i t h t h e c o n i c nozz le plume decay curve . ' Good agreement i s aDparent f o r bo!h t h e c o n v e n t i o n a l two-d imens iona l n o z z l e s and t h e 5 f l a r e ang le D e l t a nozz le . i n Eq. ( 4 ) do n o t appear t o r e q u i r e a

l i n e v e l o c i t y decay i s independent o f t h e n o z z l e f l a r e ?ng le . t h e 30 f l a r e ang le d a t a d i d n o t d e p a r t f r o m t h e

Note t h a t t h e c o r r e l a t i o n parameters 6-term sug-

gesting t h a t i n t h e fully-mixed region the center- were cor re la ted in t h e Same manner

However, t h i s may be f o r t u i t o u s s i n c e

4

o f 1.0 as i n Eq. ( 4 ) . Thus, t h e plume c e n t e r l i n e tempera tu re decay i n t h e f u l l y - m i x e d r e g i o n i s g i ven by :

The c o r r e l a t e d plume c e n t e r l i n e tempera tu re decay d a t a a r e shown i n F i g . 20 t o g e t h e r w i t h t h e r e f e r - ence c o n i c n o z z l e c u r v e of Ref. 1. I n genera l , good c o r r e l a t i o n f o r b o t h n o z z l e and o r i f i c e d a t a has been ob ta ined.

Plume C e n t e r l i n e V e l o c i t y l S t a t i c Temperature

D e c a y 1 a t i o n s h i p

A un ique r e l a t i o n s h i p e x i s t s between t h e plume c e n t e r l i n e v e l o c i t i e s , U c / U j , and t h e s t a t i c tempera tures , ( t c - t a ) / ( t j - t ) , a t a l l a x i a l s t a t i o n s downstream o f t h e nozz fe e x i t p1ane. l T h i s r e l a t i o n s h i p , a c c o r d i n q t o Ref . 1, i s g i v e n b y t h e f o l l o w i n g equa t ion :

( t c - t a ) / ( t j - t a ) = [l + 4.3 ( ( u c / u . ) 8 - 1 ( 8 )

J

Equa t ion ( 8 ) app l ie : t o a l l s i ng le -s t ream n o z z l e plumes, and w i t h t h e i n c l u s i o n o f t h e p roper geometry v a r i a b l e s t o two-stream n o z z l e plumes. F i n a l l y Eq. ( 8 ) i s a l s o v a l i d f o r e x c i t e d j e t plumes. f

I n F i g . 21, t h e plume c e n t e r l i n e s t a t i c temper- a t u r e r a t i o , ( t - t . , ) / t j - t a ) , i s shown p l o t t e d as a f u n c t i o n o f t h e plume c e n t e r l i n e v e l o c i t y r a t i o ( U c / U j ) , f o r v a r i o u s a x i a l d i s t a n c e s downstream o f t h e n o z z l e e x i t p lane . The c u r v e shown i n t h e f i g u r e was genera ted b y t h e use o f Eq. (8 ) . d a t a shown i n t h e f i g u r e group about t h i s c u r v e and a r e w e l l w i t h i n t h e s c a t t e r expec ted from e x p e r i - men ta l d a t a o f t h i s na tu re . Note t h a t a l t hough d i f - f e r e n t plume decay r e s u l t s a r e o b t a i n e d f o r o r i f i c e s and n o z z l e s i n t h e i n i t i a l - and t r a n s i t i o n - f l o w r e g i o n s o f t h e plume as s t a t e d e a r l i e r , b o t h con- f i g u r a t i o n - t y p e s e t s o f d a t a c o r r e l a t e on t h i s p l o t .

As a consequence o f t h e s t a t i c tempera ture- t o - v e l o c i t y r a t i o r e l a t i o n s h i p shown i n F i g . 21, plume c e n t e r l i n e s t a t i c t empera tu re decay cu rves can b e genera ted f o r two-dimensional nozz les o f va r ious n o z z l e aspec t r a t i o s when o n l y t h e plume c e n t e r l i n e v e l o c i t y decay d a t a f r o m c o l d f l o w exper imen ta l s t u d i e s a r e a v a i l a b l e as a f u n c t i o n o f a x i a l d i s t a n c e f r o m t h e n o z z l e e x i t p lane .

A l l t h e

R a d i a l P r o f i l e ?

R a d i a l v e l o c i t y and tempera tu re p r o f i l e s o f c o n i c n o z z l e j e t plumes a r e f r e q u e n t l y separa ted i n t o two r e g i o n s . The f i r s t r e g i o n i n c l u d e s t h e r a d i a l p r o f i l e s i n t h e v i c i n i t y o f t h e c o r e f l o w w h i l e t h e second r e g i o n i n c l u d e s t h e r a d i a l p r o f i l e s downstream o f t h e c o r e f l o w . t h e r a d i a l p r o f i l e s a r e r e f e r r e d t o as " s i m i l a r i t y p r o f i 1 es. 'I

I n t h e l a t t e r reg ion ,

F o r two-d imens iona l nozz les , two co re : reg ions e x i s t as d e p i c t e d i n F i g . 2. r e g i o n s i s assoc ia ted w i t h t h e n o z z l e h e i g h t dimen- s ion , Z , and t h e second o f t h e s e r e g i o n s i s assoc i - a t e d w i t h t h e n o z z l e w i d t h dimension, Y. I n these c o r e r e g i o n s s i m i l a r i t y p r o f i l e s a r e g e n e r a l l y no t c o n s i d e r e d t o e x i s t because t h e p r o f i l e has a

The f i r s t of t hese

u n i f o r m segment b e f o r e decay ing i n t h e r a d i a l d i r e c - t i o n , as shown s c h e m a t i c a l l y i n F i g . 22. ment decreases i n r a d i a l d i s t a n c e w i t h i n c r e a s i n g a x i a l d i s t a n c e u n t i l t h e w i d t h apex i s reached ( F i g . 2 ) . l a r i t y r e g i o n f o r b o t h v e l o c i t y and tempera tu re becomes i n c r e a s i n g l y more i m p o r t a n t w i t h i n c r e a s i n g n o z z l e aspec t r a t i o s . However, i t w i l l be shown l a t e r t h a t b y c o n s i d e r i n g o n l y t h e r a d i a l decay segment o f t h e r a d i a l p r o f i l e t h a t s i m i l a r i t y does e x i s t i n b o t h Y- and Z -d i rec t i ons . A l s o i t w i l l b e shown t h a t s i m i l a r i t y i n t h e c o r e a p p l i e s t o b o t h t h e v e l o c i t y and t h e s t a t i c t empera tu re p r o f i l e s .

Core Regions

T h i s seg-

I t i s obv ious t h a t t h i s apparent nons im i -

I n t h e h e i g h t dimension, Z, o f two-dimensional n o z z l e s few, i f any, plume r a d i a l v e l o c i t y and tem- p e r a t u r e measurements have been made. However, some plume r a d i a l measurements have been made i n t h e w i d t h dimension, Y. measurements a r e shown i n F i g . 23 f o r b o t h v e l o c i t y and tempera tu re r a d i a l p r o f i l e s . The d a t a shown a r e i n c o n v e n t i o n a l t e rms o f UR/U, as a f u n c t i o n o f YlY0.5. The s t a r t of t h e r a d i a l decay i s des igna ted b y t h e t e r m ( Y / Y O . ~ ) ~ .

I n F i g . 23 (a ) , r a d i a l v e l o c i t y decay d a t a l 9 a r e shown f o r a two-dimensional n o z z l e w i t h an aspec t r a t i o o f 6. The r a d i a l v e l o c i t y decay a t t h e X/De s t a t i o n o f 2 i s es t ima ted t o s t a r t a t YlYo.5 equa l t o 0.3, wh ich i s t h e ( Y / Y o . ~ ) ~ v a l u e f o r t h i s case. I n F i g . 23(b) , r a d i a l t empera tu re decay d a t a 8 a r e shown f o r an o r i f i c e w i t h an aspec t r a t i o o f 40. The d a t a shown a r e f o r X/De va lues o f 2.8, 5.6, 16.8. F o r t h e s e s e t s o f d a t a t h e r a d i a l decay s t a r t s a r e e s t i m a t e d a t ( Y / Y O , ~ ) ~ 0.8, 0.64, and 0.05 f o r t h e p reced ing t h r e e X/De s t a t i o n s , r e s p e c t i v e l y .

The d a t a s e t s shown i n F i g . 23 a r e now p l o t t e d i n te rms o f (Y/Yo,5) - (Y/Yo. ) i n F i g . 24 excep t f o r t h e tempera tu re d a t a a t f/6e o f 16.8 wh ich i s a l r e a d y a lmos t a s i m i l a r i t y p r o f i l e . i n o n l y t h e a c t u a l r a d i a l decay p o r t i o n o f t h e p ro - f i l e s b e i n g shown. A l s o shown i n t h e f i g u r e a r e t h e c o n i c n o z z l e r a d i a l decay cu rves f r o m Ref . 1. Good agreement between t h e two-dimensional c o n f i g u r a t i o n s and t h e c o n i c n o z z l e c u r v e i s e v i d e n t f o r b o t h t h e r a d i a l v e l o c i t y and r a d i a l t empera tu re decay. Thus, when ana lyzed i n t h i s manner s i m i l a r i t y p r o f i l e s a r e e s t a b l i s h e d i n t h e c o r e r e g i o n s .

T r a n s i t i o n and F u l l y - M i x e d F low Re=

I n t h e t r a n s i t i o n and f u l l y - m i x e d f l o w r e g i o n s o f two-d imens iona l n o z z l e s / o r i f i c e s s i m i l a r i t y r a d i a l p r o f i l e s a r e o b t a i n e d i n b o t h t h e h e i g h t ( Z ) and w i d t h (Y ) dimensions o f t h e plume.

p r o f ' es a r e shown f o r a n o z z l e w i t h an aspec t r a t i o o f 6ib i n t h e h e i g h t d imens ion o f t h e nozz le . S i m i l a r d a t a a r e shown i n F i g . 25 (b ) f o r t h e w i d t h d imens ion of t h e nozz le . The u rves shown i n t h e f i g u r e a r e f o r a c o n i c nozz le . f A d d i t i o n a l d a t a i n Refs . 23 and 8 i n c l u d e b o t h r a d i a l v e l o c i t y and tempera tu re p r o f i l e s f o r a n o z z l e (AR,6) and an o r i f i c e (AR, l o ) , r e s p e c t i v e l y . These d a t a a r e reproduced i n F igs . 26 and 27, t o g e t h e r w i t h s i m i l a r i t y p r o f i l e cu rves f o r a c o n i c nozz le . I t i s apparent t h a t t h e c o n i c n o z z l e s i m i l a r i t y p r o f i l e cu rves r e p r e s e n t t h e r a d i a l v e l o c i t y and tempera tu re decay f o r two-dimensional n o z z l e s and

Represen ta t i ve d a t a o f such

va lues o f

T h i s r e s u l t s

I n F i g . 25 (a ) t y p i c a l plume r a d i a l v e l o c i t y

tlhe

5

o r i f i c e s s a t i s f a c t o r i l y i n b o t h t h e h e i g h t and w i d t h d imens ions o f t he t r a n s i t i o n and f u l l y mixed f l o w r e g i o n s o f t h e plume.

Spread ing C h a r a c t e r i s t i c s o f Two-Dimensional Plumes

A schematic s k e t c h of t h e sp read ing c h a r a c t e r - i s t i c s and r e f e r e n c e dimensions f o r two-d imens iona l p lumes i s shown i n F i g . 28. The sp read ing o f two- d imens iona l plumes i s a s t r o n g f u n c t i o n o f t h e con- f i g u r a t i o n type ; i.e., n o z z l e o r o r i f i c e . I n i t i a l s t u d i e s i n Ref. 7 i n d i c a t e d s i g n i f i c a n t d i f f e r e n c e s i n t h e plume spread ing between a sharp-edge o r i f i c e and a r e c t a n g u l a r channel o r i f i c e h a v i n g a channe l l e n g t h o f 50 channel he igh ts , b o t h h a v i n g an aspec t r a t i o o f 10. F u r t h e r work9 o f measurements o f t h e mean f l o w f i e l d c o r r o b o r a t e d t h e r e s u l t s o f t h e i n i t i a l s tudy . T y o i c a l plume sp read ing o f t h e p r e - c e d i n g two c o n f i g u r a t i o n t ypes i s shown i n F i g . 29. The plume spread inq i n t h i s f i g u r e i s shown i n b o t h p l a n e s o f symmetry. The Y0.5 and 20.5 symbols shown i n t h e f i g u r e a re va lues o f Y and Z a t t h e l o c a l r a d i a l one-ha l f plume v e l o c i t i e s , o r UR = 0.5 Uc. I n t h e h e i g h t dimension ( Z ) o f t h e two con- f i g u r a t i o n s , t h e plume spread ing i s o n l y s l i g h t l y l e s s f o r t h e channel- type o r i f i c e t h a n t h a t f o r t h e sharp-edge o r i f i c e . I n t h e w i d t h d imens ion (Y ) , l a r g e d i f f e r e n c e s i n t h e plume sp read ing a r e observed. The channel- type o r i f i c e sp read inq i s g e n e r a l l y much g r e a t e r t h a n t h a t o f t h e sharp-edge o r i f i c e , e s p e c i a l l y nea r t h e e x i t , due t o t h e l a t t e r ' s vena c o n t r a c t a e f f e c t .

When t h e plume sp read ing o f a channe l - type o r i f i c e i s compared w i t h t h a t o f a n o z z l e (Ref. 1 9 d a t a ) much more s i m i l a r plume sp read inq c h a r a c t e r - i s t i c s were ob ta ined i n b o t h p lanes , as shown i n F i g . 30. A l thouq i i t h e aspec t r a t i o o f t h e two con- f i g u r a t i o n s i s d i f f e r e n t , t h e shape o f t h e plume spread cu rves w i t h a x i a l d i s t a n c e i s s i m i l a r . I t shou ld be n o t e d t h a t t h e h e i g h t s i d e s o f t h e n o z z l e a r e p a r a l l e l , as i n t h e case o f t h e channe l - type o r i f i c e , w h i l e t h e w i d t h s i d e s o f t h e n o z z l e converge.

w i d t h c u r v e s (F ig . 30) a r e b e l i e v e d caused b y one o r b o t h o f t h e f o l l o w i n g f a c t o r s : w a l l c o n v e r g m c e on a l l f o u r s i d e s o f t h e nozz le , and ( 2 ) a c o n t r a c t i o n o f t h e plume i t s e l f t oward t h e n o z z l e c e n t e r l i n e i n t h e w i d t h d imens ion as t h e plume changes f r o m a two-dimensional shape t o an ax i symmet r i c shape w i t h i n c r e a s i n g d i s t a n c e down- s t ream f rom t h e nozz le e x i t . F u r t h e r s t u d i e s o f t h e s e phenomena a re needed.

The a x i a l u n d u l a t i o n o f t h e plume r a d i a l h a l f -

(1) t h e l a c k of s ide -

I n t h e f o l l o w i n q s e c t i o n , o n l y n o z z l e and channe l - type o r i f i c e d a t a w i l l be used t o deve lop c o r r e l a t i o n parameters f o r plume spread inq .

Plume S p r e a d i n g C o r r e l a t i o n ___--

I n F i g . 31, t h e co ld - f l ow plume v e l o c i t y spread i n t h e h e i g h t and w i d t h d imens ions o f two- d imens iona l nozz les a r e shown i n te rms of t h e n o z z l e aspec t r a t i o X ( t ~ / t a ) 0 . 2 5 / 0 e ~ ~ ~ . A l s o shown i n t h f i g u r e i s i h e plume spread lng o f a c o n i c nozzle. lg The two-d imens iona l nozz le h e i g h t d imens ion (Z) d a t a show s i m i l a r shapes t o t h e c o n i c n o z z l e cu rve , b u t a r e d i s p l a c e d by a d d i t i o n a l f u n c t i o n s of aspec t r a t i o . C o r r e l a t i o n o f t h e da ta , shown i n F i g . 31, was o b t a i n e d by use of t h e f o l l o w i n g r e l a t i o n s h i p :

e u i v a l e n t d iamete r and

4

where :

Fz,b = [l + 0.25(AR-1)o.4]

and Fz ,x = [l + 0.000833(AR-1)3]-1

The c o r r e l a t e d d a t a i n t h e n o z z l e h e i g h t d imens ion a r e shown i n F i g . 32. The two- d imens iona l d a t a a r e g e n e r a l l y i n good agreement w i t h t h e c o n i c cu rve . n e a r t h e n o z z l e e x i t some s c a t t e r i s no ted ; how- ever , t h i s may be due t o t h e s m a l l measurement d i f f e r e n c e s , Z-b/2, i n t h e d a t a r a t h e r t h a n i n t h e c o r r e l a t i o n method.

I n t h e plume c o r e r e g i o n

I n F i g . 33 t h e c o l d f l o w plume v e l o c i t y spread on t h e n o z z l e w i d t h d imens ion i s shown t o g e t h e r w i t h t h a t f o r a c o n i c n o z z l e . g r e a t e r v a r i a t i o n i n t h e Y-dimension d a t a i s seen t o occu r t h a n t h a t shown p r e v i o u s l y i n t h e Z- dimension. Not o n l y a r e t h e d a t a d i s p l a c e d as a f u n c t i o n o f t h e n o z z l e aspec t r a t i o n b u t a l s o as a f u n c t i o n o f a n o z z l e f l a r e ang le , 6. C o r r e l a - t i o n o f t h e d a t a was o b t a i n e d w i t h t h e f o l l o w i n q r e l a t i o n s h i p :

A much

where :

F Y , a = [{l + 2.67(AR - 1)o-6){1 + 1 6 0 ( s i n 6)1.51]-'

and

Fy,x = [ ( l + 0 , 3 6 7 f i - 1}(1 + 4 . 2 5 ( s i n 6)1*51]-1 I n genera l , t h e d a t a i n t h e Y-dimension o f

t h e n o z z l e a r e c o r r e l a t e d by Eq. (10) as shown i n F i g . 34. However, t h e u n d u l a t i o n s i n t h e plume sp read ing c u r v e d i scussed f o r F i g . 30 a r e n o t accounted f o r b y Eq. (10 ) and show up i n F i q . 34 as d e v i a t i o n s f r o m t h e c o n i c cu rve . The l a r g s t

w i t h an aspec t r a t i o o f 10. o c c u r l t i t h t h e n o z z l e s h a v i n s two convergent s i d e s ( d a t a ) . The amount o f d e v i a t i o n f r o m t h e c o n i c n o z z l e c u r v e appears t o be a complex f u n c t i o n o f t h e n o z z l e f l a r e ang le and aspec t r a t i o . l e a s t d e v i a t i o n f r o m t h e c o n i c n o z z l e c u r v e was o b t a i n e d w i t h t h e n o z z l e h a v i n g an aspec t r a t i o o f 6 nd converg ing s i d e s i n t h e h e i g h t d imens ion ( d a t a 9 ) . On t h e b a s i s o f t h e a v a i l a b l e l i m i t e d da ta , i t i s recommended t h a t t h e r e l a t i o n s h i p expressed b y Eq. (10) and F i g . 34 be used f o r e s t i m a t i n g t h e plume sp read ing i n t h e n o z z l e w i d t h d imens ion u n t i l a d d i t i o n a l da ta , p a r t i c u l a r l y , w i t h n o z z l e s h a v i n g a l l f o u r s i d e s converg ing , become a v a i l a b l e .

d e v i a t i o n s o c c u r f o r t h e channe l - type o r i f i c e 5 Lesser d e v i a t i o n s

The

Plume Spread ing Ang le

The plume h a l f - v e l o c i t y sp read ing ang le f o r a two-d imens iona l n o z z l e w i t h an aspec t r a t i o o f 6 was b r i e f l y examined t o de te rm ine t h e d i f f e r e n c e i n t h e n o z z l e h e i g h t and w i d t h sp read ing ang les . B o t h t h e o v e r a l l and l o c a l sp read inq ang les were i n c l u d e d i n t h e e v a l u a t i o n .

.

I n F i g . 35 schematic ske tches d e p i c t i n g t h e nomenc la tu re used t o d e f i n e t h e o v e r a l l , A , and l o c a l , e l , sp read ing ang les a r e shown. I n F i g . 36, plume o v e r a l l and l o c a l h a l f - v e l o c i t y s p r e a d i n g angles, based on d a t a f r o m Ref . 19, a re shown. F o r comparison, sp read ing ang les f o r a c o n i c n o z z l e a r e a l s o shown i n t h i s f i g u r e .

I n F i g . 36 (a ) i t i s e v i d e n t t h a t t h e plume s p r e a d i n g ang le i n t h e n o z z l e h e i g h t ( Z ) d imension reaches a maximum n e a r l y 3 t i m e s t h a t i n t h e noz- z l e w i d t h ( Y ) d imension. d imens iona l n o z z l e sp read ing ang le i n b o t h dimensions i s l a r g e r t h a n t h a t o f t h e c o n i c nozz le . However, a t X/D, va lues >12, t h e sp read ing r a t e i n t h e w i d t h d imens ion tends t o l e v e l o f f and i s l e s s t h a n t h a t o f t h e c o n i c nozz le . A f t e r an X / D e o f 25, t h e h e i g h t d imens ion sp read ing a n g l e decreases r a p i d l y and approaches t h a t o f t h e c o n i c nozz le a t an X/D, o f 40.

sp read ing ang le i n t h e h e i g h t d imens ion i nc reases r a p i d l y w i t h a x i a l d i s tance , r e a c h i n g a maximum o f about 7" a t an r a p i d l y t o about 1.5 . The plume sp read ing ang le i n t h e w i d t h d imens ion shows a v e r y e r r a t i c and o s c i l l a t o r y v a r i a t i o n w i t h X / D w i t h a maximum sp read ing ang le o f j u s t o v e r 3.5 o f 35. As a comparison, t h e c o n i c n o z z l e l o c a l sp read ing ang le i nc rease? c o n t i n u o u s l y w i t h X/De and reaches a va lue o f 4 a t an X / D e o f 35. The o s c i l l a t o r y n a t u r e o f t h e l o c a l sp read ing ang le i n t h e w i d t h d imens ion i s a l s o e v i d e n t i n t h e o v e r a l l sp read ing ang le d a t a ( F i g . 3 6 ( a ) ) ; t h a t case, t h e ang le v a r i a t i o n i s l e s s t h a n 0.4 .

I n i t i a l l y , t h e two-

I n F i g . 36 (b ) t h e l o c a l plume h a l f - v e l o c i t y

X/Deo o f 23 &?ore dec reas ing

a t an X / D e

however, i n e

Conc lus ions -__- On t h e b a s i s o f t h e p r e s e n t c o r r e l a t i o n s t u d y

concerned w i t h two-dimensional p lume decay and sp read ing c h a r a c t e r i s t i c s , t h e f o l l o w i n g conc lus- i o n s a r e made:

1. Two-dimensional plume c e n t e r l i n e v e l o c i t y and s t a t i c t empera tu re decay d a t a were e m p i r i c a l l y c o r r e l a t e d b y s u i t a b l e geometry and f l o w param- e t e r s t h a t i n t h e i r l i m i t s reduce t o p r e v i o u s l y p u b l i s h e d s ing le -s t ream c o r r e l a t i o n s .

2. I n t h e p r e s e n t c o r r e l a t i o n , t h e two- d imens iona l plume c e n t e r l i n e v e l o c i t y and s t a t i c t empera tu re decay a r e ana lyzed i n te rms o f t h r e e d i s t i n c t r e g i o n s p r e v i o u s l y i d e n t i f i e d i n t h e l i t e r a t u r e , namely:

( a ) An i n i t i a l m i x i n g r e g i o n i n wh ich t h e f l o w i s e s s e n t i a l l y asymmetr ic.

i s e s s e n t i a l l y ax isymmet r ic .

and f u l l y mixed reg ions .

sp read ing of t h e plume were c o r r e l a t e d s e p a r a t e l y t o t h e sp read ing c h a r a c t e r i s t i c s o f a c o n i c n o z z l e because o f t h e i r i n h e r e n t d i f f e r e n t spread ing c h a r a c t e r i s t i c s i n t h e s e two n o z z l e p lanes .

( b ) A f u l l y mixed r e g i o n i n wh ich t h e f l o w

( c ) A t r a n s i t i o n r e g i o n between t h e i n i t i a l

3. The two-dimensional h e i g h t and w i d t h

4. The two-dimensional plume v a r i a t i o n o f s t a t i c t empera tu re w i t h v e l o c i t y was s i m i l a r t o t h a t f o r c o n i c nozz les .

5. The c o r r e l a t i o n s deve loped h e r e i n p r o v i d e a means o f e s t i m a t i n g t h e plume c e n t e r l i n e s t a t i c t empera tu re decay f r o m c o l d - f l o w plume c e n t e r l i n e v e l o c i t y decay measurements.

1.

2.

3 .

4.

5.

6.

7.

8.

9.

10.

11.

12.

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7

13. Chambers, F.W., and Goldschmidt, V.W., " A c o u s t i c I n t e r a c t i o n W i t h a T u r b u l e n t P lane J e t - E f f e c t s on Mean Flow," A I A A Paper 81-0057, Jan. 1981.

14. Goldschmidt, V.W., and Ka ise r , K.F., " I n t e r - a c t i o n o f an Acous t i c F i e l d and a T u r b u l e n t P lane J e t : Mean Flow Measurements." AIChE Chemical Eng ineer ing P rog ress S y m p o s i u m Ser ies , Vo l . 67, No. 109, 1971, pp. 91-98.

15. Thomas, F.O., and Goldschmidt, V.W.: " I n t e r - a c t i o n o f an Acous t i c D is tu rbance and a Two- D imens iona l Tu rbu len t J e t : Exper imeq ta l Data," Jou rna l o f F l u i d s Eng ineer ing , Vo l . 105, No. 2, June 1983, pp. 134-139.

16. K r o t h a p a l l i , A., Basanoff , D., and Karamchet i , K.; "Bas i c S t u d i e s o f M u l t i p l e F r e e and Conf ined Je ts , " AFOSR TR-84-1176, 1984.

17. Groesbeck, D.E., H u f f , R.G., and von Glahn, U.H.: "Comparison o f J e t Mach Number Decay Data Wi th a C o r r e l a t i o n and J e t Spread ing Contours f o r a L a i y e V a r i e t y o f Nozzles," NASA T N D-8423, 1977.

18. H igg ins , C.C., K e l l y , D.P., and Wainwr igh t , T.W., "Exhaust J e t Wake and T h r u s t C h a r a c t e r i s t i c s o f Severa l Nozz les Designed f o r VTOL Downwash Suppression," NASA CR-373, 1966.

19. H igg ins , C.C., and Wainwright, T.W., "Dynamic P ressu re and T h r u s t C h a r z c t e r i s t i c s o f Co ld J e t s D i s c h a r g i n g f r o m Severa l Exhaust Nozzles Des igned f o r VTOL Downwash Suppression," NASA TN D-2263, 1964.

20. Rockwel l , D., " E x t e r n a l E x c i t a t i o n o f P l a n a r Jet ," J o u r n a l of A p p l i e d Mechanics, - Vol . 39, No. 4, Dec. 1972 , pp. 883-890.

21. Balsa, T. e t a l . : "H igh V e l o c i t y J e t No ise Source L o c a t i o n and Reduct ion : Task 2- T h e o r e t i c a l Developments and Bas ic Exper iments," FAA Repor t No. FAA-RD-76-79, 11, May 1978.

22. Fzrthmann, E., "Tu rbu len t J e t Expansion,"

23. Davies, A.E., K e f f e r , J.F., and Baines, W.D., "Spread o f a Heated P lane T u r b u l e n t Je t , " Phys i cs o f F l u i d s , Vo l . 18, No. 7, J u l y 1975,

NACA TM-789, 1934.

pp. 770-f75.

8

1

BASIC ORIFICES

CHANNEL

CHANNEL-WALL ORIFICE WALL NOZZLE

WALL AND PARALLEL PLATES

FIGURE 1. - SCHEMATIC SKETCHES OF VARIOUS ORlF ICEA lALL CONFIGURATIONS REPORTED ON I N THE LITERATURE.

VELOCITY TEMPERATURE -_-

2

INNER Y

INNER

FIGURE 3. - SCHEMATIC SKETCH OF INNER AND OUTER PLUME MIX- ING REGIONS.

x\ t Z m1/5 / A . cbl , 4 I N N E R

:

- ORIFICE/NOZZLE FLOW -- ENTRAINED FLOW

AXIAL DISTANCE. X

FIGURE 5. - SCHEMATIC SKETCH OF THE EFFECT OF TWO-DIMEN- SIONAL NOZZLE ASPECT RATIO ON THE PLUME CENTERLINE VEL- OCITY AND TEMFERATURE DECAY.

0

TYPE

0 ORIFICC 0 NOZZLE

0 O C P

0.8 1.05

0

(A ) NOMINAL AR. 6.0. 1 1 1 > 'L1 E

0 12 ORIFICE 0 12 ORIFICE

I 01 0 13.3 NOZZLE -~ ~ .1 1 2 4 6 8 1 0 20 30

(B) NOMINAL AR. 12.0; REFERENCE 17; M j . 0.8. F l G U R t 7. - COMPARISON OF PLUME CENTERLINE VELOCITY DECAY

FOR VARIOUS TWO-DIMENSIONAL ORIFICES AND NOZZLES. COLD FLOW.

OR I F I C E

NOZZLE w----= F I G W E 6. - SCHEMATIC SKETCH SHOWING GROSS

DIFFERENCES BETWEEN ORIF ICE AND NOZZLE PLUME STREAMLINES.

AR M j REFER-

1.0 0.78 19 0 0 6.0 .78 19

13.3 .80 17 0 21.7 .lo 22 A

ENCE

- CONIC NOZZLE, REFERENCE 1 n

A Q n

-

FIGURE 8. - EFFtCT OF N O l l l € ASPFCT RATIO. AR. ON THE PEAK CENTERLINE VELOCITY DFCAY OF IWO-DIMENSIONAL NOZZLES. COLD FLOW.

10

0 5 0.78

0 30 1.05 0 30 .78

- CONIC NOZZLE. REFERENCE 1 .

O 0 O O \ 0 B

FIGURE 9. - EFFECT OF FLARE ANGLE (DELTA NOZZLE) ON PLUME CENTERLINE VELOCITY DECAY. REFERENCE 19; COLD FLOW.

1 .o .8 -

.6 -

.4 - .- a \ 3

- Tj , 0 K O

. 1 7 2 4 6 8 1 0 20 1

FIGURE 11. - EFFECT OF JET TEMPERATURE ON DELTA NOZZLE CENTERLINE VELOCITY DECAY. Mi, 1.07; 0, 5'. REFER- ENCE 18.

FIGURE 10. - PLUME CENTERLINE VELOCITY DECAY FOR TWO- DIMENSIONAL NOZZLE OF AR = 5. M , 0.967; REFERENCE 21

294 90 1

CONIC NOZZLE, REFERENCE 1

0 0

FIGURE 12. - PLUME CENTERLINE STATIC STATIC TEMPERATURE DECAY FOR A DELTA NOZZLE OF AR = 5 AND p = 5' T i , 901 K; REFERENCE 18.

1 1

1 .o

.8

.6

. 4

r , n "I

- - - -

- 0 1.0 0.78 19 0 6.0 .78 19 0 13.1 .80 17 n 21.7 .lo 22

-

- CONIC NOZZLE. REFERENCE 1

* 2 4 6 8 10 20

.2

1

.- a 'U 3

FIGURE 13. - CORRELATED PLUME CENTERLINE VELOCITY DECAY I N THE I N I T I A L MIXING REGION OF TWO-DIMENSIONAL NOZZLES. COLD FLOW

AR M j REFER- ENCE

0 6.0 0.78 19 0 13.3 .80 17 0 21.7 .10 22

6.0 .04 23 SOLID SYMBOLS INDICATE CALCULATED

DEPARTURE POINTS

.o

.8

.6

. 4 4 6 8 10 20

CONIC NOZZLE

I I I I l l 20

. 4 4 6 8 10

FIGURE 15. - CORRELATION OF PLUME CENTERLINE VELOCITY DECAY DATA I N THE TRANSITION REGION OF TWO-DIMENSIONAL NOZZLES. COLD FLOW.

1

E u 0 i % 5- w ' lU

.6

.4

.- a 'U x

. 2

. 1

0 5 294 1.07 0 5 901 1.07 0 30 294 .78 A 30 294 1.05 - CONIC NOZZLE. REFERENCE 1

FIGURE 14. - CORRELATED PLUME CENTERLINE VELOCITY DECAY I N THE I N I T I A L MIX ING REGION OF TWO-DIMENSIONAL DELTA NOZZLES. REFERENCE 18 DATA.

CONIC NOZZLEJ' \

0 901

SOLID POINTS INDICATE DEPARTURE POINT

20 40

FIGURE 16. - CORRELATION OF PLUME CENTERLINE VELOCITY DECAY DATA I N THE TRANSITION REGION OF TWO-DIMENSIONAL DELTA NOZZLES. p, 5': M j . 1.07: REFERENCE 18.

12

-

- 1.0 >: U .8 g 2

a 4 ' V 3

a .2 - AR Po Mi Tj I REFER- $ 2 e 6 -

W I n. LT .- K ENCE

0 1 0 0.80 294 19 F 7 E , . 4 w 2

o v

0 6 0 0 . 7 8 294 19 0 13 0 0.80 294 17

5 5 1.07 294 18 v 5 5 1.07 901 18

CONIC NOZZLE,

2

w-. k z w U - z -I n.

.2 10 20 40

. 1

FIGURE 1 7 . - CORRELATION OF P L U M CENTERLINE VELOCITY DE- CAY DATA I N FULLY-MIXED REGION FOR UNFLARED AND FLARED TWO-DIMENSIONAL NOZZLES.

AR Po T j / T a REFER- ENCE

0 6 0 1.05 23 0 5 5 3.07 18 (DELTA)

- - - -

-

- CONIC NOZZLE

-

I I I I l l 1

AR Po Tj I T a REFER- ENCE

0 6 0 1.05 23 0 5 5 3.07

1.0 - SOLID SYMBOLS INDICATE

DEPARTURE POINTS

/SLOPE, -0.5 -

.4 -

-

18

CALCULATED

FIGURE 19. - CORRELATED PLUME CENTERLINE TEMPERATURE DECAY I N TRANSITION REGION OF TWO-DIMENSIONAL NOZZLES.

FIGURE 18. - CORRELATED PLUME CENTERLINE TEMPERATURE DE- CAY I N I N I T I A L MIXING REGION OF TWO-DIMENSIONAL NOZZLES.

I AR REFER- AR REFER- ENCE I ENCE

1 10 20 40 10 20 40

(A) DELTA NOZZLE: M j , 1.07: T j / T a . 3.07.

( B ) SHARP-EDGE ORIFICES: M j ,

1 .o

m

I

c

.- c \ -- .5 u -

0

AR TYPE REFER- ENCE

0 6 NOZZLE 23

0 1 0 ORIFICE A 2 0 V 40 0 10 1 1

- D 5 DELTA NOZZLE

- CONIC NOZZLE. REFERENCE 1

0

I

. 5 J

1.0

FIGURE 21. - TYPICAL VARIATION OF LOCAL PLUME CENTER- L I N E TEMPERATURE RATIO WITH LOCAL VELOCITY RATIO FOR TWO-DIMENSIONAL NOZZLES AND ORIFICES.

1 .o

m - I

U I

\ m

I

@z

- 1

U a

a ‘@z

0 0 RADIAL DISTANCE FROM NOZZLE CENTERLINE

( A ) CORE REGIONS. (B) DOWNSTREAM OF CORE REGIONS.

FIGURE 22. - SCHEMATIC REPRESENTATION OF PLUME RADIAL MCAY PROFILES I N NOZZLE WIDTH ( Y ) AND HEIGHT (Z) DIRECTIONS.

c

..

1 4

. START OF RADIAL I DECAY, 1.0

.8

.6 > u h 3

3 'p: - .4

. 2

1

0

0 a ( A ) NOZZLE AR. 6: M j . 0.78: REFERENCE 19: X/De. 2:

COLD FLOW.

START OF RADIAL DECAY,

5 ) s

.o

.8

.6

.4

W D e 0 2 . 8 0 5.6 0 1 6 . 8

CL u I-

0 .4 .8 1.2 1.6 2.0 y/yo. 5

(B) ORIFICE AR, 40; T i , 3 7 3 K: REFERENCE 8. FIGURE 2 3 . - REPRESENTATIVE RADIAL VELOCITY AND TEMPER-

ATURE DECAY DATA I N WIDTH DIMENSION ( Y ) OF TWO-DIPEN- SIONAL CORE REGION.

1 .o

. 8

.2

0

S I M I L A R I T Y PROFILE, CONIC t \ - NOZZLE, REFERENCE 1

I ( A ) NOZZLE AR, 6; M i , 0.78 ; X/D,, 2; REFERENCE 19. COLD

FLOW.

.6 - > U

p:

A

a \

3 u .4 -

.2 -

. 5 2 2 . 5 1 , 1 . 5 \ 0 y /y0 .5 - ( y / y 0 . 5 ) s

(B) ORIFICE AR. 40: Ti, 373 K: REFERENCE 8. FIGURE 24. - CORRELATED RADIAL VELOCITY AND TEMPERATURE

DECAY DATA I N WIDTH DIMENSION ( Y ) OF TWO-DIMENSIONAL CORE REGION.

1 5

N - 3"

'2 3 u

z/zO. 5 ( A ) NOZZLE HEIGHT. Z .

( B ) NOZZLE WIDTH. Y .

FIGURE 2 5 . - RADIAL VELOCITY DECAY I N P L U M TRANSITION FLOW REGION OF A TWO-DIMENSIONAL NOZZLE. AR. 6: M j , 0.78: COLD FLOW: REFERENCE 1 9 DATA.

1.0

.8

.6 N

h

3 ' 3

.-

v

.4

. 2

0 1

1.0

.8

.2

0

I (A) RADIAL VELOCITY.

r

z/zO. 5

( B ) RADIAL TEMPERATURE. FIGURE 2 6 . - RADIAL VELOCITY AND TEMPERATURE PROFILES OF

REFERENCE 23: U j , 1 3 . 5 W S : A TWO-DIMENSIONAL NOZZLE. Tj - T a , 1 4 . 6 K; AR. 6 .

Z

I r HEIGHT CORE

AR PLANE T i ,

10 z 473 10 Y 473 1 RADIAL 448

1.0 K

CONIC NOZZLE, REFERENCE 1

.8

.6

. 4 TRANSITION REGION

.2

U

CL

a \ 3

YN0.5* z/z0.5 (B) X/De. 19.6.

FIGURE 27. - RADIAL VELOCITY AND TEMPERATURE PROFILES OF A TWO-DIMENSIONAL ORIFICE. REFERENCE 8: AR, 6.

b/2

7-- (A) NOZZLE HEIGHT DIRECTION.

Y

. -

X --

NOZZLE k ----- '. WIDTH CORE-/- --

(B) NOZZLE WIDTH DIRECTION. FIGURE 28. - SCHEMATIC SKETCH ILLUSTRATING RADIAL SPREADING

DINENSIONS FOR THE LOCAL HALF-VELOCITY. Uc/2.

10

8 n x 0

N

. 6 x 0

n

2

0 20 40 60 80 100 120 X/ b

FIGURE 29. - EFFECT OF ORIFICE TYPE ON JET SPREAD. h. 0.4 CM; 1. 4 CM: De, Re. 12200: 1.427 CM: AR, 10;

REFERENCE 5 .

17

3.0

2.5

na 2.0 'm 0

N . 1.5 nw \ m 0 1 > c , AR REFER- ENCE - NOZZLE 6.0 19 J ---- CHANNEL NOZZLE 10.0 9

c 1 CONIC NOZZLE CURVE 7

1

0 0

0

50 100 .01

1 5 10

FIGURE 31. - LOCAL PLUME HALF-VELOCITY (U,/2) VARIATION I N NOZZLE HEIGHT ( Z ) DIMENSION AS A FUNCTION OF AXIAL E X I T PLANE.

10

1 .o

n N

t A

100 .01

1 10

~~ X ( t j / t a ) 0 . 2 5 fi (Fz,x) De

FIGURE 32. - CORRELATED LOCAL PLUME HALF-VELOCITY (U,/2) I N NOZZLE HEIGHT ( Z ) DIMENSION.

.01 1 5 10 50 1 0 0

FIGURE 33. - LOCAL PLUME HALF-VELOCITY (U,/2) VARIATION I N NOZZLE WIDTH ( Y ) DIMENSION AS A FUNCTION OF AXIAL DISTANCE FROM NOZZLE E X I T PLANE.

AR Po 0 1 0 0 6 0 0 10 0 A 5 5 v 2 30 0 5 30

.1

- I

-1-4

> ‘

NOZZLE E X I T PLANE

2.Y AXES

t b/2, P/2

NOZZLE - - x * (A ) OVERALL PLUME HALF-VELOCITY SPREADING ANGLE.

b/2.8/2

X-- 1.- NOZZLE k ( B ) LOCAL PLUME HALF-VELOCITY SPREADING ANGLE.

FIGURE 35. - SCHEMATIC SKETCH OF PLUME HALF-VELOCITY SPREADING ANGLE.

7

6

W

n

i s W -1 W L 4

W

E 4 n 4 W z n v )

cu \ 2 3 F

2 2

-1 n -1

? 0

1

0

7

6

a x .- 5 a

tu -1 W L 4

E 4

Qu 3

n

n

4 W c*

v)

a

A m

$ 2 s U

1

0

- 0 NOZZLE HEIGHT 0 NOZZLE WIDTH 0 CONIC NOZZLE

10 20 30 40 X/De

( B ) LOCAL PLUME HALF-VELOCITY SPREADING ANGLE.

FIGURE 36. - REPRESENTAl lVt TWO-DIENSIONAL NOZZLt PLUME HALF-VELOCITY SPREADING ANGLt CHARACTCHISTICS. R t F t R - ENCE 19 DATA: AR. 6; COLD FLOW; NOMINAL M j . 0.8.

20

2. Government Accession No. NASA 1M-89812 AIAA-87-2111

1 Report No

4 Title and Subtitle

Two-Dimensional Nozzle Plume Characteristics

~ ~~

3. Recipient's Catalog No

5 Report Date

7 Author(s)

Uwe H. von Glahn

~ ~~~

9 Performing Organization Name and Address

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

6. Performing Organization Code

505-62-91 8. Performing Organization Report No.

E-3456 10. Work Unit No.

~ ~~ ~- - 1 Technical Memorandum 2 Sponsoring Agency Nane and Address

~- - - 9 Security Classif (of this report) 20 Security Classif (01 'age) 21 No of pages

Unclassified Unclassified 21 . ~~~~

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

22 Price'

A02

I ~~

5 Supplementary N o t ~ s

Prepared for the 23rd Joint Propulsion Conference, cosponsored by the AIAA, SAE, ASME, and ASEt, San Diego, California, June 29 - July 2, 1987.

-~ - 6 Abstract

Future high performance aircraft will likely feature asymmetric or two-dimensiona nozzles with or without ejectors. ejector systems o f minimum size and weight, the plume decay and spreading char- acteristics of basic two-dimensional nozzles must first be established. The present work deals with the experimental analyses of these plume characteristics and includes the effects of nozzle aspect ratio and flow conditions (jet Mach number and temperature) on the plume decay and spreading of two-dimensional noz- zles. Correlations including these variables are developed in a manner similar to those previously developed successfully for conic and dual-flow plumes.

In order t o design two-dimensional nozzle/

_____ - ~___- 7 Key Words (Suggested by Author(s))

Jet plume Jet characteristics

18. Distribution Statement

Unclassified - unlimited STAR Category 02