mean flow and turbulence measurements in a triangular turbulent free jet

7/27/2019 Mean Flow and Turbulence Measurements in a Triangular Turbulent Free Jet

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M e a n f l o w a n d t u r b u l e n c e m e a s u r e m e n t sin a t r i a n g u l a r t u r b u l e n t f r e e j e tW . R . Q u i n nD e p a r t m e n t o f E n g i n e e r i n g , S t . F r a n c i s X a v i e r U n i v e r s it y , A n t i g o n i s h , N o v a S c o t ia , C a n a d a

D e t a i le d m e a n f l o w a n d t u r b u l e n c e m e a s u r e m e n t s w e r e m a d e , u s in g h o t - w i r e a n e m o m e t r y ,in t h e n e a r f l o w f i e ld o f a tu r b u l e n t , i n c o m p r e s s i b l e a i r j e t i s s u in g f r o m a s h a r p - e d g e de q u i la t e r a l t r ia n g u l a r s l o t i n t o s t a g n a n t a i r s u r r o u n d i n g s . T h e m e a s u r e d q u a n t i t ie s i n c l u d e dt h e t h r e e c o m p o n e n t s o f t h e m e a n v e l o c i t y v e c t o r , t h e t h r e e t u r b u l e n c e i n t e n s i t i e s , a n dt wo o f t he Reyno l ds shear s t resses . The resu l t s i nd i ca t e t ha t t he j e t sp reads f as t e r on i t sbase s i de t han a t i t s apex . Th i s d i f f e rence i n sp read i ng l eads t o an i nve rs i on o f t he j e ts h a p e a t a b o u t f i v e e q u i v a l e n t s l o t d i a m e t e rs d o w n s t r e a m f r o m t h e s l o t e x i t p la n e . T h eR e y n o l d s s h e a r s t re s s le v e ls , c o m p a r e d t o t h o s e f o u n d i n r o u n d t u r b u l e n t f r e e j e t s a t t h es a m e d o w n s t r e a m l o c a t io n s , a r e h i g h e r i n t h e t ri a n g u l a r j e t, i m p l y i n g i m p r o v e d m i x i n g .K e y w o r d s : t r i a n g u l a r j e t ; t u r b u l e n c e ; s h a r p - e d g e d s l o t

I n t r o d u c t i o nTr i a n gu l a r t u r bu l e n t f r e e j e t s , l ike o t he r t u r bu l e n t f r ee j e t si s s u i ng f r om nonc i r c u l a r s l o t s o r noz z l e s , a r e u s e d o r ha ve t hepo t e n t i a l f o r u s e i n t e c hn i c a l a r e a s o f i n te r e s t r a ng i n g f r oma e r os pa c e t o c he m i c a l t o m e c ha n i c a l e ng i ne e r i ng . Som e a r e a so f a p p l i ca t i o n o f tr i a n g u l a r t u r b u l e n t j e t s a r e i n c o m b u s t i o nc ha m be r s o f e t e ng i ne s , bo i l e r f u r na c e s , a nd ga s - t u r b i ne p l a n t sof e lec t r i c po we r u t il it ies . Ra pid mix ing i s a prerequ is i t e forg o o d p e r f o r m a n c e i n m o s t a p p l i c a ti o n s . E c o n o m i c e x p ed i e n cym a y , in s om e a pp l i c a t i ons , r e qu i r e t ha t s h a r p - e dge d s l o ts beus e d i n p r e f e r e nc e t o noz z l e s w i t h c on t o u r e d ups t r e a m s ha p i ng .P r e v i ous e xpe r i m e n t a l w or k on t r i a ngu l a r t u r bu l e n t f r e eje t s 1-3 has invo lved je t s i ssuing f rom e i ther i sosceles an de qu i l a t e r a l t r i a ng u l a r duc t s ~ o r f r om i sos ce le s a nd e qu i l a t e r a lt r i ang ular or if ices , 2 '3 wi th smal l u ps t re am bel l -m outh radi i ,a t t a c he d t o p i pe s o f c i r c u l a r c r os s s e c ti on . The s e f l ow c on f i gu r -a t i ons oc c u r , a l on g w i t h s ha r p - e d ge d s l o t s , i n p r a c t i c a l s y s t e m s .The f l ow o f a t u r bu l e n t f r ee j e t , i s s u i ng f rom a s ha r p - e d ge dt r i a ngu l a r s l o t ha s t hus f a r , how e ve r , no t be e n s t ud i e d .Th i s s t udy p r e s e n t s de t a i l e d m e a n f l ow a nd t u r bu l e nc e da t af o r t he f l ow , i n t he ne a r f l ow fi el d, o f a t u r bu l e n t , i nc om pr e s s i b l ea i r j e t i s s u ing f r om a s ha r p - e dge d e qu i l a t e r a l t r i a ngu l a r s l o ti n t o s t a g n a n t a i r s u r r o u n d i n g s . T h e d e c a y o f t h e m e a n s t re a m -w i se ve l oc i t y a l ong t he j e t c e n t e r l i ne i s a ls o p r e s e n t e d . The s l o te x it p l a n e R e y n o l d s n u m b e r , b a s e d o n t h e e q u i v a l e n t d i a m e t e ro f t he t r i a ngu l a r s l o t ( s a m e a s t he d i a m e t e r o f a r oun d s l o t w i t ht he s a m e e x i t a r e a a s t he t r i a ngu l a r s l o t) , w a s a bo u t 2 .08 x 105 .T h e m e a n s t r e a m w i s e v e l o c i t y a n d s t r e a m w i s e t u r b u l e n c ei n t e ns i ty a t t he c e n t e r o f t he s l o t e x i t p l a ne w e r e 60 m s - 1 a nd0 .5% , r e s pe c ti ve ly .

E x p e r i m e n t a l a r r a n g e m e n t a n d p r o c e d u r eTh e f low fac i l i ty , descr ib ed in de ta i l e l sewhere , 4 is o f theb l ow - dow n t ype a nd c ons i s t s o f a s m a l l c e n tr i f uga l f a n , a s e t tl i ngAddress reprint requests to Dr. Quinn at the D epartment of Engin-eer ing, St. Francis Xavier U niversi ty , Ant igonish, No va Scot ia,Canada B 2G 1C 0 .Received 10 Ju ly 1989; accepted 12 February 1990 1990 Butterworth-Heinemann

c h a m b e r , a t h r e e -d i m e n s i o n a l ( 3 - D ) c o n t r a c t i o n a n d t h e s h a r p -e dge d e qu i l a t e r a l t r i a ngu l a r s l o t . The e qu i l a t e r a l t r i a ngu l a r s l o tw a s a s s e m bl e d , i n a m a c h i ne d r e t a i n i ng p l a t e , f r om t h r e em a c h i n e - m i t e r e d p i ec e s o f a l u m i n u m . O n e o f th e a l u m i n u mpi e c e s is s how n by s o l i d l ine s in F i gu r e 1 ; t he o t he r t w o p i e c e sa r e s h o w n b y d a s h e d li ne s. T h e f a n d r a w s a i r f r o m a r o o ma d j a c e n t t o t he l a bo r a t o r y a nd f e e ds i t t o t he s e t t l i ng c ha m be r ,w h i c h i s f i t t e d w i t h a ba f f l e a t i t s ups t r e a m e nd , a n a l um i numho ne y c om b w i th he x a gona l c el ls a nd f i ve m e s h - w i r e s c r e e ns o f6 9 % p o r o s i t y . T h e 3 - D c o n t r a c t i o n , w h i c h i s a t t a c h e d t o t h ed o w n s t r e a m e n d o f th e s e t tl in g c h a m b e r , h a s a c o n t o u r t h a t isba s e d on a t h i r d - de g r e e po l ynom i a l w i t h z e r o de r i va t i ve e ndc ond i t i ons . Th e s ha r p - e dge d e q u i l a t e ra l t r i a ngu l a r s l o t c a ps t hed o w n s t r e a m e n d o f t h e 3 - D c o n t r a c t io n . T h e je t i s su e s f ro mt he s l o t i n t o a c a ge , w h i c h i s ope n a t t he dow ns t r e a m e nd a ndc ove r e d on t he t o p a n d s i de s w i th s te e l da m p i ng s c r e e ns o f 42%p o r o s i t y .The s e ns i ng p r obe i s m ove d i n t he f l ow f i e l d by a s t e pp i ng -m ot o r - d r i ve n , m i c r oc om pu t e r - c on t r o l l e d , 3 - D t r ave r s i ng s ys te m .Pos i t i on i ng a c c u r a c y i s 0 . 3 m m i n t he s t r e a m w i s e ( x ) d i r e c t iona nd 0 .01 m m i n t he s pa nw i s e ( y ) a nd l a t e ra l ( z) d i re c t i ons . Ade f in i t ion s ke t c h o f t he c oo r d i na t e s ys t e m a nd t he c o r r e s po nd i ngc o m p o n e n t s o f th e m e a n v e l o c it y v e c t o r i s p r e s e n te d i n F i g u r e 2 .A r a c k - a nd - p i n i on s ys t e m i s u s e d f o r t r a ve r s i ng i n t he xd i r e c t i on , a nd l e a d s c r e w s a r e u s e d f o r t r a ve r s i ng i n t he y a ndz di rec t ions .X - a r r a y h o t - w i r e p r o b e s w e r e u s e d f o r t h e m e a n f l o w a n dt u r b u l e n c e m e a s u r e m e n t s . T h e h o t - w i r e p r o b e s , o p e r a t e d b yl i ne a r i z e d c ons t a n t t e m pe r a t u r e a ne m om e t e r s a t a r e s i s t a nc era t io of 1 .8 , were ca l ib ra ted in the in i t i a l region of the t es t j e t .T h e t w o w i re s o f t h e X - a r r a y p r o b e s w e r e m a t c h e d b y y a w i n gt he p r obe s s l i gh t l y (by a bo u t 0 .5 ) . C or r e c t i ons f o r t e m pe r a t u r eva r i a t i ons f r om t he c a l i b r a t i on t e m pe r a t u r e a nd f o r t he e f f e c to f t a nge n t i a l c oo l i ng w e r e m a de i n t he da t a r e duc t i on s o f t w a r e .A 12 -b it A / D boa r d , w i t h 16 a na l og i np u t c ha nne l s , a m u l t i p le xe r ,a nd a s a m pl e - a nd - ho l d un i t , w a s u s e d t o d i g i t i z e t he ho t - w i r es i gna ls . S i gna l c ond i t i on i ng w a s e f fe e te d b y t w o o t he r s a m pl e -a nd - ho l d un i t s , l ow - pa s s a na l og f i l t e r s w i t h a 5 - kH z c u t - o f ff r e que nc y a nd 4 0 - dB / de c a d e r o l l - o f f a nd a m pl i fi e rs . The m e a na nd r m s f l uc t ua t i ng ve l oc i t i e s w e r e ob t a i ne d by s a m pl i ngbe t w e e n 75 ,000 a nd 100 ,000 po i n t s a t 1 kH z , de pe n d i ng on t hel oc a t i on i n t he f l ow .

220 Int . J. Heat and Flu id Flow, Vo l . 11, No. 3, Septemb er 1990


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w 2 Re y n o ld s n o rm a l s t r e s s i n t h e z d i r e c t io nx St rearnwise ca r tesian coo rd in a tey Sp a n w ise c a r t e s i a n c o o rd in a t ez La t e ra l c a r t e s i a n c o o rd in a t eV 2 La p la c i a n o p e ra to r"Greek symb olsv K in e m a t i c v i sc o s i ty o f f lu idf l~ M e a n s t r e a m w ise v o r t i c i tyf~y M e a n sp a n w ise v o r t i c i tyfl = M e a n l a t e ra l v o r t i c i tySubscrip tsC1 Cen te r l ine va luee x i t V a lu e a t t h e c e n t e r o f t h e s l o t e x i t p l a n em a x M a x im u m v a lu e o n t h e j e t c e nt er li n e

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mixing . The p otentia l core length s o f the sharp-edged triangulara n d ro u n d s lo t j e t s, d ed u ced f rom F ig u re 3 (b ) , a re 3 . 1D = a n d4 . 4 D = , r e s p e c t i v e l y . T h e s h o r t e r p o t e n t i a l c o r e l e n g t h o f t h et r i a n g u la r j e t , a l s o e v i d e n t i n F i g u r e 3 ( a ) a n d i n a g r e e m e n t w i t ht h e r e su l ts o f G u t m a r k e t a l . , 1 ndicates be t ter near- f i e ld mix ing .M e a n s t r ea m w i s e v e l o c it y c o n t o u r s p l o t s a t f i ve d o w n s t r e a ms t a t i o n s a r e p r e s e n t e d i n F i g u r e 4 . I n t h e r e g i o n c l o s e t o t h es lo t ex i t p lane ( x / D , = 0 . 2 8 a n d x / D = = 0 . 5 ) , t h e c o n t o u r s h a v et h e t r i a n g u l a r s h a p e p r e s c r i b e d b y t h e s l o t . F u r t h e r m o r e , t h e0 . 5 c o n t o u r i s fa r th e r f r o m t h e c e n t e r o f t h e j e t - - s h o w n b y ac r o s s i n F i g u r e 4 a n d i n a l l s u b s e q u e n t f i g u r e s - o n t h e a p e xs ide than o n th e base s ide o f the je t . This d i f ference ind icatesf as te r s p r e a d i n g o f t h e j e t o n i t s a p e x s i d e i n t h i s r e g i o n o f t h ef l o w . A t x / D , = 1 , t h e c o n t o u r s h a v e a q u a s i - a x i s y m m e t r i cs h a p e , a n d s p r e a d i n g o n t h e b a s e s i d e is n o w f a s te r t h a n o n t h ea p e x s i d e . F a r t h e r d o w n s t r e a m ( a t x / D , = 5 a n d a t x / D . = 10),t h e c o n t o u r s h a v e a n i n v e r t e d t r i a n g u l a r s h a p e , b u t f a s t e rs p r e a d i n g s ti ll o c c u r s o n t h e b a s e s i d e o f t h e j e t a s v i e w e d f r o mt h e s l o t e x it p l a n e . T h e c h a n g i n g s h a p e o f t h e m e a n s t r e a m w i s ev e l o c i t y f ie ld o f t h e j e t a s i t d e v e l o p s d o w n s t r e a m , in v i e w o fth e su b seq u en t d i scu ss io n in co n n ect io n w i th th e R ey n o ld ss t r e s s e s , i s n o t e w o r t h y . T h e d i f f e r e n c e i n t h e s i z e o f t h et r ia n g u la r s lo t - - su p er im p o sed w i th d a sh ed f in es o n a l l th ef i g u r e s s h o w i n g c o n t o u r m a p s - - - i s c a u s e d b y t h e c o n t o u r -p l o t t i n g s o f t w a r e , w h i c h e n l a r g e s t h e m e a s u r e m e n t g r i d f o rx / D = _ 1 a n d c o n t r a c t s i t f o r x /D= > 1 .C o n t o u r s o f t h e m e a n s p a n w i s e v e l o c it y a n d t h e m e a n l a te r a lvelocity are shown in F igure 5 (a ) and (b) , respect ively . Thes e c o n d a r y f l o w p a t t e r n , i n t h e n e a r - f l o w f i e l d , i s m a d e u p o ff o u r c o u n t e r r o t a t i n g c e l l s . T h e s p a n w i s e s e c o n d a r y f l o w c e l l s

su g g es t in flo w a t th e b a se s id e a n d o u t f lo w a t th e a p ex s id e o fthe jet . The la tera l second ary f low cel ls suggest f low from thea p ex s id e in to th e b a se s id e o f th e j e t. T h e co m b in ed e f f ec t o fthe spanwise and la tera l secondary f low cel ls i s consistent withthe faster spreading o f the jet on i ts base s ide, as no ted earl ier .T u r b u l e n c e q u a n t i t ie sT h e s t re a m w i s e t u r b u l e n c e i n t e n s i t y v a r i a ti o n a l o n g t h e j e tc e n t e r l in e i s s h o w n i n F i g u r e 6 . T h e r e s u l ts f o r j e t s i s s u in g f r o ma s h a r p -e d g e d r o u n d s l o t a n d f r o m a c o n t o u r e d r o u n d n o z z l ea r e i n c lu d e d f o r c o m p a r i s o n . A s t e e p i n c r e a s e i n t h e s t r e a m w i s eturbulence in tens i ty i s observed in a l l three f lows in i t ia l ly . Thisi n c r e a s e i s a c o n s e q u e n c e o f s h e a r l a y e r g r o w t h a n d t h e r e s u l t i n gh i g h p r o d u c t i o n o f t u r b u l e n c e , w h i c h i s t h e n d i ff u se d f r o m t h eshear l ayer s t o t he j e t cen t er l ine . Th e h igher s t r eamw iseturbulence in tensity va lues in the tr iangular jet f low, in thein it ia l reg ion , prov ide further ev idence o f better near-f ie ldmix ing in the tr iangular jet . The decrease in the streamwiseturbulence in tensity in the tr iangular jet f low, in the reg ionx / D = = 8-10 , ref lects the drop in turbulent act iv i ty that accom-panies the m erg ing o f the shear layers eman ating from the threesides of the equilateral triangular slot.

The streamwise turbulence in tensity contours are presentedin F ig u re 7 . T h e sh a p es o f th e m ea n s t rea m w ise v e lo c i tyco n to u rs , p resen ted in F ig u re 4 , a n d th o se o f th e s t ream w isetu rb u len ce in ten s i ty co n to u rs a t th e co rresp o n d in g d o w n strea m

2 . 5 4

t . 2 7

- 2 . 5 4 - 2 . 5 4

/ \/ \

- 1 . 2 7 0 1 . 2 7 2 . 5 4Y k m )(=)

\ \

2 . 5 4

! . 2 7

N~ 0

- 2 . 5 4

F i g u r e 5x / D . = 1 .0

- 2 . 5 4

/ \/ \

- ! . 2 7 0 ! . 2 7Y t ~(w

\\

2 . 5 4

( a ) V / U c , c o n t o u r s a t x / D , = 1 .0 ; ( b ) W / U c , c o n t o u r s a t

2 2 2 I n t . J . H e a t a n d F l u i d F l o w , V o l . 1 1 , N o . 3 , S e p t em b e r 1 9 9 0


4/5

30x/De

Figure 6 Streamwise turbulence intensity variation along the jetcenterline

Figure 7 n/UC, contours

stations in Figure 7 correspond closely. Furthermore, largestreamwise turbulence intensity gradients are found, as ex-pected, in regions where the local shear in the mean streamwisevelocity is high and vice versa. The spanwise and lateralturbulence intensity contours are shown in Figures 8 and 9,respectively. The shapes of the spanwise and lateral turbulenceintensity contours are similar to those of the streamwiseturbulence intensity contours. However, the maximum valuesof the spanwise and lateral turbulence intensities are less thanthose of the streamwise turbulence intensities at all the down-stream stations. These results reflect the fact that the spanwiseand lateral velocity fluctuations acquire their energy, by meansof pressure fluctuations, from the streamwise velocity fluctu-ations. The Reynolds normal stresses, derivable from theturbulence intensities by squaring, are clearly anisotropic. Suchanisotropy of the spanwise and lateral Reynolds normal stresses

Flow and turb ulence measurements in a tr iangular jet : W. R. Quinntriggers turbulence-generated secondary flowss (Prandtls sec-ondary flows of the second hind), which represent streamwisevorticity production. The transport of the mean streamwisevorticity in a steady, incompressible flow is given by

Figure 8 fl/U,, contours

(1)

Int. J. Heat and Fluid Flow, Vol. 11, No. 3, September 1990 223


5/5

F l o w a n d t u r b u l e n c e m e a s u r e m e n t s i n a t r i a n g u l a r j e t : W . R . O u i n n/ \

x ~ . . . . / \

0

'2 2" 2 ' S 4 2 . 5 4 - 1 . 27 Y{cOml 1 .2 7 2 .5 4

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X/0 =10019 4 -- - ~ - 31 -

- , o . % 5 o 8 , o , .

F i gu r e 1 0 ( - u ' V l ~ c , x 100 ) c on t ou r s

The f ou r t h , f i f t h , a nd s i x t h t e r m s on t he r i gh t - ha nd s i de o fE q u a t i o n 1 r e p r es e n t s e c o n d a r y f lo w s o f P r a n d t r s s e c o n d k i n d .Th e s ix th t e rm i s usual ly negl ig ibly smal l , as a resul t of theb o u n d a r y l a y e r a p p r o x i m a t i o n , c o m p a r e d t o t h e o t h e r t w o , sw h i c h a r e r e s pons i b l e f o r the c ha n ge i n s ha pe o f t he m e a ns t r e a m w i s e ve l oc i t y fi el d w i t h d ow ns t r e a m d i s t a nc e , 9 a s no t e dearl ier .T h e R e y n o l d s s h e a r s tr e ss c o n t o u r s a r e s h o w n i n F i g u re s 1 0a nd 11 . L i ke t he s t r e a m w i s t u r bu l e nc e i n t e ns i t y , la r ge R e yn o l dss he a r s t r e ss g r a d i e n t s a r e a l s o f oun d i n r e g i ons o f t he f l ow w he r et he l oc a l s he a r i n t he m e a n s t r e a m w i s e ve l oc i t y is l a rge . Th em a x i m u m R e yn o l ds s he a r s t r e ss l eve ls a r e ge ne r a l l y l a r ge r t ha nt h o s e f o u n d i n r o u n d t u r b u l e n t f r ee j e ts a t t h e c o r r e s p o n d i n gdow ns t r e a m s t a t i ons , 1 '1~ i m p l y i ng i m p r ove d m i x i ng . T he- v ' w ' R e yno l ds s he a r s t r e s s w a s no t m e a s u r e d . The d if fi cu lt ie sa nd r e s u l t i ng l a r ge e r r o r s a s s oc i a t e d w i t h t he m e a s u r e m e n t o ft h is c om pon e n t o f t he R e yn o l ds s t r es s t e ns o r a r e w e l l kno w n , s '9

C o n c l u s i o n sThe m e a n f l ow a nd s om e t u r bu l e nc e c ha r a c t e r i s t i c s i n t henear - f ie ld of an inco mp ress ible , tur bule nt f ree a i r j e t , i s suingf r om a s ha r p - e dge d e qu i l a t e r a l t r i a ngu l a r s l o t , w e r e e xa m i ne di n de t ai l. W e f ou nd t ha t t he j e t s p r e a ds f a s t e r a t i t s ba s e s i det ha n a t i t s a pe x s i de . The f a s t e r ba s e - s i de s p r e a d i ng l e a ds t oa n i nve r s i on o f t he s ha pe o f t he je t a t a bo u t f ive e qu i va l e n t s l o td i a m e t er s d o w n s t r e a m f r o m t h e s lo t e x it p l a n e. T h e m a x i m u mR e yn o l ds s he a r l eve ls i n t he t r i a ngu l a r j e t a r e h i ghe r t ha n t hos ei n r o u n d t u r b u l e n t f r ee j e ts a t t h e c o r r e s p o n d i n g d o w n s t r e a ml oc a t i ons , i nd i c a t i ng i m pr ove d m i x i ng .

/\x,~=,-0 / \2 . 5 ( . . . . . .

~ o

Ylem)

x/oe,S,O

- 5 . 0 8

- 10 .16-7 .62 -3.8 1 Y~cr0

5 - - 50 - -10

5 . 0 8

- 5O8

X/De= 10-0

-1o.lst0.~s - 5 . 0 8 0 5 , O 8 1 0 . 1 6Yee

Fi gu re 11 ( - u 'vv '/ I .Fc, x 1 0 0 ) c o n t o u r s

A c k n o w l e d g m e n t sT h e s u p p o r t o f t h e N a t u r a l S c ie n c es a n d E n g i n e e r in g R e s e a rc hC oun c i l o f C a n a da , t h r ou gh g r a n t A 5484 , is g r a te f u l l ya c k n o w l e d g e d .Refe rences

1 Gu tma rk , E . , Schadow , K. C . , Pa r r , D. M. , Har r i s , C . K. , andWilson , K. C . The me an and tu rbu len t s t ruc tu re o f nonc i rcu la rje t s . AIAA pa per no . 85 -0543 , 19852 Kosh igo , S . , Gu tm ark , E ., and Schadow , K. C . Wa ve s t ruc tu resin je t s o f a rb i t ra ry shape . I I I . T r iang u la r je t s . Phys. Fluids,1988, 31, 1410-14193 S c h a d o w , K . C . , G u t m a r k , E ., P a r r , D . M . , a n d W i l so n , K . C .Se lec tive con t ro l o f f low coherence in t r iang u la r je t s . Exp. F luids,1988, 6, 129-1354 Quinn , W. R . and Mil i tze r , J . E f fec ts o f nonpara l le l ex i t f lowon rou nd tu rbu len t f rcc je t s . Int. J . Heat and Fluid Flow, 1989,10, 139-1455 Daug her ty , R . L . , F ranz in i , J . B . , and F innem ore , E . J . FluidMechan ics with Engineering Applications, M c G r a w - H i l l , N e wYork , 19856 Wygnan sk i , I . and F ied le r , H. Som e measurem ents in theself-preserving jet. J . F lu id Mech . , 1969, 38, 577-6127 Bradshaw, P . An Introduction to Turbulence and its Measure-ment, Pergamon , Oxford , Eng land , 19758 Perk ins , H. J . The fo rma t ion o f s t reamwise vor t ic i ty in tu rbu len tflow. J. Fluid Mech. , 1970, 44, 721-7409 Bradshaw, P . Turbu len t secondary f lows . Ann. Rev. Fluid Mech. ,1987, 19, 53-7410 Sami , S . , Carm ody , T . , and Rouse , H. Je t d i ffusion in the reg ionof f low es tab l i shment . J. Fluid Mech. , 1967, 27, 231-25211 Boguslawsk i , L . and Pop ie l , Cz . O. F low s t ruc tu re o f the f reeround tu rbu len t je t in the in i t ia l reg ion . J. Fluid Mech. , 1979,90, 531-539

224 I n t. J . Hea t and F l u id F l ow , V o l . 11 , No . 3 , S ep t em ber 199 0

mean flow and turbulence measurements in a triangular turbulent free jet

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