Combustion Instability Vortex Shedding

8/22/2019 Combustion Instability Vortex Shedding

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Prog. Energy Combust. Sci. 1992, Vol . 18, pp. 117-132 0360--1285192 $15.00Pr in t ed in Gre a t Br i ta in . 1992 Pe rgam on P res s p i e

C O M B U S T I O N I N S T A B IL I T Y R E L A T E D T O V O R T E X S H E D D I N G I ND U M P C O M B U S T O R S A N D T H E I R P A S SI V E C O N T R O L

K. C. Scrt~oow and E. GUTMARKNaval Weapons Center, China Lake, CA 93555-6002, U.S.A.

Received 24 July 1991

Ab strac t - -T his review summarizes recent research program re la ted to the dr iving mechanism of dum pcom bus tor instabil ity, Its scope includes experimental research in du mp c om busto rs using gaseous fuel. Theemphasis here is on vo rtex shedding as a drivin g mechanism of combustion instabil it ies. It is shown th atthe development of coherent flow structures and their breakdown into fine-scale turbulence can lead toperio dic heat release, which, when in p hase w ith the pressure oscil lation, can d rive the oscil lations as statedby the Rayleigh criterion. The physical processes associated w ith the vortex break dow n are described. Thisunderstanding is used to passively con trol and reduce the pressure oscil lations, as dem onstra ted for dum pand bluff body stabil ized com nbust ion f lows.

CONTENTS

1. Int roduct ion2. Experimental Configurations3. Large-Scale Structures in Is otherm al Shear Layers4. Large-Scale Structures in Reacting Shear Layers5. Large-Scale St ruc ture Break dow n--Enh ancem ent of Fine-Scale M ixing6. Driving Mechanism7. Passive Control8. Summary and ConclusionsReferences

117119120122123127127129131l . INTRODUCT ION

I n d u m p c o m b u s t o r s a n d c o m b u s t o r s w i t h b l u f f -b o d y f l a m e h o l d e r s , v o r t i c e s a r e f o r m e d i n t h e s h e a rl a y e r b e t w e e n t h e h i g h a n d l o w s p e e d s t r e a m s a t t h er e a r w a r d f a c i n g s t e p ( d u m p ) o r a t t h e w a k e f l o wd o w n s t r e a m o f t h e b l u f f b o d y ( f la m e h o l d e r ) . T h ev o r t e x f o r m a t i o n i s s t a b i li z e d i n t h e p r e s e n c e o fa c o u s t i c p r e s s u r e o s c i l l a t i o n s . I n g e n e r a l , t h e h i g hs p e e d s tr e a m c o n s i s t s o f a n u n b u r n t m i x t u r e o f a i ra n d f u e l , w h i l e t h e l o w s p e e d s t r e a m i s c o m p o s e dl a r g e ly o f h o t c o m b u s t i o n p r o d u c t s f o r m i n g t h ef l a m e h o l d i n g re c i r c u l a ti o n z o n e b e h i n d t h e d u m pp l a n e o r t h e b l u f f b o d y . T h e v o r t e x s t r u c tu r e h a s as i g n i f i c a n t i n f lu e n c e o n t h e c o m b u s t i o n p r o c e s s( F i g . i ) . I n t h e e a r l y p h a s e o f t h e v o r t e x d e v e l o p m e n t ,w i t h t h e u n b u r n t m i x t u r e o n o n e s i d e o f a n i n t e rf a c ea n d t h e h o t c o m b u s t i o n p r o d u c t s o n t h e o t h e r s i d e ,i n t e n s e ( f in e - s c a le ) m i x i n g a n d b u r n i n g a r e l i m i t e d .W h e n t h e v o r t e x r o l l - u p p r o c e s s is f o l lo w e d b y i n t e r -a c t i o n b e t w e e n v o r t ic e s , o r i s o b s t r u c t e d b y s i d e w a l l s ,a l a r g e i n t e r fa c e b e t w e e n t h e a i r / f u e l m i x t u r e a n d t h eh o t p r o d u c t s d e v e l o p s , l e a d i n g t o f i n e - s c a l e t u r b u -l e n ce e n h a n c e m e n t a n d s u d d e n h e a t r e le a s e. T h i sp r o c e s s i s r e p e a te d d u r i n g e a c h c y c l e o f t h e p r e s s u r eo s c i l l a t i o n s r e s u l t i n g i n p e r i o d i c h e a t r e l e a s e . W h e n ap r o p e r p h a s e r e l a t i o n s h i p b e t w e e n t h e p e r i o d i c h e a tr e l e a s e a n d p r e s s u r e o s c i l l a t i o n s e x i s t s ( R a y l e i g h

c r i t e ri o n ) 1 h i g h a m p l i t u d e p r e s s u r e o s c i l la t i o n s m a yb e e x c it e d . R a y l e i g h f o u n d t h a t a c o u s t i c o s c i ll a t io n sc a n b e e x c i t e d a n d s u s t a i n e d b y a d d i t i o n o f h e a t. H i sc r i t e r i o n s t a t e s t h a t t h e i n s t a b i l i t y w i l l b e a m p l i f i e dw h e n h e a t i s s u p p l i e d w h i l e th e p r e s s u r e i s m a x i m u m .S u p p r e s s i o n o c c u r s f o r t h e i n v e r s e c o n d i t i o n . T h u s ,t h e e x c i t a t i o n i s m a x i m a l w h e n t h e e n e r g y a n dp r e s s u r e o s c i l l a t io n s a re i n p h a s e w i t h e a c h o t h e r .

T h i s c r i t e r i o n w a s r e f o r m u l a t e d b y P u t n a m 2 u s i n gt h e R a y l e i g h i n t e g r a l to d e f in e c o n d i t i o n o f i n s t a b i l i t ya m p l i f i c a t i o n :

T' I p ' q ' d t > 0 ,w h e r e p" a n d q ' a r e t h e p r e s s u r e a n d h e a t r e l e a s eo s c i l l a t i o n a n d t i s t i m e .

T h i s c r i t e r io n i s v a l id p r o v i d e d t h a t t h e e x t e n t o ft h e f l a m e z o n e i s s m a l l r e l a t iv e t o t h e a c o u s t i c w a v e -l e n g t h . S e l f e x c i t e d o s c i l l a t io n s c a n n o t o c c u r w h e n t h ep h a s e r e l a t i o n s h i p i s n e a r 1 8 0 d e g r e e s .

E x p e r i m e n t a l s t u d y o f t h e R a y l e i g h c r i t e r i o n w a sp e r f o r m e d i n a d u m p c o m b u s t o r u s i n g r a d i a t i o n o s c il -l a t i o n a s a n i n d i c a t o r o f o s c i l l a to r y h e a t r e le a s e. 3 T h i se x p e r i m e n t i s d i s c u s s e d i n m o r e d e t a i l l a t e r .

A l t h o u g h m u c h o f t h e r e c e n t re s e a r c h is d i re c t e d a tu n d e r s t a n d i n g t h i s l ik e l y m e c h a n i s m f o r r a m j e tc o m b u s t i o n i n s t a b il i ti e s , i t c a n n o t b e s e p a r a t e dc o m p l e t e l y f r o m o t h e r p h e n o m e n a , s u c h a s s p r a y

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118 K .C . SCHAOOW nd E. GUTMARKREARWARD

FACING STE P./

umUMT / \MIXTURE OFREACTANTS VORTEX BRAID

FIG. I. Vortex roll-up in dum p combustor.co m b u s t i o n . In f ac t , it h a s b een l o n g k n o w n q u a l i t a -t ive ly f rom exper ience ga ined in eng ine developmenttha t the fue l d i s t r ibu t ion has a subs tan t ia l e f fec t oninstabili t ies . Fu el redistribu tion w as success ful ly usedt o ex t en d o p e ra t i o n a l r eg i m es w i t h r ed u ced co m b u s -t ion ins tab il it ies . Ho we ver , i t can be argu ed tha t evenwi t h s p ray co m b u s t i o n t h e d y n am i cs o f t h e v o r t exs t ru c t u re s r em a i n t h e d o m i n an t f ea t u re , wh e reb y d is -t r i b u t i o n o f fu e l/ a ir r a t i o i n t h e f l o w ch an g es t h ein i ti a l con d i t ion o f the reac t ing uns tab le she ar l ayers.In fac t , the labora to ry tes t s which wi l l be d i scussedhave fo r the mos t par t used gaseous fue l s . Th is i s ag rea t s impl i f ica t ion , done in o rder to fac i l i t a te theresearch w hich seems jus t if i ed , becau se i t app earstha t , in opera t ing eng ines , the l iqu id d rop le t s a rel a rg e l y v ap o r i zed b e fo re t h e f l o w r each es t h e s h ea rl ay er . Un d o u b t ed l y , m o re r e s ea rch i s n eed ed co n ce rn -i n g t h e co u p l i n g b e t ween s p ray co m b u s t i o n an dvor tex s t ruc tu res .

T h e ev o l u t i o n o f t h e v o r t i c e s a re d i s cu s s ed i n t h eg en e ra l co n t ex t o f t h e i n t e r ac t i o n s b e t ween s h ea r l ay e rinstabili t ies an d acou st ic instabil i t ies in the com -b u s t o r . R ecen t d ev e l o p m en t s i n t h i s a r ea s h o w t h a tt h e c o m m o n l y k n o w n v o r t e x s h e d d in g f r o m r e a r w a r dfac ing s teps and b lu ff bod ies i s a spec ia l case o f f lowins tab i li ty . In the gene ra l f low ins tab i l i ty con tex t , thevor t ices wi l l be refer red to as l a rge-sca le coheren ts t ru c tu re s . F ro m t h e d i scu s s io n s o f t h e r ecen t r e s ea rchres ul ts , a d e t a il ed u n d e r s t an d i n g o f t h e co m b u s t i o nins tab i l i ty d r iv ing me chan ism i s der ived , which can b eused to pass ive ly and ac t ive ly con t ro l the p ressu ream p l i t u d e . B y ap p l y i n g t h e n ew u n d e r s t an d i n g o ff l ow i n s t ab il i ty t o t h e co m b u s t i o n i n s tab i l it y p ro b l em ,the p resen t research i s d i f feren t f rom ear l ie r researchin th i s a rea .

As p o i n t ed o u t b y C u l i ck 4 i n a r ecen t r ev i ew o fcombus t ion ins tab i l i t i es in l iqu id -fue led p ropu ls ions y s tem s , t h e g en e ra l i d ea o f p e r i o d i c co m b u s t i o n a s s o -c ia ted wi th uns tab le shear l ayers was f i rs t indepen-d e n t ly r e p o r t e d b y K a s k a n a n d N o r e e n 5 a n d R o g e r sand M arb le 6 in the mid-fi ft ies . In par t icu lar , the la t te r

wo rk , d i s cu s s i n g p rem i x ed g as eo u s fu e l an d a i rfo w i n g p as t a f l am eh o l d e r , p ro p o s e d t h a t d e l ay edp e r i o d i c co m b u s t i o n i n s h ed v o r t i c e s can d r i v e anacous t ic f i e ld , associa ted , in the i r t es t ing r ig , wi tht ransverse osc i l l a t ions a t h igh f requency . Pressureo s c i l l a t i o n s a t l o w f r eq u en c i e s b ecam e a g ro wi n gc o n c e r n d u r i n g t h e d e v e l o p m e n t o f c o m p a c t r a m j e tco m b u s t o r s i n t h e ea r l y -e i g h t i e s . T h es e l o n g i t u d i n a losc i l l a t ions in ter fered wi th the in le t shock sys temcau s i n g l o ss o f p e r fo rm an ce d u e t o i n le t u n s t a r t . 7'8B y r n e9.10 sugg ested vorte x s hed ding as a l ikely causeof the osc i l la t ions , a l so po in t ing o u t a re la t ionsh ipb e t ween f l o w d y n am i cs o b s e rv ed i n aco u s t i c a l l yexci ted je t s and ram je t p ressu re o sc i l la t ions .

The p resen t rev iew i s re la ted to the low f requencyo s c i l l a t i o n , an d ad d re s s e s i n a b ro ad e r co n t ex t s h ea rf low ins tab i li t ies a ssocia ted wi th je t s , wak es , an dm i x i n g l ay e r s an d t h e ro l e o f l a rg e - s ca l e s t ru c t u re s a sthe source fo r per iod ic hea t re lease fo r d i f feren t com-b u s t i o n s i t u a t i o n s o f i n te r e s t t o t h e co m b u s t o rd es i gn e r . T h e r e s ea rch r e s u l ts d o n o t p ro v i d e co m -bus to r des ign cr i t e r ia to reduce p ressure osc i l l a t ions .M o re i m p o r t an t , t h e r e s ea rch p ro v i d es i n s i g h t i n t o ad o m i n an t d r i v i n g m ech an i s m , wh i ch can g u i d e t h ed es i g n e r i n t h e d ev e l o p m en t o f p a s s i v e s h ea r - fl o wco n t ro l m e t h o d s fo r r ed u ced p re s s u re o s c i l l a t i o n .E x am p l e s o f p a s si v e co n t ro l a r e p re s en t ed . A l s o ,i n c rea sed p h y s i ca l u n d e r s t an d i n g o f t h e p ro b l em canp ro v i d e t h e b a s i s fo r i m p ro v i n g p red i c t iv e m o d e l s fo rthe occurrence o f combus t ion ins tab i l i t i es .

In the fo l low ing sec t ions , recen t bas ic research f lowin the in terac t ions o f flow an d a cous t ic ins tab il i ti es i sr ev iewed a s r e l a ted t o b l u f f -b o d y an d r ea rwa rd f ac i n gs t ep f l am e s t ab i l i z ed co m b u s t i o n p ro ces s e s . T h eev o l u t i o n , i n t e r ac t io n , a n d b reak d o wn o f l a rg e- s ca les t ruc tu res in to smal l sca le tu rbu lence i s descr ibed asan i n t ro d u c t i o n t o t h e d i s cu s s i o n o n t h e co m b u s t i o ninstabil i ty research results .

In o rd e r t o ex p l o re t h e ro l e o f v o r t ex d y n am i cs inthe d r iv ing o f ramje t co m bus t ion ins tab il it ies , i t i sn eces s a ry t o co n s i d e r t h e ro l e o f o rg an i zed v o r t i c e s i n


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Com bustion instability related to vortex shedding 119V O R T E X M E R G I N G

O [ ~ u o0.20 + O.S

C O L L E C T I V E I N E R A C T I O N

FIG. 2. Shear-flow dynamics of forced jets.t h e s h ea r l ay e r d y n am i cs . T h i s ap p ro ac h wa s i n it i a tedb y t h e d i s co v e ry o f l a rg e - s ca le s t ru c t u re s b y B ro w na n d R o s h k o It a n d h a s b e e n r e v i ew e d b y H o a n dH u e r r e . t2 B a s e d o n l a b o r a t o r y l o w - R e y n o l d s n u m b e rs t u d ie s o f v a r i o u s t u rb u l en t f l ows , it was s h o w n t h a tthe shear l ayer develops ins tab i l i ty waves in i t s in i t i a lr eg i o n . W h en t h e am p l i f i ed wav es r each a ce r t a i nenergy level they ro l l up in to vor t ices (F ig . 2 ) . Thein i t ia l vo r tex s hedd ing f requ ency , f i , w h ich i s a l soca l l ed t h e m o s t am p l i f i ed f r eq u en cy , is d e t e rm i n ed b yvar iou s charac ter i s t i cs o f the ex i t ve loc i ty p ro f i le , suchas shape , tu rbu lence s t ruc tu re , in i t i a l shear l ayerm o m e n t u m t h i ck n es s , 0 0 , an d t h e je t ex i t v e l o c it y U0 .T h e i n i t i a l m o s t am p l i f i ed f r eq u en cy , wh en s ca l edwi t h 0 0 , an d U0 y i e ld s a n o n d i m en s i o n a l f r eq u en cyca l l ed t h e S t ro u h a l n u m b er , S t i = f O o / U o t h a t i sp red i c t ed t o b e c l o s e t o S t i = 0 .017 by l inear ins ta-b i li t y t h eo ry ) 3 T h e i n it ia l v o r t i c e s o f t h e s h ea r l ay e rg r o w a n d m e r g e a s t h e y a r e c o n v e c t e d d o w n s t r e a m .D u e t o m e r g i n g a n d e n t r a i n m e n t , t h e s h e a r l a y e rs p read s , an d t h e f r eq u en cy a s s o c i a ted w i t h t h ed o m i n an t l a rg e v o r t i c e s d ec rea s e s . I n t h e s h ea r l ay e ro f a j e t, s ev e ra l v o r t ex i n t e r ac t i o n s can o ccu r b e t weent h e i ni t ia l s ep a ra t i o n o f t h e s h ea r l ay e r an d t h e en d o ft h e j e t ' s p o t en t i a l co re . T h e re fo re , t h e s h ea r l ay e r i scharac ter ized by severa l ins tab i l i ty f requencies asso -c ia ted w i th d i f feren t sizes o f vor t ices . Th e reg ion a t theen d o f t h e p o t en t i a l co re i s g o v e rn ed b y t h e j e t - co l u m ni n s t ab i l i ty ) 4 T h e v e l o c i t y f l u c t u a t io n s i n t h is r eg i o nwere o b s e rv ed t o h av e a ch a rac t e r i s t i c f r eq u en cy ,c a ll e d th e p r e fe r r e d m o d e f r e q u e n c y , , w h i c h is ty p i -c a l ly in t h e s e c o n d o r t h i rd s u b h a r m o n i c r a n g e o f t h ein i t i a l shear l ayer ins tab i l i ty f requency . Th is f re-q u en c y s ca le s w i t h t h e j e t ex i t d iam e t e r , D , an d U0 t oy i e l d t h e p r e f e r r e d m o d e S t r o u h a l n u m b e r o fS tj = f j . D / U o . T h e r a n g e o f S t j w a s f o u n d i np rev i o u s i n v es t i g a ti o n s t o b e b e t ween 0 .2 5 an d 0 .5 ) 5

W h en aco u s t i c wav es i n t e r ac t w i t h t h e s h ea r l ay e r ,

v o r t ex s i ze can b e s t ab i l i z ed d ep en d i n g o n t h em a t ch i n g b e t ween t h e aco u s t i c f r eq u en cy an d t h eshear l ay er ins tab i li ty f requencies . T he s ize o f thev o r t i c e s w il l b e s m a l l e st w h en t h e aco u s t i c f r eq u en cyequals the in i t i a l vo r tex shedd ing f requency ; i t wi l lb e l a rg e s t wh en t h e aco u s t i c f r eq u en cy i s n ea r t h ep re fe r r ed -m o d e f r eq u en cy . S i g n i f i c an t l a rg e - s ca l em i x i n g e n h a n c e m e n t c a n b e o b t a i n e d a t t h e p r e fe r r e d-m o d e fo rc i n g f r eq u en cy . I f t h e aco u s t i c f r eq u en cy i sm u ch l o w er t h an t h a t o f t h e i n it ia l s h ea r l ay e r i n s ta -b i l i ty , co l lec t ive in terac t ion occurs (F ig . 2 ) as thein i t i a l ly shed vor t ices ro l l -up in to a s ing le la rgevor te x . 16

Dev e l o p m en t o f l a rg e -s ca l e s t ru c t u re s i s b en e fi c ia lfo r t h e en h an c em en t o f l a rg e -s ca l e m i x i n g o r b u l kmix ing in the shear l ayer . However , i t h inders f ine-s ca le m i x i n g o r m o l ecu l a r m i x i n g , n eces s a ry t o i n i t i a teco m b u s t i o n . I n t h e p re s en ce o f la rg e - s ca l e s t ru c t u re st rans i t io n to f ine-sca le mix in g i s in i t i a ted a t th e b ra idso f t h e v o r t i c e s , wh e re h i g h s t r a i n r a t e s (v e l o c i t yg rad i en t s ) b e t ween t h e h i g h an d l o w s p eed s t r eam sexist (Fig. 1). However, the ini t ial f ine-scale turbo-i en ce p ro d u c t i o n i s l i m i t ed t o t h e i n t e r f ace b e t weent h e t wo s t r eam s . I t c an b e co n j ec t u red t h a t t h e f i n e -s ca l e t u rb u l en t p ro d u c t i o n i s ab ru p t l y en h an ced ,d u r i n g t h e ro l l -u p o f t h e v o r t ic e s an d b y t h e m erg i n gor vor t ices .

T h e ro l e o f v o r t ex d y n am i cs i n d r i v i n g p re s s u reosc i l l a t ions was s tud ied by severa l inves t iga to rs overa p e r i o d o f ab o u t 5 y ea r s (1 9 8 4 -1 9 8 8 ) . E x p e r i m en t a ls e t -u p s an d m e t h o d s a r e s u m m ar i zed i n t h e fo l lo wi n g .

2. EXPERIMENTAL CONFIGURATIONS

T h e ex p e r i m en t a l co n f i g u ra t i o n s t o s t u d y t h e ro l eo f la rg e - s ca le s t ru c t u re s an d t h e i r b r eak d o wn i n t of i n e - s ca l e t u rb u l en ce i n d u m p -s t ab i l i z ed an d d i s k -s t ab i l i z ed co m b u s t i o n p ro ces s e s a r e s u m m ar i zed i n


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120 K .C . SCHAOOW nd E. GUTMARK

( a )

AXISYM

( b ) . . . . . ~ - - -2 1 )

/ - - .

( d )

( e )

( c ) - - ~__. / - - O ( 0

F I G . 3. E x p e r i m e n t a l f a c i l i t ie s . ( a ) R e f s 1 7 , 1 9 ; ( b ) R e f s 2 0 - 2 2 ; ( c ) R e f . 2 3 ; ( d ) R e f . 2 4 ; ( e ) R e fo 2 5 ; ( f ) R e f .26 .F i g . 3 . No n reac t i n g an d co m b u s t i o n ex p e r i m en t swere p e r fo rm ed .

C o ax i a l d u m p co m b u s t o r t e s t s (F i g . 3 ) we red es c r i b ed b y S ch ad o w e t a l ) 7 ( ex p e r i m en t a l m e t h o d si n c lu d e d h o t - w ir e a n e m o m e t r y , P l a n a r L a s e r I n d u c e dF l u o re s c e nc e ( P L I F ) i m a g i n g o f i n s i t u OH -rad i ca l s , Isi o n i za t i o n p ro b es , t h e rm o co u p l e s , an d h i g h f r eq u en cyre s p o n s e p re s s u re t r an s d u ce r s ) an d S i v as eg a ram an dW h i t e l aw t9 (m i c ro p h o n es ) . B o t h ex p e r i m en t s u s edg as eo u s fu e l . Gu t m ark e t a L ~s a l s o u s ed an an n u l a rd i f fu s i o n f lam e t o s t u d y r eac t i n g v o r t ex d y n am i cs .

T w o - d i m e n s i o n a l d u m p c o m b u s t o r s ( F ig . 3 b ) w e reu s e d b y M c M a n u s e t a l . 2 ( h o t - w i r e a n e m o m e t r y ,p re s s u re t r an s d u ce r , C H em i s s i o n d e t ec t o r , S ch l i e renp h o t o g r a p h y ) , Y u e t a l . 21 ( h o t - w i r e a n e m o m e t r y ,p re s s u re t r an s d u ce r , S ch l i e r en p h o t o g rap h y fo r h i g hs p e e d c i n e m a t o g r a p h y a n d s p a r k p h o t o g r a p h s ) ,S m i t h an d Z u k o s k i 22 ( s p a rk s h ad o wg rap h y , h i g h -s p eed p h o t o g rap h y , p r e s s u re t r an s d u ce r , h o t -w i rean em o m et ry , r ad i a t i o n i n t en s i t y d e t ec t o r ) , an d Dav i se t a l . 23 ( laser shee t f low v isual iza t ion , p ressu re t rans -d u ce r , h i g h s p eed p h o t o g rap h y ) . T h e f i r st t h r ee ex p e r -i m en t s u s ed a p rem i x ed f l o w o f g a s eo u s fu e l an d a i r ,the la t te r exper imen t used gaseous fue l in jec t ionth rou gh the s ide wal l dow ns t ream of the s tep (F ig . 3c).

T h e f l owf ie ld i n a s i m u l a t ed s i d e -d u m p co m b u s t o r(F i g . 3 d ) was s t u d i ed b y No s s e i r an d B eh a r24 usingh y d ro g en -b u b b l e s f l o w v i s u a l iz a t i o n.

E x p e r i m en t s w i t h f lam eh o l d e r s (F i g . 3 e an d f ) we rep e r f o r m e d b y H e g d e e t a l . 2 s ( s h ad o wg rap h y , l a s e rd o p p l e r v e i o c i m e t e r (L DV) , C H rad i a t i o n d e t ec t o r ,p re s s u re t r an s d u ce r ) an d P o i n s e t e t a L 26 (h igh speedp h o t o g rap h y , C 2 rad i a l em i s s i o n d e t ec t o r , p r e s s u ret r an s d u ce r , m i c ro p h o n e ) . B o t h ex p e r i m en t s u s edp rem i x ed a i r an d g a s eo u s fu e l w i t h t h e co m b u s t i o ns tab i l ized on one o r two cy l indr ica l f l am eholders 25an d r ec t an g u l a r b ack w ard - f ac i n g s t ep s . 26

In t h e fo l l o wi n g , t h o s e a s p ec t s o f t h e ex p e r i m en t swi l l b e s u m m ar i zed wh i ch p ro v i d e i n s i g h t i n t o t h ed ev e l o p m en t o f l a rg e -s ca l e s tru c t u re s i n n o n re ac t i n gand reac t ing f lows and the i r b rea kdo wn in to f ine-scalet u rb u l en ce , wh i ch m ay l ead t o s u d d en i n c rea s e s i nreac t ion ra tes and u l t imate ly to per iod ic hea t re lease .

3 . L A R G E -S C A LE S T R U C T U R E S I N I S O T H E R M A LS H E A R L A Y E R S

T h e d ev e l o p m en t o f l a rg e - sca l e , co h e ren t s t ru c t u re sd ep en d s o n t h e r e l a t i o n s h i p b e t ween aco u s t i c f r e -quencies and f low ins tab i l i ty f requencies . Forex am p l e , t o g en e ra t e co h e ren t s t ru c t u re s a t t h e en d o ft h e p o t en t i a l co re o f an ax i s y m m et r i c j e t , t h e aco u s t i cf r eq u en cy h as t o m a t ch t h e p re fe r r ed m o d e f r eq u en cy .Th is i s i l lu s t ra ted in F ig . 4 , descr ib ing exper im en ts inwh i ch t u rb u l en t f l u c t u a t i o n s we re m eas u red n ea r t h een d o f t h e p o t en t i a l co re o f a f r ee j e t . :7 T h e p re fe r r edm o d e f r eq u en cy was i d en t i f i ed f ro m t h e m ax i m a i nt h e t u rb u l en t v e l o c i t y f l u c t u a t i o n s s p ec t r a a s s h o w nfo r t h e u n fo rced (U N F ) ca s e w i t h U0 = 7 1 m / s ecy i e l d i n g fj - - 3 40 H z wi th a co r r e s p o n d i n g n o n d i m en -s i o n a l f r eq u en cy o f S t j = 0 .30 . In a second tes tw i t h l o w -am p l i t u d e fo rc i n g a t fF = 1 9 0 H z an dU0 = 5 0 m / s ee , t h e t u rb u l en ce s p ec t r a f ro m t h ep o t en t i a l co re s h o wed , i n ad d i t io n t o t h e f j -m ax i m a a t2 7 0 Hz , a d i s t i n c t s eco n d p eak a t t h e fo rc i n g f r e -que ncy (do t ted l ine) . F or th i s t es t cond i t ion , am i s m a t ch b e t ween fF a n d j~ ex is ted . W h en U0 wasfu r t h e r r ed u ced t o 3 5 m / s ec , f j was r ed u ced t o 1 9 0 Hz ,an d a m a t ch b e t w een fF an d J ~ was o b t a i n ed , r e s u l t in gi n o n e h i g h -en e rg y p eak a t fF = f j . T h e h i g h eV p eaki n d i ca te s t h a t a s a r e s u l t o f m a t c h i n g b e t ween t h en a t u ra l f l ow i n s tab i li t y f r eq u en cy n ea r t h e en d o f t h ep o t en t i a l co re , f j , an d t h e aco u s t i c fo rc i n g f r eq u en cy ,fF , h i g h l y co h e ren t , l a rg e - s ca l e s t ru c t u re s we re


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Co mb ustion instab il i ty related to vortex shedding 1213 . 1 0 - 3

2 . 1 0 - 3 1

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U , - 3 6 n t is ( f F " 1 1 1 0 H a d. . . . . 6 0 ro le ( fF - 1 0 0 H z ). . . . 7 1 m l s ( IX IF . )

. ~ , ~ t ( S ~ - 0 . 3 0 )

x = 2 Dr = OI I I I

2 0 0 ~ n O N O l l m

FIG. 4. H ighly coherent flow with jet preferred m ode frequency m atching acoustic forcing frequency(Schadow e t a l . 2 7 ) .g e n e r a t e d . T h e f l o w s t r u c t u r e s w e r e s h o w n t o h a v eh i g h a z i m u t h a l c o h e r e n c e a n d h i g h s p a t i a l a n dt e m p o r a l p e r i o d i c i t y n e a r t h e d u m p u s i n g h o t -w i r ea n e m o m e t r y ; h o w e v e r , t h e i r c o h e r e n c e w a s r e d u c e dw h i l e c o n v e c t e d d o w n s t r e a m , w h i c h w a s a l s o v i s u a l -i z e d i n w a t e r t u n n e l e x p e r i m e n t s . 2 8 F o r c i n g a t t h ep r e f e r r e d m o d e f r e q u e n c y g e n e r a t e s t h e m o s t e n e r -g e t ic c o h e r e n t s t r u c t u r e a n d t h e r e f o r e c h a n g e s t h es h e a r - f l o w c h a r a c t e r i s t i c s m o s t e f f e c t iv e l y . F o r c i n g a th i g h e r f r e q u e n c ie s p r o d u c e s s m a l l e r c o h e r e n t v o r t ic e sw h i c h a r e l e s s a m p l i f i e d b y t h e f l o w i n s t a b i l i t y a n dc o n s e q u e n t l y l e s s e f f e c t i v e i n m o d i f y i n g t h e s h e a rl a y e r s p r e a d i n g r a t e.

O r g a n i z e d f l o w s t r u c t u r e s w e r e a l s o v i s u a l i z e d i nt h e t w o - d im e n s i o n a l d u m p c o m b u s t o r . W h e n t h e fl oww a s f o r c e d w i t h a s p a n w i s e r o t o r a t t h e e x i t o f th et u n n e l , c o h e r e n t s t r u c t u r e s w e r e v i s u a l i ze d b y s m o k ei l l u m i n a t e d w i t h a p l a n a r l a s e r sh e e t. C o h e r e n t s t ru c -t u r e s w e r e g e n e r a t e d a t s e l e c t e d f o r c i n g f r e q u e n c i e s ,w h i c h w e r e n o t a c o u s t i c f r eq u e n c i es o f t h e t u n n e l , b u tw e r e c a l c u l a te d t o b e u n s t a b l e f r e q u e n c i e s o f t h e s h e a rl a y e r .23 T h e v o r t i c e s d i d n o t a l t e r t h e a c o u s t i c f i e ld i nt h e t e s t s e c t i o n , s i n c e a s a n a c o u s t i c q u a d r u p l e t h e ya r e a w e a k s o u r c e . H o w e v e r , w h e n c o m b u s t i o n i sp r e s e n t t h e y c a n f e e d b a c k a n d a f fe c t t h e c o m b u s t i o nc h a m b e r a c o u s t i c s .

I n a d d i t i o n t o p l a n a r a n d a x i s y m m e t r ic sh e a rl a y e r s , l a r g e - s c a l e s t r u c t u r e s d e v e l o p i n o t h e r f l o wc o n f i g u r a t i o n s . F o r e x a m p l e , i n a s i d e - d u m p c o m -b u s t o r c o u n t e r - r o t a t i n g v o r t e x p a i r s w e r e g e n e r a t e di n t h e i m p i n g i n g r e g i o n o f t w o r e c t a n g u l a r j e t s w i t h a ni m p i n g e m e n t a n g l e o f 1 80 ( F i g . 5 ) . V o r t i c i t y m e a s u r e -m e n t i n d i c a t e d t h a t t h e s t r e n g t h o f th e s e v o r t ic e sc h a n g e d p e r i o d i c a l l y d u e t o t h e i r s t r e t c h i n g i n t h ed o w n s t r e a m d i r e c t io n . 4 T h e s t r e n g t h a n d r o t a t i o no f t h e v o r t ic e s w e r e p h a s e l o c k e d w i t h t h e je t so s c i l la t i o n s r e l a ti v e t o t h e d o m e s e c ti o n . T h e m o t i o nc a u s e s p e r i o d i c e n h a n c e m e n t o f t h e t u r b u l e n t m i x in g ,

t h u s i n d u c i n g u n s t a b l e p e r i o d i c h e a t r e l e a s e i nc o m b u s t i o n .

T h e p r e s e n c e o f t h e c o h e r e n t s t r u c t u r e s s i g n i f i -c a n t l y c h a n g e s t h e s h e a r l a y e r c h a r a c t e r i s t i c s r e l a ti v et o u n f o r c e d s h e a r l a y er s . T h e y e n h a n c e l a r g e- s c a lem i x i n g a s s h ow n b y O s t e r a n d W y g n a n s k i .29 Th ei rp o s s i b l e ef f e ct o n f i n e - s ca l e m i x i n g a n d c o m b u s t i o n i sd i s c u s s e d l a t e r . T o s t u d y t h e e f f e c t o f l a r g e - s c a l em i x i n g i n a t w o - d i m e n s i o n a l d u m p c o m b u s t o r ,p r o f il e s o f t h e m e a n v e l o c it y w e r e o b t a i n e d d o w n -s t r e a m o f t h e s e p a r a t i o n w i t h o u t a n d w i t h s h e a r - la y e rf o r c i n g u s i n g a l o u d s p e a k e r . F r o m t h e s e m e a s u r e -m e n t s , t h e s h e a r l a y e r g r o w t h r a t e s w e r e c a lc u l a t e d .2T h e r e s u l t s a r e p r e s e n t e d i n F i g . 6 i n t h e f o r m o fm o m e n t u m t h i c k n e s s ( 0 ) v e r s u s S t r o u h a l n u m b e r ,S ty : = f ~ X / U o w i t h a x i a l d i s t a n c e f r o m t h e s t e p , X .T h e i n i t i a l s h e a r l a y e r g r o w t h r a t e s w i t h f o r c i n g a r eg r e a t e r t h a n t h o s e o f t h e u n f o r c e d f lo w . T h e f o r c in gf r e q u e n c i e s o f f r = 9 8 H z a n d 1 6 0 H z w e r e s ig n i f i-c a n t l y b e l o w t h e i n i t i a l i n s t a b i l i t y f r e q u e n c y , w h i c hw a s e s t i m a t e d t o b e f = 1 36 0 H z . T h e s p r e a d i n g - r a t ee n h a n c e m e n t i s d u e t o c o l le c t i v e i n t e r a c t i o n b e t w e e nt h e i n i t i a l ly s h e d v o r t i c e s w h i c h a r e f o r c e d t o r o U - u pi n t o o n e l a r g e v o r te x . L a r g e - s c a l e m i x i n g e n h a n c e m e n tw a s a l s o d e m o n s t r a t e d i n a c o a x i a l d u m p c o m b u s t o r .O p t i m u m r e s ul ts w e re o b t a i n e d w h e n t h e d u c t r e s o n a n tf r e q u e n c y w a s n e a r t h e p r e f e r r e d m o d e f r e q u e n c y , b o t hi n n o n r e a c t in g a n d c o m b u s t i o n e x p e r i m e n ts .27"2s

T h e p r e s e n ce o f c o h e r e n t s t r u c tu r e s i n n o n r e a c t i n gf l o w s m a y a l t e r t h e a c o u s t i c p r e s s u r e c h a r a c t e r i s t i c s .S u c h a f e e d b a c k f r o m t h e c o h e r e n t s t r u c t u r e s t o t h ea c o u s t i c s w a s s u g g e s t e d b y L a u f e r a n d M o n k e w i t z 3a n d K i b e n s ) ~ S u c h f e e d b ac k m e c h a n is m w a s n o to b s e r v e d i n a n o n r e a c t i n g f lo w w i t h a d u m p . T h e o r -e t i c a l ly , i t w a s s h o w n t h a t t h e c o h e r e n t s t r u c t u r e s a r ea c o u s t i c q u a d r u p o l e s h a v i n g o n l y a w e a k a c o u s t i cf i e ld o f t he i r ow n . 32"33 E x pe r im en ta l l y , t he sam ep r e s s u r e a m p l i t u d e d i s t r i b u t i o n a s f u n c t i o n o f f o r c i n g


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122 K. C. SCHAOOWand E . GUTMARKI IA II M E I I 0 S I I I ~

FIG. 5. Counter-rotating vortex pairs in side-dump combustor (Nosseir and Behar24).f r e q u e n c y w a s f o u n d i n a t w o - d i m e n s i o n a l d u m pc o m b u s t o r w i t h a n d w i t h o u t c o h e r e n t s t r u c t u r e sp r e s e n t i n t h e f l o w 23 (F ig . 7 ) . Th e s ud den s t ep de s ignw a s u s e d f o r t h e e x p e r i m e n t s w i t h f o r c i n g o f c o h e r e n ts t r u c tu r e . T o a v o i d d e v e l o p m e n t o f c o h e r e n t s t r u c-t u r es a t t h e s a m e f o r c i n g c o n d i t i o n s , t h e s t e p w a sr e p l a c e d b y a r a m p , e l i m i n a t i n g fl o w s e p a r a t i o n . 34

T h e c r i t i c a l r o l e o f l a r g e - s c a l e , c o h e r e n t s t r u c t u r e sf o r d r i v i n g p r e s s u r e o s c i l l a t i o n s b e c o m e s c l e a r ,

h o w e v e r , w h e n t h e i r e f fe c t o n t h e c o m b u s t i o n p r o c e s si s c o n s i d e r e d .

4 . L A R G E ~ C A L E S T R U C T U R E S I N R E A C T IN GS H E A R L A Y E R S

E x p e r i m e n t s i n a n n u l a r d i f f u s i o n f l a m e s p r o v i d e di n s i g h t i n t o t h e e f f e c t o f t h e v o r t e x d y n a m i c s o nc o m b u s t i o n. ~ 7 ' ~8 A n i n s t a n t a n e o u s p i c t u r e ( 18 n s e c ) o f

STANFORD

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FIG. 6. Shear-layer growth dow nstream of du mp w ith and w ithout forcing (Mc M anus e t a l . 2 ) .


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Com bustion instability related to vortex shedding 123

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F I G . 7 . P r e s s u r e s p e c t r a f o r t w o d u m p c o n f i g u r a t i o n ( D a v i s e t a l . 23 ) .t h e aco u s t i c a l ly ex c it ed f l am e a t t h e p re fe r r ed m o d e o fthe a i r j e t (S t = 0 .35) i s shown in F ig . 8a . The d i f -ference in b lack /whi te tones ind ica te d i f feren t in ten -s it ies o f OH -f luoresc ence , which in th i s f l ame ind ica tet h e l o ca t i o n o f t h e r eac t i o n zo n e . I t m ay b e s een t h a tthe f lame cons is ted o f la rge-sca le s t ruc tu res , s im i lar tot h o s e o b s e rv ed i n n o n reac t i n g s h ea r f l o ws . T h e co m -bus t ion was in i t i a ted (h ighes t OH levels ) a t the c i r -cu m fe ren ce o f l arg e - s ca le s t ru c t u re s, w h e re s eco n d a rys t reamwise smal l -sca le edd ies a re g rowing , in i t i a t ingt h e p ro ces s o f t r an s i t i o n t o fu l ly t u rb u l en t f l o w(s i m i l a r o b s e rv a t i o n s we re r ep o r t ed i n R e f . 2 0 ) . T h eb ra i d s co n n ec t i n g ad j acen t v o r t i c e s h ad l o w O H l ev e lsa s a r e s u l t o f l o ca l q u en ch i n g d u e t o h i g h s t r a i n i n gra t e s i n t h e s e r eg i o n s . T h e v o r t i c e s we re co n v ec t edd o w n s t r e a m , a n d t h e c o m b u s t i o n r e a c h e d t h e v o rt e xco re (F i g . 8 b ). F r o m t h e s e ex p e r im en t s i t i s c l ea r t h a tt h e co m b u s t i o n i s r e l a t ed t o t h e f l o w s t ru c t u re sg en e ra t ed b y aco u s t i c fo rc i n g i n t h e s h ea r l ay e r. D u et o t h e fl u i d d y n a m i c / co m b u s t i o n i n t e r ac t i o n , t h e h ea tr e lea s e was p e r i o d i c an d p o ck e t s o f h i g h - t em p e ra t u ref l o w w e r e c o n v e c t e d d o w n s t r e a m f r o m t h e b u r n e rexit.

T h e P L IF v i s u a l i z a t i o n t e s t s we re a l s o d o n e i n t h ec o a x ia l d u m p c o m b u s t o r ) ~ T h e s e t e s ts , a t c o n d i t io n swh i ch l ed t o h i g h am p l i t u d e p re s s u re o s c i l l a t i o n s ,co n f i rm ed t h a t , ev en a t r e a l i s t i c co m b u s t o r co n -d i t i o n s , t h e co m b u s t o r o s c i l l a t i o n s we re a s s o c i a t edwi t h p e r i o d i c f lo w s t ru c t u re s g en e ra t ed t h ro u g h i n t e r-ac t i o n b e t ween f l o w i n s t ab i l i t i e s an d ch am b eraco u s t i c s . M eas u rem en t s w i t h i o n i za t i o n p ro b ess h o wed t h a t h e a t was r e l ea s ed p e r i o d ica l l y d u e t o t h econ vec t ing vor t ices , m7 Osc i l l a to ry hea t re lease asso -c i a t ed w i t h v o r t ex d y n am i cs was a l s o o b s e rv ed b yo t h e r i n v es t i g a t o r s u s i n g r ad i a t i o n m eas u rem en t an dhig h spe ed ph ot og ra ph y. 22'26"35"36

B efo re d i scu s s i n g t h e p o s s i b le d r i v i n g m ech an i s m s

associa ted w i th per iod ic hea t re lease , f u r the r de ta i l s o fthe la rge-sca le s t ruc tu re b reak-up in to f ine-sca le tu r -b u l en ce i s d i s cu s s ed . Dep en d i n g o n t h e co m b u s t o rco n f i g u ra t i o n , d i f f e r en t f l u i d d y n am i c p ro ces s e s canlead to the sudden increase in f ine-sca le mix ing andsudden heat re lease .

5 . L A R G E - S CA L E S T R U C T U R E B R E A K D O W N - -E N H A N C E M E N T O F F I N E *S C A LE M I X I N G

In ad d i t i o n t o t h e ab o v e m en t i o n ed v o r t ex ro l l -u pin shear l ayers , the i r g rowth invo lves in terac t ionsb e t ween v o r t i c e s wh i ch m erg e t o g e t h e r t o p ro d u cen ew l a rg e r s t ru c tu re s . O n e s u ch i n t e r ac t i o n p ro ces s ist h e p a i r i n g o f t wo v o r t ic e s . T h e h i g h s t r a i n r a t e s an dt h e co n co m i t an t s m a l l - s ca l e t u rb u l en ce g en e ra t edd u r i n g t h e m erg i n g p ro ces s acce l e r a t e co m b u s t i o n .T h e p ro ces s m ay r e i n fo rce t h e p e r i o d i c h ea t r e l ea s e o fa fo rced r eac t i n g s h ea r l ay e r f l

An o t h e r c au s e o f s u d d en h ea t r e lea s e can b eo b s e rv ed i n d u m p co m b u s t o r s w i t h lo w s t ep h e ig h t . I na t w o - d i m e n s i o n a l d u m p c o m b u s t o r t h e d e v e l o p i n gv o r t ex d o w n s t r e a m o f t he d u m p i m p i n g e d a g a i n s t th el o w e r c o m b u s t o r w a l l ) S i n c e th e d o w n w a r d v e l o c it yo f t h e v o r t ex i s l arg e , v i g o ro u s m i x i n g o ccu r s b e t weent h e r e m a in i n g u n b u r n t r e a c t an t s a n d t h e c o m b u s t i o np ro d u c t , ag a i n l e ad i n g t o s u d d en h ea t r e l ea se (F i g . 9 ).T h ey s h o wed t h a t en e rg y i s s u p p l i ed t o t h e aco u s t i cf ie ld becau se the hea t re lease osc i ll a t ions (as meas uredf ro m f l am e em i s s i o n ) a r e i n p h as e w i t h t h e p re s s u ref l u c t u a t io n s d u r i n g t h e fo rm a t i o n o f t h e v o r t ex an du n t i l i t i m p i n g es o n t h e co m b u s t o r wa l l , wh en t h eh ighes t energy re lease i s observed . The acous t icr e s o n an t m o d e i s t h u s r e i n fo rced , l e ad i n g t o h i g ham p l i t u d e v e l o c i t y f l u c t u a t i o n s wh i ch i n d u ce t h e fo r -m a t i o n o f th e n e w v o r t ex . I n a s i m i la r 2 - D c o m b u s t o r


8/16

12 4 K.C. SCrtADOW and E. GUTMARK

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F I G . 8, F l a m e c h ar a ct e ri s ti c s f c i rc u la r u r n e r ( G u t m a r k e t a l . 8 ) , a ) 7 n s ~ ( a v er a g e) x p o su r e a n d ( P L I Fimaging of OH S t F = 0.44) and (b) 5 sec (average exposure (PLI F imaging o f OH S t F = 0.88).


9/16

Combustion instability related to vortex sheddingCALTECH

125

STABLE FLOW

UNSTABLE FLOWFIG. 9. Shear-flow development in du m p com bustor (Sm ith and Zukoski22).

h av i n g a r e l a t i v e l y s h o r t l en g t h , t h e d ev e l o p i n gv o r t ex i n t e r ac t s w i t h t h e ex i t n o zz l e (F i g . 10 ) . 21'37 T h ev o r t ex s h ed d i n g w as co n t ro l l ed b y t h e i n l e t a co u s t i c s.T h e s t r o n g m i x i n g b e t w e e n t h e c o l d r e a c ta n t s a n d t h eh o t p ro d u c t s o ccu r s a f t e r t h e v o r t i c e s i m p i n g e o n t h eex h au s t n o zz l e g en e ra t i n g s m a l l- s ca le v o r t i c e s . T h i s i sfo l l o wed b y h i g h h ea t r e l eas e , wh i ch b e i n g i n t h e r i g h tp h as e r e l a t i v e t o t h e p re s s u re f l u c t u a t i o n s , f u r t h e rd r i v e s t h e i n s t ab i l i t y . I n s i d e d u m p co m b u s t o r s ,p e r i o d i c f i n e - s ca l e m i x i n g en h an cem en t can b e a s s o -c i a t ed w i t h t h e d ev e l o p m en t o f t h e ax i a l v o r t i c e s a t t h eimp ing ing area as d i scu ssed ear l ie r . 24

In co m b u s t o r s w i t h f l am eh o l d e r s , m u l t ip l e s h ea rlayer in terac t ion i s a l ike ly sourc e o f f ine-sca le mix ingen h a n cem en t an d s u d d en h ea t re lea se . I n co m b u s t i o nex p e r i m en t s 2s w i t h t wo cy l i n d r ica l f l am eh o l d e r s (F i g .11 ), i t was f o u n d t h a t d u r i n g o n e cy c l e o f t h e p re s s u reo s c i l l a ti o n t wo v o r t i c e s o f o p p o s i t e s i g n a r e s h eds y m m e t r i c a ll y f r o m b o t h t h e t o p a n d b o t t o m s u rf a c e so f t h e f lam eh o l d e r . A s t h e se v o r t i c e s co n v ec t d o wn -s t r eam , t h ey d i s t o r t t h e f l am e s u r f ace an d cau s ef l ap p i n g o f t h e f l am e b ran ch es . T h i s d i s t o r t i o n r e s u lt si n an o s c i l l a t o ry i n c rea s e i n t h e f l am e s u r f ace a r ea a n d

h en ce r e s u l t s i n an o s c i l l a t o ry h ea t r e l ea s e r a t e . T h ef l ap p i n g o f t h e f l am e b ran ch es m ay a l s o cau s ep e r i o d i c i n t e r ac t i o n o f th e f l am e f ro n t w i t h t h e s i d ewal l , con t r ibu t ing to the per iod ic hea t re lease . S incet h e p h as e r e l ea s e v a r i e s f a s t e r t h an t h e aco u s t i cp re s s u re p h as e , t h e re a r e r eg i o n s i n t h e f l am e t h a tf l u c t u a te i n p h as e w i t h t h e p re s s u re an d s o m e t h a t a r eo u t o f p h as e . E x c i t a t i o n o f h ig h p re s s u re o s c i l l a ti o n sw a s o b s e r v e d w h e n t h e i n t e g ra t e d a m o u n t o f h e a tp h a s e e x c e ed s t h e o u t o f p h a s e c o n t r i b u ti o n . I t w a sa l s o s h o wn t h a t wh en t h e h ea t r e l ea s e f l u c t u a t i o n slead the acous t ic p ressu re f luc tua t ions , the ins tab i l i tyf r eq u en cy i s h i g h e r t h an t h e n a t u ra l f r eq u en c y o f t h ec o m b u s t o r a n d v ic e ve r sa .

In b l u f f -b o d y f l am eh o l d e r ex p e r i m en t s , v o r t i c e sf o r m e d o n n e i g h b o r i n g s l ot j e ts i n t e r a c t p r o d u c i n gf i n e - s ca l e t u rb u l en ce an d s u d d en h ea t r e l ea s e a sd e m o n s t r a t e d w i t h S c h li e re n p h o t o g r a p h y a n d r a d i -a t i o n m eas u rem en t s . 26 T h e s t ru c t u re o f t h e v o r t i c e san d t h e r e s u l t i n g i n st ab il i ti e s w e re s t ro n g l y d ep en d en to n t h e o p e ra t i n g co n d i t i o n s , s u ch a s t em p e ra t u re an da i r f lo w r a t e s. T w o t y p es o f i n s tab i l it y w e re o b s e rv ed .At t h e r i ch co n d i t i o n s t h e v o r t i c e s o s c i l l a t ed i n a


10/16

126 K .C . SCHADOWand E. GUTMARK

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11/16

Com bustion instability related to vo rtex sheddingGEORGIA TECH

1 2 7

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WALL FLAMEINTERACTION

FIG. 11. Combustion instabilities in disk-stabilized flames (Hegde e t a 1 . 2 5 ) .s t ro n g f l ap p i n g m o d e wh i ch r e s u l t ed i n co u p l i n gb e t ween ad j acen t i n j ec to r s . A t t h e l e an co n d i t i o n s , t h ef r eq u en cy was h i g h e r an d t h e s h ea r l ay e r ex h ib i t ed as y m m et r i c m o t i o n , w h i ch r e s u lt ed i n i n t en s e m i x i n gan d h ea t r e l ea s e wh en t h e m i x i n g l ay e r s co l l i d ed . Inb o t h ca s e s a r e s o n an t co u p l i n g b e t ween t h e u n s t ead yh ea t r e lea s e an d t h e aco u s t i c m o d e s i s e s t ab li s h ed .

6 . D R I V I N G M E C H A N I S M

T h e p reced i n g r e s ul t s s u g g est t h a t a co m b u s t o r f lo wwh i ch i s d o m i n a t ed b y v o r t ex f l o w in t h e f l am eh o l d i n greg ion i s associa ted wi th pe r iod ic hea t re lease . I f theheat re lease i s in phase wi th the p ressu re osc i l l a t ions ,d r i v i n g o ccu r s a s s t a t ed b y t h e R ay l e i g h c r i t e r io n . T od e t e rm i n e i f th e p e r i o d i c h ea t r e l ea s e i s a d r i v i n gfo rce , it is n eces s a ry t o h av e a c o m p l e t e k n o w l ed g e o ft h e s p a t ia l an d t em p o ra l d i s t r i b u t i o n s o f h ea t r e l ea sean d aco u s t i c p re s s u re . T h es e m eas u rem en t s we re d o n ei n th e p re s en t r e s ea rch u s i n g p re s su re t r an s d u ce r a n drad iat i on inten si ty m eas ure me nts . 3"26'36 It w asp rev i o u s l y s h o wn t h a t t h e o s c i l l a t o ry h ea t r e l ea s e i sl i n ea r l y p ro p o r t i o n a l t o t h e em i t t ed r ad i a t i o n . ~2 B yt ak i n g t h e c ro s s s p ec t ru m a n d p h as e o f th e p re s s u rean d r ad i a t i o n i n t en s i t y a t a g i v en l o ca t i o n i n t h ec o m b u s t i o n c h a m b e r , t h e r e la t iv e m a g n i t u d e o f t h ed r i v i n g a t t h a t l o ca t i o n can b e d e t e rm i n ed . F o r t h eex am p l e i n F i g . 1 2, th e d r i v i n g o ccu r s p r i m a r i l y a t t h ef r o n t o f th e c o m b u s t o r ) D a m p i n g o c c u rs f u r th e rd o w n s t r e a m . T h e n e t v a l u e o f t h e i nt e g ra l o f t h e c u rv ed e t e rm i n es i f d r i v i n g (p o s i ti v e n e t v a l u e ) o r d am p i n g(n eg a t iv e n e t v a l u e ) o cc u r s ) 6

T h e n e t v a l u e w ill c h a n g e i f c o m b u s t o r p a r a m e t e r swh i ch d e t e rm i n e t h e h ea t r e l ea s e an d p re s s u re d i s tr i -b u t i o n s a r e v a r i ed . T h e h ea t r e l ea se d ep en d s o n f l u i dd y n am i c m i x i n g an d ch em i ca l r e ac t i o n an d i st h e re fo re a f f ec ted b y d u m p g e o m e t ry , in i ti a l co n d i t i o no f s h ea r l ay e r, f u e l t y p e , an d l o ca l eq u i v a l en ce r a t i o ,wh i l e t h e p re s s u re d i s t r i b u t i o n d ep en d s o n t h ed o m i n an t a co u s t i c m o d e , wh i ch i s ex c i t ed d u r i n g t h eco m b u s t i o n i n s tab i l it y . 3

Vo r t ex d y n am i cs a l s o p l ay ed a c r i t i c a l ro l e i n

d r i v in g p u l sa t i n g c o m b u s t i o n i n a d u m p c o m b u s t o r ,wh ere the in le t l eng th w as s ign i f ican t ly long er than thec o m b u s t o r l e n g t h . I n a 2 - D d u m p c o m b u s t o r , t h em a x i m u m h ea t r el ea se r a t e o ccu r r ed wh en t h e v o r t ic e si m p i n g e o n t h e ex h au s t n o zz l e .2~ T h e f r eq u en cy o f t h eo s c i l la t i o n s was d e t e rm i n ed b y t h e aco u s t i c s o f t h ei n le t d u c t an d t h e v o r t ex co n v ec t i o n ti m e i n t h e co m -b u s t o r , an d t h e am p l i t u d e was d e t e rm i n ed b y t h e ra t ea t wh i ch t h e r eac t an t s en t e r ed t h e ch am b er , t h e h ea tre lease ra te , and the ven t ing ra te th rough the ex i tn o zz l e . T h e p ro ces s i s n o t a r e s o n an t o n e . T h ep re s s u re i s g ro wi n g n o t b ecau s e a r e s o n an t a co u s t i cm o d e i s b e i n g f ed a t an ap p ro p r i a t e p h as e (R ay l e i g hc r i te r i o n ) , b u t b ecau s e o f m as s a n d en e rg y i m b a l an cei n t h e co m b u s t o r . T h e f r eq u en cy i s we l l b e l o waco u s t ic m o d e f r eq uen c i es o f t h e c o m b u s t o r , i n c l u d i n gt h e b u l k m o d e f r eq u en cy . T h e i n s tab i li ty m ech an i s m i ssimilar to tha t o f a series of v ented explosion s. 2j'3s

7 . P A S S I V E C O N T R O L

B as ed o n t h e d e s c r i b ed d r i v i n g m ech an i s m , t h ep as s iv e co n t ro l m e t h o d s can m i n i m i ze p re s su re o s c i l-l a t i o n am p l i t u d es . T h ey d o n o t p ro v i d e d e s i g nc r i t e r i a , b u t c an g u i d e t h e en g i n ee r i n t h e co m b u s t o rdes ign .

Vo r t ex co h e ren ce an d t h e r e l a t ed p e r i o d i c h ea tr el ea se can b e m i n i m i zed b y m an i p u l a t i n g t h ech am b er aco u s t i c s t o r ed u ce t h e s h ea r - l ay e r fo rc i n gl e v e l . F o r a n a x i s y m m e t r i c d u m p c o m b u s t o r w i t hfu l ly op en as wel l as cons t r ic te d ex i ts , p ressu re am pl i -t u d es we re r ed u ce d b y u s e o f a s t r a t eg i cal l y l o ca t edo r if i ce in t h e u p s t r eam d u c t an d u s e o f q u a r t e r -wa v et u b es a n d H e l m h o l z r e s o n a t o r s a t ta c h e d t o t h e c o m -b u s t o r a t a l o ca t i o n c l o s e t o a p re s s u re an t i n o d e o f t h el o n g i t u d i n a l f r e q u en cy ) 9 A l s o , t h e am p l i t u d e o f t h eo s c i l la t i o n can b e r ed u ced b y ad j u s t i n g t h e i n l et an dc o m b u s t o r l e n g t h s . I n t h e s a m e c o m b u s t o r w i t h t h eu p s t r eam en d aco u s t i c a l l y c l o s ed (p e r fo ra t ed p l a t e ) ,t h e p re s s u re am p l i t u d e w as a m a x i m u m w h en t h e in l e tl en g t h was o n e h a l f o f t h e wav e l en g t h o f th e q u a r t e r -wav e o f th e aco u s t i c a l ly o p en en d ed c o m b u s t o r , w i t h


12/16

12 8 K. C. SCHADOWand E. GUTMARKGALTECH

t0 :

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-1 0

Fro . 12. Rayleigh 's cr i ter ion for dump c omb ustor instab i l i ty (S ter l ing and Zukos k iL)a p re s su re m o d e a t t h e d u c t ex it an d an an t i n o d e n ea rt h e d u m p (F i g . 1 3 ) . T h e p re s s u re am p l i t u d e w asred u ced w i t h a s h o r t e r o r l o n g e r i n l e t d u c t l en g t hw h i ch d i d n o t m a t ch t h e h a l f -w av e l en g t h ) 9 T h i ss o l u t i o n is p r ac ti c a l w h en t h e g eo m e t ry o f th e co m -b u s t o r c an b e v a r i ed acco rd i n g t o t h e aco u s t i c c r i te r i ao r w h e n t h e c o m b u s t o r c a n b e r u n w i t h a n o p e nexit.T h e r e l a t io n s h i p o f th e ex c i ted aco u s t i c m o d e f r e -que ncy to the f low ins tab i li t i es o f the sys tem i s c r i ti ca la n d c a n b e c o n t r o l l e d . F o r a c o a x i a l d u m p c o m -b u s t o r , i t c an b e a rg u ed t h a t t h e v o r t i c e s a s s o c i a t edw i t h t h e p re fe r r ed -m o d e fo rc i n g a r e t h e m o s t

p ro b ab l e t o d r i v e l o w - f r eq u en cy o s c i l l a t i o n s .Therefo re , i t i s des i rab le to have a s ign i f ican tm i s m a t ch b e t w een t h e aco u s t i c f r eq u en cy an d t h eprefer red mode f requency . Prac t ica l ly , th i s i s a d i f -f i cu l t t a s k b ecau s e t h e p re fe r r ed -m o d e f r eq u en cy an do ther f low ins tab i l i ty f requencies , which depend onthe f low veloc i ty , var y dur in g the f l igh t envelope wi thch an g i n g a i r m as s f l o w an d p re s s u re . A l s o , fo r acom plex sys tem, i t i s d i f f icu l t to p red ic t a p r io r i , w h icho f t h e aco u s t i c m o d es w i l l b e ex c it ed . M o reo v e r , i t i sm o s t l i k e l y t h a t t h e d o m i n an t a co u s t i c m o d e i n s t a -b i l i ty w i l l be a t a f requency which i s c loses t to thed o m i n an t f l o w i n s t ab i l i t y f r eq u en cy a s s o c i a t ed w i t h

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13/16

Com bustion instability related to vortex shedding 129l a rg e v o r t i c e s . F o r ex am p l e , i n a co ax i a l d u m p co m -b u s t o r , i t was s h o wn t h a t t h e p re fe r r ed -m o d e f r e -q u e n c y d e t e r m i n e d w h i c h a c o u s t i c f r e q u e n c y w a sexci ted . ~7 In c om bu s to rs wi th h igh e nerg y re lease , thep re s s u re o s c i l l a t i o n s can o v e rwh e l m t h e f l o wd y n am i cs an d fo rce i t t o d ev e l o p v o r t i c e s a t f r e -q u en c i e s wh i ch a r e a t t h e ed g e o f t h e i n s t ab i li t yen v e l o p e .

In t h e p re s en ce o f p e r i o d i c h ea t r e lea se , m a x i m u mdriv ing occ urs wh en the R ay le igh cr i t e r ion i s sa t is fied.T h e d r i v i n g c o n d i t io n s c a n b e c h a n g e d b y v a r y i n g t h em i x i n g t i m e ( fo r ex am p l e b y v a ry i n g l o ca l m i x t u rera t i o o r fu e l i n j ec t i o n p a t t e rn ) . Ho wev e r , i n l i g h t o fo p e ra t i o n a l ch an g e s o f a ir an d fu e l m as s f lo w an dp re s s u re , t h i s ap p ro ac h r em a i n s a t r i a l - an d -e r ro r t a s k .

P as s iv e s h ea r - f l o w co n t ro l w as i n v es t ig a t ed t o a l t e rt h e co m b u s t i o n p ro ces s , w i t h a g o a l , t o av o i d p e r i o d i ch ea t r e l eas e i n d ep en d en t o f v a ry i n g a i r an d fu e l m as sf low. Th is method was inves t iga ted in dump-s tab i l i zedan d d i s k - st ab i li z ed co m b u s t o r s an d i s d e s c r i b ed i n t h efo l lowing .

N o n r e a c t i n g a n d r e a c t i n g s h e a r f l o w d y n a m i c s o fn o zz l e s w i t h co rn e r s ( t r i an g u l a r n o zz l e ) an d m u i t i s t epn o zz le s we re i nv es t ig a t ed i n a co ax i a l d u m p co m b u s t o r .

S t u d i e s o f j e t s em erg i n g f ro m n o zz l e s w i t h co rn e r s ,e . g . t r i an g u l a r o r s q u a re n o zz l e s , s h o wed t h a t t h ei n t ro d u c t i o n o f s h a rp co rn e r s i n t h e n o zz l e can s ig n if i-can t ly increase the smal l -sca le tu rbu lence a t theco rn e r s r e l at i v e t o t h e f l a t s eg m en t s o f t h e n o zz l e .E v en wi t h aco u s t i c fo rc i n g o f t h e t r i an g u l a r s h ea rl ay e r, o n l y s m a l l- s ca le t u rb u l en t f l o w em an a t e d f ro mt h e co rn e r s wh i l e h i g h l y co h e ren t s t ru c t u re s we regene ra ted a t the f la t s ides . 39 In a reac t ive f low ofn o n c i r cu l a r f l am es , t h e co m b u s t i o n a t t h e f l a ts eg m en t s was co n f i n ed i n p e r i o d i c , l a rg e - s ca l eco h e ren t s t ru c t u re s wh i l e t h e co rn e r co m b u s t i o no ccu r r ed i n r an d o m l y d i s t r i b u ted s m a l l -s ca le f l am e l et s(Fig. 14).4o

E x p e r i m e n t s w i t h t h e c o e x i a i d u m p c o m b u s t o rwere p e r fo rm e d t o co m p are fu e l i n j ec ti o n i n t o c i r cu la rand t r iangu lar in le t ducts . Fuel in jec t ion in to theh igh ly tu rbu len t f low fie ld reg ion a t the ver t ices o f at r i an g u l a r i n l e t d u c t s u p p re s s ed t h e p re s s u re am p l i -t u d e b e l o w 1 0 % o f th e m ea n p re s s u re (AP R M s /Pc < 0 .10) over the e n t i re equ iva lence-r a t io range(Fig. 15).4~ In o t h e r d u m p c o m b u s t o r t e s t s, t h e t r i-an g u l a r i n l e t d u c t a l s o ex t en d ed t h e l e an an d r i chf lamm abi l i ty l imi ts . 42 The co m bin at io n o f l a rge-sca lean d f i n e - s ca l e m i x i n g p ro d u ced b y t h e t r i an g u l a rnozzle i s benef ic ia l fo r com bu s t ion w here bo th bu lkm i x i n g b e t ween t h e r eac t an t s an d m o d u l a r m i x i n g t op ro m o t e t h e r eac t i o n a r e r eq u i r ed fo r ef fi ci en t co m -b u s t i o n . Ho w ev e r , t h e p ro x i m i t y o f t h e l a rg e an dsmal l sca le f low reg ions in th i s nozzle requ i res carefu ld e s i gn o f t h e fu el i n jec t i o n p a t t e rn . I t was s h o w n t h a tt h e fu e l s h o u l d b e i n j ect ed a t t h e n o zz l e ' s co rn e r s t oavo id in ter ac t ion wi th the vor t ices shed a t the f ia t s ide .B u t i t was fo u n d t h a t i n j ec t o r o r i en t a t io n , d e p t h , an di n j ec ti o n v e l o c i t y a r e i m p o r t an t t o ach i ev e t h is g o a l . I ft h e i n j ec ti o n co n f i g u ra t i o n i s n o t o p t i m i zed t o g e t t h eJPEC$ 1 8 : 2 - D

fue l in to the des i red f low reg ion , osc i l l a t ions are no tsuppressed ef fec tive ly an d the f lam ma bi l i ty l imi t s canbe adverse ly af fec ted .

A m u l t i - s t ep d u m p h av i n g s ev e ra l b ack ward f ac i n gs t ep s en h an ces f i n e - s ca l e t u rb u l en ce an d p rev en t sl a rg e - s ca l e s t ru c t u re d ev e l o p m en t a s s h o wn i n n o n -reac t ing and reac t ing exper im en ts . 43 U s ing a mul t i -s t ep d u m p co m b u s t o r , t h e p re s s u re o s c i l l a t i o n s we rered u ced b e l o w APRMs/P = 0 .10 . The lean f lameb l o w-o u t l i m i t was s l i g h t l y ex t en d ed t o l o wer ~ swi t h t h e m u l t i - s t ep d u m p r e l a t i v e t o t h e s u d d end u m p ; h o wev e r , r i ch f l am e b l o w-o u t o ccu r r ed a t al o wer eq u i v a l en ce r a t i o fo r t h e m u l t i - s t ep d u m p(0 .8 < 4 ) < 0 .9 ) th an fo r the sudde n du m p(~ > 1 .3 ) .

T o o b t a i n s u p p re s s i o n o v e r a w i d e r an g e o f eq u i v a -lence ra t io , the d i s t r ibu t ion o f fue l in jec t ion in to thef low over the s teps i s c r i t i ca l . I t has to be d i s t r ibu tedalong the s teps so tha t i t i s mixed in to the f ine-sca let u rb u l en ce d o w n s t r eam o f each s tep . P re fe rab l y , its h o u l d b e i n j ec t ed p e rp en d i cu l a r t o t h e f l o w a t t h er igh t ve loc i ty , such th a t the fue l j e t does n o t in ter ferewi t h t h e r ea t t a ch m en t o f t h e a i r fl o w o v e r th e s t ep san d ed g es. T h e l en g t h t o h e i g h t r a t i o o f th e s t ep s h a st o b e o p ti m i zed t o o b t a i n r ea t t a ch m en t n ea r t h e ed ge .S h o r t e r s t ep s d o n o t h av e a co m p l e t e r ec i r cu l a t i o nzo n e t o en s u re g o o d m i x i n g , wh i le l o n g e r o n es cau s ed ecay o f th e t u rb u l en ce en e rg y .

In a d i s k - s tab i li z ed co m b u s t o r , c o m b u s t i o n o s c il la -t i o n s we re r ed u ced b y co n t ro l l i n g t h e aco u s t i c d r i v i n g ,p ro v i d ed b y t h e f l am e m erg i n g an d wa l l - f l am e i n t e r -ac t ion reg ions . Speci f ica l ly , re la t ive to the p ressu reo s c i l la t i o n t h e l o ca l p h as e o f t h e u n s t ead y h ea t r e l ea s ewas m an i p u l a t ed t o b e o u t o f p h as e w i t h t h e aco u s t i cp re s s u re . T h i s was acco m p l i s h ed b y d i s p l ac i n g t h et wo f l am eh o l d e r s r e l a t i v e l y t o each o t h e r , t h e reb ych an g i n g t h e v o r t ex t rav e l t i m e f ro m each f l am eh o l d e rt o t h e f l am e m erg i n g an d wa l l fl am e i n t e r ac t io n zo n es .T h e f ea s ib i li t y o f t h is t e ch n i q u e i s d em o n s t r a t ed i nF i g . 1 6 wh e re t h e am p l i t u d e an d f r eq u en cy o f t h eexci ted p ressu re osc i l l a t ion are p lo t ted as a funct iono f t h e v e r ti c a l s ep a ra t i o n b e t ween t h e f l am eh o l d e r s . As t ro n g v a r i a t i o n i n p re ss u re am p l i t u d e i s ev id en t w i t hvary ing the ver t ica l separa t ion . ~

8. SUMMARY AND CONCLUSIONS

Combus t ion ins tab i l i t i es were s tud ied in a var ie tyo f d u m p c o m b u s t o r a n d b l u f f- b o d y f l a m e h o ld e rg eo m e t r i e s , i n c l u d i n g t wo -d i m en s i o n a l an d ax i s y m -m e t r i c d u m p co m b u s t o r s , s i d e -d u m p , cy l i n d ri ca l , an drec tan gu lar f l am e stabi li zers . Al l the exper im en tss h o wed t h a t t h e i n s t ab i l i t y was a s s o c i a t ed w i t h t h efo rm a t i o n o f l a rg e -s ca l e v o r ti c e s i n t h e m i x i n g l ay e rwh i ch co u p l ed wi t h t h e aco u s t i c p re s s u re t o ex c i t es t rong osc i l l a t ions .

C o l d f l ow t e s ts s h o w ed t h a t t h e ro l l -u p o f v o r ti c e si s r e l a t ed t o Ke l v i n -He l m h o l z i n s t ab i l i t y i n t h es ep a ra t i n g s h ea r l ay e r b eh i n d t h e v a r i o u s f l am e-ho lders . Th e f req uenc y o f th is ins tab i l ity sca les wi th a


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7 n sE X P O S U R E

P L I FI M A 6 1 N GO F O Hf F = 1 0 0 H z |

CDA I R ~ c

130 K.C. SCHADOWand E. GUTMARK

0 1 0 2 0 3 0 4 0 5 0 6 0D I S T A N C E , m m

7 0

f v 2 2 . 0 50 . 5 7

FIG. 14. Flame characteristics of equilateral triangular burner (Gutmark e t a/.4).typical length scale which can be either the initialthickness of the shear layer or the jet inlet diameter,and the flow velocity.

When the flow is forced by either the upstream ordownstream duct resonant acoustic modes or by anexternal source, vortices can be generated at a muchlarger scale relative to the Kelvin -Hol mholz insta-bility. However, since the acoustic emission of thenonreacting vortices is low, there was no detectable

feedback between the flow and the acoustic pressurein the chamber.

This fact changed when a reacting mixing layer wasconsidered. The large periodic energy release associ-ated with the burnin g inside the vortices provides themissing link for the necessary feedback loop. Thefollowing scenario was suggested by all the exper-iments described above. The mixing layer rolls up in tovortices in which combustion occurs. The energy

O CIRCULAR NLETA TRIANGULAR CO MB . NOT SUSTAINED

0 . 40

0 . 3 5 - r e al. = 1 .7 k g / s / ~ ' ' ' 0

FLAT SIDE0 . 2 5 - = 1 42c 0 . 2 0 -0 . 1 5 -

NER INJECTION0 .10 - ~ / . ~ & T= 130c0 . 0 5 - . ~

_ l I = I = I I I I J , _0 "0 .3 00 :'~ - 0 . 4 0 . 5 0 . 6 " 0 . 7 0 . 8 0 . 9 1 1 . 1 1 . 2FIG. 15. Pressure amplitude vs equivalence ratio for circular and triangular inlet duct (Schadow el a l . 4 ~ ) .


15/16

6 E O l l G I A T ( ' C H|

3 .

I

0 .0

1 1 0* A M P L I T U D E O F P '

, J 2 o ~ o , o : ,m m u a o s m u u m o , o m u c E , ~ ,~

t oo- 1 4 o

- 1 2 0

- 1 0 0 i. am . .o . 6 0

. 4 0

FIG. 16. Passive control of pressure oscillations in

Combustion instability related to vortex shedding 131

Z 0

oI. O

disk-stabilized flames (Hegde et al.44).release is thus periodic in nature and reaches amaximum when the vortices break down to smallscale turbulence. There are different mechanisms thatlead to this transition depending on the combustorgeometry such as vortex interaction, vortex impinge-ment or collision with each other or on a solid surface,and vortex merging. The fluctuating heat release canfeed energy into the acoustic pressure oscillations,provided tha t the two are in phase with each other, asstated by the Rayleigh criterion. As the pressure oscil-lations are amplified, they drive velocity oscillation atthe mixing layer which further enhance the genera tionof coherent vortices in the shear layer.

The under stan ding of this process suggests possiblemethods for controlling the oscillations in unstablecombustion. The methods described are based ongeometrical changes in the design of the combustorand thus are referred to as passive control. Thecommon goal is to disrupt the feedback loop betweenthe periodic heat release and the acoustic pressureoscillations. One approach was to decouple the twoby driving them out of phase with each other, i.e.using Rayleigh criterion. The other was to change thegeometrical design of the inlet duct or the bluff-bodyflameholders such that the evolution of large-scalestructures is hampered and production of small-scaleturbulence is promoted, thus mai ntaini ng a uniformrather than pulsating combustion process. Themethods described showed a certain success in sup-pressing combustion instabilities but require carefuldesign of the fuel injection system such that adverseeffects can be minimized.

R E F E R E N C E S

1. RAYLEIGH, J. W. S., T h e T h e o r y o f S o u n d , DoverPublications, New York (1945).2. PUTNAM, A. A., Combus t ion-Dr iven Osc i l la t ions inIndus try , Elsevier (1971).

3. STERLING, . D. and ZUKOSK1,E. E., A IA A P a p . 8 7 -0 2 2 0(1987).4. CULICK , F. E. C . , A G A R D 7 2 B P E P M e e t. , 126pp.(1988).5. KASKAN,W. E. and NOgEEN, A. E., A S M E T ra ns. 77,885-895 0955).6. ROGERS, D. E. and MARRLE, F. E., Jet Propuls . 26,456--462 (1956).7. HALL, P. H., A I A A P a p . 8 0 -1 1 1 8 (1980),8. SCHAOOW,K. C., CRUMP,J. E. and BLO~SHIELO,F. S.,P r o c. 1 8 th J A N N A F C o m b u st . M e e t ., CPIA Pub. No.

347, Vol. III (1981).9. BYRr,~E, R. W., P r o c . 1 8 t h J A N N A F C o m b u s t . M e e t . ,CPIA Pub. No. 347 (1981).10. BYRNE, R. W., A I A A P a p . 8 3 -2 0 1 7 (1983).1 . BROWN, G. L. and ROSHKO,A . , J . F lu id Me c h . 6 4 ,775-816 (1974).12. Ho, C. M. and HUERRE, P., A. R e v . F lu id Me c h . 16,365--424 (1984).13. MICHALKE,A., J . F lu id Mech . 23 , 521-544 (1965).14. CRow, S. C. and CHAMPAGNE,F. H., J. F l u i d M e c h . 4 8 ,547-591 (1971).15. GUTMARK,E. and Ho, C. M., Phys. Fluids 26, 2932-2938(1983).16. Ho, C. M. and NOSSEIR,N. S . , J . F lu id Mech . 105 ,119-142 (1981).17. SCHAOOW,K. C., GUTMARK,E., PARR, T. P., PARR, D.M. and WILSON, W. J., Combust. Sci. Technol. 64,167-186 (1989),18. GUTMARK,E., PARR, T. P., PARR, D. M. and SCHADOW,K. C. , d . Heat Trans fer 111, 148-155 (1989).19. SIVmEOAgAM,S. and WHlaXLAW,J. H., 'Oscillations inaxisymmetric dump combustors,' Imperial College,Mechanical Engineering Report FS/86/33 (July, 1986).20. McMANuS, R. R., VArCDSmm~ER, V. and BOWMAN,C . T . , C o m b u s t . F la m e 82, 75-92 (in press).21. Yu, K., TROt:rE, A. C., KEAN]NI,R., BAUWENS,L. andDAILY, J. W., A IA A P a p . 8 9 -0 6 2 3 (1989).22. SMITH,D. A. and ZUKOSKI,E. E., A IA A P a p . 8 5 -1 2 4 8(1985).23. DAws, J. A., KomEgA'rrl,N. M., WALTEmCK,R. E. andSTRAHLE, W. E., A IA A P a p . 8 6 -0 0 0 3 (1986).24. NOSSEIR, N. S. and BEHAR, S., A I A A J . 2 4 , 1752-1757(1986).25. HEGDE,U. G., REUTER,D. and ZINN, B. T., A I A A P a p .88-0150 (1988).26. POINSOT, T. J., TROUVE, A. C., VEYNANTE,D. P.,CANDEL,S. M. and ESPOS]TO, E. J., J . F lu id Me c h . 177,265-292 (1987).


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132 K .C . SCHADOWand E. GUTMARK27. SCHADOW,K. C., GU'rMARK,E., PARR, D. M ., MAHAN,V . A . an d FERRELL,G. B., J. Combust. Sci . Technol. 54,103-116 (1987).28. SCHADOW, K. C., WILSON, K. J. an d GUTMARK, E.,A I A A J. 25, 1164-1170 (1987).29. OS~R, D. and WYGNANSKI,I . , J. Fluid Mech. 123,91-130 (1982).30. LAUFER, . an d M ONKEWITZ,P. A. , AIAA Pap. 80-0962(1980) .31. KmENS,V ., AIAA Pap. 81-1960 (1981).32. KOSmGOE, S., YANG , V. a nd CULICK, F. E. C., A I A APap. 85-0043 (1985).33. Jo u, W .-H. a nd MENON, S., Phys. Fluids (1988). (AlsoAIAA-75-1422.)34. DAVIS, . A. an d STRAHI~, W. A., AIAA Pap. 88-0595(1988).35 . D A vis , D . L ., ' Coaxia l dump combu s tor s com bus t ioninstabil i t ies , Par t I - -Parametr ic tes t data , ' AeroPr opuls ion Labor a tor y , A i r For ce Wr ight A er onaut ica lLabor a tor ies , Wr ight - Pa t te r son A FB, O hio , I n te r imRepo r t (1981).

36. HEGDE,U. G ., REUTER,D., DANIEL,B. R. and ZINN,B.T., Combust. Sci. Technol. 55, 125-138 (1987).37. Y u, K., LEE, S., TROUVE,A. C., STEWART,H. a nd DAILY,J. W. , AIAA Pap. 87-1871 (1987).38. BAUWENS,L. an d DAILY, J. W ., Spring Meet. WesternStates Section Combust. Inst. Pap. 89-29 (1989).39. SCHADOW, K. C., GUTMARK, E., PAR R, D. M . an dWILSON, K . J., Ex p. Fluids J. 6, 129-135 (1988).40. GUTMARK,E., SCHADOW,K. C., PARR, T. P. , PARR, D.M . an d WILSON, W. J. , Exp. Fluids 7, 248-258 (1989).41. SCHADOW, K. C., GUTMARK, E., WILSON, K. J. an dSMITH, R . A.,. 9 t h IS ABE (1989).42. WHITELAW, . H., SIVASEGARAM,S., SCHADOW, K. C.and GUTMARI,E ., 7 2n d A G A R D M e e t . (1988).43. SCHADOW, K. C., GUTMARK, E., WILSON, K. J. an dSMITH,R. A. , J . Propuls . Pwr 6, 406-411 (1990).44. HEGDE, U., REUTER, D. an d ZINN, B., A I A A P a p .89-0979 ( i 989).

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