bluff- body stabilization wright.pdf

8/10/2019 bluff- body stabilization wright.pdf

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B lu f f -B ody F lam e Stabi l i za ti on

B lockage E f f ec ts

F. H. WRIGHT

Experiments have been performed to define the influence of blockage on flame

stabilization by bluff bodies in dueted flow. Flameholders of a particularly simple

geometry were studied over a wide range of blockage ratios. The studies were made

while combustion was taking place and showed that flow speeds and flame geometry

depend strongly on blockage. However, the experiments demonstrated convincingly

that, at flame bIowoff, the particular combination of these variables known as the

characteristic mechanical time is independent of blockage as well as of other gross

fluid dynamic parameters'. Further experiments explored the influence of Mach number

on the flows and showed quantitatively tile changes in flow speeds and flame

geometry to be expected at high Mach numbers. The experiments showed that the

value of the mechanical time at blowoff remains unchanged at high Mach numbers

despite large changes in the flow speeds and lengths that constitute this mechanical

time. As a guide for the experiments, a free-streamline theory was developed. This

purely fluid dynamic theory, supplemented by a few simple experimental results,

suffices to predict most of the features of bluff-body flameholding. A result of practical

importance, predicted by the theory and confirmed by experiment, is that maximum

bIowoff speed occurs at a relatively low blockage ratio.

EXPERIMENTAL studies by E. E. ZUKOSKI and F. E. MARBLE of bluff-body

flameholders have demonstrated that flameholding ability depends directly

on the length L of the recirculation zone, the sheltered region just down-

stream from the bluff body (Figure 1). Flameholding limits also depend

on the nature of the combustible mixture. Fortunately, experiments 1 have

shown that the influence of mixture properties may be expressed by a

single parameter, the chemical time r. As a result, the blowoff speed from

a bluf-body flameholder may be written very simply as

(V~)Bo=(L/r)

where V._, is the flow speed past the flame.

This equation is a powerful tool in the correlation and prediction of

flameholder blowoff, since the chemical time depends only on the pressure

and temperature of the combustible mixture and on fuel type and fuel/air

ratio; chemical time is independent of the gross fluid dynamic variables

such as flow speed and flameholder geometry. For a given combustible

mixture the chemical time is the same for all flameholders. On the other

hand, the recirculation-zone length depends essentially only on the fluid

dynamic variables.

The blowoff equation shows how the blowoff flow speed V2 past the

wake varies with recirculation-zone length and chemical time at blowoff.

Of greater practical interest, however, is the speed V~ far upstream. In

terms of this speed the blowoff relation becomes (V~)Bo=(V,/V~_)(L/r).

The velocity ratio V~./Vj depends on flameholder geometry and is strongly

influenced by the proximity of duct walls or other flameholders: it depends

on blockage. Blockage also affects the length of the recirculation zone.

319


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F H WRIGHT

, X

Duct wall RecJrculatlon zo ne

F l a m e h o l d e r

/

v

~

J

D u c t w a l t i

\ \ .? - \ \ \~ \ ' ~ \~ , ~ , \ \ \ \ \ \ \ \ \ \ , \ \ , ,~ . \N \ \ \ , \ \ \ \ - - 3 \ . , , \N \ , ~ \ \ \ \ \ \ \ \ \ \ \ \ . \ , \ \ \ \ \ \ \ \ \ \ \ , \ - , - ( , .

F ig u r e 1 . F la me h e ld o n f l at - p la t e f l a me h o ld e r

I n f a c t , e x p e r i m e n t s 2, : i n d i c a t e d t h a t r e c i r c u l a t i o n - z o n e l e n g t h v a r i e s

i n v e r s e l y a s t h e s q u a r e r o o t o f th e b l o c k a g e a n d t h a t f l o w s p e e d p a s t t h e

w a k e i n c re a s e s a l m o s t li n e a r ly w i t h b lo c k a g e . H o w e v e r , f u r t h e r s tu d y w a s

r e q u i r e d t o e l u c i d a t e t h e e f fe c ts o f b l o c k a g e a n d o t h e r f l u id d y n a m i c

v a r ia b l es . H e n c e a n e x p e r i m e n t a l a n d t h e o r e t ic a l i n v e s t ig a t i o n o f t h e

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

s i m p l e g e o m e t r y w a s i n it ia t ed . T h e fl o w a b o u t f ia t p l a te s o r i e n t e d n o r m a l

t o t h e s t r e a m w a s s t u d i e d ; t h i s p a p e r p r e s e n t s t h e r e s u l t s o f t h e s t u d y .

EXPERIMENTAL STUDIES

Equipment

T h e e x p e r i m e n t s w e r e r u n i n a 1 i n . x 4 i n . d u c t w i t h t h e f l a m e h o l d e r s e t

a c r o ss t h e n a r r o w d i m e n s i o n a n d c o m p l e t e l y s p a n n i n g th e d u c t . T h e d u c t

e x t e n d e d 6 i n . d o w n s t r e a m f r o m t h e f l a m e h o l d e r ; f o r c o m p a r i s o n p u r p o s e s

a f e w e x p e r i m e n t s w e r e c a r r ie d o u t w i t h a 9 i n. d u c t l e n g t h . D u c t s i d e

w a l l s w e r e o f V y c o r g la s s.

F l a m e h o l d e r s w e r e t h i n f l a t p l a t e s w i t h b e v e l l e d e d g e s , o r i e n t e d s o t h a t

t h e f la t s id e s f a c e d u p s t re a m . E x c e p t f o r a fe w c o m p a r i s o n r u n s, t h e

f l a m e h o l d e r s w e r e w a t e r - c o o l e d .

F u e l w a s S t a n d a r d O i l C o . t h i n n e r N o . 2 0 0 , a g a s o l i n e - l i k e h y d r o c a r b o n

w h i c h w a s i n j e c t e d i n t o h e a t e d a i r f a r u p s t r e a m f r o m t h e f l a m e h o l d e r ,

f o r m i n g a h o m o g e n e o u s g a se o u s c o m b u s t i b le m i x t u r e . N o r m a l m i x t u r e

t e m p e r a t u r e w a s 3 3 9 K .

F l a m e s h a p e s a n d w i d t h s w e r e o b t a in e d f r o m s p a r k s c h li e re n p h o t o g r a p h s .

R e c i r c u l a t i o n - z o n e l e n g t h s w e r e m e a s u r e d b y i n j e c t i n g s a l t w a t e r i n t o

t h e f la m e . S a l t i n j e c t e d i n t o t h e r e c i r c u l a t i o n z o n e c o l o u r s t h e w h o l e

r e g i o n ; s a l t i n j e c t e d d o w n s t r e a m f r o m t h e e n d o f t h e r e c i r c u l a t i o n z o n e

l e a v e s t h e r e c i r c u l a t i o n r e g i o n u n c o l o u r e d .

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BLUFF BODY F LAME STABILIZATION: BLOCKAGE EFFECTS

Recirculation-zone length

T h e r e c i r c u l a t i o n z o n e i s t h e s h e l t e r e d r e g i o n j u s t d o w n s t r e a m f r o m a

b l u f f - b o d y f l a m e h o l d e r i n w h i c h h o t g a s r e c i rc u l a te s , a n d t h e l e n g t h L

o f t h i s r e g i o n p l a y s a n e x t r e m e l y i m p o r t a n t r o l e i n Z u k o s k i a n d M a r b l e ' s

v i ew o f f l ame s t ab i l i za t i on 1. H en ce one o f t he f i r st exper im en t s t o be

p e r f o r m e d w a s t h e s t u d y o f t h e i n f l u e n c e o f v a r i o u s f l u i d d y n a m i c a n d

c h e m i c a l p a r a m e t e r s o n t h e l e n g t h L .

S e v e r a l v a r ia b l e s w e r e f o u n d t o h a v e l it tl e ef f e c t o n t h e r e c i r c u l a ti o n - z o n e

l e ng t h. F o r e x a m p l e , c h a n g i n g f l a m e h o l d e r t e m p e r a t u r e m a d e n o m e a s u r -

a b l e d i f f e r e n c e i n t h e l e n g t h , n o r d i d c h a n g i n g f l a m e h o l d e r a s p e c t r a t i o b y

r u n n i n g a f l a m e h o l d e r i n d u c t s o f d i f f e r e n t w i d t h s .

O n t h e o t h e r h a n d , t h e f l o w s p e e d i s a f lu i d d y n a m i c v a r i a b l e t h a t m i g h t

b e e x p e c t e d t o i n fl u e n c e t h e r e c ir c u l a t io n - z o n e le n g t h . E x p e r i m e n t s w e r e

p e r f o r m e d t o t e s t t h i s i n f l u e n c e , a n d s o m e o f t h e r e s u l t s a r e s h o w n i n

Figure 2.

T h e d i m e n s i o n l e s s l e n g t h

L / d

of t he r ec i r cu l a t i on zone i s p lo t t ed

30

20

Figure 2. Recirculation-zone ~ 10

lengths versus Mach number: -4

8

~=1 0

0.08 0 20 0.40

MI

3R:1 :4

0.60

0-80

v e r s u s t h e u p s t r e a m M a c h n u m b e r M 1 f o r v a r i o u s b l o c k a g e r a t i o s ( B R ) .

T h e l e n g th d o e s in d e e d d e p e n d u p o n M I a n d h e n c e u p o n t h e u p s t r e a m

s p e e d , b u t o n l y w e a k l y . V a r i a t i o n o f l e n g t h w i t h sp e e d i s a l w a y s le s s

r a p i d t h a n s p e e d r a i se d t o t h e o n e - q u a r t e r p o w e r . T h e l e n g t h c h a n g e s

shown i l l Figure 2 a r e sm a l l b u t c o m p l e x . F o r v e r y l ow R e y n o l d s n u m b e r s

t h e f l a m e s a r e l a m i n a r a n d t h e i r r e c i r c u l a t io n z o n e s a r e l o n g . A s s h o w n

in Figure 2, t h i s is s o f o r B R = 1 : 3 2 a n d 1 : 16 a t v e r y l o w M a c h n u m b e r s .

A s t h e s p e ed ( a n d R e y n o l d s n u m b e r ) i n c r ea s e s, t h e f l a m e b e c o m e s t u r b u l e n t

a n d t h e r e c i r c u l a t io n z o n e s h o r t e n s . T h i s b e h a v i o u r is e a s i ly e x p l a i n e d b y

c o n s i d e r a t i o n o f t h e m i x i n g z o n e s

(Fig ure 1).

R e c i r c u l a t i o n - z o n e l e n g t h

d e p e n d s o n t h e s p r e a d in g r a te o f t h e m i x in g z o n e s. W h e n t h e m i x i n g z o n e s

s p r e a d r a p i d l y , a s t h e y d o w i t h t u r b u l e n t f l a m e s , t h e r e c i r c u l a t i o n z o n e i s

s h o r t , w h e r e a s w h e n t h e z o n e s s p r e a d s lo w l y , a s t h e y d o w h e n t h e m i x t u r e i s

l aminar , t he r ec i r cu l a t i on zone i s l ong .

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F H W R I G H T

A t l o w R e y n o l d s n u m b e r s , t h e u p p e r t w o c u r v e s o f

Figure 2

d e c r e a s e

w i t h i n c r e a s i n g s p e e d ; t h e n t h e y p a s s t h r o u g h a m i n i m u m , a n d t h e r e a f t e r

i n c r ea s e u n t i l a p l a t e a u is r e a c h e d . R e c i r c u l a t i o n - z o n e l e n g t h th e n r e m a i n s

c o n s t a n t a s t h e s p e e d i n c re a s e s . O n l y w h e n t h e f lo w p a s t t h e fl a m e b e c o m e s

s u p e r s o n i c d o e s th e r e c ir c u l a t io n - z o n e le n g t h a g a i n c h a n g e . I f t h e

b l o c k a g e i s h i g h , t h i s c h a n g e m a y o c c u r a t a r e l a t i v e l y l o w v a l u e o f t h e

u p s tr e am M a c h n u m b e r , a s th e B R = 1 : 4 c u rv e in

Figure 2

shows .

H o w e v e r , f o r m o d e r a t e b l o c k a g e r a t i o s a n d f l a m e h o l d e r s i z e s , b l o w o f f

o c c u r s i n t h e p l a t e a u r e g i o n w h e r e l e n g t h d o e s n o t c h a n g e w i t h s p e e d , a n d

f l o w p a s t t h e f l a m e i s n e v e r s u p e r s o n ic .

R e c i r c u l a t i o n - z o n e l e n g t h c h a n g e s s l o w l y w i t h s u c h v a r i a b l e s a s f l a m e -

h o l d e r t e m p e r a t u r e , a s p e c t ra t i o , a n d f lo w s p e e d . L e n g t h d o e s , h o w e v e r ,

v a r y r a p i d l y a n d c o n s i s t e n t ly w i t h f l a m e h o l d e r b lo c k a g e , a s

Figure 3

shows .

T h e d i m e n s i o n l e s s l e n g t h

L / d

v a r ie s i n v e r se l y w i t h t h e s q u a r e r o o t o f t h e

b lockag e ra t i o ( t he ac tua l s l ope i s -0 46 ) . Th i s i s t he va r i a t i on fo un d -% 3

f o r c i r c u l a r c y l i n d e r s b u t , a s s h o w n i n

Figure 3,

t he f l a t -p l a t e l eng ths a re

2O

4 ~

0 04 0-06 0'0B 0:10 0'20 0'30

B/:?

F i g u r e 3 . R e c i r c u l a t i o n - z o u e

l e n g t h v e r s u s b l o c k a g e r a t i o

17 p e r c e n t g r e a t e r . T h e d a t a f o r t h e u p p e r c u r v e o f

Figure 3

w e r e

ob ta ined by run n ing f l a t p l a t es o f d i f f e ren t s izes i n t he 1 i n . .x 4 i n . duc t .

H e n c e b o t h b l o c k a g e a n d a s p e c t r a t i o s v a r i e d a s t h e p l a t e s w e r e c h a n g e d ;

b u t t h e e n t i re e f f e c t w a s a s c r i b e d t o b l o c k a g e , s in c e p r e v i o u s e x p e r i m e n t s

h a d s h o w n th a t a s p e c t r a t i o h a d n e g l ig i b le i n fl u e n c e . T h e b l o c k a g e e f f e c t

is f lu i d d y n a m i c a n d m a y b e c o m p u t e d w i t h t h e a i d o f t h e f r e e - s tr e a m l i n e

t h e o r y ( s e e A p p e n d i x ) .

I n a d d i t io n t o th e fl u id d y n a m i c p a r a m e t e r s , a c h e m i c al p a r a m e t e r - - t h e

m i x t u r e s t r e n g t h - - w a s s t u d i e d , a n d i ts in f l u e n c e o n r e c i r c u l a t io n - z o n e l e n g t h

w a s e x p lo r e d . L e n g t h s w e r e m e a s u r e d h o l d i n g f l a m e h o l d e r g e o m e t r y a n d

f l o w s p e e d c o n s t a n t .

Figure 4

s h o w s t y p i c a l r e s u l t s o f s u c h m e a s u r e m e n t s

f o r a b l o c ka g e r a ti o o f 1 : 3 2. T h e f l a m e s a t M 1 = 0 2 4 a n d M 1 = 0 4 7 a r e

t u r b u l e n t , o r n e a r l y s o , a n d t h e t w o c u r v e s a r e s i m i l a r i n t h a t r e c i r c u l a t io n -

z o n e l e n g t h is a m i n i m u m c l o se t o s t o i c h i o m e t r i c a n d i n c re a s e s a p p r e c i a b l y

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B L U FF B O D Y L A M E S T A B IL IZ A T IO N : L O C K A G E F F E C T S

as the mixture ratio departs from stoichiometric. A possible explanation

for this behaviour is that the spreading rate of the mixing zones is greatest

close to stoichiometric, where the temperature is highest, and that recir-

culation-zone length is a minimum for the highest spreading rate.

The third curve of Figure 4 Ml =0.13) corresponds to a set of laminar

flames and is different from the curves for turbulent flames. In general,

the recirculation zones are longer than the zones that would be expected for

turbulent flames at this speed, and the length increases monotonically with

fuel/air ratio. Again, this curve may be explained by the spreading rates

2 5

F i g u r e 4 . R e c i r c u l a t i o n - ~ 2 0

~ . 1 3

z o n e l e n g t h v e r s u s [ u e l / a i r -4

r a t i o ; B R = 1 : 3 2

X X M 0 . 2 4

i Re : 1 6 x 104

0 .5 1 , 0 15

of the mixing zones. Rich laminar flames are very smooth and mixing is

slow if the fuel has a molecular weight greater than that of air). On the

other hand, lean flames are frequently distorted by large-scale waves which

increase the mixing rates; recirculation-zone lengths may be even shorter

than at stoichiometric.

In

Figure 4,

the situation approaching blowoff indicated by short vertical

lines) is interesting. The propagating flame, downstream from the recir-

culation zone (Figure 1), becomes more and more tenuous until finally it

disappears altogether, an event which has been defined to be blowoff. How-

ever a residual flame frequently remains beyond this point if flow conditions

are very stable. The residual flame occupies just the recirculation-zone

region, and the recirculation-zone length remains unchanged. As conditions

become slightly more stringent, cold air enters the downstream end of the

recirculation zone and the zone shortens. A point is plotted on the lean

end of the M, =0.24 curve in Figure 4 to show the decrease in length that

may be observed under these circumstances, even though this point is

beyond the normally defined blowoff. The curves of Figure 4 show that

a chemical parameter, the mixture strength, does not greatly affect

recirculation-zone length, nor do most of the fluid dynamic parameters that

have been studied. Only the blockage has been shown to have a strong

influence on recirculation-zone length. Hence it will be especially interesting

to study the influence of blockage on other flame characteristics.

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F H WRIGHT

Wake width

Closely related to the recirculation-zone length is the flame or wake width.

This width may readily be measured on a schlieren photograph (see

Figure 1).

Unfortunately, the outer edges of the wake are not smooth and

regular, and in measuring the width it is necessary to pick an average width

and also to average several pictures. When this is done, the results are

remarkably consistent. For a given blockage ratio, the width is virtually

constant, independent of mixture ratio, and independent of speed (Figure 5)

except when the Mach number of the flow past the flame approaches unity,

at which time the wake width decreases.

6 .0

5.0'

4.C

3 0

2.0

1 5

o r a

~ . n

. /

BR = 1 :3 2

rh 'h

/

BR=1:16

I

B R = I : 8

B R = I : 4

,%

1 0

0 1 0 2 0'3 0'4 0 5 0 6

M 1

Figure 5. Wake width versus

Mach number; @= l'0

The width plotted in Figure 5 was measured at the middle of the recir-

culation zone. Actually, for all blockage ratios except the smallest, this

width applies to the entire downstream half of the recirculation zone; in

this region, width does not change with distance from the flameholder.

The data of Figure 5 yield another interesting result: the ratio of wake

width to flameholder diameter

W / d

varies inversely with the square root of

the blockage, which is exactly the variation previously found for L / d .

Hence the ratio of recirculation-zone length to wake width may be expected

to be independent of blockage ratio. This supposition is confirmed

experimentally for turbulent flames at high speeds

(Figure

6): the

L / W

ratio is independent of flameholder size and blockage ratio and varies only

slightly with speed, approaching a constant value at very high speeds.

(Measurements for M~ close to unity are not reliable and should be

disregarded.)

The observations show, then, that the L / W ratio is independent of

blockage and nearly independent of speed, at least for speeds close to

blowoff. Also, the L / W ratio is nearly the same as that found for other

bluff-body flameholders2.

These results have several interesting applications. They show that the

wake width multiplied by a constant factor may be used in the blowoff

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BLUFF BODY FLAME STABILIZATION: BLOCKAGE EFFECTS

,..4

B R = 1 : 3 2

B R = 1 : 1 6

B R

1 : 8

B R

1:4

0.5 0-6 (>7 0 8

;'1 0'2 0'3 0 4 1 0

M2

F ig u r e 6. R a t i o o / r e c ir c u la t i o n - zo n e l e n g th t o w id th v e r s u s

M a e h n u m b e r ; q ,= l O

f o r m u l a i n p l a c e o f t h e r e c i r c u l a ti o n - z o n e l e n g th . G . M A t rO N ~ a n d o t h e r s

h a v e u s e d t h is m e t h o d . ) T h e r e c i r c u l a t io n - z o n e l e n g t h m a y b e d e t e r m i n e d

f r o m t h e w a k e w i d t h b y m e a n s o f t h e r e l a t i o n

L = ( L / W ) W .

T h i s

p r o c e d u r e i s c o n v e n i e n t e x p e r i m e n t a l l y , s i n c e t h e w a k e w i d t h i s m o r e e a s i l y

m e a s u r e d t h a n t h e r e c i r c u la t i o n - z o n e l e n g th . C o n c e p t u a l l y , h o w e v e r , i t

s e e m s a p p r o p r i a t e t o r e g a r d t h e l e n g t h L a s t h e p r i m a r y p a r a m e t e r .

T h e

L / W

r a t i o h a s a n o t h e r in t e r e s ti n g a p p l i c a t io n . I t g iv e s a n a p p r o x i -

m a t e m e a s u r e o f th e r a te o f s p r e a d in g o f th e m i x i n g z o n e s. T h e m i x i n g

z o n e s s t a r t a t t h e f l a m e h o l d e r a n d s p r e a d u n t i l , a t t h e d o w n s t r e a m e n d o f

t h e r e c i r c u l a ti o n z o n e , t h e y c o m p l e t e l y fill t h e w a k e . T h e w i d t h o f t h e

w a k e a t t h e e n d o f th e r e c i r c u l a t i o n z o n e i s a p p r o x i m a t e l y W , a n d t h e

d i s t a n c e a l o n g t h e f l a m e f r o m f l a m e h o l d e r t o t h e e n d o f t h e r e c i r c u l a t i o n

z o n e is o n l y sl ig h t ly g r e a t e r t h a n L . H e n c e th e s p r e a d i n g r a t e f o r o n e

m i x i n g z o n e is a p p r o x i m a t e l y

W / 2 L ,

o r a b o u t o n e i n e i g h t f o r t u r b u l e n t

f la m e s . T h e m i x i n g - z o n e s p r e a d i n g a n g l e is r o u g h l y 7 , o r a b o u t o n e - h a l f

t h e s p r e a d i n g a n g l e o b s e r v e d in s o m e i s o t h e r m a l m i x i n g z o n e s . T h i s

d i f f e re n c e m a y b e p a r t l y a m a t t e r o f d e f i n it io n . ) M i x i n g - z o n e s p r e a d i n g

r a te m a y a ls o b e m e a s u r e d d i r e c tl y fr o m s o m e o f t h e s c h l ie r e n p h o to g r a p h s .

T h e m e a s u r e d s p r e a d i n g a n g l e o f t h e t h e r m a l m i x i n g z o n e s i s a b o u t 7 .

Pressure and velocity distributions

S t a t i c a n d t o t a l p r e s s u r e s w e r e m e a s u r e d a t m a n y p o i n t s i n t h e d u c t , a n d

v e l o c i t i e s w e r e c a l c u l a t e d f r o m t h e p r e s s u r e s ; f r o m t h e s e m e a s u r e m e n t s

s e v e ra l i n t e re s t in g c o n c l u s i o n s c a n b e d r a w n . I n t h e fr e e s tr e a m o u t s i d e

t h e f l a m e , t h e t o t a l p r e s s u r e is c o n s t a n t . O n t h e o t h e r h a n d , i n t h e

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

r a p i d l y in a l l d i r e c t io n s . F o r e x a m p l e , Figure 7 s h o w s t h e v a r i a t i o n o f

v e l o c i ty a n d h e n c e o f s t a t i c p r e s su r e i n t h e s t r e a m w i s e d i re c t i o n a l o n g a

l in e c l o se t o t h e d u c t w a l l b l o c k a g e r a t i o 1 : 4 ) . S p e e d s t a r ts t o i n c r e a s e

a b o u t t w o f l a m e h o l d e r w i d t h s a h e a d o f t h e f l a m e h o l d e r ; it in c r e as e s r a p i d l y

o v e r a d i s t a n c e o f f o u r f l a m e h o l d e r w i d t h s a n d t h e n r e m a i n s p r a c t i c a l l y

325


8/19

F. H. WRIGHT

c o n s t a n t f o r t h e r e st o f t h e t r a v e l p a s t t h e r e c i r c u l a t i o n z o n e . T h e v e l o c i t y -

d i s t r ib u t i o n c u r v e is s h o w n f o r s t o i c h i o m e t r i c b u t is t h e s a m e f o r a ll f u e l / a i r

r a t io s a t l e a s t t o t h e e n d o f t h e r e c i r c u l a t i o n z o n e .

S t a t i c p r e s s u r e a n d s p e e d a l s o v a r y i n t h e d i r e c t i o n n o r m a l t o t h e d u c t

a x is . T h i s v a r i a t i o n i s s h o w n i n

F i g u r e 8

f o r t h r e e d i f f e r e n t s t a t i o n s a l o n g

t h e d u c t . U p s t r e a m f r o m t h e f l a m e h o l d e r t h e s p ee d i s n e a r l y c o n s t a n t

a c r o s s t h e d u c t . O p p o s i t e t h e f l a m e h o l d e r h o w e v e r s p e e d c h a n g e s r a p i d l y

f r o m a m o d e r a t e l y lo w v a l u e at t h e d u c t w a l l to a m a x i m u m a t t h e

f l a m e h o l d e r e d g e . D o w n s t r e a m a t t h e m i d d l e o f t h e r e c i rc u l a t io n z o n e

s p e e d i s a g a i n c o n s t a n t o u t s i d e t h e f l a m e a n d e q u a l t o t h e s p e e d n e a r t h e

f l a m e a t th e fl a m e h o l d e r . I n f a c t f lo w s p e e d a l o n g t h e f l a m e s u r f a c e i s

n e a r l y c o n s t a n t t h r o u g h o u t th is e n t i re r e gi o n . A t lo w b lo c k a g e s t h e

v e l o c i t y d i s t r i b u t i o n i s n o t f l a t o p p o s i t e t h e m i d d l e o f t h e r e c i r c u l a t i o n z o n e

b u t p e a k s a t t h e f l a m e s u r f a c e . N e v e r t h e l e s s t h e v e l o c i t y a l o n g th e f l a m e

i s c o n s t a n t a n d t h e s t a ti c p r e s s u r e i n si d e t h e re c i r c u l a t i o n z o n e i s p r a c t i c a l l y

c o n s t a n t .

D u c t w a l l

J / / / / / / / / / / // / / / / / / / / / / / / // / / / / / / / / / / / / // /

2 0

Figure 7. Ve loc i ty var ia tion in

s treamwise d irec t ion a long a l ine

c lo s e to d u c t wa l l; BR = 1 :4

1 5 /

1 < - ~ J

-3 -2 -1 0 1 2 3 4 5 6

x /d

V e l o c i t y - d i s t r i b u t i o n c u r v e s s u c h a s t h o s e o f

F i g u r e s 7

a n d 8 c a n a l s o

b e u s e d to e s t im a t e t h e m a s s f lo w i n t o t h e w a k e . F o r e x a m p l e t h e m a s s

f lo w t h r o u g h t h e s c h l ie r e n b o u n d a r y u p t o t h e m i d d l e o f t h e r e c ir c u l a ti o n

z o n e i s r o u g h l y 1 0 p e r c e n t o f t h e t o t a l m a s s f l o w f o r 1 : 4 b l o c k a g e . T h e

p e r c e n t a g e i s s m a l l e r f o r l o w e r b l o c k a g e r a t i o s .

T h e v e l o c i t i e s o f

F i g u r e s 7

a n d 8 w e r e m e a s u r e d a t r e l a t i v e ly l o w s p e e d s .

A t h i g h e r sp e e ds a ll p re s s u r es a n d v e l o c it ie s v a r y w i t h M a c h n u m b e r .

F o r e x a m p l e

F i g u r e 9

s h o w s th e v a r i a ti o n w i t h M a c h n u m b e r o f t h e s t a ti c

p r e s s u r e o n t h e d o w n s t r e a m f a c e o f t h e f l am e h o l d e r . M e a s u r e m e n t s m a d e

a t d i ff e re n t t e m p e r a t u r e s h a v e c l e a rl y d e m o n s t r a t e d t h a t t h e p r e s s u r e

v a r ia t io n d o e s i n d e ed d e p e n d o n M a c h n u m b e r a n d n o t o n a n o t h e r v a r i a b le

s u c h a s R e y n o l d s n u m b e r . F o r l ow a n d m o d e r a t e M a c h n u m b e r s th e

p r e s s u r e c o e ff i ci e n t v a r i e s a s M ~ w h i l e a t v e r y h i g h M a c h n u m b e r s t h e

v a r i a t i o n is f a s te r . M o d e l s c a n b e d e v i s e d t h a t w i ll p r e d i c t t h e p r e s s u r e

3 2 6


9/19

BLUFF=BODY FLAME STABILIZATION: BLOCKAGEEFFECTS

variation with Mach number, but for reasonable accuracy at very high

Mach numbers the models are complex and will not be discussed.

2-0,

1.C

Duct wal l

/ / 1 ( / / / / / / / / / / / / / / ( / / / / /

,~/d=-2.11 /d=O x /d=3.5

\ \ \ ~ , \ \ \ \ \ \ \ x \ \ ~ \ \ \ \ / x \ N \

~ e a r ~ m i d d [e~of

rec i rcu la t ion zone

x/ f f -- 0 ,

opposite flame-

ho lde r

x /d= -2 .1 ,

up s t r eam

I

0.5 1 0 1-5 2.0

y / d

F i g u r e 8 . V e l o c i t y v a r ia -

t i o n i n d i r e c t i o n n o r m a l

t o f l o w ; B R = 1 : 4

The variation of velocity ratio

V . , / V ,

with Mach number strongly

influences blowoff speed (V~)Bo. The effect is especially marked at high

blockage ratios and is also influenced by the actual size of the flameholder,

since blowoff speed increases with flameholder size and Mach-number

influence is more severe for higher speeds. This is an important result that

-1.C

F i g u r e 9 . F l a m e h o l d e r s t a ti c ~ . 2 . 0

p r e s s u r e c o e f f i c i e n t v e r s u s

M a c h n u m b e r / o r se v er a l

b l o c k a g e r a t i o s

-3 C

" - - "< " - - - ~ " e ~ ~

-4'0

0

327

0 1

\ \

0 2 0 3 '0'4

M ~

" B R =

1:32

o BR=l:16

[]

B R = I : 8

B R = I :4

0'5 0 6 0 7


10/19

F. H. WRIGHT

has been obtained from the velocity measurements. The measurements have

revealed several other striking features of the flow about flat-plate flame-

holders. The recirculation zone lies largely in a region of constant pressure;

inside the recirculation zone, the pressure actually increases slightly going

upstream along the centre line, and the flow direction is contrary to that

of the main stream: gas recirculates. The mixing zones bordering the

recirculation zone are regions of almost constant pressure, and flow speed

along the flame edge is nearly constant. Hence the mixing may be studied

as a constant-pressure process.

C O M P R I S O N O F

EXPERIMENT WITH FREE-STREAMLINE THEORY

The fact that the wake of a bluff-body flameholder is a region of almost

constant pressure suggests that a free-streamline model may accurately

simulate flow conditions about the flameholder. In order to check this

supposition, flow conditions about the flat-plate flameholders have been

compared with flows computed on the basis of a free-streamline theory

see Appendix). This theory was developed to represent the flow about a

bluff body in a channel, and includes both the Betz-PetersohnGand Roshko 7

theories as special cases.

The free-streamline theory yields all flow quantities in terms of two

parameters, which may be chosen to be the blockage ratio BR and the

velocity ratio

V 2 / V 1 .

If a relation between

V ~ _ / V ,

and blockage ratio can

be found from experiment, then all flow quantities can be expressed in

terms of the blockage ratio alone. Wake width, wake spreading length

the distance required for the theoretical wake to reach its maximum width),

free-streamline shape, and velocity at every point in the duct will be

20

~-1 5 E d g ef lame ~

~ . ~ f f ~ Ductwall

1.0

O 0'1 0-2 03

R

Figure 10 . F low speed oppos i te midd le o f rec ircu la t ion

zone versus b lockage ra t io

predicted by the theory as functions of the blockage ratio for the particular

experimental arrangement, and the predictions may be compared with

measured values.

The flat-plate flameholder experiments yield the V2/V~ versus BR curve

shown in

F i g u r e 1 0 .

From this curve, the wake width and wake spreading

328


11/19


length were computed and are shown in Figure 22 for blockage ratios up to

1 : 4. Figure 11 shows that experimental values of the wake width agree

well with the predicted curve. The experimental values are the separations

between the mass flow boundaries, and the resulting wake widths are slightly

smaller than the widths between schlieren boundaries Figure 5).

The upper curve of Figure 21 may also be compared with an experimental

quantity.

The experiments showed that the wake reaches a maximum

width at approximately the middle of the recirculation zone, and that

downstream from this point the wake width is practically constant. As a

result, the recirculation-zone half-length may be compared with the wake

spreading length.

Downstream from this point the theoretical wake has

constant width.

15

4l~o

Figure II. Wake wid th

and recircu la t ion - Zone

, a

hal f- length

WW S

block- ?

age ratio

5

Theoretical (x d)

v

xperimental

(W/d)

0

xperiqental

(L/2d)

Agreement between recirculation-zone half-lengths and theoretical wake

spreading lengths is surprisingly good. In fact, considering the idealizations

of the model, the agreement is better than might be expected.

The model

has sharp boundaries between wake and outer flow, while in reality inner

and outer flows are separated by moderately thick shear zones.

Down-

stream from the recirculation zone the model has little resemblance to

reality, yet it accurately simulates the flow over the important forward part

of the recirculation zone and serves as a useful guide for prediction of the

influence of blockage on the flow.

For small blockage ratios, this model

is appreciably better than the Betz-Petersohn model62 *, which assumes that

the flow speed far downstream is equal to the free-streamline speed.

Experimentally, this assumption is found to be good for blockage ratios

larger than 1 : 4 but is not justified for smaller blockages.

For small blockages the free-streamline speed is not equal to the speed

far downstream: nor is the speed far downstream equal to the free-stream

speed as would be required in Roshkos theory for zero blockage.

Proper

choice of the velocity ratio leads to better agreement with experiment than

is possible with either of the limiting theories Figure 12 .

329


12/19

F H WRIGHT

F i g u r e 1 2

s h o w s t h a t u s e o f t h e z e r o b l o c k a g e c u r v e t o p r e d i c t w a k e

w i d t h s i s m i s l e a d in g . O n t h e o t h e r h a n d , d r a g c a l c u l a t io n s b a s e d o n t h e

z e r o b l o c k a g e m o d e l m a y b e f a i r ly g o o d i f t h e p r o p e r v a l u e o f V ~ / V t is

u s e d. T h e z e r o b lo c k a g e t h e o r y p re d i ct s a p p r o x i m a t e l y th e s a m e v a l u e f o r

the p res su re -d rag coef f i c i en t , C D = O . 8 9 ( V , , / V , ) 2, a s d o e s t h e t h e o r y t h a t

t a k e s b l o c k a g e i n t o a c c o u n t . H o w e v e r , th e z e r o b lo c k a g e th e o r y d o e s n o t

6 . 0

/

\

\

2 . 0

1'0

1'0 1'1

z t M e a s u r e d w i d t h s b e t w e e n

m a s s f l o w b o u n d a r i e s

r

.BETZ :PETERSO HN heory

/

BR =0 (ROSHKO the ory )

~ ,Theory w i th pa ram e te rs

d e t e r m i n e d f r o m

~xmeasu red ve l oc i t y

x , N , , ~ a t i o v s b o c k a g e

x . ,

1 . 2 1 . 3 1 . 4 1 . 5 1 . 6 1 . 7 1 . 8 1 . 9 2 ' 0

5 V l

F i g u r e 1 2. W a k e w i d t h

versus V ~ V ] exper imen -

ta l and theore t ica l

p r e d i c t t h e v a r i a t i o n o f

V . ~ / V 1

w i t h b l o c k a g e ; t h e p r e s e n t t h e o r y p r o v i d e s

t h i s i n f o r m a t i o n a n d l e a d s t o a n e x p r e s s i o n f o r C D f o r f l a t p l a t e s a t l o w

speeds

CD ~ 1. l + 6-2 (BR ) + 9 1 (BR ) 2 . . . . [1]

( A t h i g h s p e e d s , CD i n c re a s e s m o r e r a p i d l y w i t h b l o c k a g e t h a n t h is e q u a t i o n

i n d ic a t e s. ) T h e t h e o r y p r o v i d e s a n e a s y c a l c u l a t i o n o f t h e f l a m e h o l d e r

p r e s s u r e d r a g , a n i m p o r t a n t q u a n t i t y t h a t is d i ff ic u l t t o m e a s u r e . T h e

c a l c u l a t i o n m a y b e p r e s u m e d t o b e a c c u r a t e , s i n c e t h e o r e t i c a l a n d m e a s u r e d

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

A f i na l p lo t

( F i g u r e 1 3 )

f u r t h e r d e m o n s t r a t e s t h e u t il it y o f t h e t h e o r y a s

a n a i d t o e x p e r i m e n t . T h e e n t i r e fl o w f ie ld c l o se to t h e f l a t p l a t e is s h o w n

f o r b l o c k a g e 1 : 4 . A l t h o u g h t h e p l o t i s b a s e d o n t h e o r y , i t a l m o s t p e r f e c t ly

r e p r e s e n t s t h e e x p e r i m e n t a l l y m e a s u r e d f l o w f ie ld . I t i s u s e f u l in t h a t i t

g i v es a c o n s i s t e n t p i c tu r e o f t h e v a r i a t i o n s o f v e l o c i ty t h r o u g h o u t t h e e n t i r e

f ie ld . T h e t h e o r e t i c a l p l o t s u p p li e s o t h e r i n f o r m a t i o n t h a t i s o f v a l u e i n

a n e x p e r i m e n t a l s t u d y o f t h e f lo w . F o r e x a m p l e , i t s h o w s p r o p e r l o c a t i o n s

f o r s t a t i c - p r e s s u r e r e f e r e n c e t a p s , p r o p e r o r i e n t a t i o n s f o r s t a t i c - p r e s s u r e

tubes , ve loc i t y g rad i en t s t o be exp ec t ed , e t c .

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

d o e s a g r e e s u r p r i s i n g l y w e l l w i t h e x p e r i m e n t a l r e s u l t s f o r f l a t - p l a t e f l a m e -

330


13/19

B L U F F B O D Y F L A M E S T A B I L IZ A T I O N ; B L O C K A GE E F F E C T S

h o l d e r s h e l d n o r m a l to t h e s t r e a m i n a d u c t. T h e t h e o r y l ea d s t o r e a s o n a b l y

a c c u r a t e p r e d i c t i o n s o f f la m e h o l d e r c h a ra c t e r is t ic s f o r v a r y i n g b l o c k a g e

r a t io s . I f o n e q u a n t i t y s u c h a s t h e co e f f ic i e n t o f s t a ti c p r e s s u r e b e h i n d t h e

f l a m e h o l d e r i s k n o w n , t h e n t h e t h e o r y e x h i b i t s t h e e n t i r e f l o w f i e l d .

2 0

- 2

I

/ / / / , ' / / / / ,

r

\

-1 0

/ / / / / i . ~ / / . / , / / / / / / / / / ,

I

/

, t

~ t_ . ~ _ 1 8 0 = ~

W a k e b o u n d a r y

V--O

2

x O

Figure 13 . T heor e t ica l ve loc i ty d i s t r ibu t ion a bou t a f la t -p la te f lame-

h o ld e r; B R = 0 2 5 0 7

F L A M E B L O W O F F

A n i m p o r t a n t a i m o f t h e f l a t - p la t e - f l a m e h o l d e r e x p e r i m e n t s w a s t o f i n d

w h e t h e r o r n o t t h e f l a t p l a t e s f o l l o w e d t h e b l o w o f f r u l e v a l i d f o r o t h e r

b l u f f - b o d y f l a m e h o l d e r s . T h i s r u l e s ta t e s t h a t i f t h e b l o w o f f p a r a m e t e r ,

KB, ,=(V. ,_r /L) , i s g r e a t e r t h a n u n i t y , t h e f la m e w i ll b l o w o f f. T h e r u l e

f u r t h e r s a y s t h a t t h e c h e m i c a l ti m e r d o e s n o t d e p e n d u p o n t h e f l a m e h o l d e r ;

h e n c e a p l o t o f T v e r s u s 9 t h e f u e l / a i r r a t io , f r a c t i o n o f s t o i c h i o m e t r ic ) w i ll

b e a u n i q u e c u r v e f o r a ll f l a m e h o l d e r s t h a t s a t i s f y t h is r u le . I n v e r s e l y ,

f r o m t h e r / 9 c u r v e t h e b l ow o f f s p e ed c a n b e o b t a i n e d f o r a n y f l a m e h o l d e r

f o r w h i c h L a n d V ~ / V , a r e k n o w n . F i g u r e 1 4 s h o w s t h e r/q, c u r v e f o r t h e

f l a t -p l a t e f l am eho lder s . A l l t he f l a t -p l a te r e su l ts f a l l c l o se t o t h i s cu rve .

F u r t h e r , t h e c u r v e i s i d e n t ic a l w i t h t h a t f o u n d 2 f o r o t h e r f l a m e h o l d e r s , s u c h

a s c i r c u l a r c y l i n d e r s , i n t h e s a m e d u c t .

T h e c h e m i c a l t im e s f o u n d i n t h e 1 i n . x 4 i n. d u c t a r e s l ig h t l y l o n g e r t h a n

t h o s e o b s e r v e d i n a d u c t t w i c e a s w i d e , p o s s i b l y b e c a u s e o f g r e a t e r h e a t

t r a n s f e r t o t h e w a l l s i n t h e n a r r o w d u c t . M e a s u r e m e n t s i n d i c a te t h a t

r e c i r c u l a t i o n - z o n e t e m p e r a t u r e s a r e l o w e r i n t h e n a r r o w e r d u c t , t h u s

s u p p o r t i n g t h e v ie w t h a t h e a t lo s t t o t h e w a l l s m a y b e i m p o r t a n t . A l s o ,

b l o w o f f s p e e d s a n d r e c i r c u l a t io n - z o n e t e m p e r a t u r e s a r e l o w e r w i t h m e t a l

d u c t w a l l s t h a n w i t h g la s s. T h e c h a n g e in b lo w o f f s p e e d m a y b e d u e t o

c h a n g e i n c h e m i c a l t i m e w i t h r e c i r c u l a ti o n - z o n e t e m p e r a t u r e . H o w e v e r ,

i f w a l l h e a t t r a n s f e r i s i m p o r t a n t , t h e n t h e a g r e e m e n t i n t h e r /q , c u r v e s f o r

d i f f e r e n t b l o c k a g e r a t io s i n t h e s a m e d u c t i s s u r p ri s in g , s in c e t h e a s p e c t

r a t i o a n d t h e r e l a ti v e i m p o r t a n c e o f e n d e f f e c ts c h a n g e w i t h b lo c k a g e . T h e

d i s c r e p a n c y i n r b e t w e e n d i f f e r e n t d u c t s r e q u i r e s f u r t h e r s t u d y .

T h e b l o w o f f p a r a m e t e r d o e s , t h e n , a p p l y t o fl a t- p l a te fl a m e h o l d e r s .

B l o w o f f s p e e d s m a y b e p r e d i c t e d i f t h e b e h a v i o u r o f t h r e e v a r i a b l e s , V ~ ,

331


14/19

F. H. WRIGHT

L and r, is known close to blowoff. Fortunately, V~ and L depend in simple

fashion on factors such as flameholder size and blockage ratio, and their

values may be found from fluid dynamic experiments or from free-streamline

I l l

3

t ,

~2

' \

0

0'5

/ ~, BR=I:4

o BR=I:8

'~D'~. ~ ~ BR=1:16

*' BR--1:32

1 0 1 5 2 ' 0

,

Figure 14. C hem ica l t im e

v e r s u s m ix tu r e r a t io 9

theory.

ments.

written

In addition, the chemical time T is known from previous experi-

Hence, for the flat-plate flameholders, the blowoff speed may be

V1 L d

where h is the duct height, d is the flameholder size, L is the length of the

recirculation zone, BR is the blockage ratio d / h , and C~ and Co are

constants. The last part of the formula is approximate and applies only

for moderate blockage ratios and at low speeds. The formula predicts

that maximum blowoff speed will be found for blockage ratio C~/C~_.

This blockage turns out to be roughly 0 35 for flat plates and roughly 056

for circular cylinders.

Blockage for peak blowoff speed is even less than the preceding values

when the Mach number of the flow past the flame is high. Indeed, the

entire blowoff formula is subject to correction when this Mach number is

high: blowoff speeds are lower than those predicted by the low-speed

formula. The correction increases with blockage ratio, and the peak of

the blowoff versus blockage curve is shifted toward low values of the

blockage. This shift is apparent in an experimental curve presented in

F i g u r e 1 5 .

Peak blowoff occurs at a blockage less than 1 : 10. However,

the top of the curve is flat and blowoff speeds at the higher blockage ratios

are only slightly lower than the peak velocity.

Corrections to be applied to the blowoff formula depend upon flameholder

shape and size as well as upon blockage ratio. The corrections are larger

332


15/19

BLUFF-BODY FLAME STABILIZATION BLOCKAGE EFFE CTS

fo r f l a t p la tes than fo r o the r shapes such as wedg es o r cy l inder s . Th e

cor rec t ions a re l a rge fo r l a rge f l ameho lder s whose no rmal b lowof f speed i s

h igh and hence , fo r a g iven b lockage r a t io , the co r rec t ions a re g rea te r in a

la rge duc t than in a smal l one . Fu r the r , s ince l ean b lowof f speeds a re

lower , the Ma ch num ber has l e ss in fluence on l ean b lowo f f s than on

blowoffs c lose to s to ichiometr ic .

F o r s e v e ra l r e a so n s , t h e v e r y l o w v a l u e o f b l o c k a g e f o r m a x i m u m b l o w o f f

s h o w n i n

Figure 15

probably does not have great s ignif icance for pract ica l

appl ica t ions . Fa cto rs such as f low osci l la t ions , turbule nce , in ter ference

ef fec t s, Re yno lds num ber , a nd m ix tu re inhomogene i t i e s, wh ich we re

ca re fu l ly avo ided in these exper imen ts , m ay have l e ss in f luence upo n b low of f

speeds f rom la rge f l ameho lder s than up on b lowof f s f rom smal l ft ameho lder s

opera t ing a t low b lockage r a t io s .

700

~ 7

g

~r

50 00 0.05 010 015 0'20 0'25

B R

M a x i m u m b l o w o f f s p e e d s [ o r f la t -H a t e ll a m e -

h o l d e r s i n 1 i n . 4 i n . d u c t

F i g u r e 1 5 .

CONCLUSIONS

P r e v io u s w o r k ~ h a d s h o w n th a t t he p r o b l e m o f b l u f f - M y f la m e h o ld in g c a n

be d iv ided in to two pa r ts : the chemis t ry o f the com bus t io n r eac t ion and the

f lu id dyna m ics o f the f low . Ev en mo re conv inc ing ly than pa s t wo rk , the

e x p e r i m e n t s r e p o r t e d h e r e d e m o n s t ra t e d t h a t t h e t w o p a r ts o f t h e p r o b l e m

m ay be s tud ied s epara te ly . Th e fl a t -p la te exper im en ts were pa r t i cu la r ly

s ignif icant in show ing that th e f low pat terns ab ou t b luf f -b od y f lam ehold ers

a r e n e a r l y i n d e p e n d e n t o f t h e c o m b u s t i o n c h e m i s t r y a n d d e p e n d o n l y o n

f lu id dyna m ic va r iab les . In f ac t , the f low pa t t e rns can be p red ic ted by a

pure ly f lu id dynamic theo ry deve loped in th i s paper a s a gu ide fo r the

exper imen ts .

F l a m e b l o w o f f d e p e n d s o n t h e f lo w p a t te r n s a n d h e n c e d e p e n d s d i r ec t ly

on f lu id dyn am ic pa ram ete r s . A n in te res t ing exam ple o f an es sen ti a lly

f lu id dynam ic va r iab le tha t in fluences b lowo f f is fu rn ished by the b lockage .

The f r ee - s t r eaml ine theo ry p red ic t s the p r inc ipa l e f f ec t s o f b lockage on

f lame s tab il i za t ion , thus emph as iz ing the es sen t ia l ly f lu id dynam ic charac te r

o f o n e p a r t o f t h e f la m e h o l d i n g p r o b l e m . T h e o r y a n d e x p e r i m e n t b o t h

show tha t bo th the f low speed V~ pas t the f l ame and the r ec i r cu la t ion -zone

l e n gt h L d e p e n d u p o n f l a m e h o l d e r b l o c k a g e. H e n c e t h e v a l u e o f t h e

b l o w o f f p a r a m e t e r

(rV,~/L)

depe nds d i rec t ly on the b lockage . I f the

exp l ic i t va r ia t ions o f speed and r ec i r cu la t ion -zone l eng th a re t aken in to

a c c o u n t , t h e b l o w o f f s p e e d m a y b e w r i t te n a s a f u n c ti o n o f t h e b l o c k a g e

as fo l lows

(B R y , ~

333


16/19

F H WRIGHT

where V1 is the upstream speed, BR is the blockage ratio, h is the duct

height, r is the chemical-time parameter, and C1 and C2 are constants.

The formula predicts that maximum blowoff speed will occur at

BR'~C1/C, , ;

for flat-plate flameholders this blockage turns out to be

0-35, a surprisingly low value.

When the Mach number of the flow past the flame is very high,

compressibility affects the flow patterns and it is necessary to apply a

correction to the preceding blowoff formula. Fortunately, the correction

may be made by straightforward application of fluid dynamic principles;

the validity of this procedure is a further demonstration of the essentially

fluid dynamic character of one portion of the blowoff problem.

The experiments and the analysis showed the manner in which various

fluid dynamic parameters influence flame blowoff as well as demonstrating

the fact that the influence is nearly independent of chemical parameters.

On the other hand, experiments demonstrated that the combustion

chemistry is also an important factor governing blowoff and that the

chemistry is not influenced by gross fluid dynamic variables such as flow

Reynolds number, Mach number, or blockage. An impressive example of

the independence of the chemistry is afforded by Figu re 14, in which the

chemical-time parameter is plotted versus fuel/air ratio. The chemical

time at a given mixture strength is identical for different-sized flameholders

and is indeed the same as the chemical time found for other types of

flameholders1.

The experiments with flat-plate flameholders and the associated fluid

dynamic theory furnished convincing proof that the complex flame-

stabilization problem may be split into two simple and nearly independent

parts, one fluid dynamic and the other chemical.

NOMENCLATURE

BR = blockage ratio = d/ h

CD = pressure drag coefficient

CF=(flameholder static pressure minus upstream static pressure)/

upstream dynamic pressure

d = flameholder width or diameter (in y direction)

h = duct height (in y direction)

KBo= V2r /L= blowof f parameter, reciprocal of Damkohler s para-

meter I

L = recirculation-zone length

M = Mach number

M~ = Mach number far upstream

M2 = Math number at edge of flame

Q = source strength

Re=Reynolds number, based on flameholder width and flow speed

far upstream

v = conjugate of complex velocity

V = flow speed

V~ =flow speed far upstream

V2 = flow speed at edge of flame

V~ = flow speed far downstream

W = wake width opposite middle of recirculation zone, x = L

334


17/19


x = ax i a l c o o r d i n a t e m e a s u r e d f r o m f r o n t f a c e o f t ta m e h o l d e r

x w = d i s t a n c e f r o m f l a m e h o l d e r t o b e g i n n i n g o f c o n s t a n t w a k e w i d t h

the o r e t i c a l )

y = t r a n s v e rs e c o o r d i n a t e m e a s u r e d f r o m d u c t c e n t r e l in e

z = x + i y

0 = a n g u l a r c o o r d i n a t e i n h o d o g r a p h p l a n e

r = c h e m i c a l- t im e p a r a m e t e r

= f u e l / a i r r a ti o , f r a c t i o n o f s t o i c h io m e t r ic

q , = c o m p l e x p o t e n t i a l o f fl o w i n z p l a n e

Su b s cr i p t s :

1 = c o n d i t i o n s f a r u p s t r e a m

2 - c o n d i t i o n s a t o u t e r e d g e o f f l a m e

3 = c o n d i t io n s f a r d o w n s t r e a m

B O = b l o w o f f

F = fl a m e h o l d e r

W = i n i ti al p o i n t o f c o n s t a n t w i d t h w a k e

A P P E N D I X

FREE STREAMLINE FLOW ABOUT FLAT PLATES ORIENTED NORMAL TO

THE FLOW IN A CHANNEL

A n e w f r e e - s t r e a m l i n e t h e o r y f o r t h e f l o w a b o u t a f l a t p l a t e i n a d u c t

(F igure 16) h a s b e e n d e v e l o p e d . T h i s t h e o r y d o e s n o t r e q u i r e t h e sp e e d

V 3 f a r d o w n s t r e a m t o e q u a l t h e s p e e d V 2 a l o n g t h e f r e e s t r e am l i n e , a n d

t h u s is m o r e g e n e r a l t h a n t h e t h e o r y o f A . B E T Z a n d E . PE TE RS OH N .

A 3 ,

A 2 - - ~ V ~ - -

A 1 = , -

C2

el

Figure 16. Free-streamline flow pattern

T h e f l o w m a y b e o b t a i n e d b y c o n s i d e r i n g t h e h o d o g r a p h ,

Figure 17 .

T h e h o d o g r a p h i s d r a w n f o r t h e c o n j u g a t e v o f t h e c o m p l e x v e l o c i t y .

T h a t i s ,

v = V e x p - i O ) . . . . [3]

w h e r e V i s t h e m a g n i t u d e o f th e v e l o c i t y a t a n y p o i n t i n t h e p h y s i c a l p l a n e

a n d t h e a n g l e 0 s p e c if ie s i ts d i r e c t i o n . T h e c o m p l e x p o t e n t i a l o f t h e

f l o w i n t h e p h y s i c a l o r z p l a n e i s e a s i l y f o u n d f r o m a d i s t r i b u t i o n o f s o u r c e s

a n d s i n k s i n t h e h o d o g r a p h p l a n e

(Figure 18).

335


18/19

F H WRIGHT

V v= V O

F ig u r e 1 7. Ho d o g r a p h f o r f r e e - s tr e a m-

l ine pa t tern

T h e n , s i n c e

h ) V , ) l n ~ - V ~ / ~ V ~

I , ~ ~ , ~ _

. . . . [ 4 1

= d < I > / d z . . . . [5 1

t h e c o o r d i n a t e z ( = x + i y ) o f a n y p o i n t i n t h e p h y s i c a l p l a n e i s g i v e n i n

t e r m s o f

(v/V.), (V1/V~.), and (V3/V2)

b y

f l

d~

z = v dZ ~vd ~ . . . . [61

T h e e x p l i c it f o r m u l a f o r z is l e n g t h y a n d w i ll b e o m i t t e d . A f e w s p e c i a l

c a s e s a r e :

B l o c k a g e r a t i o :

d g l )

BR=~= 1 V~

V~ , V, V:

[ l _ v ~ ) t a n = ( ~ , ) + ( V ~ V ~ V , ]

( ' f l

- ~ . _ ~ t a n I ~ j . _ ,

. . . . [ 7 ]

F ig u r e 1 8. S o u r c e d i s t r ib u t i o n i n h o d o g r a p h p la n e

3 3 6


19/19

B L U F F - B O D Y F L A M E S T A B I L I Z A T I O N : B L O C K A G E E F F E C T S

W a k e s p r e a d i n g l e n g t h :

y w = _ l ( V t ' ~ V t + V , , h _ 1 V V 3 V ,, 1 V 3

h z k V : J [ ( V . ,

i? ~) t a n ( ~ ) - ( V . , + v ; ) t a n h - ( ~ , , ) ] . . [ 8 ]

W a k e w i d t h :

- h . . . . . [91

A p p l y i n g f o r m u l a 7 , t h e v e l o c i t y r a t i o

V : / V ~

m a y b e p l o t t e d v e r s u s

b l o c k a g e r a t io w i t h V3 / V~ a s p a r a m e t e r . F o r c o m p a r i s o n w i t h e x p e r i m e n t a l

r e a l i t y t h e a p p r o p r i a t e v a l u e o f V 3 / V ~ m u s t b e c h o s e n f o r e a c h b l o c k a g e

r a ti o . T h e n a l l o t h e r q u a n t it ie s m a y b e e x p r e s se d i n t e r m s o f t h e b l o c k a g e

r a t i o a l o n e . ( I t i s, o f c o u r s e , u n n e c e s s a r y t o s t a r t w i t h t h e b l o c k a g e ra t i o .

I n s o m e c a s e s t h e w a k e w i d t h o r t h e f r e e -s t re a m l i n e s h a p e m a y p r o v e t o

b e c o n v e n i e n t s t a rt i n g p o i n t s .)

T h i s f r e e - s t r e a m l i n e t h e o r y i n c lu d e s b o t h t h e z e r o b l o c k a g e 7 a n d t h e

V:~ = V ,

t h e o r i e s ~, ~ a s s p e c i a l c a s e s b u t i n v o l v e s a n a d d i t i o n a l p a r a m e t e r .

T h e t h e o r y h a s b e e n d e v e l o p e d f o r f l a t p l a t e s o n l y b u t c a n e a s i l y b e

e x t e n d e d t o o t h e r b l u f f b o d i e s , s u c h a s w e d g es , b y a s u i t ab l e a r r a n g e m e n t

o f so u r c e s a n d s in k s in th e h o d o g r a p h p l a n e.

T h i s p a p e r p r e s e n t s t h e r e s u l t s o f o n e p h a s e o f r e s e a r c h c a r r i e d o u t a t

t h e J e t P r o p u l s i o n L a b o r a t o r y , C a l if o rn i a I n s ti t u t e o f T e c h n o l o g y u n d e r

C o n t r ac t N o . D A - O 4 - 4 9 5 - O r d 1 8, s p o ns o r ed b y th e D e p a r t m e n t o f t h e

A r m y , O r d n a n c e C o r p s .

J e t P r o p u l s i o n L a b o r a t o r y ,

C a l i [ o r n i a I n s t i t u t e o f T e c h n o l o g y

( R e c e i v e d S e p t e m b e r 1 9 5 8 )

RE FE RE NCE S

1 Z U K O S K I

E. E. and MARBLE, F. E. Pa pe r in

Proceedings of the Gas Dynam ics

Symposium on Thermochemistry (held at Northwestern University, Evanston,

Illinois, 22-24 Augu st 1955), pp 205 210. Northwestern University P ress

- FOSTER, J. R . Th e effects of com bustion ch am be r blockage on bluff bo dy flame

stabilization. Thesis in Aeronautical Engineering, California Institute o f Tech-

nology, June 1956

3 Z U K O S K I E. E.

Sixth Symposium (International) on Combustion,

pp 942-943.

Reinhold: New York, 1956

.1ZUKOSKI, E. E. and MARBLE, F. E . P ape r No. 14 in A G A R D og rap h No. 9,

Combus-

;ion Research es and Review s 1955. Butterworths : London, 1955

: MATRON, G . Rech. Adro. 195 7, 57, 11

~; BETZ, A . a n d PETERSOHN, E.

Tech . No te Nat . A dv . Comm. Aero . , Wash . , No . 667

(1932)

z ROSHKO,A.

Tech. No te Nat. Adv . Comm . Aero., Wash., No . 3168

(1954)

CORNELL, W . G .

Trans. Am er. So c. mech. Engrs,

1956 , 78, 573

337

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