Upload
kirubhakaran2000
View
226
Download
0
Embed Size (px)
Citation preview
8/10/2019 bluff- body stabilization wright.pdf
1/19
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
8/10/2019 bluff- body stabilization wright.pdf
2/19
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 .
320
8/10/2019 bluff- body stabilization wright.pdf
3/19
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 .
321
8/10/2019 bluff- body stabilization wright.pdf
4/19
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
322
8/10/2019 bluff- body stabilization wright.pdf
5/19
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.
323
8/10/2019 bluff- body stabilization wright.pdf
6/19
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
324
8/10/2019 bluff- body stabilization wright.pdf
7/19
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
11/19
BLUFF BODY FLAME STABILIZATION: BLOCKAGE EFFECTS
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
17/19
BLUFF BODY FLAME STABILIZATION: BLOCKAGE EFFECTS
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
8/10/2019 bluff- body stabilization wright.pdf
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
8/10/2019 bluff- body stabilization wright.pdf
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