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Premixed flame propagating into a narrow channel at a high speed, part 1: Flame behaviors in the channel
COMBUSTION A N D F L A M E 60: 245-255 (1985)
245
Premixed Flame Propagating into a Narrow Channel at a High Speed, Part 1: Flame Behaviors in the Channel NORIMASA IIDA, OSAMU KAWAGUCHI, and G. TAKESHI SATO Faculty of Science and Technology, Keio University, 14-1, Hiyoshi, 3-Chome, Kohoku-Ku, Yokohama 223, Japan
This paper deals with the transient behavior of a flame flowing into a narrow channel from a chamber filled with a propane-air mixture. The flame was observed through direct or schlieren high speed photography, and at the same time the arrival at the entrance and exit of the channel were detected by ion gaps. From the experimental results it was found that in some cases the flame extinguished or hesitated in the channel before passing through. These behaviors were dependent on the equivalence ratio of the mixture, the channel width, and the flame inflow velocity. Flame standstill in the channel is assumed to be caused by continuous quenching of hot reacting gas due to turbulent mixing with cold unburned gas at the contraction region established near the entrance of the channel. For any specific mixture, when the channel entrance is rounded or the inflow velocity is low, the m i n i m u m width of the channel for which a flame will run through without any retardation becomes smaller compared with the case of a sharp-edged entrance or a high inflow velocity. On the contrary, the m i n i m u m width of the channel for which a flame cannot pass through does not depend on the corner roundness of the channel entrance or the inflow gas velocity.
INTRODUCTION The problem of premixed gas flame propagation through narrow channels followed by a flame jet flow has been studied by Wolfhard and Bruszak [1], Phillips [2], and Maekawa and Takeichi [3]. In those studies the ignition of a flammable mixture by a flame jet or hot gas ejected from a chamber through a narrow channel has been treated. Yamaguchi et al. [4], Furukawa and Gomi [5], Wakai et al. [6], and Klomp and Deboy [7] have made experimental studies of the flame propagation process in a chamber filled with a flammable gas which has a partition with a hole and have reported upon the effects of the whole diameter and the gas jet velocity on ignition probability and flame velocity in the mixture of the other side of the partition. Ono et al. [8] have obtained flame extinguishment conditions through measurements of flame velocity in a small channel with electrostatic Copyright © 1985 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
probes and reached the conclusion that there are two kinds of velocity limits of flame quenching, that is, a limit at low flow velocities mainly caused by cooling by the channel wall and another limit at high flow velocities which could not be explained using the cooling effect concept. They surmised that the entrainment of surrounding gas into a flame jet after it passes through the channel was the main controlling factor for this type of flame quenching, because the transient time of the flame in the channel is shorter for flame extinguishment under a high velocity condition than it is for a low velocity condition. In the studies referred to above, it is not clear whether the external flammable mixture is ignited by a propagating flame jet or by a hot jet of combustion products. Furthermore the factors controlling the flame propagation process in a narrow channel were not investigated. Because of this the authors of this paper have carried out
0010-2180/85/$03.30
246
NORIMASA IIDA ET AL.
and report on some experimental studies of the characteristics of a premixed flame passing through a narrow channel at a high speed and measured flame properties in the channel to determine the factors affecting these characteristics.
EXPERIMENTAL A P P A R A T U S AND PROCEDURES Detailed experiments were systematically carried out using a simple two-dimensional windowed chamber with a narrow channel leading to the open air shown in Fig. 1. The combustion chamber has dimensions of 110 mm in width, 200 mm in length, and 70 mm in depth. The narrow channel set on the short upper side of the chamber has the same depth as the chamber. The side walls are made of common transparent acrylic plates to observe the flame propagating in the chamber and through the channel. The
length of the channel is 200 mm and the width can be set to any dimension ranging from 0 to 12.5 ram. An electric spark igniter is installed on the central axis of the chamber but the point of ignition is movable in the vertical direction. The apparatus is mounted vertically as shown to avoid nonsymmetrical flame propagation due to buoyancy effects which occur when a flame propagates in a quiescent premixed gas in a chamber. Prior to an experiment, the chamber is filled with a well mixed propane-air mixture at room temperature and pressure, and left till the mixture becomes perfectly still. After the flammable mixture in the chamber is ignited by the igniter, the propagating flame is recorded on a high speed motion picture camera or a 35 mm still camera by a direct photographic method or a schlieren method. The pressure in the chamber is also measured and recorded with a pressure transducer and a memory storage
+-
I///
f / ~
I COMBUSTION CHAMBER 2 CHANNEL 3 MIXTURE GAS INLET 4 MIXTURE GAS OUTLET 5 SPARK IGNITER 6 PRESSURE TRANSDUCER 7 ELECTROSTATIC PROBE or
15 ION GAP 16 PITOT TUBE 17 PRESSURETRANSDUCER Z IGNITION POSITION b CHANNEL WIDTH B COMBUSTIONCHAMBERWIDTH
Fig. 1. Experimental apparatus.
FLAME PROPAGATION IN NARROW CHANNELS (I) synchroscope. A short time after ignition, a part of the propagating flame penetrates into the narrow channel and either runs through the channel or extinguishes in the channel, depending on the initial conditions. The times at which the flame enters the channel and leaves it are detected using ion gaps at the entrance and the exit of the channel. The velocity and temperature of the gas or flame ejected out of the channel are measured using a fine pitot tube of 1.0 mm in outer diameter with a highly sensitive and quick response pressure transducer and a thermocouple (type-R) of 25 #m diameter. OBSERVATION AND RESULTS
Appearance of Propagating Flame When a mixture is ignited at the closed end of the chamber, a flame propagates in the mixture with a semispherical shape at the beginning and with a warhead like shape later. As the flame propagates and the mixture burns, the pressure in the chamber rises and the unburned gas flows toward the channel entrance. The top of the flame is pointed as it approaches the channel entrance due to the flow velocity distribution in the unburned gas ahead of the flame. The flame flows into the channel at a very high speed together with the unburned gas. The shapes of the flames propagating in the chamber are shown in Fig. 2 with flame contours traced from the motion picture films at 5 or 10 ms intervals.
LI
(a) Z/L=1.0
247
In these examples the propane-air mixtures are stoichiometric and ignited at four different positions. The width of the channel is 6.3 mm and the channel entrance is not rounded (i.e., R = 0). In this figure, R = 0 means that the entrance to the channel has sharp-edged corners and Z / L = 1.0 means that the mixtures are ignited at the closed end of the chamber. After flowing into the channel, the flame travels at a high speed. Figure 3 shows a few frames of a motion picture film during the time that the flame propagates through the channel for conditions quite similar to those of Fig. 2a. The position of the flame tip in the channel can be traced from the motion picture film. Three examples are plotted for stoichiometric propane-air mixtures as a function of time elapsed from ignition in Fig. 4. When the channel width is large (b = 10 mm), the flame propagates into the channel together with the high speed gas flow and quickly runs through the channel. When the channel width is somewhat smaller (b = 6.3 mm), the flame behavior is different from that of the former case. Just after the flame penetrates into the channel, it stops its motion for few milliseconds at a distance of about 40 mm from the entrance, and then runs through the rest of the channel at a high speed. In this case the flame penetrating into the channel appears to be extinguished for a short period of time at this special position. The authors call this phenomenon "Passing Through After Retardation." When the channel width is still
b=6.3mm
(b) ZIL=0.75
(c)
Z/L=0.5
(d) Z/L= 0.25
Fig. 2. Flame contours for mixture ignition at four different ignition positions.
248
NORIMASA IIDA ET AL. b=6.3 mm, B=II0 mm, R=0, Z/L=1.0, @=i.0, C3H 8
®---~=30.0 ms (Z,N)~ 30.5 ms
® 33.0 ms
© 37.5 mstcour}®/,2.5 ms
Fig. 3. Flame positions after the flame flows into the channel: times are elapsed time from ignition.
smaller (b = 1.6 mm), the position of the flame tip in the channel cannot be judged from the film, but may be judged from ion gap signals which show that flame remains in the channel until all the mixture has burned out. The authors named this phenomenon " N o n Passage," to avoid confusion with the transient extinguishment of the former case.
Passage Characteristics of Flames The motion picture films are not suitable for tracing the flame movement and for judging whether or not the flame has passed through the channel. For this reason ion gaps were installed at the entrance and the exit of the channel as shown in Fig. 1 to detect the flame and to measure its electrical conductivity which indicate the activity of the reacting gas.
E E x 200 _ Z / L = 1 . 0
0=1.0 C3H8
O.
E u_
Four examples of ion current records are shown in Fig. 5, which were recorded with a synchroscope. The lower trace of each picture is that detected by the probe set at the channel entrance and the upper one is that at the channel exit. When a flame passes a probe, a high ionization current appears and it is clear that a flame has passed the probe. The time which a flame requires to pass through the channel can be estimated from the time interval between the rise times of the two ionization currents and the apparent flame velocity Uf can be calculated using the following equation, Uf---
l
m/s,
where l is the channel length, 200 mm, and ti. and to.t indicate the times (ms) that the flame passes the respective ion gaps.
f~-=-!-
/
C
~-200 0
c
~{b) b: 6.3rnrn z
0
.o
(1)
t o u t - tin
.~'~'N~(c)
b =l.6mm ,
20
t
40
ms
60
Fig. 4. The position of the top of the flame in the chamber and the channel as a function of time.
FLAME PROPAGATION IN NARROW CHANNELS (I) B=ll0
u,
R=0,
Z/L=I.0,
~=l.0,
249
CsH 3
\
0
50
100 ms
0
(a) b=10 u
50
100 ms
(b) b:6.3 u
i l l m l w u , ~ ' N m m r n l l r ~ n m mn
0
50
100 ms
(e) b=l.6mn
0
50
100 ms
(d) b=1.25 m
Fig. 5. Some examples of ion current waves of passing-through-the-channel flames. Lower and upper beams indicate those detected at the channel entrance and exit, respectively. The velocity of premixed gas ejected from the channel is estimated from the dynamic pressure measured with the pitot tube and pressure transducer at the channel exit. If the exit velocity at tin is called Uti., the ratio of Utin to Uf can be used to judge the passage characteristics of the flames, because the gas velocity Uti n should not change rapidly during the time interval between tin and tout. When a high speed flame propagates in the premixed gas toward the channel exit without retardation, the ratio Uti./Uf will be smaller than unity. However, if this ratio is found to be larger than unity, one cannot but conclude that the flame stays somewhere in the channel for a while before passing through the channel because negative burning velocities are impossible. The relations between Utin/Uf and the equivalence ratio, th, of the mixture are shown in Fig. 6 for various channel widths b. For the widest channel, b = 12.5 mm, Uti./Uf is always smaller than unity, which means that the flame runs through the channel without retardation. For the 10 m m width channel, Utin/Uf is larger than unity for off-stoichiometric mixtures because the flame hestitates for a while in the
channel. When the channel is narrower than 6.3 m m the flame passes through the channel after some retardation over the whole range of equivalence ratio. In the case of a narrower channel for off-stoichiometric mixtures, the ion gaps at
rI -I T - -I -
"~/I.~=1.0
} I
If
; I
LI
0.8
1.0
1.2
1.4
1
1.6
Fig. 6. Ratio o f the ejected gas velocity at the time the
flame flows into the channel, Utin, to the flame velocity, Uf, as a function of equivalence ratio of the mixture for various channel widths.
250
NORIMASA IIDA ET AL.
I
JO PASSINGTHROUGH. . . . . (~)
I R= 0 I | A, TER RETARDATION--(b) Z/L=1 0 l l-/k PARTIALLY PASSING - C H "~j [ A PASSING THROUGH
2o j
THROUGH. . . . . . . . . . . . C~)
3 8 1
II
/ e NOT PASSING THROUGH -(d)
E E
16 j
0 60 I
6 0 6 0 61 I ~ I
I0 --~~'~"~'----ZX--Z~--A--~,
--I
A
ZX ix
ZX ZX ZX A
ZX ,~ I
A
Z~ A
A
•
o, A
At Q
U I
I/ " " "
"
I l--O--•--•--•--•--•--•--•--•II
0.8
,
r
1.0
,
I
1.2
,
I
1.4
,
I
1.6
F i g . 7. C h a r a c t e r i s t i c s o f f l a m e f l o w i n g t h r o u g h n a r r o w c h a n n e l s s h o w n as d o m a i n s f o r the t h r e e f l a m e b e h a v i o r o b s e r v e d , p l o t t e d as a f u n c t i o n o f c h a n n e l w i d t h b a n d e q u i v a l e n c e r a t i o 4~.
the channel exit no longer detect the presence of any flame at the channel exit. Finally, flame cannot pass through channels narrower than 1.25 mm at any equivalence ratio. The flame characteristics in various narrow channels are replotted in the (4), b) plane in Fig. 7. Flame behaviors are divided into three domains as follows: a. b.
c.
a domain where flame runs through the channel with the gas flow; a domain where flame passes through the channel after a transient hesitation in the channel; a domain where flame does not pass through the channel.
Transient Flame Extinguishment The flame penetrates into the channel with a smooth flame front together with unburned premixed gas. Figure 8 shows an instantaneous schlieren photograph taken at the moment just
after the flame penetrates into the channel. The flame is constricted by the flow contraction region near the channel entrance, and then expands gradually in the channel and changes from a laminar state to a turbulent state. The flame penetrating into the channel is schematically illustrated in Fig. 9 using the image from the schlieren photographs for various channel widths. All the characteristic dimensions of the flame observed in the channel are related to b in the same way over the range of the channel widths examined. The position, x¢, where the flame is most constricted is about b / 2 away from the entrance and the transition from a laminar state to a turbulent state occurs at the position xl = b. The flame expands to fill the channel after the position Xm = 3b and the unburned gas flowing into the channel mixes with the flame and burned gas. The flame which reaches the channel entrance continuously penetrates into the channel in the laminar state with unburned gas on both sides and it suffers strong shear produced by the steep velocity gradient in the contraction region. Subsequently the flame is cooled through turbulent mixing with unburned gas and continuously extinguished, and appears to be held at the position x f = 5b. The value of wf/b, which indicates the relative minimum laminar flame width near the channel entrance, increases as time passes as shown in Fig. 10. we/b is almost equivalent to the ratio of the volume flow rate of the burned gas to the unburned gas flowing into the channel if the velocity distribution is uniform at the channel entrance, which was confirmed with an experiment of cold flow. As the remaining unburned gas in the chamber continues to burn and flows into the channel, the unburned gas inflow rate decreases relative to the initial inflow rate and the resulting decrease of flame quenching by turbulent mixing allows the flame to propagate downstream in the channel. Such flame behavior is called "Passing Through After Retardation." As described above, the characteristics of the flame passing through a narrow channel will be closely related to the aerodynamic characteristics of the flow in the channel. Accordingly, the
FLAME PROPAGATION IN NARROW CHANNELS (I)
251
Fig. 8. Schlieren image of a flame passing through a channel with sharp-edged entrance corners. effects of gas velocity in the channel and the roundness of the entrance corner on the flame characteristics will now be considered. The inflow velocity of the unburned gas from the chamber at the instant when the flame propagates into the channel can be artificially changed by moving the ignition point Z / L for any combination of equivalence ratio and channel width. Thus, some experiments were carried out to examine the effects of the gas velocity on the flame characteristics, by setting the igniter
at various positions. Figure 11 shows the relations between Utin, which was used as a reference gas velocity, and equivalence ratio 4~, for several ignition points Z / L for the case where the channel width b = 1.6 mm. As the ignition point approaches to the channel entrance, the gas velocity at the instance of flame penetration, Utin, is reduced. The flame characteristics are shown in Fig. 12 for the location of the ignition point Z / L = 0.25. The borderline between the domain where
252
NORIMASA IIDA ET AL. ~
Laminar flame Fully laminar
region ~
300 1
Turbulentflame
I
Fully Turbulent region
_~
E .---
~o°tbustion product
.
Cool combustible mixture
X~3b
,^^
_
I
l
=
~
..---o-- o ~ o
loi"°
105
the flame passes through the channel and the domain where it passes through after retardation shifts to the side of narrower channel width when compared with the case where the ignition point is at Z / L = 1.0 (shown in Fig. 7). This is because a flame propagating into the channel together with a lower velocity gas will be less influenced by the cooling action of turbulent mixing just downstream of the contraction region. Flame characteristics for stoichiometric mixtures are replotted in Fig. 13 to show the relationship between Uti n and b for various ignition positions. The borderline between the passing-through domain and the passing-afterretardation domain is almost a straight line on the semilogarithmic graph and may be represented by the equation (Utin)crit= O/ In b +/),
(2)
b--lOmm / I Z/L=1.0 ~ - - A ~ ;~'A=j.o I oI I
0 /
0
1
lo
-
-O-o-o_o~_
t
-
0.8
Ii °'; I
1.2
1 .&
1.6
Fig. ] l . Gas velocity at the channel exit at the time that the f l a m e enters the channel as a function of mixture equivalence ratio for different ignition positions.
where o~ and /3 are empirical constants which depend on the fuel, equivalence ratio, and the radius of curvature of the channel entrance. (Utin)crit is the limiting reference gas velocity in the channel that just allows a flame to run through the channel. ~ r 1 PASSING THROUGH ..... (a> PASSING THROUGH ^ AFTER RETARDATION--(b)l"(= U A, PARTIALLY PASSING THROUGH . . . . . . . . . . . . (c) C3H 8 • NOT PASSINGTHROUGH-(d) 0 A
20
r--I
IN I
l
I
ZIL=0.25]
i
E
0
E
I
•
tin
1.0
0
,
0
0
,
0
I
zx z x ~ o
8 ms
Fig. 10. N o r m a l i z e d flame width at the path entrance as a function o f elapsed time f r o m the m o m e n t of flame entry to the channel.
I[
,..
I
4
r\°\l
I
0
I
,
0
0
I
/ /
I I
(3 I
II
.o /* - ? - - 0 - - 0 - - 0 - - 0 --0 - ZX--ZX--~,
i
2
I
m _......,o ~ o - o ~ o .,....0 x , o I i ~'~ 0~0~-- \ ~ "
/ 0 l
7r2 ol.Y"
o,,
l"°'-oI\
/ UU I~ u
Fig. 9. R e l a t i v e d i m e n s i o n s o f the f l a m e near the channel entrance as estimated f r o m schlieren i m a g e s .
1.0
C3H 8
0.75 \
I I
"~
Xf =5b
Z/L=I.0
200 ? =
XC= b / 2 I --
R=0
I
.~..0 ~ O .....0
~ ~,-m",.~ _z ~,'.-='-.
" /
Laminar flame - . front )
b=1.6 rnm
l
I
1 / /
O/A
O'~A~A/O E I
ZX * / i
•
1 --0--0--0--0--0--0--0 0.8
1.0
1.2
• I
•
•
• I ,
--0--0
1 .&
1.6
Fig. 12. Passage characteristics o f the f l a m e for the case w h e n the mixture is ignited at the position Z / L = 0.25.
FLAME PROPAGATION IN NARROW CHANNELS (I) 3O0
I
R=O ~=l.u
.,, z L ~ . Z I L = I . 0 / _ _
C3H8 ' '
--o~ E
=
200
i
~
-°-"
lOO
,I--L_q. 5 I a~l
•I o
~.~.~5"-'_o \_ ~"
~'£')
£)
I
t-----?-'-'o-o
2
4
1
6 8 10 b mm Fig. 13. Passage characteristics shown as the relation between the channel width, b, and the reference gas velocity, Ut~,, for four different ignition positions.
It is seen that the limit velocity that just allows a flame to pass through the channel without any retardation is higher for a wider channel. When the channel is wide, the length of the turbulent shear region in the contraction region near the entrance is relatively small compared with the channel width and the flame is less influenced by turbulent mixing with cold unburned gas and runs through the channel without retardation. The radius of curvature of the channel entrance affects the characteristics of a flame propagating into the channel from the chamber. Some experiments were carried out to examine the effects of radius of curvature of the entrance on the passage characteristics of flame. Figure 300
E
d:101m~
200
t
,,-a~,,..__.
I -
o
I 1
~0 /
_~'~~L
"" " ' ~ Z / L = 1.0
"
•
C3H8 ~!
I --A~--o'-ZL--o____.__[
2
b
I /..
i ?..o o J I~ ° P - o - .o---o 6 8 10 mm
Fig. 14. Passage characteristics for a channel with rounded entrance corners.
253
14 indicates the characteristics for a channel with an entrance corner radius of curvature of 10 mm. The borderline between the passing domain and the passing-through-after-retardation domain shifts to higher gas velocities. This is because, when the channel entrance is rounded, severe contraction does not occur and the turbulence intensity near the wall just behind the channel entrance is lower, which causes the flame to pass through the channel with less retardation or without retardation. The instantaneous schlieren photograph of Fig. 15 justifies this conjecture concerning the effect of a rounded channel entrance. The contraction of the burned region just downstream of the entrance does not exist and the position where the flame reaches the wall shifts far downstream when compared with the case shown in Fig. 8. The limit condition for which a flame does not pass through the channel does not change even if the corner of the path entrance is rounded. For a specific mixture it depends only on the channel width and not on the gas velocity, as is clearly indicated in Figs. 13 and 14. From this fact, it is assumed that flame extinguishment in a very narrow channel, which is called " N o t Passing T h r o u g h " in this paper, is caused by absorption of active species and heat by the wall. The nonpassing limit width is independent of the gas velocity and is the same order as that for a steady laminar flame. The flame retardation phenomenon seems to be caused by the gas flow from the combustion chamber to the channel. The ratio b / B (where B is the width of the chamber) was selected as a nondimensional parameter relating to the hydrodynamic characteristics of the flow produced about the channel entrance, and the influence of this parameter on the passage characteristics was examined for various combinations of b and B shown in Table 1. Figure 16 shows the passage characteristics of flame plotted in the (Uti,, b/B) plane. The value of b/B indicates a ratio of the channel width of the combustion chamber width. This ratio will influence the gas flow just downstream of the entrance of the channel. Finally Eq. (2) may be changed to take into
254
NORIMASA IIDA ET AL.
Fig. 15. Schlieren image of a flame propagating into a channel with rounded entrance corners.
TABLE 1 Relations among b, B and ratio b / B
~ b B (mm) 110 80 63 47.5 37.5
(mm) 10
6.3
4.0
2.5
1.6
1.0
0.091 0.13 0.16 0.21 0.27
0.067 0.079 0.10 0.13 0.17
0.036 0.050 0.063 0.084 0.10
0.023 0.031 0.040 0.030 0.067
0.015 0.020 0.025 0.034 0.043
0.009 0.013 0.016 0.02 1 0.027
FLAME PROPAGATION IN NARROW CHANNELS (I)
255
300
6,
:3"/~
~
A
A A&'
h,
0 PASSING THROUGH. . . . . (a) •'%. PASSING IHROUGH AFTER RETARDATION- - ( b )
A AAA
100
J ~
A - - "
OOU
o 00 0
~
~
n ~
O°o 0
, I
I
R:O ~ : I. 0 C3He
L
I
I
0.01
I
0.05
oOooO I
I
nO ~o o 0 08 0
o0
I L
0.1
b/a Fig. 16. Passage characteristics shown as a function of the ratio of channel width to chamber width, b / B , and the reference gas velocity, Ut~o.
account the influence of B on the limit of flame passage without retardation in a narrow channel: (Utin)crit :
O/ ln(b/B) + {3'.
(3)
The limit of flame extinguishment has no unique behavior in the (Utah, b/B) plane, because the limit condition depends only on the channel width. CONCLUSIONS Experiments were systematically carried out on the behavior of a premixed flame flowing into a narrow channel from a chamber with an accompanying high speed gas flow and some conclusions have been obtained within the limit of the experiments as follows. 1. Flames flowing into a narrow channel from a chamber exhibit three kinds of behaviors, i.e., passing-through, passing-through-afterretardation, and not-passing-through, depending on the channel width, equivalence ratio, and ignition position (that is, flame penetrating velocity). 2. Passing-through-after-retardation is caused by the quenching effect of turbulent mixing of hot reacting gas with the cold unburned gas that is flowing into the channel together with the flame. 3. The limit width of the channel for which a flame passes through without retardation decreases as the inflow velocity goes down,
and the relation between gas velocity and channel width for the passing-through-without-retardation limit can be expressed by an empirical equation. . The limit width described in conclusion 3 decreases when the contraction near the path entrance is relieved by rounding the corner of the entrance. . For a specific mixture, the limit condition for which no flame will pass through, with or without retardation, depends only on the channel width, and not on the inflow velocity or the radius of curvature of the path entrance.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Wolfhard, H. G., and Bruszak, A. E., Combust. Flame 4:149-159 (1960). Phillips, H., Combust. Flame 7:129-135 (1963). Maekawa, M., and Takeichi, M., Fire Research 1:317-322 (1978/1979). Yamaguchi, S., et al., Trans. JSME419:1390-1399 (1981) (in Japanese). Furukawa, J., and Gomi, T., Trans. JSME414:380391 (1981) (in Japanese). Wakai, K., et al., Trans. J S M E 417:872-879 (in Japanese). Klomp, E. D., and Deboy, G. R., Trans. S A E 85:739-752 (1976). Ono, S., and Wakuri, U., Trans, J S M E 365:269-279 (1977) (in Japanese).
Received 12 N o v e m b e r 1984; revised 4 January 1985
245
Premixed Flame Propagating into a Narrow Channel at a High Speed, Part 1: Flame Behaviors in the Channel NORIMASA IIDA, OSAMU KAWAGUCHI, and G. TAKESHI SATO Faculty of Science and Technology, Keio University, 14-1, Hiyoshi, 3-Chome, Kohoku-Ku, Yokohama 223, Japan
This paper deals with the transient behavior of a flame flowing into a narrow channel from a chamber filled with a propane-air mixture. The flame was observed through direct or schlieren high speed photography, and at the same time the arrival at the entrance and exit of the channel were detected by ion gaps. From the experimental results it was found that in some cases the flame extinguished or hesitated in the channel before passing through. These behaviors were dependent on the equivalence ratio of the mixture, the channel width, and the flame inflow velocity. Flame standstill in the channel is assumed to be caused by continuous quenching of hot reacting gas due to turbulent mixing with cold unburned gas at the contraction region established near the entrance of the channel. For any specific mixture, when the channel entrance is rounded or the inflow velocity is low, the m i n i m u m width of the channel for which a flame will run through without any retardation becomes smaller compared with the case of a sharp-edged entrance or a high inflow velocity. On the contrary, the m i n i m u m width of the channel for which a flame cannot pass through does not depend on the corner roundness of the channel entrance or the inflow gas velocity.
INTRODUCTION The problem of premixed gas flame propagation through narrow channels followed by a flame jet flow has been studied by Wolfhard and Bruszak [1], Phillips [2], and Maekawa and Takeichi [3]. In those studies the ignition of a flammable mixture by a flame jet or hot gas ejected from a chamber through a narrow channel has been treated. Yamaguchi et al. [4], Furukawa and Gomi [5], Wakai et al. [6], and Klomp and Deboy [7] have made experimental studies of the flame propagation process in a chamber filled with a flammable gas which has a partition with a hole and have reported upon the effects of the whole diameter and the gas jet velocity on ignition probability and flame velocity in the mixture of the other side of the partition. Ono et al. [8] have obtained flame extinguishment conditions through measurements of flame velocity in a small channel with electrostatic Copyright © 1985 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
probes and reached the conclusion that there are two kinds of velocity limits of flame quenching, that is, a limit at low flow velocities mainly caused by cooling by the channel wall and another limit at high flow velocities which could not be explained using the cooling effect concept. They surmised that the entrainment of surrounding gas into a flame jet after it passes through the channel was the main controlling factor for this type of flame quenching, because the transient time of the flame in the channel is shorter for flame extinguishment under a high velocity condition than it is for a low velocity condition. In the studies referred to above, it is not clear whether the external flammable mixture is ignited by a propagating flame jet or by a hot jet of combustion products. Furthermore the factors controlling the flame propagation process in a narrow channel were not investigated. Because of this the authors of this paper have carried out
0010-2180/85/$03.30
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NORIMASA IIDA ET AL.
and report on some experimental studies of the characteristics of a premixed flame passing through a narrow channel at a high speed and measured flame properties in the channel to determine the factors affecting these characteristics.
EXPERIMENTAL A P P A R A T U S AND PROCEDURES Detailed experiments were systematically carried out using a simple two-dimensional windowed chamber with a narrow channel leading to the open air shown in Fig. 1. The combustion chamber has dimensions of 110 mm in width, 200 mm in length, and 70 mm in depth. The narrow channel set on the short upper side of the chamber has the same depth as the chamber. The side walls are made of common transparent acrylic plates to observe the flame propagating in the chamber and through the channel. The
length of the channel is 200 mm and the width can be set to any dimension ranging from 0 to 12.5 ram. An electric spark igniter is installed on the central axis of the chamber but the point of ignition is movable in the vertical direction. The apparatus is mounted vertically as shown to avoid nonsymmetrical flame propagation due to buoyancy effects which occur when a flame propagates in a quiescent premixed gas in a chamber. Prior to an experiment, the chamber is filled with a well mixed propane-air mixture at room temperature and pressure, and left till the mixture becomes perfectly still. After the flammable mixture in the chamber is ignited by the igniter, the propagating flame is recorded on a high speed motion picture camera or a 35 mm still camera by a direct photographic method or a schlieren method. The pressure in the chamber is also measured and recorded with a pressure transducer and a memory storage
+-
I///
f / ~
I COMBUSTION CHAMBER 2 CHANNEL 3 MIXTURE GAS INLET 4 MIXTURE GAS OUTLET 5 SPARK IGNITER 6 PRESSURE TRANSDUCER 7 ELECTROSTATIC PROBE or
15 ION GAP 16 PITOT TUBE 17 PRESSURETRANSDUCER Z IGNITION POSITION b CHANNEL WIDTH B COMBUSTIONCHAMBERWIDTH
Fig. 1. Experimental apparatus.
FLAME PROPAGATION IN NARROW CHANNELS (I) synchroscope. A short time after ignition, a part of the propagating flame penetrates into the narrow channel and either runs through the channel or extinguishes in the channel, depending on the initial conditions. The times at which the flame enters the channel and leaves it are detected using ion gaps at the entrance and the exit of the channel. The velocity and temperature of the gas or flame ejected out of the channel are measured using a fine pitot tube of 1.0 mm in outer diameter with a highly sensitive and quick response pressure transducer and a thermocouple (type-R) of 25 #m diameter. OBSERVATION AND RESULTS
Appearance of Propagating Flame When a mixture is ignited at the closed end of the chamber, a flame propagates in the mixture with a semispherical shape at the beginning and with a warhead like shape later. As the flame propagates and the mixture burns, the pressure in the chamber rises and the unburned gas flows toward the channel entrance. The top of the flame is pointed as it approaches the channel entrance due to the flow velocity distribution in the unburned gas ahead of the flame. The flame flows into the channel at a very high speed together with the unburned gas. The shapes of the flames propagating in the chamber are shown in Fig. 2 with flame contours traced from the motion picture films at 5 or 10 ms intervals.
LI
(a) Z/L=1.0
247
In these examples the propane-air mixtures are stoichiometric and ignited at four different positions. The width of the channel is 6.3 mm and the channel entrance is not rounded (i.e., R = 0). In this figure, R = 0 means that the entrance to the channel has sharp-edged corners and Z / L = 1.0 means that the mixtures are ignited at the closed end of the chamber. After flowing into the channel, the flame travels at a high speed. Figure 3 shows a few frames of a motion picture film during the time that the flame propagates through the channel for conditions quite similar to those of Fig. 2a. The position of the flame tip in the channel can be traced from the motion picture film. Three examples are plotted for stoichiometric propane-air mixtures as a function of time elapsed from ignition in Fig. 4. When the channel width is large (b = 10 mm), the flame propagates into the channel together with the high speed gas flow and quickly runs through the channel. When the channel width is somewhat smaller (b = 6.3 mm), the flame behavior is different from that of the former case. Just after the flame penetrates into the channel, it stops its motion for few milliseconds at a distance of about 40 mm from the entrance, and then runs through the rest of the channel at a high speed. In this case the flame penetrating into the channel appears to be extinguished for a short period of time at this special position. The authors call this phenomenon "Passing Through After Retardation." When the channel width is still
b=6.3mm
(b) ZIL=0.75
(c)
Z/L=0.5
(d) Z/L= 0.25
Fig. 2. Flame contours for mixture ignition at four different ignition positions.
248
NORIMASA IIDA ET AL. b=6.3 mm, B=II0 mm, R=0, Z/L=1.0, @=i.0, C3H 8
®---~=30.0 ms (Z,N)~ 30.5 ms
® 33.0 ms
© 37.5 mstcour}®/,2.5 ms
Fig. 3. Flame positions after the flame flows into the channel: times are elapsed time from ignition.
smaller (b = 1.6 mm), the position of the flame tip in the channel cannot be judged from the film, but may be judged from ion gap signals which show that flame remains in the channel until all the mixture has burned out. The authors named this phenomenon " N o n Passage," to avoid confusion with the transient extinguishment of the former case.
Passage Characteristics of Flames The motion picture films are not suitable for tracing the flame movement and for judging whether or not the flame has passed through the channel. For this reason ion gaps were installed at the entrance and the exit of the channel as shown in Fig. 1 to detect the flame and to measure its electrical conductivity which indicate the activity of the reacting gas.
E E x 200 _ Z / L = 1 . 0
0=1.0 C3H8
O.
E u_
Four examples of ion current records are shown in Fig. 5, which were recorded with a synchroscope. The lower trace of each picture is that detected by the probe set at the channel entrance and the upper one is that at the channel exit. When a flame passes a probe, a high ionization current appears and it is clear that a flame has passed the probe. The time which a flame requires to pass through the channel can be estimated from the time interval between the rise times of the two ionization currents and the apparent flame velocity Uf can be calculated using the following equation, Uf---
l
m/s,
where l is the channel length, 200 mm, and ti. and to.t indicate the times (ms) that the flame passes the respective ion gaps.
f~-=-!-
/
C
~-200 0
c
~{b) b: 6.3rnrn z
0
.o
(1)
t o u t - tin
.~'~'N~(c)
b =l.6mm ,
20
t
40
ms
60
Fig. 4. The position of the top of the flame in the chamber and the channel as a function of time.
FLAME PROPAGATION IN NARROW CHANNELS (I) B=ll0
u,
R=0,
Z/L=I.0,
~=l.0,
249
CsH 3
\
0
50
100 ms
0
(a) b=10 u
50
100 ms
(b) b:6.3 u
i l l m l w u , ~ ' N m m r n l l r ~ n m mn
0
50
100 ms
(e) b=l.6mn
0
50
100 ms
(d) b=1.25 m
Fig. 5. Some examples of ion current waves of passing-through-the-channel flames. Lower and upper beams indicate those detected at the channel entrance and exit, respectively. The velocity of premixed gas ejected from the channel is estimated from the dynamic pressure measured with the pitot tube and pressure transducer at the channel exit. If the exit velocity at tin is called Uti., the ratio of Utin to Uf can be used to judge the passage characteristics of the flames, because the gas velocity Uti n should not change rapidly during the time interval between tin and tout. When a high speed flame propagates in the premixed gas toward the channel exit without retardation, the ratio Uti./Uf will be smaller than unity. However, if this ratio is found to be larger than unity, one cannot but conclude that the flame stays somewhere in the channel for a while before passing through the channel because negative burning velocities are impossible. The relations between Utin/Uf and the equivalence ratio, th, of the mixture are shown in Fig. 6 for various channel widths b. For the widest channel, b = 12.5 mm, Uti./Uf is always smaller than unity, which means that the flame runs through the channel without retardation. For the 10 m m width channel, Utin/Uf is larger than unity for off-stoichiometric mixtures because the flame hestitates for a while in the
channel. When the channel is narrower than 6.3 m m the flame passes through the channel after some retardation over the whole range of equivalence ratio. In the case of a narrower channel for off-stoichiometric mixtures, the ion gaps at
rI -I T - -I -
"~/I.~=1.0
} I
If
; I
LI
0.8
1.0
1.2
1.4
1
1.6
Fig. 6. Ratio o f the ejected gas velocity at the time the
flame flows into the channel, Utin, to the flame velocity, Uf, as a function of equivalence ratio of the mixture for various channel widths.
250
NORIMASA IIDA ET AL.
I
JO PASSINGTHROUGH. . . . . (~)
I R= 0 I | A, TER RETARDATION--(b) Z/L=1 0 l l-/k PARTIALLY PASSING - C H "~j [ A PASSING THROUGH
2o j
THROUGH. . . . . . . . . . . . C~)
3 8 1
II
/ e NOT PASSING THROUGH -(d)
E E
16 j
0 60 I
6 0 6 0 61 I ~ I
I0 --~~'~"~'----ZX--Z~--A--~,
--I
A
ZX ix
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ZX ,~ I
A
Z~ A
A
•
o, A
At Q
U I
I/ " " "
"
I l--O--•--•--•--•--•--•--•--•II
0.8
,
r
1.0
,
I
1.2
,
I
1.4
,
I
1.6
F i g . 7. C h a r a c t e r i s t i c s o f f l a m e f l o w i n g t h r o u g h n a r r o w c h a n n e l s s h o w n as d o m a i n s f o r the t h r e e f l a m e b e h a v i o r o b s e r v e d , p l o t t e d as a f u n c t i o n o f c h a n n e l w i d t h b a n d e q u i v a l e n c e r a t i o 4~.
the channel exit no longer detect the presence of any flame at the channel exit. Finally, flame cannot pass through channels narrower than 1.25 mm at any equivalence ratio. The flame characteristics in various narrow channels are replotted in the (4), b) plane in Fig. 7. Flame behaviors are divided into three domains as follows: a. b.
c.
a domain where flame runs through the channel with the gas flow; a domain where flame passes through the channel after a transient hesitation in the channel; a domain where flame does not pass through the channel.
Transient Flame Extinguishment The flame penetrates into the channel with a smooth flame front together with unburned premixed gas. Figure 8 shows an instantaneous schlieren photograph taken at the moment just
after the flame penetrates into the channel. The flame is constricted by the flow contraction region near the channel entrance, and then expands gradually in the channel and changes from a laminar state to a turbulent state. The flame penetrating into the channel is schematically illustrated in Fig. 9 using the image from the schlieren photographs for various channel widths. All the characteristic dimensions of the flame observed in the channel are related to b in the same way over the range of the channel widths examined. The position, x¢, where the flame is most constricted is about b / 2 away from the entrance and the transition from a laminar state to a turbulent state occurs at the position xl = b. The flame expands to fill the channel after the position Xm = 3b and the unburned gas flowing into the channel mixes with the flame and burned gas. The flame which reaches the channel entrance continuously penetrates into the channel in the laminar state with unburned gas on both sides and it suffers strong shear produced by the steep velocity gradient in the contraction region. Subsequently the flame is cooled through turbulent mixing with unburned gas and continuously extinguished, and appears to be held at the position x f = 5b. The value of wf/b, which indicates the relative minimum laminar flame width near the channel entrance, increases as time passes as shown in Fig. 10. we/b is almost equivalent to the ratio of the volume flow rate of the burned gas to the unburned gas flowing into the channel if the velocity distribution is uniform at the channel entrance, which was confirmed with an experiment of cold flow. As the remaining unburned gas in the chamber continues to burn and flows into the channel, the unburned gas inflow rate decreases relative to the initial inflow rate and the resulting decrease of flame quenching by turbulent mixing allows the flame to propagate downstream in the channel. Such flame behavior is called "Passing Through After Retardation." As described above, the characteristics of the flame passing through a narrow channel will be closely related to the aerodynamic characteristics of the flow in the channel. Accordingly, the
FLAME PROPAGATION IN NARROW CHANNELS (I)
251
Fig. 8. Schlieren image of a flame passing through a channel with sharp-edged entrance corners. effects of gas velocity in the channel and the roundness of the entrance corner on the flame characteristics will now be considered. The inflow velocity of the unburned gas from the chamber at the instant when the flame propagates into the channel can be artificially changed by moving the ignition point Z / L for any combination of equivalence ratio and channel width. Thus, some experiments were carried out to examine the effects of the gas velocity on the flame characteristics, by setting the igniter
at various positions. Figure 11 shows the relations between Utin, which was used as a reference gas velocity, and equivalence ratio 4~, for several ignition points Z / L for the case where the channel width b = 1.6 mm. As the ignition point approaches to the channel entrance, the gas velocity at the instance of flame penetration, Utin, is reduced. The flame characteristics are shown in Fig. 12 for the location of the ignition point Z / L = 0.25. The borderline between the domain where
252
NORIMASA IIDA ET AL. ~
Laminar flame Fully laminar
region ~
300 1
Turbulentflame
I
Fully Turbulent region
_~
E .---
~o°tbustion product
.
Cool combustible mixture
X~3b
,^^
_
I
l
=
~
..---o-- o ~ o
loi"°
105
the flame passes through the channel and the domain where it passes through after retardation shifts to the side of narrower channel width when compared with the case where the ignition point is at Z / L = 1.0 (shown in Fig. 7). This is because a flame propagating into the channel together with a lower velocity gas will be less influenced by the cooling action of turbulent mixing just downstream of the contraction region. Flame characteristics for stoichiometric mixtures are replotted in Fig. 13 to show the relationship between Uti n and b for various ignition positions. The borderline between the passing-through domain and the passing-afterretardation domain is almost a straight line on the semilogarithmic graph and may be represented by the equation (Utin)crit= O/ In b +/),
(2)
b--lOmm / I Z/L=1.0 ~ - - A ~ ;~'A=j.o I oI I
0 /
0
1
lo
-
-O-o-o_o~_
t
-
0.8
Ii °'; I
1.2
1 .&
1.6
Fig. ] l . Gas velocity at the channel exit at the time that the f l a m e enters the channel as a function of mixture equivalence ratio for different ignition positions.
where o~ and /3 are empirical constants which depend on the fuel, equivalence ratio, and the radius of curvature of the channel entrance. (Utin)crit is the limiting reference gas velocity in the channel that just allows a flame to run through the channel. ~ r 1 PASSING THROUGH ..... (a> PASSING THROUGH ^ AFTER RETARDATION--(b)l"(= U A, PARTIALLY PASSING THROUGH . . . . . . . . . . . . (c) C3H 8 • NOT PASSINGTHROUGH-(d) 0 A
20
r--I
IN I
l
I
ZIL=0.25]
i
E
0
E
I
•
tin
1.0
0
,
0
0
,
0
I
zx z x ~ o
8 ms
Fig. 10. N o r m a l i z e d flame width at the path entrance as a function o f elapsed time f r o m the m o m e n t of flame entry to the channel.
I[
,..
I
4
r\°\l
I
0
I
,
0
0
I
/ /
I I
(3 I
II
.o /* - ? - - 0 - - 0 - - 0 - - 0 --0 - ZX--ZX--~,
i
2
I
m _......,o ~ o - o ~ o .,....0 x , o I i ~'~ 0~0~-- \ ~ "
/ 0 l
7r2 ol.Y"
o,,
l"°'-oI\
/ UU I~ u
Fig. 9. R e l a t i v e d i m e n s i o n s o f the f l a m e near the channel entrance as estimated f r o m schlieren i m a g e s .
1.0
C3H 8
0.75 \
I I
"~
Xf =5b
Z/L=I.0
200 ? =
XC= b / 2 I --
R=0
I
.~..0 ~ O .....0
~ ~,-m",.~ _z ~,'.-='-.
" /
Laminar flame - . front )
b=1.6 rnm
l
I
1 / /
O/A
O'~A~A/O E I
ZX * / i
•
1 --0--0--0--0--0--0--0 0.8
1.0
1.2
• I
•
•
• I ,
--0--0
1 .&
1.6
Fig. 12. Passage characteristics o f the f l a m e for the case w h e n the mixture is ignited at the position Z / L = 0.25.
FLAME PROPAGATION IN NARROW CHANNELS (I) 3O0
I
R=O ~=l.u
.,, z L ~ . Z I L = I . 0 / _ _
C3H8 ' '
--o~ E
=
200
i
~
-°-"
lOO
,I--L_q. 5 I a~l
•I o
~.~.~5"-'_o \_ ~"
~'£')
£)
I
t-----?-'-'o-o
2
4
1
6 8 10 b mm Fig. 13. Passage characteristics shown as the relation between the channel width, b, and the reference gas velocity, Ut~,, for four different ignition positions.
It is seen that the limit velocity that just allows a flame to pass through the channel without any retardation is higher for a wider channel. When the channel is wide, the length of the turbulent shear region in the contraction region near the entrance is relatively small compared with the channel width and the flame is less influenced by turbulent mixing with cold unburned gas and runs through the channel without retardation. The radius of curvature of the channel entrance affects the characteristics of a flame propagating into the channel from the chamber. Some experiments were carried out to examine the effects of radius of curvature of the entrance on the passage characteristics of flame. Figure 300
E
d:101m~
200
t
,,-a~,,..__.
I -
o
I 1
~0 /
_~'~~L
"" " ' ~ Z / L = 1.0
"
•
C3H8 ~!
I --A~--o'-ZL--o____.__[
2
b
I /..
i ?..o o J I~ ° P - o - .o---o 6 8 10 mm
Fig. 14. Passage characteristics for a channel with rounded entrance corners.
253
14 indicates the characteristics for a channel with an entrance corner radius of curvature of 10 mm. The borderline between the passing domain and the passing-through-after-retardation domain shifts to higher gas velocities. This is because, when the channel entrance is rounded, severe contraction does not occur and the turbulence intensity near the wall just behind the channel entrance is lower, which causes the flame to pass through the channel with less retardation or without retardation. The instantaneous schlieren photograph of Fig. 15 justifies this conjecture concerning the effect of a rounded channel entrance. The contraction of the burned region just downstream of the entrance does not exist and the position where the flame reaches the wall shifts far downstream when compared with the case shown in Fig. 8. The limit condition for which a flame does not pass through the channel does not change even if the corner of the path entrance is rounded. For a specific mixture it depends only on the channel width and not on the gas velocity, as is clearly indicated in Figs. 13 and 14. From this fact, it is assumed that flame extinguishment in a very narrow channel, which is called " N o t Passing T h r o u g h " in this paper, is caused by absorption of active species and heat by the wall. The nonpassing limit width is independent of the gas velocity and is the same order as that for a steady laminar flame. The flame retardation phenomenon seems to be caused by the gas flow from the combustion chamber to the channel. The ratio b / B (where B is the width of the chamber) was selected as a nondimensional parameter relating to the hydrodynamic characteristics of the flow produced about the channel entrance, and the influence of this parameter on the passage characteristics was examined for various combinations of b and B shown in Table 1. Figure 16 shows the passage characteristics of flame plotted in the (Uti,, b/B) plane. The value of b/B indicates a ratio of the channel width of the combustion chamber width. This ratio will influence the gas flow just downstream of the entrance of the channel. Finally Eq. (2) may be changed to take into
254
NORIMASA IIDA ET AL.
Fig. 15. Schlieren image of a flame propagating into a channel with rounded entrance corners.
TABLE 1 Relations among b, B and ratio b / B
~ b B (mm) 110 80 63 47.5 37.5
(mm) 10
6.3
4.0
2.5
1.6
1.0
0.091 0.13 0.16 0.21 0.27
0.067 0.079 0.10 0.13 0.17
0.036 0.050 0.063 0.084 0.10
0.023 0.031 0.040 0.030 0.067
0.015 0.020 0.025 0.034 0.043
0.009 0.013 0.016 0.02 1 0.027
FLAME PROPAGATION IN NARROW CHANNELS (I)
255
300
6,
:3"/~
~
A
A A&'
h,
0 PASSING THROUGH. . . . . (a) •'%. PASSING IHROUGH AFTER RETARDATION- - ( b )
A AAA
100
J ~
A - - "
OOU
o 00 0
~
~
n ~
O°o 0
, I
I
R:O ~ : I. 0 C3He
L
I
I
0.01
I
0.05
oOooO I
I
nO ~o o 0 08 0
o0
I L
0.1
b/a Fig. 16. Passage characteristics shown as a function of the ratio of channel width to chamber width, b / B , and the reference gas velocity, Ut~o.
account the influence of B on the limit of flame passage without retardation in a narrow channel: (Utin)crit :
O/ ln(b/B) + {3'.
(3)
The limit of flame extinguishment has no unique behavior in the (Utah, b/B) plane, because the limit condition depends only on the channel width. CONCLUSIONS Experiments were systematically carried out on the behavior of a premixed flame flowing into a narrow channel from a chamber with an accompanying high speed gas flow and some conclusions have been obtained within the limit of the experiments as follows. 1. Flames flowing into a narrow channel from a chamber exhibit three kinds of behaviors, i.e., passing-through, passing-through-afterretardation, and not-passing-through, depending on the channel width, equivalence ratio, and ignition position (that is, flame penetrating velocity). 2. Passing-through-after-retardation is caused by the quenching effect of turbulent mixing of hot reacting gas with the cold unburned gas that is flowing into the channel together with the flame. 3. The limit width of the channel for which a flame passes through without retardation decreases as the inflow velocity goes down,
and the relation between gas velocity and channel width for the passing-through-without-retardation limit can be expressed by an empirical equation. . The limit width described in conclusion 3 decreases when the contraction near the path entrance is relieved by rounding the corner of the entrance. . For a specific mixture, the limit condition for which no flame will pass through, with or without retardation, depends only on the channel width, and not on the inflow velocity or the radius of curvature of the path entrance.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Wolfhard, H. G., and Bruszak, A. E., Combust. Flame 4:149-159 (1960). Phillips, H., Combust. Flame 7:129-135 (1963). Maekawa, M., and Takeichi, M., Fire Research 1:317-322 (1978/1979). Yamaguchi, S., et al., Trans. JSME419:1390-1399 (1981) (in Japanese). Furukawa, J., and Gomi, T., Trans. JSME414:380391 (1981) (in Japanese). Wakai, K., et al., Trans. J S M E 417:872-879 (in Japanese). Klomp, E. D., and Deboy, G. R., Trans. S A E 85:739-752 (1976). Ono, S., and Wakuri, U., Trans, J S M E 365:269-279 (1977) (in Japanese).
Received 12 N o v e m b e r 1984; revised 4 January 1985