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Limiting factor of flame propagation in low-volatility fuel clouds
E i g h t e e n t h S y m p o s i u m (International) on C o m b u s t i o n
The C o m b u s t i o n Institute, 1981
L I M I T I N G F A C T O R OF F L A M E P R O P A G A T I O N IN LOW-VOLATILITY FUEL CLOUDS S. HAYASHI
National Aerospace Laboratory, lindaiii-machi, Chofu, Tokyo, 1apan T. OHTANI
Fuel Research Laboratory, NYK Line, Naka-ku, Yokohama, 1apan AND
K. IINUMA AND S. KUMAGAI*
Department of Aeronautics, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, 1apan The limit of flame propagation, in terms of the number density or spacing of droplets and fuel concentration, in low-volatility fuel clouds has been determined, varying the droplet size. The stream of mono-sized droplets, produced by a rotating-disk atomizer, enters d o w n w a r d into the test section. The droplet size and n u m b e r density are controlled by adjusting the rotating speed of the atomizer and the fuel feed rate, respectively. With increasing n u m b e r density for a given droplet size, the following occur in sequence: droplet ignition with mispropagation; upward propagation of isolated diffusion flames surrounding the droplets; flame spread over the stream cross section. As the droplet size is increased, the critical n u m b e r density for propagation decreases rapidly, whereas the droplet spacing increases at a very small rate according to a mathematical relation. The critical fuel concentration decreases sharply with increasing droplet size in the range from a few I~m to about 40 ~m, where transition from ignition of the premixed gases to relay ignition of the neighboring droplets occurs, and then decreases moderately toward less than half of the lower flammability limit. This creates a serious explosion hazard, since a fuel-air mixture which is not flammable in the premixed state, may become flammable through condensation of the fuel into droplets.
1. Introduction
one extreme model of fuel spray combustion, although the actual flame is supported by a mixture of fuel droplets, fuel vapor and air. Studies in this field will be useful for understanding the mechanism of spray combustion and will yield fundamental knowledge on the prevention of explosions in oil mists. In the present study, the propagation limits in droplet-air systems of low-volatility fuels have been determined with respect to the droplet-size effect.
Intensive experimental and theoretical investigations on the combustion of single fuel droplets have been carried out, and the fundamental features are now fairly well understood. ~'2) As a next step, the study of the combustion of fuel clouds or droplet-air systems is essential in order to understand the much more complicated process of spray combustion. Along this line, the authors have been studying flame propagation and flame structure in droplet-vapor-air systems. 3'4's) As shown in previous studies, prevaporization as well as droplet size has a predominant effect on the combustion characteristics. The droplet-air system of a low-volatility fuel is
2. Experimental Apparatus and Procedure Figure i shows a schematic drawing of the experimental apparatus, which consists of a rotating-disk atomizer, and settling and test sections. A fiat disk (2) of 100-mm diameter with a sharp edge is driven
*Professor Emeritus. 361
362
COMBUSTION OF DROPLETS AND SPRAYS
T |
~E ~E
l oD_ _7_ Flc. 1. Experimental apparatus. directly by an ac electric motor (3). A fuel (1) is fed to the center of the rotating disk from a 0.8-mm inner diameter nozzle through a rotometer. The atomizer housing is loosely connected to a cylinder (8) which serves as the settling section through a port with a 20-mm diameter throat, whose axis coincides with a vertical line tangent to the disk periphery. The fuel is atomized into droplets in all directions and every droplet that reaches the wall adheres there. Therefore, only a fraction of the atomized fuel enters the settling section. The fuel that adheres to the wails of the atomizer housing and the connecting port is drained, to keep it from flowing into the test section. The droplets originally produced by the atomizer consist of two groups: monosized droplets and satellite droplets of much smaller sizes. The latter are successfully eliminated by sectioning off part of the atomized fuel, by means of a pump and a collector (4), through 2-mm diameter holes arranged circularly on the housing wall. The size of droplets is controlled by adjusting the rotating speed of the disk, whereas their number density is varied by changing the fuel feed rate. The dependence of the initial droplet diameter, d, determined by the immersion method using silicone oil, on the rotating speed, n, reduces to d o: n -1, showing the same trend as the result obtained by Walton and Prewett. ~ After passing through the settling section, the stream of droplets enters into test section through a rectangular channel (9), 25 mm wide and 10 mm deep. A spark gap for ignition (13) (5 mm in width), formed by 0.5-mm thick electrodes, is placed 40 mm below the exit of the channel along the center line of the stream cross section. A pair of glass windows are fitted in to the wall of the test section,
and are used to photograph the droplets and flames with a camera (12). The number density of the droplets in the test section is determined by shadow photography. The light beam from the spark gap (10) is collimated with a lens system (11) to illuminate the droplet stream through the window. In the preliminary tests, the spatial distribution of the droplets along the light path was found to be practically uniform. It was also shown that the 10-mm thick droplet stream is thin enough for all the droplets in the light path to be recorded. The number density is determined by counting the number of droplets in a sampling volume, 15 mm wide, 20 mm high and 10 mm deep. In the case of dilute clouds, for which this sampling volume has often been found to be too small, larger sampling volumes are used. Experiments are conducted with n-decane and n-dodecane, keeping the air in the test section practically stationary. The vapor pressures of the fuels at the experimental temperature (20~ are listed in Table I, together with some physical properties and the limits of flammability. Since n-decane is more volatile than n-dodecane, the effect of prevaporization on the propagation limits of the droplet-air systems is expected to be larger for the former. One trial in the propagation-limit tests consists of eight spark passages at a rate of 34 sparks per second. This number of repetitions has been selected so that one droplet at least can be ignited, even under conditions where no flame propagation is established. Any flame that enters the atomizer housing and becomes stabilized at the exit is extinguished by injecting nitrogen (7), and the gas in the apparatus is purged by fresh air (6) before the next trial.
3. Experimental Results 3.1. Fuel Clouds and Flames
The results of all trials can be classified into three modes: (i) mispropagation--up to a certain value the number density is not sufficiently high for flames to propagate through the fuel cloud even though there is ignition of individual droplets, (ii) isolated blue-flame propagation--as the number density increases to a certain value, a mass of flame consisting of isolated blue diffusion flames surrounding the droplets propagates upwards, often in a column extending from the spark gap, (iii) interacting yellow-flame propagation--as the number density increases further, the flame becomes yellow and usually spreads over the cross section of the droplet stream. Figure 2 shows the fuel clouds in the test section. In determining the propagation limits, one droplet
FLAME PROPAGATION IN LOW-VOLATILITY F U E L CLOUDS
363
TABLE I Properties of fuels
Fuel
Density g/cm 3
Boiling point ~
Vapor pressure at 20~ mmHg
Stoichiometric mixture vol%
C lo H 22 C 12H26
0.75 0.75
174.1 216.3
1.3 0.1
1.33 1.11
at least must exist in the region of the ignition spark. However, at larger droplet sizes, the droplet spacing at which a propagating flame can be established is not as small, compared with the size of the ignition spark. The successive-spark method is convenient from this point of view. Direct photographs (Fig. 3) show that some droplets ignite and burn in isolated diffusion flames ahead of a continuous flame, which in reality consists of many small flames supported by individual droplets. In the case of dense clouds, these flames interact to form a homogeneous flame similar to a premixed flame. 4'7~ For much less volatile fuels, discretness of the flames becomes apparent, as shown for tetraline droplets 20-40 Ixm in diameter. 7'~ The flame shown in Fig. 3 is quite luminous, since the fuel concentration is rather higher than the propagation limit. At fuel concentrations near the propagation limits, a blue flame is seen on each
: /ji(i~!84184 il/
n -CI2H26 d = 164 lath
Limit of flammability vol% mg/ltr 0.75 0.60
48 46
droplet. The flame speed increases especially in the early stage of propagation. 3.2. Propagation Limit
Critical Number Density Figure 4 shows the results of propagation limit tests in terms of the number density for n-decane. Mispropagation, isolated blue-flame propagation and interacting yellow-flame propagation are represented by solid circles, triangles and hollow circles, respectively. Flame propagation becomes possible, when the number density increases to a certain value, and the value at the propagation limit, called the critical number density, decreases sharply with increasing initial droplet diameter. Though there is no qualitative difference between the results for n-decane and n-dodecane the critical number den-
,
n -CtoH22 I 0 0 #rn FIG. 2. Shadow photographs of droplet clouds.
n- CI2H26 6 4 pm
364
COMBUSTION OF DROPLETS AND SPRAYS
Time
n-decane
60
oo o
40
o
o
o o
o
8
o o
o o
i
o
~ 2o
o
o
o
o
o
8
O
o o
9 o
9
J
io
40
e
~l 8
80
! ", L IZO d , pm
i I
I
I
160
F](.. 5. Effects of fuel concentration and droplet size d on modes of flame propagation, n-Decane. Fie. 3. Direct photographs of flame propagation in n-decane droplet-air system. Frame interval, 0.005 SeC.
sity for the former is lower than that for the latter at any, given droplet size. Critical Fuel Concentration It is to be expected that if the mechanism of flame propagation in a droplet-air system is similar to that in a premixed gas, the propagation limit will occur at a fuel concentration corresponding to the lower limit of flammability of the premixed gas. From this point of view, the results are expressed in terms of fuel concentration (Fig. 5). As far as the present tests are concerned, the fuel concentration at the propagation limit, called the critical fuel concentra-
I
0 0
600
0
n-decane
4o0
?E
/.
0
0
0 0
0
0 o 0
9
0
i
4O
e 9
I
8TO
' 120
' 160
d , pm
FI(,. 4. Effects of number density N and size d of droplet on modes of flame propagation, n-Decane.
tion, decreases moderately with increasing initial droplet diameter. Droplet-air systems of n-decane give a reduction in the critical fuel concentration to about 13 mg/ltr for an initial droplet diameter of 55 p.m, for example, from the limit of flammability of 48 mg/ltr (53~ (see Table I). For droplet-air systems of n-dodecane also, the corresponding reduction amounts to more than 50% for initial droplet diameters larger than 40 p.m. This fact suggests a serious problem with respect to explosion hazards, since a fuel-air mixture, even though it is not flammable in the premixed state, may become flammable when the vapor condenses into rather large droplets. The discrepancy between the propagation limits for premixed gases and for droplet-air mixtures can be attributed to the difference in the mechanism of flame propagation between the two systems. Since fine droplets vaporize readily to form a mixture with air prior to ignition, the fuel cloud including such droplets is practically the same as the corresponding premixed gas. Therefore, the propagation limit is expected to appear at a fuel concentration corresponding to the limit of flammabilityof the premixed gas of the same fuel. As the droplet size increases, the degree of prevaporization diminishes and flame propagation occurs through successive ignition of unburnt droplets by the hot gas surrounding neighboring burning droplets. Thus, for the fuel clouds involving large droplets, no flame propagates if the average droplet spacing exceeds a critical value. The limiting droplet size for complete vaporization in the preheat zone of the usual hydrocarbon flames is estimated to be of the order of a few micrometers, 5's'9~and the estimated degree of vaporization is rather small for a droplet of 40-1xm initial diameter. The sharp decrease in the critical fuel concentration is consistent with the transition of
FLAME PROPAGATION IN LOW-VOLATILITY FUEL CLOUDS the mechanism of flame propagation in this range of droplet diameter.
365
for n-dodecane over the whole range of initial diameters tested, which is attributed to the difference in volatility.
Critical Droplet Spacing Consideration on the propagation limit in the preceeding paragraph and some photographic evidences in the present and previous experiments suggest that droplet spacing is probably a more appropriate concept than fuel concentration for characterizing the propagation limit of fuel clouds with droplets larger than about 40 ~m in initial diameter. Figure 6 shows the results of propagation limit tests in terms of nondimensionaldroplet spacing, viz. the average droplet spacing, l, divided by the initial droplet diameter, d. The average droplet spacing is calculated as (1/N~/a). The value of nondimensional droplet spacing, t/d, at the propagation limit, which is simply called the critical droplet spacing, increases at a very small rate with increasing initial droplet diameter. This increase, if any, is much smaller than the increase that should occur in the range of droplet size below 40-1xminitial diameter, since on the basis of the data in Table I the critical droplet spacing is estimated to tend to about 20 for both n-decane and n-dodecane at d = 0 or complete vaporization. The variation in the critical droplet spacing with the initial droplet diameter is consistent with the disproportional relation between the size of the hot-gas zone and the droplet diameter in single-droplet combustion. The critical droplet spacing is larger for n-decane than
n-decone 80
6o
i--
:
40
i
9
a
0
4
0
4.1. Spark Ignition of Fuel Clouds The propagation limit of droplet-air systems is very sensitive to the ignition source employed. A small city gas diffusion flame, used as an ignitor in the early stage of the present study, was sometimes less effective than an electric spark in igniting smaller droplets. Such droplets are more likely to be entrained by the convection current due to the open flame before they can ignite. The high temperature and rapid heat release of a spark shorten the heating-up period of the droplets and favor their ignition. The only problem associated with spark ignition is that droplet spacing is not always very small compared to the dimension of the spark even in the propagation limits. This means that droplets are not always in the effective region of the spark. The probability of flame propagation obtained by single sparks, Pob, may be given by the product, P~g P,,,, where P,, is the probability that one droplet at least will be ignited, and Pp, is the probability that a propagating flame will be established after ignition. Since P,g is strongly influenced by the number density, P oa is expected to differ appreciably from Pp,, especially near the propagation limits. Some examples of P oh are presented in Fig. 7, where P o~ actually increases but hardly approaches 100% or even 90% with increasing N. If the curves were steep enough with respect to N, 50% points, for example, could be used as a measure of the propagation limit. To obtain a more realistic value of Pp, from Pob, the dependence of P,~ on N is estimated using a simple model, where droplets are assumed to be located at every node of an orthogonal lattice with an average spacing L A typical value of P~ based on such a model is also shown in Fig. 7. Comparison of P~gand Pos in this figure suggests that the increase
o 08
20
4. Discussion
1~
I.OF
I~
t
i
80
12o
120
i
160
d, pm Fie. 6. Nondimensional droplet spacing lid vs. droplet size d. n-Decane.
~176
~
io
,6o
,~o
N , om"3
FIG. 7. Variation of P~g and P,,h with N for singlespark method Kerosene.
366
COMBUSTION OF DROPLETS AND SPRAYS
of Pp, with N is more than that of P,,b in single sparks. As the number of sparks passed in one trial is increased, P~g increases towards unity, and Pub obtained with successive sparks is expected to approach P,r. 4.2. Propagation Limit of Fuel Clouds In droplet-air systems, burning droplets act as ignition sources for neighboring droplets. Thus, the droplet spacing rather than the fuel concentration has a predominant influence on the propagation limit. Some investigators studied the propagation and appearance of flame in one-dimensional droplet arrays. Reichenbach et al lo~showed that the immersion depth in the hot-gas zone is important for ignition and flame propagation. It was shown by Iinuma that air flow in the direction of flame propagation shortens the propagation time." The estimated critical droplet spacing based on [inuma's results is several times smaller than that obtained in the present study. Under gravity the hot-gas zone develops upwards, and hence upward propagation is easier than horizontal propagation. Nuruzzaman et al ~2~established stationary flames in single streams of free-falling fuel droplets. The maximum value of the critical droplet spacing is estimated to be about 20 for kerosine. In the present study, the direction of ignition is random. This may explain the fact that the values of critical droplet spacing in one-dimensionalarrays are relatively small. Isoda and Kumagai13~showed that the maximum ratio of
n -decone " ' ' ~
hot-gas zone diameter to droplet diameter is around 30 for n-heptane. The order-of-magnitude agreement with the values of critical spacing in the present study seems meaningful. Figure 8 compares the results of the present study with those for tetraline droplets of smaller sizes.8't4~ The gradual change for larger droplet sizes is due to the effect of gravity on the shape and size of the flame and the hot-gas zone of burning droplets.
5. Conclusions 1) The propagation limit of droplet-air systems is very sensitive to the method of ignition, especially for small droplets. 2) The transition from the normal type of premixed gas ignition to relay ignition occurs for a range from a,few micrometers to about 40 vtm in initial droplet diameter. This brings about an appreciable reduction in the critical fuel concentration. 3) With increasing droplet diameter from about 40 Ixm, the critical fuel concentration decreases gradually and the critical number density decreases sharply, while the critical droplet spacing increases slightly. 4) The volatility of the fuel has an appreciable influence on the limit of flame propagation in droplet-air systems. REFERENCES 1. HEDLEY,A. B., NURUZZAMAN,A. S. M. ANDMARTIN, G. F.: J. Inst. Fuel. 44, 38 (1971). 2. WILLIAMS, A.: Combustion and Flame, 21, 1
.........
(1973). 3. HAYASHI,S. AND KUMAGAI,S.: Fifteenth Sympo-
dode6ane
sium (International) on Combustion, p. 445, The 2O o
Combustion Institute, 1975. l
I0 5O
I
4. HAYASHI,S. AND KUMAGAI,S.: Archiwum Termodynamik i Spalani. 6, 479 (1975). 5. HAYASHI,S., KUMACAI,S. ANDSAKAl,T.: Combustion Science & Technology. 15, 169 (1977). 6. WALTON,W. H. ANDPREWETT, W. C.: Proc. Phys. Sue. 62-B, 341 (1949). 7. HAYASHI, S.: Flame Propagation in DropletVapor-Air Mixtures, Ph.D. Thesis, University of
I
\ \ 3o
'\ tetraline
\
\
20 I
Tokyo, 1975. 8. BURCOYNE,J. H. ANn COHEN, L.: Proc. Roy. Soc. A-225, 375 (1954).
n-dodecane
9. WILLIAMS, F. A.: Progress in Astronautics and
n-dec~e" . . . . . . . . .
o
0
I
40
I
BO d,pm
I
120
160
Fit.. 8. Propagation limits in terms of critical droplet spacing and critical fuel concentration vs. droplet size d.
Rocketry (L. E. Bollinger et al., Ed.), Vol. 2, p. 229, Academic Press, 1960. 10. REICHENBACH,R., SQUIRES,n . AND PENNER, S. S.: Eighth Symposium (International) on Combustion, p. 1068, The Combustion Institute, 1961.
11. hNUMA, K.: Combustion and Flame, 6, 127 (1962).
F L A M E P R O P A G A T I O N IN L O W - V O L A T I L I T Y F U E L C L O U D S
12, NURUZZAMAN,A. S. M., HEDLEu A. B. AND BEER, ]. B.: ]. Inst. Fuel. 43, 301 (1970). 13. ISODA, H. ANO KUMAGM, S.: S e v e n t h S y m p o s i u m (International) on C o m b u s t i o n , p. 523, T h e
367
C o m b u s t i o n Institute, 1959.
14. WILLIAMS, A.: O x i d a t i o n a n d C o m b u s t i o n Rev i e w s (C. F. T i p p e r , Ed.), Vol. 3, p. 1, Elsevier, 1968.
COMMENTS R. L. Rogers, IC1 Organics Division, England. As the a u t h o r s p o i n t out, their f i n d i n g s that the lower f l a m m a b i l i t y limits of f u e l / a i r m i x t u r e s m a y be s u b s t a n t i a l l y decreased if t h e fuel is in the form of d r o p l e t s rather t h a n v a p o r will lead to a s e r i o u s alteration in the interpretation of the e x p l o s i o n h a z a r d s of mists. H o w e v e r in the evaluation of data w h e r e droplets fall t h r o u g h stationary air into the f l a m e front it is essential that a true rather t h a n a static f u e l / a i r c o n c e n t r a t i o n will be d e t e r m i n e d ) T h u s B u r g o y n e 2 h a s d e f i n e d the kinetic concentration of a mist as the ratio of the rates of arrival o f l i q u i d air in the c o m b u s t i o n zone. I n order that their results m a y therefore be of m o r e general use, c o u l d the a u t h o r s please e s t i m a t e the s e d i m e n t a t i o n velocity of the droplets, the velocity a n d direction of the f l a m e front in their investigation a n d t h u s calculate the kinetic or true concentration of the droplet air m i x t u r e s u n d e r l i m i t i n g conditions.
REFERENCES
Is. J, C()()K, C, F. CULLLSANO A. J. GoorJ. Combustion and Flame 30, 3 0 9 - 3 1 7 (1977). 2BuReOYN~:, J. H. Proc. (2nd) S y m p . C h e m . Process H a z a r d s Spec. Ref. P l a n t D e s i g n . M a n c h e s t e r , 1963, p. 1.
Author's Reply. T h e s e d i m e n t a t i o n velocity of droplets is e s t i m a t e d to be a b o u t 3.6 - 58 c m / s e c by Stokes's e q u a t i o n for the droplet d i a m e t e r of 40 160 p.m. T h e kinetic c o n c e n t r a t i o n d e f i n e d by B u r g o y n e c o u l d be also calculated. Your k i n d c o m m e n t is appreciated, b u t the a u t h o r s t h i n k that t h e u s e of the kinetic c o n c e n t r a t i o n m a y not n e c e s s a r i l y m a k e their results more g e n e r a l at the l i m i t i n g c o n d i t i o n s , w h e r e the c l o u d s are too dilute to f o r m a " f l a m e front" a n d the direction o f discrete f l a m e p r o p a g a t i o n is r a n d o m .
The C o m b u s t i o n Institute, 1981
L I M I T I N G F A C T O R OF F L A M E P R O P A G A T I O N IN LOW-VOLATILITY FUEL CLOUDS S. HAYASHI
National Aerospace Laboratory, lindaiii-machi, Chofu, Tokyo, 1apan T. OHTANI
Fuel Research Laboratory, NYK Line, Naka-ku, Yokohama, 1apan AND
K. IINUMA AND S. KUMAGAI*
Department of Aeronautics, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, 1apan The limit of flame propagation, in terms of the number density or spacing of droplets and fuel concentration, in low-volatility fuel clouds has been determined, varying the droplet size. The stream of mono-sized droplets, produced by a rotating-disk atomizer, enters d o w n w a r d into the test section. The droplet size and n u m b e r density are controlled by adjusting the rotating speed of the atomizer and the fuel feed rate, respectively. With increasing n u m b e r density for a given droplet size, the following occur in sequence: droplet ignition with mispropagation; upward propagation of isolated diffusion flames surrounding the droplets; flame spread over the stream cross section. As the droplet size is increased, the critical n u m b e r density for propagation decreases rapidly, whereas the droplet spacing increases at a very small rate according to a mathematical relation. The critical fuel concentration decreases sharply with increasing droplet size in the range from a few I~m to about 40 ~m, where transition from ignition of the premixed gases to relay ignition of the neighboring droplets occurs, and then decreases moderately toward less than half of the lower flammability limit. This creates a serious explosion hazard, since a fuel-air mixture which is not flammable in the premixed state, may become flammable through condensation of the fuel into droplets.
1. Introduction
one extreme model of fuel spray combustion, although the actual flame is supported by a mixture of fuel droplets, fuel vapor and air. Studies in this field will be useful for understanding the mechanism of spray combustion and will yield fundamental knowledge on the prevention of explosions in oil mists. In the present study, the propagation limits in droplet-air systems of low-volatility fuels have been determined with respect to the droplet-size effect.
Intensive experimental and theoretical investigations on the combustion of single fuel droplets have been carried out, and the fundamental features are now fairly well understood. ~'2) As a next step, the study of the combustion of fuel clouds or droplet-air systems is essential in order to understand the much more complicated process of spray combustion. Along this line, the authors have been studying flame propagation and flame structure in droplet-vapor-air systems. 3'4's) As shown in previous studies, prevaporization as well as droplet size has a predominant effect on the combustion characteristics. The droplet-air system of a low-volatility fuel is
2. Experimental Apparatus and Procedure Figure i shows a schematic drawing of the experimental apparatus, which consists of a rotating-disk atomizer, and settling and test sections. A fiat disk (2) of 100-mm diameter with a sharp edge is driven
*Professor Emeritus. 361
362
COMBUSTION OF DROPLETS AND SPRAYS
T |
~E ~E
l oD_ _7_ Flc. 1. Experimental apparatus. directly by an ac electric motor (3). A fuel (1) is fed to the center of the rotating disk from a 0.8-mm inner diameter nozzle through a rotometer. The atomizer housing is loosely connected to a cylinder (8) which serves as the settling section through a port with a 20-mm diameter throat, whose axis coincides with a vertical line tangent to the disk periphery. The fuel is atomized into droplets in all directions and every droplet that reaches the wall adheres there. Therefore, only a fraction of the atomized fuel enters the settling section. The fuel that adheres to the wails of the atomizer housing and the connecting port is drained, to keep it from flowing into the test section. The droplets originally produced by the atomizer consist of two groups: monosized droplets and satellite droplets of much smaller sizes. The latter are successfully eliminated by sectioning off part of the atomized fuel, by means of a pump and a collector (4), through 2-mm diameter holes arranged circularly on the housing wall. The size of droplets is controlled by adjusting the rotating speed of the disk, whereas their number density is varied by changing the fuel feed rate. The dependence of the initial droplet diameter, d, determined by the immersion method using silicone oil, on the rotating speed, n, reduces to d o: n -1, showing the same trend as the result obtained by Walton and Prewett. ~ After passing through the settling section, the stream of droplets enters into test section through a rectangular channel (9), 25 mm wide and 10 mm deep. A spark gap for ignition (13) (5 mm in width), formed by 0.5-mm thick electrodes, is placed 40 mm below the exit of the channel along the center line of the stream cross section. A pair of glass windows are fitted in to the wall of the test section,
and are used to photograph the droplets and flames with a camera (12). The number density of the droplets in the test section is determined by shadow photography. The light beam from the spark gap (10) is collimated with a lens system (11) to illuminate the droplet stream through the window. In the preliminary tests, the spatial distribution of the droplets along the light path was found to be practically uniform. It was also shown that the 10-mm thick droplet stream is thin enough for all the droplets in the light path to be recorded. The number density is determined by counting the number of droplets in a sampling volume, 15 mm wide, 20 mm high and 10 mm deep. In the case of dilute clouds, for which this sampling volume has often been found to be too small, larger sampling volumes are used. Experiments are conducted with n-decane and n-dodecane, keeping the air in the test section practically stationary. The vapor pressures of the fuels at the experimental temperature (20~ are listed in Table I, together with some physical properties and the limits of flammability. Since n-decane is more volatile than n-dodecane, the effect of prevaporization on the propagation limits of the droplet-air systems is expected to be larger for the former. One trial in the propagation-limit tests consists of eight spark passages at a rate of 34 sparks per second. This number of repetitions has been selected so that one droplet at least can be ignited, even under conditions where no flame propagation is established. Any flame that enters the atomizer housing and becomes stabilized at the exit is extinguished by injecting nitrogen (7), and the gas in the apparatus is purged by fresh air (6) before the next trial.
3. Experimental Results 3.1. Fuel Clouds and Flames
The results of all trials can be classified into three modes: (i) mispropagation--up to a certain value the number density is not sufficiently high for flames to propagate through the fuel cloud even though there is ignition of individual droplets, (ii) isolated blue-flame propagation--as the number density increases to a certain value, a mass of flame consisting of isolated blue diffusion flames surrounding the droplets propagates upwards, often in a column extending from the spark gap, (iii) interacting yellow-flame propagation--as the number density increases further, the flame becomes yellow and usually spreads over the cross section of the droplet stream. Figure 2 shows the fuel clouds in the test section. In determining the propagation limits, one droplet
FLAME PROPAGATION IN LOW-VOLATILITY F U E L CLOUDS
363
TABLE I Properties of fuels
Fuel
Density g/cm 3
Boiling point ~
Vapor pressure at 20~ mmHg
Stoichiometric mixture vol%
C lo H 22 C 12H26
0.75 0.75
174.1 216.3
1.3 0.1
1.33 1.11
at least must exist in the region of the ignition spark. However, at larger droplet sizes, the droplet spacing at which a propagating flame can be established is not as small, compared with the size of the ignition spark. The successive-spark method is convenient from this point of view. Direct photographs (Fig. 3) show that some droplets ignite and burn in isolated diffusion flames ahead of a continuous flame, which in reality consists of many small flames supported by individual droplets. In the case of dense clouds, these flames interact to form a homogeneous flame similar to a premixed flame. 4'7~ For much less volatile fuels, discretness of the flames becomes apparent, as shown for tetraline droplets 20-40 Ixm in diameter. 7'~ The flame shown in Fig. 3 is quite luminous, since the fuel concentration is rather higher than the propagation limit. At fuel concentrations near the propagation limits, a blue flame is seen on each
: /ji(i~!84184 il/
n -CI2H26 d = 164 lath
Limit of flammability vol% mg/ltr 0.75 0.60
48 46
droplet. The flame speed increases especially in the early stage of propagation. 3.2. Propagation Limit
Critical Number Density Figure 4 shows the results of propagation limit tests in terms of the number density for n-decane. Mispropagation, isolated blue-flame propagation and interacting yellow-flame propagation are represented by solid circles, triangles and hollow circles, respectively. Flame propagation becomes possible, when the number density increases to a certain value, and the value at the propagation limit, called the critical number density, decreases sharply with increasing initial droplet diameter. Though there is no qualitative difference between the results for n-decane and n-dodecane the critical number den-
,
n -CtoH22 I 0 0 #rn FIG. 2. Shadow photographs of droplet clouds.
n- CI2H26 6 4 pm
364
COMBUSTION OF DROPLETS AND SPRAYS
Time
n-decane
60
oo o
40
o
o
o o
o
8
o o
o o
i
o
~ 2o
o
o
o
o
o
8
O
o o
9 o
9
J
io
40
e
~l 8
80
! ", L IZO d , pm
i I
I
I
160
F](.. 5. Effects of fuel concentration and droplet size d on modes of flame propagation, n-Decane. Fie. 3. Direct photographs of flame propagation in n-decane droplet-air system. Frame interval, 0.005 SeC.
sity for the former is lower than that for the latter at any, given droplet size. Critical Fuel Concentration It is to be expected that if the mechanism of flame propagation in a droplet-air system is similar to that in a premixed gas, the propagation limit will occur at a fuel concentration corresponding to the lower limit of flammability of the premixed gas. From this point of view, the results are expressed in terms of fuel concentration (Fig. 5). As far as the present tests are concerned, the fuel concentration at the propagation limit, called the critical fuel concentra-
I
0 0
600
0
n-decane
4o0
?E
/.
0
0
0 0
0
0 o 0
9
0
i
4O
e 9
I
8TO
' 120
' 160
d , pm
FI(,. 4. Effects of number density N and size d of droplet on modes of flame propagation, n-Decane.
tion, decreases moderately with increasing initial droplet diameter. Droplet-air systems of n-decane give a reduction in the critical fuel concentration to about 13 mg/ltr for an initial droplet diameter of 55 p.m, for example, from the limit of flammability of 48 mg/ltr (53~ (see Table I). For droplet-air systems of n-dodecane also, the corresponding reduction amounts to more than 50% for initial droplet diameters larger than 40 p.m. This fact suggests a serious problem with respect to explosion hazards, since a fuel-air mixture, even though it is not flammable in the premixed state, may become flammable when the vapor condenses into rather large droplets. The discrepancy between the propagation limits for premixed gases and for droplet-air mixtures can be attributed to the difference in the mechanism of flame propagation between the two systems. Since fine droplets vaporize readily to form a mixture with air prior to ignition, the fuel cloud including such droplets is practically the same as the corresponding premixed gas. Therefore, the propagation limit is expected to appear at a fuel concentration corresponding to the limit of flammabilityof the premixed gas of the same fuel. As the droplet size increases, the degree of prevaporization diminishes and flame propagation occurs through successive ignition of unburnt droplets by the hot gas surrounding neighboring burning droplets. Thus, for the fuel clouds involving large droplets, no flame propagates if the average droplet spacing exceeds a critical value. The limiting droplet size for complete vaporization in the preheat zone of the usual hydrocarbon flames is estimated to be of the order of a few micrometers, 5's'9~and the estimated degree of vaporization is rather small for a droplet of 40-1xm initial diameter. The sharp decrease in the critical fuel concentration is consistent with the transition of
FLAME PROPAGATION IN LOW-VOLATILITY FUEL CLOUDS the mechanism of flame propagation in this range of droplet diameter.
365
for n-dodecane over the whole range of initial diameters tested, which is attributed to the difference in volatility.
Critical Droplet Spacing Consideration on the propagation limit in the preceeding paragraph and some photographic evidences in the present and previous experiments suggest that droplet spacing is probably a more appropriate concept than fuel concentration for characterizing the propagation limit of fuel clouds with droplets larger than about 40 ~m in initial diameter. Figure 6 shows the results of propagation limit tests in terms of nondimensionaldroplet spacing, viz. the average droplet spacing, l, divided by the initial droplet diameter, d. The average droplet spacing is calculated as (1/N~/a). The value of nondimensional droplet spacing, t/d, at the propagation limit, which is simply called the critical droplet spacing, increases at a very small rate with increasing initial droplet diameter. This increase, if any, is much smaller than the increase that should occur in the range of droplet size below 40-1xminitial diameter, since on the basis of the data in Table I the critical droplet spacing is estimated to tend to about 20 for both n-decane and n-dodecane at d = 0 or complete vaporization. The variation in the critical droplet spacing with the initial droplet diameter is consistent with the disproportional relation between the size of the hot-gas zone and the droplet diameter in single-droplet combustion. The critical droplet spacing is larger for n-decane than
n-decone 80
6o
i--
:
40
i
9
a
0
4
0
4.1. Spark Ignition of Fuel Clouds The propagation limit of droplet-air systems is very sensitive to the ignition source employed. A small city gas diffusion flame, used as an ignitor in the early stage of the present study, was sometimes less effective than an electric spark in igniting smaller droplets. Such droplets are more likely to be entrained by the convection current due to the open flame before they can ignite. The high temperature and rapid heat release of a spark shorten the heating-up period of the droplets and favor their ignition. The only problem associated with spark ignition is that droplet spacing is not always very small compared to the dimension of the spark even in the propagation limits. This means that droplets are not always in the effective region of the spark. The probability of flame propagation obtained by single sparks, Pob, may be given by the product, P~g P,,,, where P,, is the probability that one droplet at least will be ignited, and Pp, is the probability that a propagating flame will be established after ignition. Since P,g is strongly influenced by the number density, P oa is expected to differ appreciably from Pp,, especially near the propagation limits. Some examples of P oh are presented in Fig. 7, where P o~ actually increases but hardly approaches 100% or even 90% with increasing N. If the curves were steep enough with respect to N, 50% points, for example, could be used as a measure of the propagation limit. To obtain a more realistic value of Pp, from Pob, the dependence of P,~ on N is estimated using a simple model, where droplets are assumed to be located at every node of an orthogonal lattice with an average spacing L A typical value of P~ based on such a model is also shown in Fig. 7. Comparison of P~gand Pos in this figure suggests that the increase
o 08
20
4. Discussion
1~
I.OF
I~
t
i
80
12o
120
i
160
d, pm Fie. 6. Nondimensional droplet spacing lid vs. droplet size d. n-Decane.
~176
~
io
,6o
,~o
N , om"3
FIG. 7. Variation of P~g and P,,h with N for singlespark method Kerosene.
366
COMBUSTION OF DROPLETS AND SPRAYS
of Pp, with N is more than that of P,,b in single sparks. As the number of sparks passed in one trial is increased, P~g increases towards unity, and Pub obtained with successive sparks is expected to approach P,r. 4.2. Propagation Limit of Fuel Clouds In droplet-air systems, burning droplets act as ignition sources for neighboring droplets. Thus, the droplet spacing rather than the fuel concentration has a predominant influence on the propagation limit. Some investigators studied the propagation and appearance of flame in one-dimensional droplet arrays. Reichenbach et al lo~showed that the immersion depth in the hot-gas zone is important for ignition and flame propagation. It was shown by Iinuma that air flow in the direction of flame propagation shortens the propagation time." The estimated critical droplet spacing based on [inuma's results is several times smaller than that obtained in the present study. Under gravity the hot-gas zone develops upwards, and hence upward propagation is easier than horizontal propagation. Nuruzzaman et al ~2~established stationary flames in single streams of free-falling fuel droplets. The maximum value of the critical droplet spacing is estimated to be about 20 for kerosine. In the present study, the direction of ignition is random. This may explain the fact that the values of critical droplet spacing in one-dimensionalarrays are relatively small. Isoda and Kumagai13~showed that the maximum ratio of
n -decone " ' ' ~
hot-gas zone diameter to droplet diameter is around 30 for n-heptane. The order-of-magnitude agreement with the values of critical spacing in the present study seems meaningful. Figure 8 compares the results of the present study with those for tetraline droplets of smaller sizes.8't4~ The gradual change for larger droplet sizes is due to the effect of gravity on the shape and size of the flame and the hot-gas zone of burning droplets.
5. Conclusions 1) The propagation limit of droplet-air systems is very sensitive to the method of ignition, especially for small droplets. 2) The transition from the normal type of premixed gas ignition to relay ignition occurs for a range from a,few micrometers to about 40 vtm in initial droplet diameter. This brings about an appreciable reduction in the critical fuel concentration. 3) With increasing droplet diameter from about 40 Ixm, the critical fuel concentration decreases gradually and the critical number density decreases sharply, while the critical droplet spacing increases slightly. 4) The volatility of the fuel has an appreciable influence on the limit of flame propagation in droplet-air systems. REFERENCES 1. HEDLEY,A. B., NURUZZAMAN,A. S. M. ANDMARTIN, G. F.: J. Inst. Fuel. 44, 38 (1971). 2. WILLIAMS, A.: Combustion and Flame, 21, 1
.........
(1973). 3. HAYASHI,S. AND KUMAGAI,S.: Fifteenth Sympo-
dode6ane
sium (International) on Combustion, p. 445, The 2O o
Combustion Institute, 1975. l
I0 5O
I
4. HAYASHI,S. AND KUMAGAI,S.: Archiwum Termodynamik i Spalani. 6, 479 (1975). 5. HAYASHI,S., KUMACAI,S. ANDSAKAl,T.: Combustion Science & Technology. 15, 169 (1977). 6. WALTON,W. H. ANDPREWETT, W. C.: Proc. Phys. Sue. 62-B, 341 (1949). 7. HAYASHI, S.: Flame Propagation in DropletVapor-Air Mixtures, Ph.D. Thesis, University of
I
\ \ 3o
'\ tetraline
\
\
20 I
Tokyo, 1975. 8. BURCOYNE,J. H. ANn COHEN, L.: Proc. Roy. Soc. A-225, 375 (1954).
n-dodecane
9. WILLIAMS, F. A.: Progress in Astronautics and
n-dec~e" . . . . . . . . .
o
0
I
40
I
BO d,pm
I
120
160
Fit.. 8. Propagation limits in terms of critical droplet spacing and critical fuel concentration vs. droplet size d.
Rocketry (L. E. Bollinger et al., Ed.), Vol. 2, p. 229, Academic Press, 1960. 10. REICHENBACH,R., SQUIRES,n . AND PENNER, S. S.: Eighth Symposium (International) on Combustion, p. 1068, The Combustion Institute, 1961.
11. hNUMA, K.: Combustion and Flame, 6, 127 (1962).
F L A M E P R O P A G A T I O N IN L O W - V O L A T I L I T Y F U E L C L O U D S
12, NURUZZAMAN,A. S. M., HEDLEu A. B. AND BEER, ]. B.: ]. Inst. Fuel. 43, 301 (1970). 13. ISODA, H. ANO KUMAGM, S.: S e v e n t h S y m p o s i u m (International) on C o m b u s t i o n , p. 523, T h e
367
C o m b u s t i o n Institute, 1959.
14. WILLIAMS, A.: O x i d a t i o n a n d C o m b u s t i o n Rev i e w s (C. F. T i p p e r , Ed.), Vol. 3, p. 1, Elsevier, 1968.
COMMENTS R. L. Rogers, IC1 Organics Division, England. As the a u t h o r s p o i n t out, their f i n d i n g s that the lower f l a m m a b i l i t y limits of f u e l / a i r m i x t u r e s m a y be s u b s t a n t i a l l y decreased if t h e fuel is in the form of d r o p l e t s rather t h a n v a p o r will lead to a s e r i o u s alteration in the interpretation of the e x p l o s i o n h a z a r d s of mists. H o w e v e r in the evaluation of data w h e r e droplets fall t h r o u g h stationary air into the f l a m e front it is essential that a true rather t h a n a static f u e l / a i r c o n c e n t r a t i o n will be d e t e r m i n e d ) T h u s B u r g o y n e 2 h a s d e f i n e d the kinetic concentration of a mist as the ratio of the rates of arrival o f l i q u i d air in the c o m b u s t i o n zone. I n order that their results m a y therefore be of m o r e general use, c o u l d the a u t h o r s please e s t i m a t e the s e d i m e n t a t i o n velocity of the droplets, the velocity a n d direction of the f l a m e front in their investigation a n d t h u s calculate the kinetic or true concentration of the droplet air m i x t u r e s u n d e r l i m i t i n g conditions.
REFERENCES
Is. J, C()()K, C, F. CULLLSANO A. J. GoorJ. Combustion and Flame 30, 3 0 9 - 3 1 7 (1977). 2BuReOYN~:, J. H. Proc. (2nd) S y m p . C h e m . Process H a z a r d s Spec. Ref. P l a n t D e s i g n . M a n c h e s t e r , 1963, p. 1.
Author's Reply. T h e s e d i m e n t a t i o n velocity of droplets is e s t i m a t e d to be a b o u t 3.6 - 58 c m / s e c by Stokes's e q u a t i o n for the droplet d i a m e t e r of 40 160 p.m. T h e kinetic c o n c e n t r a t i o n d e f i n e d by B u r g o y n e c o u l d be also calculated. Your k i n d c o m m e n t is appreciated, b u t the a u t h o r s t h i n k that t h e u s e of the kinetic c o n c e n t r a t i o n m a y not n e c e s s a r i l y m a k e their results more g e n e r a l at the l i m i t i n g c o n d i t i o n s , w h e r e the c l o u d s are too dilute to f o r m a " f l a m e front" a n d the direction o f discrete f l a m e p r o p a g a t i o n is r a n d o m .