Observations on the burning of droplets in the absence of buoyancy

C O M B U S T I O N AND FLAME 38: 111-I 19 (1980)

111

Observations on the Burning of Droplets in the Absence of Buoyancy B R I A N K N I G H T * and F O R M A N A. W I L L I A M S * *

Department of Applied Mechanics and EngineeringSciences. Universityof California, San Diego, La Jolla, California 92093

Experimentalresultsare reportedon the burningof freedropletsof heptaneand deeanein oxygen-nitrogenatmospheres. The burning occurred in a freelyfallingchamberproviding2.2 see of negligiblegravity.Enhanced burningratesand a phenomenon of flash extinctionwereobservedand attributedto thermophoreticbuildupand ignitionof carbonnearthe droplet surface. INTRODUCTION The study of basic combustion processes often involves theoretical idealizations which enable complex phenomena to be reduced to simpler, more tractable configurations conducive to analytical description. Of considerable aid in the understanding of certain phenomena is the availability of experimental results which can be used to test theoretical results. Accurate comparison between theory and experiment may be facilitated by performing experiments under conditions that conform to the approximations made in the development of the theory. Idealizations common to theories of droplet burning include the approximation of spherical symmetry. Experimental study of an individual droplet, however, has usually necessitated the support of the droplet on the end of a fine quartz fiber [1], and resulting flows are manifestly nonspherical. The hot flame in a gravitational field causes gases to rise buoyantly, establishing an axisymmetric flow under natural convection, thereby violating the theoretical assumption. From a fundamental viewpoint, underlying physical and chemical phenomena, such as the effects of chemical kinetics, could be studied more * Current address: United Technologies Research Center, East Hartford, CT. ** Current address: Visiting Goddard Professor, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ. Copyright © 1980 by The Combustion Institute Published by Elsevier North Holland, Inc., 52 Vanderbilt Avenue, New York, NY 10017

readily if the complicating influence of buoyancy were removed. Reduction of the influence of buoyancy upon the droplet burning has been attempted in the past by working with small droplets projected into a hot-gas stream [2-5], and by burning droplets at reduced pressure [6]. However, neither method provided complete data for the life of the burning droplet without effects of droplet supports on the flow field x. The only other way to decrease buoyancy is to reduce or eliminate gravity. Elimination of gravitational effects on droplet combustion has been pioneered by Kumagai [7] who studied the phenomenon occurring in a freely falling chamber. In his experiments, zero gravity was achieved for less than 1 sec, so that burning to completion in spherical symmetry never occurred. It was found that unsteady conditions prevailed in the gas during the entire observation time. With the hope of achieving quasisteady burning in the gas phase to droplet sizes so small that extinction could be observed, an experimental apparatus was designed and constructed to observe 1 At reduced pressures, suspended droplets have been employed; the entire history has been photographed, but the support influenced the burning. Recent work on projected droplets is quite promising [3, 4] ; effects of supports are absent and droplets may be photographed at any stage of burning, but the distance over which a droplet moves is so great that the entire burning history of a single droplet has not been recorded in a motion-picture film with good resolution.

0010-2180/80/050111+9501.75

112 droplet burning in the absence of buoyancy for a longer period of time than has previously been feasible. EXPERIMENTAL APPARATUS AND PROCEDURE The test apparatus was designed to confine a droplet in a gravity-free environment to a prespecified location without there being solid objects (e.g., glass fibers, ignition sources) near it to destroy the symmetry. A schematic of the apparatus is shown in Fig. 1. Basically, the apparatus consists of a drop frame which contains the test chamber, ignition system, batteries, electrical control system, and high-speed motion-picture camera. The drop frame is enclosed within an air-drag shield which serves to eliminate forces on the drop frame due to viscous drag from the atmosphere during free fall. Combustion of the fuel droplet under study takes place in the test chamber, a 32 X 25 × 28 cm box having Plexiglas walls 1.9 cm thick. The chamber can be evacuated and filled with any desired gas mixture from below atmospheric pressure to 2 atm. The use of clear Plexiglas enables the camera to photograph the burning within the chamber. To achieve a gravity-free environment during burning, the entire assembly consisting of the drop frame and air-drag shield is released into free fall. The two components fall as separate units, so that during the descent the drop frame will fail slightly faster than the drag shield due to the drag forces on the shield. During a 24-m fall, the drop frame will move 20.3 cm relative to the drag shield, so that upon impact the frame will rest upon the floor of the drag shield. Measured forces of 10--6 g on the drop frame are typical with this arrangement. To allow for the relative movement, the drag shield rests upon spacers which separate it from the drop frame and provide 20.3 cm clearance between the two units. The free-fall facility was designed and constructed by personnel from the NASA Lewis Research Center, where it has been employed in many other reduced-gravity experiments. The heart of the present apparatus is the droplet release mechanism, contained within the Plexi-

B. KNIGHT and F. A. WILLIAMS glas combustion chamber. This mechanism was designed to release the droplet at a specified point and provide an ignition source. As shown in Fig. 2, it consists of a piston contained in a cylinder. Into the piston are inserted a 2-mm-maximumdiameter quartz fiber and a brass push rod. The piston rests against a helical spring, and when the spring is compressed, is held in place by an electromagnetically actuated catch. A microswitch on an adjustable support is used to activate the ignition source, an automotive induction coil powered by a 4300-#F 50-V dc capacitor. The secondary voltage from the coil is caused to arc across the fine copper electrodes spaced about 1.5 mm apart at the tip of the quartz fiber. The electrodes are mounted on a sliding track which is held in place by a second electromagneticaUy actuated catch, against the tension of a stretched helical spring. Prior to a test, the piston and electrodes are set into position, and the chamber is evacuated and refilled with a desired gas mixture. A remotely controlled syringe system is used to mount a droplet on the end of the quartz fiber. The drop assembly is suspended by an overly stressed piano wire at the top of the drop tower, an eightstory structure. To initiate a test, the camera mounted on the drop frame is started at a rate of 400 frames per second. The relay securing the droplet-release piston is activated and the piston begins an upward motion, thereby pulling the fiber out of the droplet but imparting an upward vertical velocity to it. Under the influence of gravity, the droplet continues moving upward but is continually decelerated until it reaches a point of zero velocity. At this time, timers in the control panel activate a pneumatic cutter which severs the wire supporting the drop assembly, releasing it into free fall. The helical spring pushes the piston upward so that the push rod trips the microswitch which activates the spark system and releases the electrode catch. The electrodes then retract away from the droplet. In this manner, the droplet is intended to be in free fall, stationary with respect to the test chain. ber and camera, and there are no physical objects in contact with it to disturb the burning process. After 2.2 see of free fall, the drop assembly

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114

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With this apparatus, an experimental program was conducted using n-heptane and n-decane as the fuels to observe the burning of single hydrocarbon-fuel droplets in a buoyancy-free environment. In twenty-two tests, burning was achieved in atmospheres consisting of 20, 25, 30, 50, and 80 % oxygen by volume diluted with nitrogen at pressures of 1/2 and 1 atm. Data from the experiments, obtained from the 16-mm high-speed motion-picture camera, showed the time history of the droplet and flame diameters. In tests where decane was used as the fuel, a highly luminous flame surrounded the droplet and at oxygen mass fractions equal to or greater than 30% was so intense that the surface of the droplet was not visible without backlighting. Tests with heptane produced a much less luminous flame, but the droplet surface was still obscured when the oxygen mass fraction exceeded 50%. The release of the droplet using the fiberwithdrawal technique described above provided free droplets, but in no test were purely stationary droplets ignited and photographed. Critical timing accuracy is needed with this technique so that the drop frame is released into free fall precisely when the droplet reaches the apex of its trajectory. Deviation from this timing results in a droplet that is moving at a constant velocity, either up or down depending upon whether the drop frame is released too soon or too late. The difficulty in achieving accurate timing increases with the weight of the package to be released and therefore with the intended free-fall time. The timing inaccuracies within the system employed could not be resolved; all data obtained involved droplets moving between 0.8 and 3.6 cm/sec relative to the camera. The moving droplets did not remain in the camera's field of view for the entire 2.2 sec of free fall. However, in several cases droplets

115 bounced off the walls of the chamber so that they could be viewed for intervals during the 2.2 sec free fall when they passed slowly through the camera's field of view. In three tests with decane buring in 50% 02 in N2, small satellite droplets were ejected from the main droplet due to the action of the fiber withdrawal. These satellites were 600 tam in diameter and were observed to bum to extremely small diameters. These droplets were moving at low velocities (0.8 cm/sec) and were so small in diameter that the effect of their motion through the chamber upon the flame shape was negligible. For larger droplets moving at higher velocities, the flame was distorted in the expected manner with rather long luminous tails in the droplet's wake. Often luminous carbon particles could be seen in the tail, giving it an elongated spike4ike shape. DROPLET BURNING RATE

Theories of droplet combustion [8] result in an expression for the mass burning rate rh in terms of the ambient and fuel properties, showing it to be proportional to the radius rt of the liquid droplet. The theory agrees approximately with experiments in the sense that the square of the droplet diameter decreases approximately linearly with the time (the "d-square law"). A plot of the droplet diameter squared versus time should result in a straight line whose slope is given by (8#-~u) Ko =

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of liquid fuel vaporized at the wet-bulb temperature Tb, Cp represents the mean specific heat for the fuel vapor, p~ is the liquid density at T b, h is the thermal conductivity of the gas, Yo is the oxygen mass fraction and T temperature, sub-

116

B. KNIGHT and F. A. WILLIAMS

script =, denoting conditions in the ambient atmosphere. Data from our experiments were plotted in a linear regression analysis performed to determine the slope of the line of d 2 versus time. Since the droplets were moving, it was expected that the mass evaporation rate would exceed that of a stationary droplet. To correct the theoretical burning rate for forced convection, the results of work by Frdssling [9] were applied to plot "theoretical" data at each measured data point using the measured droplet diameter to determine the droplet Reynolds number Re=, and applying the correction rh/rh o = 1 + 0.276Re..112Sc= 1/a to the theoretical burning rate, where Sc=, is the Schmidt number. Consideration was given to introduction of a correction for radiant energy transfer, but estimates indicated this correction to be negligible. Figure 3 shows the theoretical and experimental results for n-heptane burning in air at 1 atm under zero-gravity conditions. The data plotted cover the time period from 1.36 to 2.16 ~..

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sec after ignition and release into free fall. This particular droplet was moving through the chamber with a constant velocity of 3.6 cm/sec in an upward direction after rebounding from the bottom of the combustion chamber. The slopes of the lines are the theoretical and experimental burningrate constants. Because of the timing error in the package release, many droplets achieved substantial velocities relative to the drop frame. At a large velocity, burning could not be sustained, and the flame was extinguished. Figure 4 shows (Re=,) 1/2 at extinction for n-heptane at various atmospheric compositions. It is interesting to note that the velocity at extinction for Yo2/YN2 = 0.25 at 1 arm was 16 cm/sec, whereas experiments on suspended heptane droplets at 1 g achieved imposed convective velocities above 30 cm/sec without extinction [10]. The supporting fiber may help to stabilize the flame in the earlier experiments. The increase in Re=, at extinction as Yoz/Ylvz increases is qualitatively consistent with theories of extinction by finite-rate chemistry, in view of the greatly reduced chemical reaction time at the elevated flame temperature of the enriched atmosphere. I

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118

B. KNIGHT and F. A. WILLIAMS

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seemed to explode. The diameter of the flame immediately prior to the explosion was 1.5 mm. The time history of the square of the flame diameter is shown in Fig. 6; photographic resolution precluded measurement of droplet diameter. Unusual extinctions of this type were not observed with heptane in any test, including burning in a mixture of 80% 0 z in N z. This type of phenomenon appears likely to necessitate the presence of impurities in the decane with relative concentrations that increase during burning; these impurities may be present initially or may accumulate during the combustion process. DISCUSSION

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FLASH EXTINCTION

As stated above, no droplet was observed to experience spherically symmetrical burning to a diameter so small that f'mite-rate gas-phase combustion kinetics dominated and caused extinction of the flame. However, two tests with decane burning in a mixture having 50% oxygen concentration resulted in an interesting phenomenon which we have termed "flash extinction". Figure 5 shows a detail from the film of one of those tests. As earl be seen, this satellite droplet burned to an extremely small diameter and then

The most likely explanation for both the observed flash extinction and the disagreement between experimental and theoretical values for the burning rate constant is the presence of hot carbon particles in and around the droplet surface. In the fuel-rich region interior to the flame sheet, solid carbon particles are produced through pyrolysis reactions at the elevated temperatures near the flame sheet. The concentration of hot carbon would increase with time of burning and with flame temperature. This is qualitatively consistent with our observations, in that decane droplets burning in 50% 02 in N 2 (with an adiabatic flame temperature of 2856 K) produced a highly luminous flame, while heptane burning in air (adiabatic flame temperature of 2160 K) produced a much less luminous flame. The hot carbon particles could be transported by thermophoresis (Soret-type thermal diffusion of particles smaller than a molecular mean free path) towards the cooler regions near the droplet surface, resulting in increased heat transfer to the droplet with a resulting increase in the evaporation rate. The effects of this carbon production would be felt more strongly late in the droplet's history. In previous droplet experiments in the absence of buoyancy [7], the droplets were not burning for a time sufficient to achieve appreciable carbon buildup. Agreement between theoretical and experimental values for the burning rate were dependent upon the temperature at which the gas and fuel properties were evaluated,

BUOYANCY-FREE DROPLET BURNING usually taken as the arithmetic mean between the ambient and the adiabatic flame temperature. In the present set of experiments, as exemplified by the data shown in Fig. 3, the burning time was effectively quadruple that of previous experiments, and in the last 0.8 see of observed burning, the experimental burning rate exceeds the theoretical rate. This trend was seen in all cases for both fuels studied. It seems likely that the buildup of hot carbon results in increased heat transfer in the later stages of combustion, resulting in increased difference between observed and calculated burning rates. The presence of the hot carbon at the droplet surface might also explain the observed flash extinction. For a small droplet, it may be possible for carbon particles in the surface to be heated to ignition under the conditions existing near the surface (where Yo :/: 0 if f'mite-rate kinetics are considered). This ignition of the carbon would result in a violent superheating of the droplet which would occur very suddenly. The flash extinction was observed only with very small decane droplets, where the rate of carbon production and heat transfer to the droplet would be maximum. The possibility of carbon ignition is consistent with the flame diameter data of Fig. 6, where it can be seen that prior to the flash extinction, the flame diameter decreased sharply, indicating a possible enhanced burning rate and substantial oxygen penetration to the carbon. Carbon production can be seen then as a possibly crucial factor in droplet combustion. The burning time, fuel composition, and atmospheric composition all are factors which affect the production of carbon, whose effect upon the burning rate has not yet been fully demonstrated. This work was supported by NASA under Grant No. NSG 3047. We wish to thank NASA

119 Lewis personnel, notably Tom Cochran and John Haggard, for help and encouragement in this work.

REFERENCES 1. Godsave,G. A. E., Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, Md, 1953, pp. 813-830. 2. Hottel, H. C., Williams, G. C., and Simpson, H. C., Fifth Symposium {International) on Combustion,

Reinhold, New York, 1955, pp. 101-129. 3. Sangiovanni, J. J., and Kesten, A. S., A theoretical and experimental investigation of the ignition of fuel droplets, Combust. Sci. Technol., 16, 59-70 (1977). 4. Lasheras, J. C., Fernandez-Pello, A. C., and Dryer, F. L., Experimental observations of the disruptive combustion of free droplets of multicomponent fuels, Paper No. 79-24, presented at the Spring 1979 Meeting of the Western States Section of the Combustion Institute, Provo, UT, Apr. 24, 1979. 5. Sangiovanni,J. J., and Dodge, L. G., Observations of flame structure in the combustion of monodispersed droplet streams, Seventeenth Symposium (lnternationalJ on Combustion, The Combustion Institute, Pittsburgh, PA, 1979. 6. Law, C. K., and Williams, F. A., Combust. Flame 19, 393--405 (1972). 7. Kumagai, S., Sakai, T., and Okajima, S., Thirteenth Symposium {International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1971, pp. 779-785. 8. Williams, F. A., Combustion Theory, AddisonWesley, Reading, MA, 1965, pp. 47-58. 9. FriSssling, N., Gerlands Beitr. Geophys. 52, 170 (1938). I0. Wise, H. and Agoston, G. A., Burning of liquid droplets, Advances in Chemistry Series, no. 20, Amer. Chem. Soc., Washington, DC, 1958, pp. 116-135.

Received 19 June 1979; revised 15 September 1979