Evaporation characteristics of fuel and multifuel droplets

300

C O M B U S T I O N A N D F L A M E 8 5 : 3 0 0 - 3 0 8 (1991)

Evaporation Characteristics of Fuel and Multifuel Droplets M. M. ELKOTB, S. L. ALY, and H. A. ELSALMAWY Faculty of Engineering, Cairo University, Giza, Cairo, Egypt The evaporation characteristics of commercial fuel droplets, such as heavy diesel fuel, light diesel fuel, gasoline and kerosene, and multifuel droplets formed by blending any two of the aforementioned commercial fuels in different proportions were experimentally investigated. The effect of interacting droplets in a parcel of droplets on evaporation characteristics was also studied. The results indicated that the evaporation characteristics are considerably affected by fuel blending and that this effect increases as the difference in volatilities between the blended fuels increases. Droplet interaction in a fuel parcel decreases droplet vaporization. However, this effect decreases as the separation distance between the droplet increases. Generalized correlations are derived for the evaporation constant and multifuel droplet. Moreover, an empirical correction factor accounting for the droplet interaction effect on evaporation constant is proposed.

NOMENCLATURE C Cp d K ~" L 1 n R Re Sc T t t*

concentration specific heat at constant pressure diameter evaporation constant normalized evaporation constant effective latent heat of gasification separation parameter exponent of the evaporation (Eq. 2) radius Reynolds number Schmidt number temperature time time for complete evaporation

Greek Symbols a 7

6

evaporation rate transfer number normalized evaporation constant of fuel blend correction factor stoichiometric oxidizer-to-fuel ratio

Subscripts ev h iso ox s

evaporation heavy component isolated oxidizer droplet surface

Copyright © 1991 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc.

vo o

oo

volatile initial condition ambient condition

INTRODUCTION Liquid fuel droplet vaporization constitutes an important step in droplet combustion. Much work, theoretical and experimental, has been done in the area of single-component hydrocarbon vaporization and combustion. The basic approach for pure component droplet combustion in a stagnant oxidizing atmosphere was formulated by Godsave [1], Williams [2], Goldsmith and Penner [3], and Wise et al. [4], and led to the d 2 law, according to which the square of droplet diameter decreased linearly with time. Law and Sirignano [5] derived the d 2 law of evaporation or burning from the conservation equations of mass and energy. Some investigators [6-8] indicated that this law was not well obeyed during the initial period of droplet combustion because of transient heating. The flame standoff ratio changed during combustion to higher values, to approach that predicted by the d 2 law, due to the transient effect resulting from vapor accumulation [9] between the droplet and flame. Law et al. [9] suggested certain modifications in the d 2 law equation to account for the effect of vapor accumulation. The behavior of fuel droplets has been determined experimentally by several researchers [10, 11], and the effect of ambient temperature, pressure, and gas composition on the burning rate has 0010-2180/91/$3.50

EVAPORATION OF FUEL DROPLETS

301

been widely investigated [12, 13]. The vaporization and combustion behavior of fuel spray, with droplet diameters less than 200 tim, was investigated by Kumagal and Isoda [6] and Labowsky

[141. Regarding the multicomponent fuel droplet, Law [15] formulated the basic spherically symmetric model for its vaporization and combustion. Law [16] and Faeth [17] considered the problem of multicomponent droplet combustion with internal circulation. Prakash and Sirignano [18] provided a detailed study for the effect of internal circulation on droplet vaporization. Law and Law [19] ignored the internal circulation and provided a steady-state boundary layer type model for multicomponent droplet vaporization and combustion. The present work describes a comprehensive experimental study of the vaporization characteristics of commercial and multicomponent fuel droplets. This study involves the effects of a wide range of operating conditions, pressure, temperature, and Reynolds number on the vaporization of a single droplet and a parcel of droplets simulating a fuel spray. Commercial fuels such as heavy diesel fuel, light diesel fuel, kerosene, and gasoline and their blends are studied.

APPARATUS AND TECHNIQUE The apparatus (Fig. 1) consisted of a high-pressure chamber with optically flat access (quartz windows), a centrally mounted injection nozzle fitted either with a single hole or multiple holes to produce either a single droplet or a parcel of droplets directed radially across the bomb within the full view of the windows. An electronically controlled injection nozzle enabled a single injection of fuel to be achieved with good repeatability. The droplet injector is fitted with a changeable cup to inject into the chamber multiple droplets with different spacing between them. Fuel could be injected into the high-pressure chamber under constant pressure drop as soon as the driving circuit activated the solenoid. A delay circuit was used to detect the start of injection and trigger the oscilloscope and delay circuit. Droplets were photographed by a high-speed camera with background light from a microflash, excited by the delay circuit. Nitrogen was introduced to the bomb at different pressures. For vaporization studies, the nitrogen was preheated in a 2-kW electrical furnace and introduced through the bomb slowly; this produced a fairly quiescent condition, with air AID CONVERTER

T ~

/'

PRESSURE REGULATOR

.

I I.~

[IRANSIENTRECORDER

OSCILLOSCOPE

~

IJ

NITROGEN BOTTLE

Fig. 1. Apparatus.

:,

302 temperature reaching about 400 K. A 2-kW heating element was incorporated inside the bomb to enable the nitrogen temperature to be increased to 673 K [20]. The chamber was fitted with a pressure transducer and thermocouples connected to a transient recorder, A/D converter, and minicomputer to calculate the injection velocity and temperature histories during the injection period. Average droplet diameters and penetration were obtained statistically from photographs magnified ten times through repeated measurements. An error analysis for the various measured quantities yielded most probable errors for the droplet diameter, velocity, and time equal to +2%, +4%, and +2.3%, respectively.

M.M. ELKOTB ET AL.

4.0 LIJ W 3.8 o_

o

E

Q

o~ no < :~ 3.6 0

e4

0 • 0 0

~,

Gasotene Kerosene L .D .F. H.O.F.

20

40

60

80

100

120

TI ME, t ( m s e c . )

Fig. 2. Variationof droplet diameterwith time for base fuels.

A

4

E E

3

(J {U

RESULTS AND DISCUSSION It was important to first study the vaporization characteristics of the different base fuels that form the multicomponent fuel. The vaporization characteristics were expressed in terms of the variation of droplet squared diameter with time. The evaporation constant for the fuel droplet, can be determined from such vaporization characteristics. The following two subsections present the results of the evaporation characteristics of base and multicomponent fuel droplet, respectively. The effect of interacting droplets on the droplet vaporization constant is presented in the third subsection.

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Vaporization Characteristics of Base Fuel Droplets The base fuels were heavy diesel fuel (H.D.F.), light diesel fuel (L.D.F.) gasoline, and kerosene. They were investigated at 1 atm. and 400"C. Figure 2 shows their variations of droplet squared diameter with time. It is easily noticed that the rate of change of droplet squared diameter with time of gasoline is the greatest, to be followed by kerosene, and then light diesel and heavy diesel fuel. The change of instantaneous evaporation constant K with time, which is the negative of the rate of change of the droplet squared diameter dd2/dt, for the base fuels is depicted in Fig. 3. It is to be noted that the value of the evaporation constant continuously changes with time. This

Gosolene Kerosene L.D.F. H.D.F.

20

I0

eg

80

i

i

~00

120

TIME, t ( m s e c . ) Fig. 3. Variation of evaporation constant with time for base fuels.

can be attributed to the continuous change of convection because of the change of droplet velocity and diameter, and to the droplet heating up. In order to separate the effect of droplet heating from that of convection it is necessary to determine the end of the droplet heatup period. This is done by comparing the normalized droplet vaporization constant to the correlation of Ranz and Marshall [21]. The normalized evaporization constant K is defined as the instantaneous droplet evaporation constant, measured under the effect

EVAPORATION OF FUEL DROPLETS

303

of droplet heating and convection heating, divided by the steady-state evaporation constant. Values of the steady-state evaporation constant are taken from Ref. [22]. The correlation of Ranz and Marshall gives a normalized evaporation constant under the effect of convection. It can be rewritten in the form

which can be written as ln{1/[1 -

= ln[Ro2/(Kt*)] + nln(t*/t).

O)

Figure 4 shows the ratio of the measured value of K to that of the Ranz and Marshall correlation at different times. The normalized evaporation constant starts from zero and increases with time. The rate of increase decreases with time until it reaches the values of the Ranz and Marshall evaporation constant. The time that the droplet takes to reach the nearly fiat portion of the curve is the heatup period, which differs from one fuel to another. At the end of droplet heating, the normalized evaporation constant assumes a constant value that represents evaporation purely due to convection. The value for gasoline is higher than that for kerosene, which is in turn higher than that for light diesel fuel. Heavy diesel fuel has the lowest value. Regarding the effect of the droplet size on the evaporation constant, Aggarwal et al. [23] proposed a modified form of the d 2 law, which takes into account the nonlinearity R 2 = Ro 2

--

Kt*O-n)tn,

(2)

1.2

f

1.0 C~ 0,8 0.6 127 t~. ¢:a 0,t. v I-~

~

0 • A o

0.2

Ga solene Kerosene L.O.F. H.O.F.

0.0

0

20

40

60 TIME,

80

100

120

140

160

t (msec.)

Fig. 4. Variation of normalized evaporation constant with time for base fuels.

(3)

From the definition of K and t*, which is the time of complete evaporation, it follows that

RoZ/Kt *= = 1 + 0.3 Re 1/2 Sc I/3.

(R/Ro)2]}

1.

(4)

Since the rate of heat transfer per unit mass is proportional to Ro -1 times Ro 2 times Ro -3, dT/dt will be proportional to Ro -2 and the total vaporization time of droplet will be proportional to R02. Thus, the initial droplet diameter does not affect the value of the evaporation constant whenever it is less than 20 #m. For droplets of diameter greater than 20/zm, E1 Wakil et al. [24] found that t* o¢ R01"75. In the present work, n ranges between 2.6 for heavy diesel fuel and 2.3 for gasoline [20]. Differences between relatively large- and small-diameter droplets arise from their velocities and shape distortion. The smaller the size of the droplet, the higher its velocity, and consequently the higher the heat transfer and evaporation rates. Shape distortion of droplet occurs more readily in relatively large droplets. On the one hand, it increases the heat transfer rate to the droplet due to the increase in its exposed surface, whereas on the other hand, it decreases it due its slowing down as a result of a large drag. In the present work, the droplet was not sufficiently large enough to cause shape distortion, and geometrical similarity with other droplets in the micrometric range was preserved. In addition, the experimental results were correlated in terms of the nondimensional quantities, namely Re and Sc, rendering the present results applicable to a broad range of droplet sizes and velocities and satisfying the range of Re covered by the experiments.

Vaporization Characteristics of Multicomponent Fuel Droplet Multicomponent fuels were formed from blending any two of the four base fuels at various percentages, All experiments were at atmospheric pressure and 400"C. Blends of heavy diesel fuel with volumetric ratios of 20%, 40%, 60%, and 80% of light diesel fuel, kerosene, and gasoline

304

M . M . E L K O T B E T AL.

O80 =I.H.D.E., 20'/o Gasolene O60%H.D.F. , / . 0 ' / . Gasotene "~"

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D 80'Id4.D.F., A60'I.H.D.F., •40"hH.D.F., O20'hHn.E, '

/ 0

TIME,t(msec.)

0

20

Fig. 5. Variation of evaporation constant with time for H.D.F.-gasoline blends.

40

60

80

20% L.D.F. 40'1,, L.D.F. 60% L.D.F. 80=•. L.D.F. ' '

100

120

TIME, t (msec.) Fig. 7. Variation of evaporation constant with time for H.D.F.-L.D.F. blends.

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0

n

0

20

40

60

80

100

3

Y Z ~03 z °

2

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TIME,t(msec.) Fig. 6. Variation of evaporation constant with time for H.D.F.-kerosene blends.

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•/~0%L.D.E, 60%Gasolene O 20%L.n.F. 80%Gasolene

were formed. Also blends with light diesel fuel as a base fuel were formed with kerosene and gasoline at different blending ratios. For all these blends, the variation of droplet squared diameter with time was measured and the evaporation constant calculated. Figures 5 - 7 show the variation of evaporation constant with time for the blends of H.D.F. with gasoline, kerosene, and L.D.F., respectively. The evaporation constant increases with the concentration of the lighter component. The same general trend is exhibited for the blends of L.D.F. with gasoline and kerosene (Figs. 8 and 9). The varia-

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0

20

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60

80

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100

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120

TIME.t(msec.) Fig. 8. Variation of evaporation constant with time for L.D.F.-gasoline blends.

tion of evaporation constant with fuel concentration for the blends formed from H.D.F. and L.D.F. as base fuels with gasoline and kerosene is shown in Figs. 10 and 11 at a time of 130 ms. Figures 10 and 11 show that the evaporation

EVAPORATION OF FUEL DROPLETS

305

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100

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T I M E , t (msec.) Fig. 9. Variation of evaporation constant with time for L.D.F.-kerosene blends.

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A H.D.F.- L . D . F BLend • H . D . F . - Kerosene Blend O H.D.F - Gasolene B l e n d Re : 6.0 z.0

60

80

100

CONCENTRATION IN H.D.F. Fig. 10. Variation of evaporation constant with concentration for H.D.F. as base fuel and L.D.F., kerosene and gasoline blends.

constant has its minimum value at a concentration of 20% of the volatile component for all blends. In Figs. 10 and 11, for low concentrations of the more volatile component, it is found that efficient mixing occurred and evaporation resembles that of a single-component droplet with properties averaged according to the mole fraction of each component. On the other hand, for a mix-

/.,0

i

60

80

100

CONCENTRATION IN L . D . F .

20%Kerosene

&0"l. Kerosene

20

i

Variation of evaporation constant with concentration for L.D.F. as base fuel and kerosene and gasoline blends. Fig.

11.

ture containing a higher concentration of gasoline, evaporation resembled batch distillation, according to the shell model, that is, ditfusional forces in the liquid phase are efficient enough to transport the more volatile component to the outer surface of the droplet, while diesel fuel remains in the core. In this case, the presence of gasoline on the outer surface of the droplet and at lower boiling point tends to decrease the overall evaporation rate of the blended droplet by limiting the droplet temperature to its low boiling point until evaporation is almost complete. Only then can the temperature of the heavy component, heavy diesel fuel, start to increase again to reach its boiling point and evaporate. Which of these two effects supersedes the other depends on the concentration of the gasoline in the mixture. It was found that beyond a limit of 20%, the amount of volatile component was sufficient to increase the overall evaporation rate of the blended fuel droplet. Similar results have been obtained by Wang [25] with heptane and hexadecane, the boiling temperatures of which vary widely. They found that for a mixture containing 70% heptane, evaporation resembled that of batch distillation, following the shell model, while for 20% heptane, evaporation followed a model of a single component liquid droplet with average properties according to the mole fraction of each component. Effect of Droplet Interaction on Vaporization Characteristics The previous discussion was limited to an isolated fuel droplet in an unbounded environment. A fuel

306

M . M . ELKOTB ET AL. oration constant decreases as Reynolds number increases.

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A N A L Y T I C A L M A N I P U L A T I O N OF E X P E R I M E N T A L RESULTS

E3.8

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2.5 / 3.0

<

m

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3.6

0

20

40

60

80

100

120

TI ME,t(msec.) Fig. 12. Effect o f separation parameter on droplet squared diameter variation with time at 4 0 0 " C .

spray, however, is a system of interacting fuel droplets. To study the effect of droplet interactions, a parcel of droplets was formed using interchangeable brass cups with different separating parameters, l, defined as the distance between the centers of two neighboring droplets divided by the droplet diameter. Each cup contains five nozzles; the separation parameter between the central nozzle and the circumferential ones differs from one cup to another. Separation parameter values were 2, 2.5, 3, and 4. The variation of droplet squared diameter with time for the central droplet in a parcel of droplets dropped through the test chamber is shown in Fig. 12, at 400"C and 1 atm. The evaporation constant decreases with the separation parameter. This is further elucidated in Fig. 13, which shows the variation of droplet evaporation constant divided by that of an isolated droplet with separation parameter for different Reynolds numbers. The effect of separation parameter upon the evap-

1.0 o o~

~-

As shown in Fig. 4, the normalized evaporation constant K of any of the base fuel droplet follows a trend similar to that of Ranz and Marshall correlation during the evaporation period. However, the value of evaporation constant relative to Ranz and Marshall correlation varies with the type of fuel. Thus, the data were correlated at various times to an expression of the following form: g = 1 + const(Re 1/2 x Scl/3).

(5)

The constant in Eq. 5 was calculated to be 0.36, 0.34, 0.32, and 0.31 for gasoline, kerosene, light diesel fuel, and heavy diesel fuel, respectively. Equation 5 can be written in terms of the evaporation rate of the fuel, aev, as follows: ~" = 1 + const(Re ]/2 x Scl/3/aev),

(6)

where Ol~v = ln(1 +/3)//3 and /3 is the transfer number, which, during the evaporation period, is defined as

rs)]/L.

(7)

The interesting feature of Eq. 6 is that the constant is independent of the type of fuel, and is calculated to be 0.17 for all fuels in the present study.

20 10

0.8

Base Fuel Droplet Evaporation Constant

/~ = [ C p g ( T , , -

e :40 \

1.2

From these experimental data, it was possible to establish empirical expressions for the evaporation constant of commercial fuel droplets. An empirical expression is also proposed for the evaporation constant of multifuel blends. Furthermore, an empirical correlation is given for the spray effect on droplet vaporization.

Multifuel Droplet Evaporation Constant

0.t. o.o

1.s

2.0

2.s

3.0

3.5

~.o

~.5

SEPARATION PARAMETER, Fig. 13. Effect of separation parameter on droplet evaporation constantrelationto that of an isolateddroplet.

A normalized evaporation constant 7 for the multifuel blend is defined by = (Kb,ond

- Xh)/(Kvo - rh),

(8)

EVAPORATION OF FUEL DROPLETS

307

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LL

I

2

,.

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,~

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.,.

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LT IJ.

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ORe:SO & Re : 7 0 oRe : 8 0 ore :90 • Re : 100 __ Equation

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,

C2

LO

0

CONCENTRATION BY VOLUME

Fig. 14. Relation between normalized evaporation constant of multifuel and concentration by volume of H . D . F . - g a s o l i n e blends.

0

10

defined by

7 = 7.8C

for0 < C < 0.2,

(9)

CONCLUSIONS

7 = 3 . 2 C - 2.2

for0.2 < C < 1,

(10)

Effect of Droplets Interaction on Droplet Vaporization A correction factor, rlev, accounting for the interaction effect on droplet evaporation constant, is

30

'tO

REYNOLDS NUMBER. Re

Fig. 15. Dependenceof C l

where Kblend, K h , and Kvo are the evaporation constants of multi fuel droplet and heavy and volatile components in the blended droplet, respectively. According to this definition, 7 would be 0 for a blend composed entirely of the heavy component, and 1 if composed entirely of the volatile component. However, it is important to note that y for the blend does not have to lie between these two values because the addition of volatile component up to a certain concentration decreases the evaporation constant of the pure heavy component, leading in this case to values of y less than 0. However, 7 cannot exceed a value of 1. Correlating this normalized evaporation constant of the blend with the concentration by volume of the base fuels forming the blend produces a set of similar curves, which are independent of the type of the base fuels. Figure 14 presents a sample of these curves at a time of 130 ms, and a generalized relation is obtained, which does not depend on the type of the base fuels of the following form:

where C is the concentration by volume of the lighter component in the blend.

20

and

C2 on Reynolds number.

nov :K/Kiso.

(11)

This correction factor depends on Reynolds number and the separation parameter. The relation among 7/ev, 1, and Re can be obtained in the form ~e, = 1 - C , / e c2,,

(12)

where C I and C 2 are constants that may depend on Re. Plots of C t and C 2 against Re in Fig. 15 show C 1 to be independent of Re, with a value of 2.14. C 2 depends on Re according to the following relation: C 2 = 0.63 + 0.01 Re.

(13)

Accordingly, the correction factor assumes the form t/ev = 1 --

(2.14/e(O'63+o'oIRe)l).

(14)

1. The vaporization characteristics of a blended fuel droplet is considerably affected by the blend. The addition of 20% gasoline to heavy diesel fuel greatly reduces the evaporation constant. 2. The effect of blending different fuels on the evaporation constant becomes more pronounced as the difference between the volatilities of the blended base fuels increases. The

308

M . M . E L K O T B ET A L .

experimental results indicate a greater change in the evaporation characteristics o f heavy diesel fuel when blended with gasoline than when blended with light diesel fuel. 3. In a parcel o f droplets where interaction occurs between the different droplets, the droplet evaporation constant decreases with the decrease in separation parameter. This reduction decreases as Reynolds number increases. 4. A generalized correlation has been obtained for the normalized evaporation constant o f the base fuel droplet o f the form J~ = 1 + const(Re 1/2 Scl/3/t~ev), where the constant has been calculated to be 0.17 for all the fuels used in the present study. 5. Evaporation constants of the various fuel blends have been correlated with the evaporation constants o f the base fuels forming them, and generalized expressions have been proposed in the forms. 3' = 7 . 8 C 3" = 3 . 2 C -

for0 < C < 0.2, 2.2

f o r 0 . 2 < C < 1.

6. A n empirical formula has been deduced for the evaporation constant correction to account for the effect o f interaction o f droplet with other droplets: T/ev =

1 -

(2.14/e(°'63+°'OIRe)t).

REFERENCES

1. Godsave, G. A. E., Fourth Symposium (International) on Combustion, Williams & Wilkins, Baltimore, 1953, pp. 818-830. 2. Williams, F. A., Combust. Flame 2:207 (1965). 3. Goldsmith, M., and Penner, S. S., Jet PropuL 24:245-251 (1954).

4. Wise, H., Lorell, J., and Wood, B. J., Fifth Symposium (International) on Combustion, Reinhold, New York, 1955, pp. 132-141. 5. Law, C. K., and Sirignano, W. A., Combust. Flame 28:175-186 (1977). 6. Kumagai, S., and Isoda, H., Sixth Symposium (International) on Combustion, Reinhold, New York, 1957, pp. 726-731. 7. Kotaki, S., and Okazaki, T., Int. J. Heat Mass Transf 12:595-609 (1969). 8. Krier, H., and Wronkiewicz, H. A., Combust. Flame 18:159-166 (1972). 9. Law, C. K., Chung, S. H., and Suprinivasan, N., Combust. Flame 28:172-198 (1980). 10. Faeth, G. M., and Lazar, R. S., NASA CR-72622, 1969. 11. Kadota, T., and Hiroyasu, H., Bull. JSME 19:1515-1521 (1976). 12. Kobayasi, K., Fifth Symposium (International) on Combustion, Reinhold, New York, 1955, 141-147. 13. Agoston, G. A., Wood, B. J., and Wise, H., Jet PropuL 28:181-188 (1958). 14. Labowsky, M., Combast. Sci. TechnoL 18:145-151 (1978). 15. Law, C. K., A I C H E J. 24:626-632 (1978). 16. Law, C. K., Combast. Flame 26:219-222 (1976). 17. Faeth, G. M., A I A A 8:1308-1314 (1970). 18. Prakash, S., and Sirignano, W. A., Int. J. Heat Mass Transl. 21:885-895 (1978). 19. Law, C. K., and Law, H. K., A I A A 19:522-527 (1981). 20. E1 Salmawy, H. A., M.Sc. thesis, Faculty of Engineering, Cairo University, 1986. 21. Ranz, W. E., and Marshall, W. R., Chem. Eng. Prog. 48:141-146, 173-180 (1952). 22. Chin, J. S., and Lefebvre, A. H., A I A A 21:1437-1443 (1983). 23. Aggarwal, S. K., Tong, A. Y., and Sirignano, W. A., A I A A 22:1448-1457 (1984). 24. E1-Wakil,M. M., and Abdou, M. I., SAE reprint 598B, 1962. 25. Wang, C. H., Lin, X. O., and Law, C. K., Combust. Flame 56:175-197 (1984). Received 4 January 1988; revised 29 September 1988