Modeling Droplet Breakup Processes in Bio-fuel Diesel Engines under Micro-explosion Conditions

Transcription

1 ILASS Americas, th Annual Conference on Liquid Atomization and Spray Systems, Chicago, IL, May 7 Modeling Droplet Breakup Processes in Bio-fuel Diesel Engines under Micro-explosion Conditions K. T. Wang and C. F. Lee * Department of Mechanical Science and Engineering University of Illinois at Urana-Champaign Urana, IL USA Astract A numerical study of micro-explosion for multi-component droplets in diesel engines is presented. The first part of the model comprises the thermodynamic description of the droplet, the mathematical formulation of the ule generation and growth inside the droplet, and the final explosion of the droplet. After the explosion that shatters the droplet, the size and velocity of secondary droplets are determined y a linear staility analysis. An extension to the previous model, which allows a generic proaility function to e inserted, is proposed. Comparison of droplet ehaviors for ethanol-tetradecane mixtures with and without micro-explosion shows that micro-explosion shortens the droplet lifetime. Amient temperature does not have a significant effect on micro-explosion. However, it is oserved that high amient pressure is more likely to induce micro-explosion. There exists an optimal composition of aout 5% of ethanol for micro-explosion. Mixture composition does not have significant effect on the secondary droplet sizes, so does the parent droplet size. But numerical results show that secondary droplets tend to e smaller with ethanol-rich mixtures. On the other hand, the initial droplet size showed a significant effect on the secondary droplet velocity with small initial droplet radius. The secondary droplet velocity for an initially 1 m is six times as high as those with initial sizes larger than 15 m. It is found that micro-explosion is possile for ethanol/tetradecane mixtures in typical diesel engine operation. The occurrence of micro-explosion and the susequent reakup promotes droplet atomization and enhance droplet dispersion which in turns improves engine performance and reduces emissions of soot and unurned hydrocaron. * Corresponding author

2 Introduction Micro-explosion is a violent disruptive ehavior due to the explosive internal gasification and is usually accompanied y a cracking sound [1] due to different volatilities and oiling points among the components in the liquid mixture. The phenomenon of micro-explosion has een extensively studied since it was firstly reported y Ivanov and Nefdov []. Engine performance can e improved with microexplosion since it enhances the atomization of fuel droplets. The air-fuel contact area is increased and therefore improves the mixing process [3]. Kadota and Yamasaki [4] note that the violent disintegration during micro-explosion disperses the secondary droplets into larger volume, which improves the comustion efficiency while reducing the formation of soot and unurned hydrocaron. Extensive experimental examinations on the micro-explosion phenomenon in multicomponent liquid droplets have een done. Experiments for oth miscile multicomponent droplets [5, 6] and water in fuel emulsions [5, 7-1] have een performed and micro-explosion is oserved in oth cases. Wang and Law [5] conducted a series of experiments using alcohol/alkane and alcohol/alcohol mixtures under elevated pressures and they showed that alcohol/diesel lends has the potential of enhancing atomization within diesel engines. Numerical models are also proposed to descrie the mechanism of micro-explosion in emulsified fuels [1, 11, 1]. Based on the linear staility analysis, Zeng and Lee [13] proposed a model enaling the determination of the size and the velocity distriutions for secondary droplets. ecently, renewale fuels such as iodiesel and ethanol have received much attention ecause they have less impact on the environment [14] and have the possiility of decreasing domestic demand on foreign petroleum. In today s commercial use, iofuels are generally mixed with petroleum-ased diesel fuels. Understanding the droplet reakup process and the comustion process for io-fuel and diesel lends is essential in optimizing engine operations and etter engine designs in the future. Due to the significant differences in volatilities and oiling points etween ethanol and diesel fuel, microexplosion is expected in ethanol-diesel fuel droplets. In this study, the micro-explosion effect in liquid mixture of diesel fuel and ethanol is studied, using tetradecane to chemically descrie diesel fuel and ethanol as an additive. A computational study of the droplet reak-up characteristics under microexplosion in diesel engines for the aforementioned fuel lend is presented. Numerical simulations are done using the KIVA-3V elease code, developed y the Los Alamos National Laoratory [15], which is a multidimensional transient computational fluid dynamic solver for chemical reacting flow. The numerical model developed y Zeng and Lee [13] is implemented into the code for enhancing its aility in micro-explosion simulations. Mathematical Formulation A droplet of radius s, with a ule of radius in the center, known as a ule-droplet system, is shown in Figure 1. Spherical symmetry is assumed throughout the droplet s lifetime as this has een experimentally oserved y Wang et al. [16]. Jin and Borman [17] show that internal circulation enhances the mixing process within the liquid droplets and this can e represented y an enlarged diffusivity. As a consequence, the full three-dimensional analysis within the liquid phase can e reduced into onedimensional y applying the effective diffusivity. Figure 1. Bule-droplet system Following the derivations y Zeng and Lee [13], the conservation equations for mass, species and energy of the ule-droplet system are shown in equations (1), () and (3), respectively, with represents mass-averaged density, Y i denotes the mass fraction of species i in the mixture and e represents internal energy, r lv, (1) r lyi 1 lvr Yi 1 Yi Dr, () i t r r r r r le 1 lvr e t r r, (3) 1 Y 1 T i Der i i kr t i r r r r r r where T is temperature, k t is effective thermal conductivity and D i is the mass diffusivity of species i. The oundary conditions at the droplet surface (r = s ) and the ule-droplet interface (r = ) can e

3 otained y satisfying the continuity of mass and energy flux, as shown in Zeng [18]. According to Lee and Merte [19], since the ule growth rate is much less than the sonic speed, the pressure distriution within the ule can e considered as uniform throughout its lifetime. Both temperature and compositions are also assumed spatially uniform [19]. The liquid and vapor are assumed in thermal and phase equilirium and thus the temperature and fugacity are continuous across the interface [19]. Following Zeng and Lee [13], the homogeneous nucleation theory is applied to descrie the ule generation process. Since homogeneous nucleation requires a higher superheat limit, the theory sets a lower ound of the onset of micro-explosion [18]. The nucleation rate, J, is determined y the formula proposed y Avedisian and Glassman [6], shown in equation (4), which has shown good predictions of superheat limit [6, 13, 18], * A J nkf exp, (4) kt where is a constant denoting the proaility of nucleation, n is the numer density, k f is the gas collision frequency and A * is the activation energy. The constant generally ranges from.1 to 1 and does not have significant effects on the nucleation rate once the temperature approaches the superheat limit. As in the previous studies [6, 13, 18], unity is chosen for in current work. The numer of nuclei can e otained y integrating equation (4) over time and the control volume [13]. Because the nucleation rate, J, is in exponential form, it is insensitive against the choice of the numer of nuclei in the determination of the onset of homogeneous nucleation. Henceforth, the numer of nuclei is chosen as unity at the onset of homogeneous nucleation as in the previous studies [13, 18]. The initial radius of the ule nucleus can e determined from the Young-Laplace equation. The ule growth rate is determined from the modified ayleigh equation [13, ]. The reakup criterion is determined y the dispersion equation derived y Zeng and Lee [13], using a linear staility analysis, 1 4 s s Wes ( ) ( 1 ) 3 We, (5) 1 Mai 3We where 3 l, Ma V c i i, s lvs s Wes, lvi We,, g, and g,. (6) The dispersion equation is an analytically solvale cuic equation in, for which the largest root dominates the growth of disturance. Zeng [13, 18] defines the reakup variale, K(t), as Kt () s l t dt. (7) exp( ) s The growing ule cannot sustain the internal disturances when K(t) reaches a critical value and reakup then occurs. In the present study, this critical value of K(t) is assumed to e five, following the suggestion in Zeng and Lee [13] for microexplosion calculations with hydrocarons. Size and Velocity of the Secondary Droplets Zeng [18] derives the size distriution and velocity of the secondary droplets following the reakup process of the ule-droplet system y assuming a functional form for the proaility density function used to descrie the distriution of the secondary droplets. Following the same procedures, the derivation is extended for a generic proaility distriution function, f(r,, ), descriing the distriution of the N secondary droplets produced following the reakup. The origin of the spherical coordinate is located at the center of the ule-droplet system; in other words, the reakup process is viewed from the center of mass of the ule-droplet efore reakup. Furthermore, assume the proaility density function is separale and spherically symmetrical, f f( r,, ) f r f f, (8) r Sustituting equation (8) into the mass conservation and integrate over the control volume and simplifying, gives r s. (9) N r f dr The radial direction momentum conservation can e manipulated in a similar manner to give, 1 NV r f dr V 3 3 r i s l. (1)

4 The velocity of the secondary droplet can then e otained y sustituting (9) into (1), which gives V 3 V i s 3 3 s. (11) Similarly, the energy conservation equation can e manipulated and gives, N r f dr r s 4 l V i V s l s. (1) The Sauter mean diameter for the secondary droplets can then e evaluated y dividing equation (1) y equation (9) which gives V 4 1 s i l V 3 3 s s 3 s.(13) esults and Discussion The KIVA-3V elease code [15, 1] is used with the aforementioned micro-explosion model for numerical simulations of ethanol-diesel droplets. A parametric study examining the effects of amient pressure, temperature, and initial composition of the mixture on the onset of ule generation is conducted for an ethanol-diesel droplet. Since commercially availale diesel fuels is a mixture of hydrocaron compounds, instead of a single, pure compound, some surrogates have een suggested as sucomponents for its description []. Tetradecane is used, throughout this study, to represent petroleumderived diesel fuels. The initial size of the ethanoldiesel droplet under consideration is 3 m and at temperature of 3 K. Numerical investigations are conducted to investigate the effects of varying pressure on microexplosion. A droplet, composed 5% ethanol and 5% tetradecane y mass, is simulated y the augmented KIVA-3V elease code mentioned earlier. Amient temperature is fixed at 3 K, the typical flame temperature during comustion for hydrocarons with pressure varying from 1 atm to 3 atm. Figure shows the relation etween normalized volume and amient pressure. The normalized volume is defined as the ratio of ule size at the onset of ule generation to its initial size, which provides a descriptive way to quantify the effect of micro-explosion. This can e done ecause the time elapsed etween ule generation and droplet reakup is negligile relative to the lifetime of droplet under micro-explosion [18]. Strong effect of micro-explosion is indicated y large normalized radius and vice versa. No micro-explosion is oserved when the amient pressure is less than atm. As oserved in Figure, the normalized volume increases from.1 for droplets under amient pressure of 3 atm until it reaches a maximum of.5 at approximately atm. Normalized volume then reduces gradually from.5 to.45 with further increment of pressure from atm to 34 atm. It can e seen from the figure that pressure has a strong effect on micro-explosion at low pressure. As pressure is increased y 5% from 4 atm to 6 atm, the normalized volume is increased y more than 5% from. to.3. On the other hand, when amient pressure is increase from 16 to 18 atm, the normalized volume increased from.48 to.5, an increment less than 5%. The slope of the curve is very steep at low pressure and gradually flattens, eventually turns negative at very high pressure. Although experimental oservations are not availale for high pressure conditions, the current prediction is in consistent with Wang and Law s experiments [5] conducted from atmosphere to 4 atm. Normalized volume ( n 3 / s3 ) Pressure (atm) Figure. Effect of amient pressure on microexplosion in the droplet-ule system. The inversion of micro-explosion intensity at high pressure is discussed y Avedisian and Glassman [3] ut not yet justified through experiments. As oserved from Figure, the inversion point is aout 4 atm and the phenomenon ecomes ovious when the amient pressure is aove 8 atm. The oserved inversion of micro-explosion effect can e explained as a result of the competition of droplet temperature and pressure. The maximum temperature the droplet can attain is determined y the saturation temperature of the heaviest component in the liquid mixture. Therefore, as pressure increases, the droplet temperature also increases, and this leads to higher nucleation rate and reduction of the droplet lifetime. However, for droplet at high amient pressure, ule generation is restrained due to the fact that the ule saturation pressure may not

5 increase fast enough to compete against the liquid pressure. Moreover, the growth rate of the ule may e restrained at high liquid pressure. These comined effects reduce the intensity of microexplosion at high pressure, as pointed out y Avedisian and Glassman [3]. Figure 3 shows the effect of amient temperature on ule generation for 5% ethanol and 5% tetradecane droplets at amient pressure of 1 atm, with temperature varies from 1 K to K. Interestingly, there are no noticeale variations of the normalized volume over this wide range of temperature variation. Equation (4) shows that the nucleation rate is determined y the droplet temperature, rather than the amient temperature. The results from KIVA indicate that the surface temperature of the droplet increases y aout 3% from 53 K to 546 K while the amient temperature is increased y over 1% from 1 K to K. This is ecause the droplet evaporation rate is increased with higher amient temperature. As a consequence, the increased heat transfer to the droplet due to higher amient temperature is reflected with faster evaporation that reduces the droplet s lifetime, instead of sensile heat transfer that could e oserved with higher droplet temperature. This explains the much smaller temperature increment in droplet temperature when the amient temperature is varied. ) 3 Normalized volume ( n 3 / s Temperature (K) Figure 3. Effect of amient temperature on microexplosion in the droplet-ule system. A parallel prediction on the occurrence and strength of micro-explosion for emulsified droplets was made y Fu et al. [1]. The authors define a variale, K, to quantify the strength of microexplosion (see equation (3) in [1]). Fu et al. [1] show that the amient temperature does not have direct effects on micro-explosion. However, it is also pointed out that higher amient temperature causes larger heat transfer and thus a quicker onset of microexplosion. Effect of composition is examined for the ethanol/tetradecane droplet at 1 atm of amient pressure and 3 K of amient temperature. Mass fraction of ethanol in the mixture is varied from % to 9%. Figure 4 shows the relationship etween the normalized volume and mixture composition. The normalized volume is % when the mixture contains % of ethanol y mass. It increases as the composition of ethanol is increased and reaches the peak value of 4% normalized volume for mixtures with 4% to 5% of ethanol that represents the optimal composition ratio of ethanol/tetradecane mixtures. The normalized volume then decreases with the further increment of ethanol in the mixture. Normalized volume ( n 3 / s3 ) Mass fraction of ethanol Figure 4. Effect of initial composition on microexplosion in the droplet-ule system. This paraola-like curve has een oserved in experiments in a numer of previous studies [5, 9, 16]. Oviously, from Figure 4, there exists an optimal mixture composition, which is aout equal composition of ethanol and diesel, for triggering micro-explosion. Generally speaking, from the viewpoint of micro-explosion, the less volatile component is used to drive up the droplet temperature. Meanwhile, the more volatile component plays the role of internal gasification [5]. Therefore it is reasonale to suggest that there is an optimal ratio of more volatile and less volatile components for micro-explosion. If the amount of more volatile component, i.e. ethanol in this study, is too low, the internal gasification may not strong enough to form a ule. On the contrary, if the droplet is in rich ethanol, heat transferred into the droplet may e consumed in the evaporation of ethanol, rather than increasing the droplet temperature. As a result, the onset of ule generation is delayed as the droplet temperature must e higher than the superheat limit for ethanol for ule generation. Thus, there exists an optimal mixture composition. Numerical calculations are done for ethanol/tetradecane droplets of different

6 compositions with initial radius of 1 m at amient conditions of 4 atm and 85 K. The temporal variations of droplet radius with and without microexplosion are shown in Figure 5. The droplet radius is normalized y initial radius and the time scale is normalized y the lifetime of droplets with no microexplosion. The droplet lifetime for droplets with 4/6, 6/4 and 8/ of ethanol and tetradecane y mass are 1.95 ms,. ms and.5 ms, respectively, for droplets without micro-explosion. Figure 5. Effect of micro-explosion on droplet lifetime for droplets with initial radius of 1 m. Amient conditions are 4 atm and 85 K. Since ethanol is more volatile than tetradecane, longer urnout time is oserved for mixtures containing more ethanol. Bule expansion is oserved at normalized time scale of aout.8 to.9 from Figure 5 for all cases eing considered y noting the arupt increase in radius. The susequent reduction in radius is due to reakup of the droplets after micro-explosion. For 4% ethanol and 6% tetradecane droplets, the droplet lifetime is reduced y 13% if micro-explosion is oserved. The droplet lifetime for droplets with 6% ethanol is shorter than those with 4% ecause ethanol facilitates internal gasification, and therefore, inducing micro-explosion to occur earlier at normalized time of.84 instead of.87 for droplets with only 4% of ethanol. However, micro-explosion is delayed for droplet with 8% ethanol y mass. In spite of facilitating internal gasification and inducing micro-explosion, it is more difficult to drive up the droplet temperature as heat transferred to the droplet is consumed in evaporating ethanol, the more volatile species, which is an isothermal process. As a result, it takes longer for the droplet to reach the superheat limit. Therefore, micro-explosion is delayed. esults from KIVA show that the micro-explosion and reakup processes occur at normalized time of.89 for a droplet with 8% of ethanol. However, as oserved in Figure 5, droplet lifetime varies insensitively with respect to compositions for 1 m ethanol/tetradecane droplets. Since evaporation is the dominating process for small droplets, the effect of micro-explosion on lifetime reduction ecomes relatively insignificant. The variations of Sauter mean radius (SM) for secondary droplets formed for parents droplets of 1 m and m with respect to mass fraction of ethanol are shown in Figure 6. Amient pressure is 4 atm, and amient temperature is 85 K as in previous calculation shown in Figure 5. The SM of the secondary droplets is aout % of initial size for oth cases considered. The results show that microexplosion can significantly enhance the atomization process. Although SM tends to decrease for droplets made of mixtures with more ethanol, the overall effect of composition on SM is small, like the effect due to initial size of the droplets as oserved in Figure 6. For ethanol-rich mixture, the evaporation of ethanol prior to micro-explosion reduces the droplet size consideraly. This contriutes to the smaller secondary droplets formed after micro-explosion. The SM increased y less than aout 1% when initial droplet radius increased from 1 m to m. Normalized SM Mass fraction of ethanol 1 micron micron Figure 6. The variation of Sauter mean radius for droplets formed after micro-explosion with respect to composition. This graph shows the facilitation of atomization y micro-explosion. From oth Figures 5 and 6, upon microexplosion, the instantaneous normalized radius of the 1 m droplets with 4% of ethanol is aout 5 m. Micro-explosion shatters the parents droplet and generates child droplets with normalized SM of aout.. For droplets with initial radius of 5 m, micro-explosion is not oserved as the vaporization process is much faster. The droplet completely evaporates efore the onset of micro-explosion. The secondary droplets formed after micro-explosion tends to e smaller, as seen in Figure 6, for ethanolrich droplets, with initial radius of 1 m and m

7 droplets. However, the effect is more significant for the former case. The initial size of the droplet exhiits a significant effect on the velocity of secondary droplets. The secondary droplet velocity for droplet composes of 5 % ethanol and 5 % tetradecane y mass and initial radius from 1 m to 5 m is shown in Figure 7. The amient pressure and temperature are 4 atm and 85 K, respectively, and initial droplet velocity is 6 m/s. Secondary velocity (m/s) Initial droplet radius (m) Figure7. Secondary droplet velocity for the optimal composition (5/5 ethanol/tetradecane) with various initial radii. The secondary droplet velocity for the 1 m radius droplet is six times higher than droplets with radius larger than 15 m. As the initial droplet size increases, the secondary droplet velocity decreases. From KIVA output, for droplets with initial radius of 1 m and initial velocity of 6 m/s, the secondary velocity is 6.4 m/s. It is ovious that, larger secondary velocity leads to wider spray angle. This improves the spray dispersion and penetration. As a result, the comustion efficiency could e improved while reducing the emissions of soot and unurned hydrocaron [3, 4]. Conclusions A numerical study on the micro-explosion phenomenon in ethanol/tetradecane droplets is performed using KIVA-3V elease code. The numerical model developed y Zeng and Lee [13] is used to descrie the micro-explosion process. The distriution of secondary droplets and their velocity are derived, in the framework of Zeng and Lee [13], for a generic distriution function. The effects of temperature, pressure, and mixture composition are verified y comparing with pulished results in previous studies on micro-explosion. The KIVA code is then applied to study micro-explosion for fuel sprays in diesel engine. Breakup of fuel droplets due to micro-explosion is analyzed quantitatively. The results conclude that, for ethanol/tetradecane droplets: 1. Amient temperature does not have significant effects on micro-explosion once the droplet temperature can reach the superheat limit of the more volatile component.. Amient pressure facilitates the onset of microexplosion indirectly y enaling the droplet to reach a higher temperature. Micro-explosion is less likely to occur at atmospheric pressure. However, an inversion in the micro-explosion effect in terms of pressure is oserved at high pressure and micro-explosion is suppressed at high pressure also. 3. There exists an optimal composition for ethanol and tetradecane mixture for the onset of microexplosion. Neither low nor high mass fraction of ethanol is in favorale in inducing microexplosion. 4. Mixture composition has minimal effect on the sizes of secondary droplets, so does the initial droplet radius. However, ethanol-rich mixture tends to generate smaller secondary droplets. Secondary droplets are aout % as ig as the parent droplets. The results indicate that microexplosion is a very effective tool for assisting in atomization of the fuel spray. 5. esults from 5% ethanol and 5% tetradecane mixture show that higher secondary droplet velocity can e achieved with smaller initial droplet. The secondary droplet velocity for a 1 m is almost six times higher than droplets larger than 15 m. Large secondary droplet velocity leads to etter dispersion of fuel spray. 6. Micro-explosion is possile for ethanol and tetradecane mixture under diesel engine environments. Breakup of the droplets due to micro-explosion enhances spray atomization and dispersion, characterized y secondary size and secondary velocity, respectively. Therefore, micro-explosion can simultaneously improve engine performance and reduce soot and unurned hydrocaron emission. Further works are required to extend the current model for simulations of multicomponent mixtures such as ethanol-iodisel-diesel lends. The model used in current study can e implemented for multicomponent mixtures y replacing the inary diffusivity with an effective diffusivity defined for the multi-component mixtures. Only miscile mixtures are considered in this study. A new computational model is needed for proper description of the mechanism controlling micro-explosion in immiscile mixture, such as those oserved in wateroil emulsions.

8 Acknowledgements This work was supported in part y the Department of Energy Grant No. DE-FC6-5NT4634, and y Department of Energy GATE Centers of Excellence Grant No. DE-FG6-5NT46. We also thank Way Lee Cheng and Valerie L. Stringer for their assistance on preparing the manuscript. Nomenclature A * activation energy c the speed of sound D mass diffusion coefficient e internal energy J nucleation rate (per volume per time) k Boltzmann s constant K reakup variale; micro-explosion strength k f gas collision coefficient k t thermal conductivity Ma Mach numer n numer density r radial coordinate ule radius s droplet radius n droplet radius at the onset of nucleation s initial droplet radius 3 Sauter mean radius t time T temperature V radial velocity V velocity magnitude of secondary droplets V i liquid velocity at ule-droplet interface We Weer numer Y mass fraction dimensionless droplet radius disturance growth rate dimensionless disturance growth rate density surface tension dimensionless density Suscripts g gas i species i l liquid Superscripts undistured property eferences 1. Fu, W.B., Hou, L.Y., Wang, L., and Ma, F.H., Fuel Proceeding Tech. 79: ().. Ivanov, V.M., and Nefdov, P.I., Experimental investigation of the comustion process in nature and emulsified fuels, NASA TT F-58 (1965). 3. Lif, A., and Holmerg, K., Advances in Colloid and Interface Science 13-16: (6). 4. Kadota, T., and Yamasaki, H., Progress in Energy and Comustion Science 8: (). 5. Wang, C.H., and Law, C.K., Comustion and Flame 59: 53-6 (1985). 6. Avedisian, C.T., and Glassman, I., ASME J. Heat Transfer 13: 7-8 (1981). 7. Sheng, H.Z., Chen, L., and Wu, C.K., SAE Paper No , Warrendale, PA (1995). 8. Segawa, D., Yamasaki, H., Kadota, T., Tanaka, H., Enomoto, H., and Tsue, M., Proceedings of the Com. Inst. 8: (). 9. Lasheras, J.C., Fernandez-Pello, A.C., and Dryer, F.L., Comustion Science and Tech., 1: 1-14 (1979). 1. Tsue, M., Yamasaki, H., Kadota, T., Segawa, D., and Kono, M., Proceedings of the 7th Symposium (International) on Comustion. The Comustion Institute, 1998, pp Tsao, K.C., and Wang, C.L., SAE Paper No. 8634, Warrendale, PA (1986). 1. Law, C.K., Comustion Science and Tech. 17: 9-38 (1977). 13. Zeng, Y., and Lee, C.F., Proceedings of the Comustion Inst. 31: (7). 14. Pang, X., Shi, X., Mu, Y., He, H., Shuai, S., Chen, H., and Li,., Atmospheric Environment, 4: (6). 15. Amsden, A., KIVA-3V: A Block-Structured KIVA Program for Engines with Vertical or Canted Valves, Los Alamos National Laoratory eport LA MS (1997). 16. Wang, C.H., Liu, X.Q., and Law, C.K., Comustion and Flame 56: (1984). 17. Jin, J.D., and Borman, G.L., SAE Paper No. 8564, Warrendale, PA (1985). 18. Zeng, Y., Ph.D. Thesis, University of Illinois, Mechanical Engineering (). 19. Lee, H.S., and Merte, H. Jr., Int. J. Heat Mass Transfer 39: (1996).. Sciven, L.E., Chemical Engineering Science 1: (196). 1. Amsden, A.A., O ourke, P.J., and Butler, T.D., KIVA-II: A Computer Program for Chemically eactive Flows with Sprays, Los Alamos National Laoratory eport LA-1156-MS (1989).. Schihl, P., Hoogterp, L., Pangilinan, H., Schwarz, E., and Bryzik, W., Modeling JP-8 fuel effects on diesel comustion systems, Army esearch Development and Engineering Command, Warren, MI., eport: DECOM/AL-1633, Sep 6 3. Avedisian, C.T, and Glassman, I., Int. J. Heat Mass Transfer, 4: (1981).