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Theoretical and numerical analysis of the evaporation of mono- and multicomponent single fuel droplets. (English) Zbl 07298876
Summary: Single fuel droplet vaporization, with special attention to the case of ethanol, is considered in this study. First, we showed, using an order-of-magnitude analysis and detailed unsteady simulations, that the commonly used quasi-steady assumption is not suitable for an accurate description of the liquid phase during the evaporation process. Second, we demonstrated that an increase in the relative importance of radiation explains the departures of the evaporation rate from the \(d^2\)-law observed experimentally when sufficiently large droplets – initial radius above 0.25 mm – evaporated in ambient temperatures around 800 K. The multicomponent formulation included here, in which the physical properties of both liquid and gas phases depend on the concentration of the different species involved, was validated by comparing our numerical results with experimental data of ethanol, \(n\)-heptane, ethanol-water and \(n\)-dodecane-\(n\)-hexadecane droplets available in the literature. Because of its technological relevance, we dedicated special attention to the effect of the droplet water content and ambient humidity on the evaporation time of ethanol droplets. Our computations showed higher vaporization rates with increasing ambient humidity as a consequence of the extra heat generated during the condensation of moisture on the droplet surface.
76T10 Liquid-gas two-phase flows, bubbly flows
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[1] Aalto, M., Keskinen, K. I., Aittamaa, J. & Liukkonen, S.1996An improved correlation for compressed liquid densities of hydrocarbons. Part 2. Mixtures. Fluid Phase Equilib.114 (1-2), 21-35.
[2] Abramzon, B. & Sazhin, S.2006Convective vaporization of a fuel droplet with thermal radiation absorption. Fuel85 (1), 32-46.
[3] Abramzon, B. & Sirignano, W. A.1989Droplet vaporization model for spray combustion calculations. Intl J. Heat Mass Transfer32 (9), 1605-1618.
[4] Assael, M. J., Charitidou, E., De Castro, C. A. N. & Wakeham, W. A.1987The thermal conductivity of \(n\)-hexane, \(n\)-heptane, and \(n\)-decane by the transient hot-wire method. Intl J. Thermophys.8 (6), 663-670.
[5] Avulapati, M. M., Ganippa, L. C., Xia, J. & Megaritis, A.2016Puffing and micro-explosion of diesel-biodiesel-ethanol blends. Fuel166, 59-66.
[6] Azimi, A., Arabkhalaj, A., Ghassemi, H. & Markadeh, R. S.2017Effect of unsteadiness on droplet evaporation. Intl J. Therm. Sci.120, 354-365.
[7] Banipal, T. S., Garg, S. K. & Ahluwalia, J. C.1991Heat capacities and densities of liquid \(n\)-octane, \(n\)-nonane, \(n\)-decane, and \(n\)-hexadecane at temperatures from 318.15 K to 373.15 K and at pressures up to 10 MPa. J.Chem. Thermodyn.23 (10), 923-931.
[8] Brown, R. J. C., Keates, A. C. & Brown, A. S.2011Optimised determinations of water in ethanol by encoded photometric near-infrared spectroscopy: a special case of sequential standard addition calibration. Anal. Chim. Acta690 (1), 47-52.
[9] Burgdorf, R., Zocholl, A., Arlt, W. & Knapp, H.1999Thermophysical properties of binary liquid mixtures of polyether and \(n\)-alkane at 298.15 and 323.15 K: heat of mixing, heat capacity, viscosity, density and thermal conductivity. Fluid Phase Equilib.164 (2), 225-255.
[10] Caudwell, D. R., Trusler, J. P. M., Vesovic, V. & Wakeham, W. A.2004The viscosity and density of \(n\)-dodecane and \(n\)-octadecane at pressures up to 200 MPa and temperatures up to 473 K. Intl J. Thermophys.25 (5), 1339-1352.
[11] Cazabat, A.-M. & Guena, G.2010Evaporation of macroscopic sessile droplets. Soft Matter6 (12), 2591-2612.
[12] Chauveau, C., Halter, F., Lalonde, A. & Gökalp, I.2008 Experimental study on high-pressure droplet evaporation using microgravity conditions. In ILASS, vol. 22, pp. 1-7. Elsevier.
[13] Coffee, T. P. & Heimerl, J. M.1981Transport algorithms for premixed, laminar steady-state flames. Combust. Flame43, 273-289.
[14] Crespo, A. & Liñán, A.1975Unsteady effects in droplet evaporation and combustion. Combust. Sci. Technol.11 (1-2), 9-18.
[15] Criado-Sancho, M. & Casas-Vázquez, J.1997 Termodinámica química y de los procesos irreversibles.
[16] Diddens, C.2017Detailed finite element method modeling of evaporating multi-component droplets. J.Comput. Phys.340, 670-687.
[17] Dombrovsky, L. A., Sazhin, S. S., Sazhina, E. M., Feng, G., Heikal, M. R., Bardsley, M. E. A. & Mikhalovsky, S. V.2001Heating and evaporation of semi-transparent diesel fuel droplets in the presence of thermal radiation. Fuel80 (11), 1535-1544.
[18] 2019 Thermal Conductivity of Hexadecane. Available at: http://www.ddbst.com/en/EED/PCP/TCN_C516.php.
[19] 2013 Water - Density, Specific Weight and Thermal Expansion Coefficient. Available at: https://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html.
[20] Erbil, H. Y.2012Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci.170 (1-2), 67-86.
[21] Fang, B., Chen, L., Li, G. & Wang, L.2019Multi-component droplet evaporation model incorporating the effects of non-ideality and thermal radiation. Intl J. Heat Mass Transfer136, 962-971.
[22] Filippov, L. P.1955Vest. Mosk. Univ., Ser. Fiz. Mat. Estestv. Nauk 8, 67-69.
[23] Fredenslund, A., Gmehling, J. & Rasmussen, P.1977Vapor-liquid Equilibria using UNIFAC: A Group-contribution Methods. Elsevier Scientific.
[24] Gao, M., Zhang, D., Kong, P. & Zhang, L.-X.2020Experimental investigation of Marangoni convection in a sessile droplet at a constant heat flux condition. Intl Commun. Heat Mass Transfer115, 104600.
[25] Ghassemi, H., Baek, S. W. & Khan, Q. S.2006Experimental study on binary droplet evaporation at elevated pressures and temperatures. Combust. Sci. Technol.178 (6), 1031-1053.
[26] Goos, E., Burcat, A. & Ruscic, B.2010 Extended third millennium ideal gas and condensed phase thermochemical database for combustion with updates from active thermochemical tables. Elke Goos, Remchingen, Germany, accessed Sept, 19, 2016.
[27] Gregson, F. K. A., Ordoubadi, M., Miles, R. E. H., Haddrell, A. E., Barona, D., Lewis, D., Church, T., Vehring, R. & Reid, J. P.2019Studies of competing evaporation rates of multiple volatile components from a single binary-component aerosol droplet. Phys. Chem. Chem. Phys.21 (19), 9709-9719.
[28] Grunberg, L. & Nissan, A. H.1949Mixture law for viscosity. Nature164 (4175), 799.
[29] Gurrala, P., Katre, P., Balusamy, S., Banerjee, S. & Sahu, K. C.2019Evaporation of ethanol-water sessile droplet of different compositions at an elevated substrate temperature. Intl J. Heat Mass Transfer145, 118770.
[30] Hallett, W. L. H. & Beauchamp-Kiss, S.2010Evaporation of single droplets of ethanol-fuel oil mixtures. Fuel89 (9), 2496-2504.
[31] Han, K., Zhao, C., Fu, G., Zhang, F., Pang, S. & Li, Y.2015Evaporation characteristics of dual component droplet of benzyl azides-hexadecane mixtures at elevated temperatures. Fuel157, 270-278.
[32] He, M., Liao, D. & Qiu, H.2017Multicomponent droplet evaporation on chemical micro-patterned surfaces. Sci. Rep.7, 41897.
[33] Hillenbrand, T. & Brüggemann, D.2020Evaporation of free falling droplets of binary alkane-ethanol blends. Fuel274, 117869.
[34] Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B.1964The Molecular Theory of Gases and Liquids. John Wiley and Sons. · Zbl 0057.23402
[35] Kadlec, P., Henke, S. & Bubnik, Z.2010Properties of ethanol and ethanol-water solutions-tables and equations. Sugar Ind.135 (10), 607-613.
[36] Kee, R. J., Warnatz, J. & Miller, J. A.1983 Fortran computer-code package for the evaluation of gas-phase viscosities, conductivities, and diffusion coefficients.[chemkin]. Tech. Rep. SAND-83-8209 ON: DE83009358. Sandia National Labs.
[37] Khasanshin, T. S., Shchamialiou, A. P. & Poddubskij, O. G.2003Thermodynamic properties of heavy \(n\)-alkanes in the liquid state: \(n\)-dodecane. Intl J. Thermophys.24 (5), 1277-1289.
[38] Koller, T. M., Klein, T., Giraudet, C., Chen, J., Kalantar, A., Van Der Laan, G. P., Rausch, M. H. & Froba, A. P.2017Liquid viscosity and surface tension of \(n\)-dodecane, \(n\)-octacosane, their mixtures, and a wax between 323 and 573 K by surface light scattering. J.Chem. Engng Data62 (10), 3319-3333.
[39] Kuo, K. K.1986Principles of Combustion, pp. 261-227. John Wiley & Sons.
[40] Lage, P. L. C. & Rangel, R. H.1993Total thermal radiation absorption by a single spherical droplet. J.Thermophys. Heat Transfer7 (1), 101-109.
[41] Law, C. K.1982Recent advances in droplet vaporization and combustion. Prog. Energy Combust. Sci.8 (3), 171-201.
[42] Lee, A. & Law, C. K.1992An experimental investigation on the vaporization and combustion of methanol and ethanol droplets. Combust. Sci. Technol.86 (1-6), 253-265.
[43] Liñán, A. & Williams, F. A.1993Fundamental Aspects of Combustion. Oxford University Press.
[44] Lupo, G. & Duwig, C.2018A numerical study of ethanol-water droplet evaporation. Trans. ASME: J. Engng Gas Turbines Power140 (2).
[45] Maqua, C., Castanet, G. & Lemoine, F.2008Bicomponent droplets evaporation: temperature measurements and modelling. Fuel87 (13-14), 2932-2942.
[46] Mathur, S., Tondon, P. K. & Saxena, S. C.1967Thermal conductivity of binary, ternary and quaternary mixtures of rare gases. Mol. Phys.12 (6), 569-579.
[47] Mcbride, B. J.1993Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species, vol. 4513. NASA Langley Research Center.
[48] Michailidou, E. K., Assael, M. J., Huber, M. L., Abdulagatov, I. M. & Perkins, R. A.2014Reference correlation of the viscosity of \(n\)-heptane from the triple point to 600 K and up to 248 MPa. J.Phys. Chem. Ref. Data43 (2), 023103.
[49] Millán-Merino, A.2020 Theoretical and numerical analysis of isolated ethanol droplets: evaporation and combustion. PhD thesis, Universidad Carlos III de Madrid.
[50] Millán-Merino, A., Fernández-Tarrazo, E., Sánchez-Sanz, M. & Williams, F. A.2020Modified multipurpose reduced chemistry for ethanol combustion. Combust. Flame215, 221-223.
[51] Muelas, Á., Carpio, J., Ballester, J., Sánchez, A. L. & Williams, F. A.2020Pyrolysis effects during high-temperature vaporization of alkane droplets. Combust. Flame217, 38-47.
[52] Niimura, Y. & Hasegawa, K.2019Evaporation of droplet in mid-air: pure and binary droplets in single-axis acoustic levitator. PloS One14 (2), e0212074.
[53] Nomura, H., Ujiie, Y., Rath, H. J., Sato, J. & Kono, M.1996 Experimental study on high-pressure droplet evaporation using microgravity conditions. In Symposium (International) on Combustion, vol. 26, pp. 1267-1273. Elsevier.
[54] Outcalt, S., Laesecke, A. & Fortin, T. J.2010Density and speed of sound measurements of hexadecane. J.Chem. Thermodyn.42 (6), 700-706.
[55] Pinheiro, A. P., Vedovoto, J. M., Da Silveira Neto, A. & Van Wachem, B. G. M.2019Ethanol droplet evaporation: effects of ambient temperature, pressure and fuel vapor concentration. Intl J. Heat Mass Transfer143, 118472.
[56] Ray, S., Raghavan, V. & Gogos, G.2019Two-phase transient simulations of evaporation characteristics of two-component liquid fuel droplets at high pressures. Intl J. Multiphase Flow111, 294-309.
[57] Sagdeev, D. I., Fomina, M. G., Mukhamedzyanov, G. K. & Abdulagatov, I. M.2013Experimental study of the density and viscosity of \(n\)-heptane at temperatures from 298 K to 470 K and pressure upto 245 MPa. Intl J. Thermophys.34 (1), 1-33.
[58] Sasaki, Y., Hasegawa, K., Kaneko, A. & Abe, Y.2020Heat and mass transfer characteristics of binary droplets in acoustic levitation. Phys. Fluids32 (7), 072102.
[59] Sazhin, S. S.2006Advanced models of fuel droplet heating and evaporation. Prog. Energy Combust. Sci.32 (2), 162-214.
[60] Sefiane, K., Tadrist, L. & Douglas, M.2003Experimental study of evaporating water-ethanol mixture sessile drop: influence of concentration. Intl J. Heat Mass Transfer46 (23), 4527-4534.
[61] Sharma, S. & Ghoshal, S. K.2015Hydrogen the future transportation fuel: from production to applications. Renew. Sustain. Energy Rev.43, 1151-1158.
[62] Shinjo, J., Xia, J., Ganippa, L. C. & Megaritis, A.2016Puffing-enhanced fuel/air mixing of an evaporating \(n\)-decane/ethanol emulsion droplet and a droplet group under convective heating. J.Fluid Mech.793, 444-476. · Zbl 1382.76264
[63] Shmuylovich, L., Shen, A. Q. & Stone, H. A.2002Surface morphology of drying latex films: multiple ring formation. Langmuir18 (9), 3441-3445.
[64] Sirignano, W. A.2010Fluid Dynamics and Transport of Droplets and Sprays. Cambridge University Press.
[65] Smoke, M. D. & Giovangigli, V.1991 Formulation of the premixed and nonpremixed test problems. In Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, pp. 1-28. Springer.
[66] Spalding, D. B.1959Theory of particle combustion at high pressures. Am. Rocket Soc. J.29 (11), 828-835.
[67] Svehla, R. A.1995 Transport coefficients for the Nasa Lewis chemical equilibrium program. NASA Lewis Research Center Cleveland Rep. 4647.
[68] Tanaka, Y., Itani, Y., Kubota, H. & Makita, T.1988Thermal conductivity of five normal alkanes in the temperature range 283-373 K at pressures up to 250 MPa. Intl J. Thermophys.9 (3), 331-350.
[69] Tseng, C. C. & Viskanta, R.2005Effect of radiation absorption on fuel droplet evaporation. Combust. Sci. Technol.177 (8), 1511-1542.
[70] Tseng, C. C. & Viskanta, R.2006Enhancement of water droplet evaporation by radiation absorption. Fire Safety J.41 (3), 236-247.
[71] 2016 Chemical-kinetic mechanisms for combustion applications. San Diego Mechanism web page, Mechanical and Aerospace Engineering (Combustion Research), University of California at San Diego (http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html), version 2016-12-14, last accessed on 24-07-2017.
[72] Wilke, C. R. & Chang, P.1955Correlation of diffusion coefficients in dilute solutions. AIChE J.1 (2), 264-270.
[73] Williams, F. A.2018Combustion Theory. CRC Press.
[74] Wohlfarth, C.2008 Viscosity of hexadecane. In Supplement to IV/18, pp. 655-656. Springer.
[75] Yang, J.-R. & Wong, S.-C.2001On the discrepancies between theoretical and experimental results for microgravity droplet evaporation. Intl J. Heat Mass Transfer44, 4433-4443. · Zbl 0986.76508
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