Abstract
Understanding the transport processes during evaporation and combustion of isolated liquid fuel droplet is highly important in several applications involving sprays. Comprehensive numerical models assist in carrying out simulations involving interlinked transport processes in liquid and gas phases using proper interface coupling conditions. The predictions from such numerical models reveal flow, temperature and species fields, with which the evaporation, as well as combustion characteristics, can be thoroughly analyzed. In this article, a detailed review of numerical models used to simulate evaporation of isolated droplets under several operating conditions is presented. This includes evaporation in high-pressure conditions, where real gas effects and solubility of ambient gas into the liquid droplet, come into play. Subsequently, a review of droplet combustion models, which are comprehensive enough to reveal the burning characteristics of an isolated droplet, is presented. Importance of liquid phase motion on evaporation and combustion behavior and water absorption in the case of alcohol droplets are reported. This review also includes modeling concepts applied to multi-component droplets.
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References
Williams A (1973) Combustion of droplet of liquid fuels: a review. Combust Flame 21:1–31
Faeth GM (1977) Current status of droplet and liquid combustion. Prog Energy Combust Sci 3:191–224
Law CK (1982) Recent advances in droplet vaporization and combustion. Prog Energy Combust Sci 8:171–201
Faeth GM (1983) Evaporation and combustion of sprays. Prog Energy Combust Sci 9:1–76
Sirignano WA (1983) Fuel droplet vaporization and spray combustion theory. Prog Energy Combust Sci 9:291–322
Dwyer HA (1989) Calculations of droplet dynamics in high temperature environment. Prog Energy Combust Sci 15:131–158
Law CK, Faeth GM (1994) Opportunities and challenges of combustion in microgravity. Prog Energy Combust Sci 20:65–113
Gilver SD, Abraham J (1996) Supercritical droplet vaporization and combustion studies. Prog Energy Combust Sci 22:1–28
Biroul M, Gökalp I (2006) Current status of droplet evaporation in turbulent flows. Prog Energy Combust Sci 32:408–423
Tong AY, Sirognanao WA (1986) Multicomponent droplet vaporization in a high temperature gas. Combust Flame 66:221–235
Gogos G, Ayyaswamy PS (1988) A model for the evaporation of a slowly moving droplet. Combust Flame 74:111–129
Aharon I, Shaw BD (1996) Marangoni instability of bi-component droplet gasification. Phys Fluids 8:1820–1827
Ha VM, Lai CL (2002) Onset of Marangoni instability of a two-component evaporating droplet. Int J Heat Mass Transf 45:5143–5158
Ha VM, Lai CL (2004) Theoretical analysis of Marangoni instability of an evaporating droplet by energy method. Int J Heat Mass Transf 45:5143–5158
Ra Y, Reitz RD (2003) The application of a multicomponent droplet vaporization model to gasoline direct injection engines. Int J Engine Res 4:193–218
Tonini S, Cossali GE (2012) An analytical model of liquid drop evaporation in gaseous environment. Int J Ther Sci 57:45–53
Law CK (1978) Internal boiling and superheating in vaporizing multicomponent droplets. Am Inst Chem Eng J 24:626–632
Abramzon B, Sirignanao W (1989) Droplet vaporization model for spray combustion calculations. Int J Heat Mass Transf 32:1605–1618
Haywood RJ, Nafziger R, Renksizbulut MA (1989) A detailed examination of gas and liquid phase transient processes in convective droplet evaporation. J Heat Transf 111:495–502
Megaridis CM, Sirignano WA (1990) Numerical modeling of a vaporizing multicomponent droplet. Proc Combust Inst 23:1413–1421
Megaridis CM, Sirignano WA (1993) Multicomponent droplet vaporization in a laminar convective environment. Combust Sci Technol 87:27–44
Chiang CH, Raju MS, Sirignano WA (1992) Numerical analysis of convecting, vaporizing fuel droplet with variable properties. Int J Heat Mass Transf 35:1307–1324
Megaridis CM (1993) Liquid phase variable property effects in multicomponent droplet convective evaporation. Combust Sci Technol 92:293–311
Megaridis CM (1993) Comparison between experimental measurements and numerical predictions of internal temperature distributions of a droplet vaporizing under high convective conditions. Combust Flame 93:287–302
Renksizbulut M, Bussmann M (1993) Multicomponent droplet evaporation at intermediate Reynolds numbers. Int J Heat Mass Transf 36:2827–2835
Haywood RJ, Renksizbulut M, Raithby GD (1994) Transient deformation and evaporation of droplets at intermediate Reynolds numbers. Int J Heat Mass Transf 37:1401–1409
Shih AT, Megaridis CM (1995) Suspended droplet evaporation modeling in a laminar convective environment. Combust Flame 102:256–270
Shih AT, Megaridis CM (1996) Thermocapillary flow effects on convective droplet evaporation. Int J Heat Mass Transf 39:247–257
Tamim J, Hallet WLH (1995) A continuous thermodynamics model for multicomponent droplet vaporization. Chem Eng Sci 50:2933–2942
Dwyer HA, Aharon I, Shaw BD, Niazmand H (1996) Surface tension influences on methanol droplet vaporization in the presence of water. Proc Combust Inst 26:1613–1619
Dwyer HA, Shaw BD (2001) Marangoni and stability studies on fiber-supported methanol droplets evaporating in reduced gravity. Combust Sci Technol 162:331–346
Aggarwal SK, Mongia HC (2002) Multicomponent and high-pressure effects on droplet vaporization. J Eng Gas Turbines Power 124:248–255
Gartung K, Arndt S, Seibel C (2002) Vaporization of multicomponent fuel droplets: numerical and experimental examination. In: Proc. of 18nd annual conference on liquid atomization and spray systems (Europe), Zaragoza, Spain, September 9–11
Sazhin SS (2006) Advanced models of fuel droplet heating and evaporation. Prog Energy Combust Sci 32:162–214
Yang S, Ra Y, Reitz RD (2010) A vaporization model for realistic multicomponent fuels. In: Proc. of 22nd annual conference on liquid atomization and spray systems (USA), Cincinnati, OH, May 16–19
Elwardany AE, Gusev IG, Castanet G, Lemoine F, Sazhin SS (2011) Mono- and multicomponent droplet cooling/heating and evaporation: comparative analysis of numerical models. Atom Sprays 21:907–931
Sazhin SS, Elwardany AE, Krutitskii PA, Depredurand V, Castanet G, Lemoine F, Sazhina EM, Heikal MR (2011) Multi-component droplet heating and evaporation: numerical simulation versus experimental data. Int J Therm Sci 50:1164–1180
Strotos G, Gavaises M, Theodorakakos A, Bergeles G (2011) Numerical investigation of the evaporation of two-component droplets. Fuel 90:1492–1507
Raghuram S, Raghavan V (2012) Numerical study of transient evaporation of moving two-component fuel droplets. At Sprays 22:493–513
Raghuram S, Raghavan V, Pope DN, Gogos G (2012) Numerical study of Marangoni convection during transient evaporation of two-component droplet under forced convective environment. Int J Heat Mass Transf 55:7949–7957
Raghuram S, Raghavan V, Pope DN, Gogos G (2013) Two-phase modeling of evaporation characteristics of blended methanol-ethanol droplets. Int J Multiph Flow 52:46–59
Tonini S, Cossali GE (2015) A novel formulation of multi-component drop evaporation models for spray applications. Int J Therm Sci 89:245–253
Azimi A, Arabkhalaj A, Ghassemi H, Markadeh RS (2017) Effects of unsteadiness on droplet evaporation. Int J Ther Sci 120:354–365
Strotos G, Malgarinos I, Nikolopoulos N, Gavaises M (2016) Predicting the evaporation rate of stationary droplets with the VOF methodology for a wide range of ambient temperature conditions. Int J Therm Sci 109:253–262
Matlosz RL, Leipziger S, Torda TP (1972) Investigation of liquid droplet evaporation in a high temperature and high pressure environment. Int J Heat Mass Transf 15:831–852
Kadota T, Hiroyasu H (1976) Evaporation of a single droplet at elevated pressures and temperatures. Bull JSME 19:1515–1521
Manrique JA, Borman GL (1969) Calculations of steady state droplet vaporization at high ambient pressure. Int J Heat Mass Transf 12:1081–1095
Lazar RS, Faeth GM (1971) Bipropellant droplet combustion in the vicinity of the critical point. Proc Combust Inst 13:743–753
Canada GS, Faeth GM (1973) Fuel droplet burning rates at high pressures. Proc Combust Inst 14:1345–1354
Curtis EW, Farrell PV (1988) Droplet vaporization in a super critical microgravity environment. Acta Astronaut 17:1189–1193
Curtis EW, Farrell PV (1992) A numerical study of high-pressure droplet vaporization. Combust Flame 90:85–102
Hsieh KC, Shuen JS, Yang V (1991) Droplet vaporization in high-pressure environments I: near critical conditions. Combust Sci Technol 76:111–132
Jia H, Gogos G (1992) Investigation of liquid droplet evaporation in sub-critical and super-critical gaseous environments. J Thermophys Heat Transf 6:738–745
Jia H, Gogos G (1993) High pressure droplet vaporization; effects of liquid phase gas solubility. Int J Heat Mass Transf 36:4419–4431
Delplanque JP, Sirignano WA (1993) Numerical study of the transient vaporization of an oxygen droplet at sub-critical and super-critical conditions. Int J Heat Mass Transf 36:303–314
Haldenwang P, Nicoli C, Daou J (1996) High pressure vaporization of LOX droplet crossing the critical conditions. Int J Heat Mass Transf 39:3453–3464
Zhu GS, Aggarwal SK (2000) Droplet super-critical vaporization with emphasis on equation of state. Int J Heat Mass Transf 43:1157–1171
Zhu GS, Aggarwal SK (2002) Fuel droplet evaporation in a super-critical environment. ASME J Eng Gas Turbines Power 124:762–770
Gogos G, Soh S, Pope DN (2003) Effects of gravity and ambient pressure on liquid fuel droplet evaporation. Int J Heat Mass Transf 46:283–296
Consolini L, Aggarwal SK, Murad S (2003) A molecular dynamics simulation of droplet evaporation. Int J Heat Mass Transf 46:3179–3188
Zhang H (2004) Numerical research on a vaporizing fuel droplet in a forced convective environment. Int J Multiph Flow 30(2):181–198
Zhang H, Raghavan V, Gogos G (2008) Subcritical and supercritical droplet evaporation within a zero gravity environment: low Weber number relative motion. Int Commun Heat Mass Transf 35:385–394
Yang JR, Wong SC (2001) On the discrepancies between theoretical and experimental results for microgravity droplet evaporation. Int J Heat Mass Transf 44:4433–4443
Nomura H, Ujiie Y, Rath HJ, Sato J, Kono M (1996) Experimental study of high-pressure droplet evaporation using microgravity conditions. In: Proc. 26th Symp. on combustion, The Combustion Institute, Pittsburgh, PA, 1267–1273
Zhang H, Raghavan V, Gogos G (2009) Subcritical and supercritical droplet evaporation within a zero gravity environment; on the discrepancies between theoretical and experimental results. Int J Spray Combust Dyn 1:317–338
Balaji B, Raghavan V, Ramamurthi K, Gogos G (2011) A numerical study of evaporation characteristics of spherical n-dodecane droplets in high pressure nitrogen environment. Phys Fluids 23(6):063601
Saroj R, Raghavan V, Gogos G (2018) Two-phase transient simulations of evaporation characteristics of two-component liquid fuel droplets at high pressures. Int J Multiph Flow. https://doi.org/10.1016/j.ijmultiphaseflow.2018.10.002
Yang JR, Wong SC (2002) An experimental and theoretical study of the effects of heat conduction through the support fiber on the evaporation of a droplet in a weakly convective flow. Int J Heat Mass Transf 45:4589–4598
Polymeropoulos CE, Peskin RL (1969) Ignition and extinction of liquid fuel drops—numerical computations. Combust Flame 13:166–172
Dwyer HA, Sanders BR (1986) A detailed study of burning fuel droplets. In: Symposium (international) on combustion. 21, 633–639
Dwyer HA, Sanders BR (1988) Calculations of unsteady reacting droplet flows. In: Symposium (international) on combustion. 22, 1923–1929
Shaw BD (1990) Studies of influences of liquid phase species diffusion on spherically symmetric combustion of miscible binary droplets. Combust Flame 81:277–288
Cho SY, Choi MY, Dryer FL (1991) Extinction of a free methanol droplet in microgravity. In: Symposium (international) on combustion, 23, 1611–1617
Chao BH, Law CK, T’ien JS (1991) Structure and extinction of diffusion flames with flame radiation. In: Symposium (international) on combustion, 23, 523–531
Madooglu K, Karagozian AR (1993) Burning of a spherical fuel droplet in a uniform flow field with exact property variation. Combust Flame 94:321–329
Saitoh T, Yamazaki K, Viskanta R (1993) Effect of thermal radiation on transient combustion of a fuel droplet. AIAA J Thermophys Heat Trans 7:94–100
Huang LW, Chen CH (1995) Flame stabilization and blow off over a single droplet. Numer Heat Transf A 27:53–71
Jiang TL, Chen WS, Tsai MJ, Chiu HH (1995) A numerical investigation of multiple flame configurations in convective droplet gasification. Combust Flame 103:221–238
Marchese AJ, Dryer FL, Colantonio RO, Nayagam V (1996) Microgravity combustion of methanol and methanol/water droplets: drop tower experiments and model predictions. In: Symposium (international) on combustion, 26, 1209–1217
Marchese AJ, Dryer FL (1996) The effect of liquid mass transport on the combustion and extinction of bicomponent droplets of methanol and water. Combust Flame 105:104–122
Lee J, Tomboulides AG, Orszag SA, Yetter RA, Dryer FL (1996) A transient two-dimensional chemically reactive flow model: fuel particle combustion in a nonquiescent environment. In: Symposium (international) on combustion, 26, 3059–3065
Huang LW, Chen CH (1997) Droplet ignition in a high-temperature convective environment. Combust Flame 109:145–162
Marchese AJ, Dryer FL (1997) The effect of non-luminous thermal radiation in microgravity droplet combustion. Combust Sci Technol 124:371–402
Marchese AJ, Dryer FL, Colantonio RO (1998) Radiative effects in space-based methanol-water droplet combustion experiments. Proc Combust Inst 27:2627–2634
Dwyer HA, Shaw BD, Niazmand H (1998) Droplet/flame interactions including surface tension influences. In: Symposium (international) on combustion, 27, 1951–1957
Balakrishnan P, Sundararajan T, Natarajan R (2000) Interference effects during burning of tandem porous spheres in mixed convective environment. AIAA J 38:1889–1898
Balakrishnan P, Sundararajan T, Natarajan R (2001) Combustion of a fuel droplet in a mixed convective environment. Combust Sci Tech 163:77–106
Kazakov A, Conley J, Dryer FL (2003) Detailed modeling of an isolated, ethanol droplet combustion under microgravity conditions. Combust Flame 134:301–314
Cuoci A, Mehl M, Buzzi-Ferraris G, Faravelli T, Manca D, Ranzi E (2005) Autoignition and burning rates of fuel droplets under microgravity. Combust Flame 143:211–226
Pope DN, Gogos G (2005) Numerical simulation of fuel droplet extinction due to forced convection. Combust Flame 142:89–106
Pope DN, Howard D, Lu K, Gogos G (2005) Combustion of moving droplets and suspended droplets: transient numerical results. J Thermophys Heat Transf 19:273–281
Raghavan V, Babu V, Sundararajan T, Natarajan R (2005) Flame shapes and burning rates of spherical fuel particles in a mixed convective environment. Int J Heat Mass Transf 48:5354–5370
Dietrich DL, Struk PM, Ikegami M, Xu G (2005) Single droplet combustion of decane in microgravity: experiments and numerical modelling. Combust Theor Model 9:569–585
Stauch R, Lipp S, Maas U, Rudman M (2006) Detailed numerical simulations of the autoignition of single n-heptane droplets in air. Combust Flame 145:533–542
Raghavan V, Pope DN, Howard D, Gogos G (2006) Surface tension effects during low-Reynolds-number methanol droplet combustion. Combust Flame 145:791–807
Raghavan V, Pope DN, Gogos G (2006) Effects of forced convection and surface tension during methanol droplet combustion. J Thermophys Heat Transf 20:787–798
Raghavan V, Pope DN, Gogos G (2008) Effect of non-luminous flame radiation during methanol droplet combustion. Combust Sci Technol 180:546–564
Raghavan V, Babu V, Sundararajan T (2009) Investigation of interaction between methanol fed tandem porous spheres burning in a mixed convective environment. Combust Theor Model 13:461–485
Jin Y, Shaw BD (2010) Computational modeling of n-heptane droplet combustion in air–diluent environments under reduced-gravity. Int J Heat Mass Transf 53:5782–5791
Sahu VK, Raghavan V (2011) A numerical study of steady diffusion flames established over ethanol fed porous spheres. Arch Combust 31:211–222
Sahu VK, Raghavan V, Pope DN, Gogos G (2011) Numerical modeling of steady burning characteristics of spherical ethanol particles in a spray environment. J Heat Transf 133:094502
Farouk T, Dryer FL (2012) Tethered methanol droplet combustion in carbon-dioxide enriched environment under microgravity conditions. Combust Flame 159:200–209
Farouk TI, Liu YC, Savas AJ, Avedisian CT, Dryer FL (2013) Sub-millimeter sized methyl butanoate droplet combustion: microgravity experiments and detailed numerical modeling. Proc Combust Inst 34:1609–1616
Awasthi I, Gogos G, Sundararajan T (2013) Effects of size on combustion of isolated methanol droplets. Combust Flame 160:1789–1802
Awasthi I, Pope DN, Gogos G (2014) Effects of the ambient temperature and initial diameter in droplet combustion. Combust Flame 161:1883–1899
Cuoci A, Frassoldati A, Faravelli T, Ranzi E (2015) Numerical modeling of auto-ignition of isolated fuel droplets in microgravity. Proc Combust Inst 35:1621–1627
Alam FE, Liu YC, Avedisian CT, Dryer FL, Farouk TI (2015) n-Butanol droplet combustion: numerical modeling and reduced gravity experiments. Proc Combust Inst 35:1693–1700
Cheng LY, Alam FE, Yuhao X, Dryer FL, Avedisian CT, Farouk TI (2016) Combustion characteristics of butanol isomers in multiphase droplet configurations. Combust Flame 169:216–228
Farouk TI, Dietrich D, Alam FE, Dryer FL (2017) Isolated n-decane droplet combustion—dual stage and single stage transition to “Cool Flame” droplet burning. Proc Combust Inst 36:2523–2530
Cuoci A, Saufi AE, Frassoldati A, Dietrich DL, Williams FA, Faravelli T (2017) Flame extinction and low-temperature combustion of isolated fuel droplets of n-alkanes. Proc Combust Inst 36:2531–2539
Ashna M, Rahimian MH, Fakhari A (2017) Extended lattice Boltzmann scheme for droplet combustion. Phys Rev E 95:053301
Giusti A, Sidey JAM, Borghesi G, Mastorakos E (2017) Simulations of droplet combustion under gas turbine conditions. Combust Flame 184:101–116
Giusti A, Sitte MP, Borghesi G, Mastorakos E (2018) Numerical investigation of kerosene single droplet ignition at high-altitude relight conditions. Fuel 225:663–670
Stagni A, Cuoci A, Frassoldati A, Ranzi E, Faravelli T (2018) Numerical investigation of soot formation from microgravity droplet combustion using heterogeneous chemistry. Combust Flame 189:393–406
Chen W, Gao R, Sun J, Lei Y, Fan X (2018) Modeling of an isolated liquid hydrogen droplet evaporation and combustion. Cryogenics 96:151–158
Irfan M, Muradoglu M (2018) A front tracking method for particle resolved simulation of vaporization and combustion of a fuel droplet. Comput Fluids 174:283–299
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Raghavan, V. Numerical Modeling of Evaporation and Combustion of Isolated Liquid Fuel Droplets: a Review. J Indian Inst Sci 99, 5–23 (2019). https://doi.org/10.1007/s41745-019-0097-5
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DOI: https://doi.org/10.1007/s41745-019-0097-5