Experiments in Fluids

, 56:1871 | Cite as

Experimental analysis and semicontinuous simulation of low-temperature droplet evaporation of multicomponent fuels

  • S. LehmannEmail author
  • S. Lorenz
  • E. Rivard
  • D. Brüggemann
Research Article


Low-pollutant and efficient combustion not only in internal combustion engines requires a balanced gaseous mixture of fuel and oxidizer. As fuels may contain several hundred different chemical species with different physicochemical properties as well as defined amounts of biogenic additives, e.g., ethanol, a thorough understanding of liquid fuel droplet evaporation processes is necessary to allow further engine optimization. We have studied the evaporation of fuel droplets at low ambient temperature. A non-uniform temperature distribution inside the droplet was already considered by including a finite thermal conductivity in a one-dimensional radial evaporation model (Rivard and Brüggemann in Chem Eng Sci 65(18):5137–5145, 2010). For a detailed analysis of droplet evaporation, two non-laser-based experimental setups have been developed. They allow a fast and relatively simple but yet precise measurement of diameter decrease and composition change. The first method is based on collecting droplets in a diameter range from 70 to 150 µm by a high-precision scale. A simultaneous evaluation of mass increase is employed for an accurate average diameter value determination. Subsequently, a gas chromatographic analysis of the collected droplets was conducted. In the second experiment, evaporation of even smaller droplets was optically analyzed by a high-speed shadowgraphy/schlieren microscope setup. A detailed analysis of evaporating E85 (ethanol/gasoline in a mass ratio of 85 %/15 %) and surrogate fuel droplets over a wide range of initial droplet diameters and ambient temperatures was conducted. The comparison of experimental and numerical results shows the applicability of the developed model over a large range of diameters and temperatures.


Droplet Diameter Droplet Generator Droplet Velocity Droplet Evaporation Initial Droplet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Orthographic projection of the droplet on a plane perpendicular to the direction of motion (m2)


Spalding molar transfer number (−)


Spalding heat transfer number (−)


Drag coefficient (−)


Average molar density of gas phase (mol m−3)


Molar density of the liquid phase (mol m−3)


Molar-specific heat capacity of the liquid phase (J mol−1 K−1)


Average molar-specific heat capacity of gas phase at surface (J mol−1 K−1)


Average molar-specific heat capacity of the vapor phase (J mol−1 K−1)


Initial droplet diameter (m)


Diffusivity of a species (m2 s−1)


Average vapor diffusivity in the surrounding gas phase (m2 s−1)


Distribution function (−)


(Drag) force (N)


Enthalpy of vaporization of the liquid phase at droplet surface (J mol−1)


Molar mass of a species (kg mol−1)


Liquid thermal conductivity (W m−1 K−1)


Droplet mass (kg)


Fraction of substance in the droplet (mol)


Molar flow rate (mol s−1)


Nusselt number (−)

\(\dot{Q},\dot{Q}_{i} , \dot{Q}_{o}\)

Heat flow, heat flow from the inside/outside of the droplet (J s−1)


Droplet radius (m)


(Modified) Sherwood number (−)


Time (s)

\(T_{a}, T_{l} , T_{s} , T_{\infty }\)

Ambient temperature, liquid temperature, droplet surface temperature, gas-phase temperature in infinite distance (K)


Relative velocity of the droplet (m s−1)


(Liquid) molar fraction of species i (−)

\(x_{g,v,s},\,x_{g,v,\infty }\)

Molar fraction of vapor in gas phase at the droplet surface and in infinite distance (−)


Correlation factor (−)


Mass density of the flow (kg m−3)


Internal recirculation factor (−)


Diffusion-limited model


Hybrid model


Well-mixed model



The authors are grateful for the financial support of the German Research Foundation (DFG) under Grant No. BR 1713/10 and the reviewers’ supportive remarks.


  1. Abdel-Qader Z, Hallett WL (2005) The role of liquid mixing in evaporation of complex multicomponent mixtures: modelling using continuous thermodynamics. Chem Eng Sci 60(6):1629–1640. doi: 10.1016/j.ces.2004.10.015 CrossRefGoogle Scholar
  2. Abramzon B, Sirignano W (1989) Droplet vaporization model for spray combustion calculations. Int J Heat Mass Transf 32(9):1605–1618. doi: 10.1016/0017-9310(89)90043-4 CrossRefGoogle Scholar
  3. Adachi M, McDonell VG, Tanaka D, Senda J, Fujimoto H (1997) Characterization of fuel vapor concentration inside a flash boiling spray. SAE Int, Warrendale. doi: 10.4271/970871 CrossRefGoogle Scholar
  4. Atherton TJ, Kerbyson DJ (1999) Size invariant circle detection. Image Vis Comput 17(11):795–803. doi: 10.1016/S0262-8856(98)00160-7 CrossRefGoogle Scholar
  5. Calvo E, García JA, Santolaya JL, García I, Aísa L (2012) A framework about flow measurements by LDA–PDA as a spatio-temporal average: application to data post-processing. Meas Sci Technol 23(5):055202. doi: 10.1088/0957-0233/23/5/055202 CrossRefGoogle Scholar
  6. Clift R, Grace JR, Weber ME (1978) Bubbles, drops, and particles. Academic Press, New YorkGoogle Scholar
  7. Drake M, Haworth D (2007) Advanced gasoline engine development using optical diagnostics and numerical modeling. Proc Combust Inst 31(1):99–124. doi: 10.1016/j.proci.2006.08.120 CrossRefGoogle Scholar
  8. Fieberg C, Reichelt L, Martin D, Renz U, Kneer R (2009) Experimental and numerical investigation of droplet evaporation under diesel engine conditions. Int J Heat Mass Transf 52(15–16):3738–3746. doi: 10.1016/j.ijheatmasstransfer.2009.01.044 CrossRefzbMATHGoogle Scholar
  9. Frohn A, Roth N (2000) Dynamics of droplets. Springer, BerlinCrossRefzbMATHGoogle Scholar
  10. Gartung K (2008) Modellierung der Verdunstung realer Kraftstoffe zur Simulation der Gemischbildung bei Benzindirekteinspritzung. Logos Verlag Berlin, BerlinGoogle Scholar
  11. Hallett W, Beauchamp-Kiss S (2010) Evaporation of single droplets of ethanol–fuel oil mixtures. Fuel 89(9):2496–2504. doi: 10.1016/j.fuel.2010.03.007 CrossRefGoogle Scholar
  12. Hallett W, Legault N (2011) Modelling biodiesel droplet evaporation using continuous thermodynamics. Fuel 90(3):1221–1228. doi: 10.1016/j.fuel.2010.11.035 CrossRefGoogle Scholar
  13. Lemoine F, Castanet G (2013) Temperature and chemical composition of droplets by optical measurement techniques: a state-of-the-art review. Exp Fluids 54(7):1572. doi: 10.1007/s00348-013-1572-9 CrossRefGoogle Scholar
  14. Nguyen D, Honnery D, Soria J (2011) Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV. Exp Fluids 50(4):949–959. doi: 10.1007/s00348-010-0962-5 CrossRefGoogle Scholar
  15. Ra Y, Reitz RD (2009) A vaporization model for discrete multi-component fuel sprays. Int J Multiph Flow 35(2):101–117. doi: 10.1016/j.ijmultiphaseflow.2008.10.006 CrossRefGoogle Scholar
  16. Renksizbulut M, Yuen MC (1983) Numerical study of droplet evaporation in a high-temperature stream. J Heat Transf 105(2):389. doi: 10.1115/1.3245591 CrossRefGoogle Scholar
  17. Rivard E, Brüggemann D (2010) Numerical investigation of semi-continuous mixture droplet vaporization at low temperature. Chem Eng Sci 65(18):5137–5145. doi: 10.1016/j.ces.2010.06.010 CrossRefGoogle Scholar
  18. Sarathy SM, Oßwald P, Hansen N, Kohse-Höinghaus K (2014) Alcohol combustion chemistry. Prog Energy Combust Sci 44:40–102. doi: 10.1016/j.pecs.2014.04.003 CrossRefGoogle Scholar
  19. Sazhin S, Elwardany A, Krutitskii P, Deprédurand V, Castanet G, Lemoine F, Sazhina E, Heikal M (2011a) Multi-component droplet heating and evaporation: numerical simulation versus experimental data. Int J Therm Sci 50(7):1164–1180. doi: 10.1016/j.ijthermalsci.2011.02.020 CrossRefGoogle Scholar
  20. Sazhin S, Elwardany A, Sazhina E, Heikal M (2011b) A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbon fuel droplets. Int J Heat Mass Transf 54(19–20):4325–4332. doi: 10.1016/j.ijheatmasstransfer.2011.05.012 CrossRefzbMATHGoogle Scholar
  21. Settles GS (2006) Schlieren and shadowgraph techniques: visualizing phenomena in transparent media with 208 figures and 48 color plates, 1st edn. Springer, BerlinGoogle Scholar
  22. Sirignano WA (2010) Fluid dynamics and transport of droplets and sprays, 2nd edn. Cambridge University Press, New YorkCrossRefGoogle Scholar
  23. Sirignano WA (2014) Advances in droplet array combustion theory and modeling. Prog Energy Combust Sci 42:54–86. doi: 10.1016/j.pecs.2014.01.002 CrossRefGoogle Scholar
  24. Stan C, Troeger R, Guenther S, Stanciu A, Martorano L, Tarantino C, Lensi R (2001) Internal mixture formation and combustion—from gasoline to ethanol. SAE Int, Warrendale. doi: 10.4271/2001-01-1207 CrossRefGoogle Scholar
  25. Tamin J, Hallett WL (1995) A continuous thermodynamics model for multicomponent droplet vaporization. Chem Eng Sci 50(18):2933–2942. doi: 10.1016/0009-2509(95)00131-N CrossRefGoogle Scholar
  26. Yang S, Ra Y, Reitz RD, VanDerWege B, Yi J (2010) Development of a realistic multicomponent fuel evaporation model. Atomiz Spray 20(11):965–981. doi: 10.1615/AtomizSpr.v20.i11.40 CrossRefGoogle Scholar
  27. Yuen MC, Chen LW (1976) On drag of evaporating liquid droplets. Combust Sci Technol 14(4–6):147–154. doi: 10.1080/00102207608547524 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • S. Lehmann
    • 1
    Email author
  • S. Lorenz
    • 1
  • E. Rivard
    • 1
  • D. Brüggemann
    • 1
  1. 1.Chair of Engineering Thermodynamics and Transport Processes (LTTT), Bayreuth Engine Research Center (BERC)University of BayreuthBayreuthGermany

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