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


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.

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A :

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

B n :

Spalding molar transfer number (−)

B h :

Spalding heat transfer number (−)

c d :

Drag coefficient (−)

\(\overline{c}_{g}\) :

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

c l :

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

C p,l :

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

\(\overline{C}_{p,g,s}\) :

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

\(\overline{C}_{p,v}\) :

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

d 0 :

Initial droplet diameter (m)

D l,I,m :

Diffusivity of a species (m2 s−1)

\(\overline{D}_{v,g}\) :

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

f :

Distribution function (−)

F (d) :

(Drag) force (N)

ΔH v,l,s :

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

I :

Molar mass of a species (kg mol−1)

k l :

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

m d :

Droplet mass (kg)

n d :

Fraction of substance in the droplet (mol)

\(\dot{n}\) :

Molar flow rate (mol s−1)

Nu :

Nusselt number (−)

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

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

r s :

Droplet radius (m)

Sh (*) :

(Modified) Sherwood number (−)

t :

Time (s)

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

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

v rel :

Relative velocity of the droplet (m s−1)

x (l,)i :

(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 (−)

κ :

Correlation factor (−)

ρ f :

Mass density of the flow (kg m−3)

χ :

Internal recirculation factor (−)


Diffusion-limited model


Hybrid model


Well-mixed model


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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.

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Correspondence to S. Lehmann.

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Lehmann, S., Lorenz, S., Rivard, E. et al. Experimental analysis and semicontinuous simulation of low-temperature droplet evaporation of multicomponent fuels. Exp Fluids 56, 1871 (2015).

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