Abstract
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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Abbreviations
- 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 (−)
- DL:
-
Diffusion-limited model
- HY:
-
Hybrid model
- WM:
-
Well-mixed model
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Acknowledgments
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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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). https://doi.org/10.1007/s00348-014-1871-9
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DOI: https://doi.org/10.1007/s00348-014-1871-9