Heating and evaporation of semi-transparent diesel fuel droplets in the presence of thermal radiation

Absorption and scattering spectral efficiency factors for spherical semi-transparent fuel droplets are approximated by simple analytical expressions as functions of imaginary and real parts of the complex index of refraction and the diffraction parameters of droplets. These expressions are applied to the modelling of thermal radiation transfer in Diesel engines. On the basis of the P-1 approximation, which is applicable due to the large optical thickness of combustion products, various ways of spectral averaging for absorption and scattering coefficients are suggested. Assuming that the concentration of fuel droplets is small, the scattering effects are ignored and the analysis is focused on approximations for the absorption coefficient. The average absorption coefficient of droplets is shown to be proportional to ard2+b, where rd is the droplet radii, and a and b are quadratic functions of gas temperature. Explicit expressions for a and b are derived for diesel fuel droplets in the range 5–50 μm and gas temperatures in the range 1000–3000 K. The expression for the average absorption coefficient of droplets is implemented into the research version of VECTIS CFD code of Ricardo Consulting Engineers. The effect of thermal radiation on heating and evaporation of semi-transparent diesel fuel droplets is shown to be considerably smaller when compared with the case of black opaque droplets.