Absorption of external thermal radiation in asymmetrically illuminated droplets

A theoretical model of thermal radiation absorption in semi-transparent droplets at the surface and inside a fuel spray is presented. Asymmetry of droplet illumination is taken into account. Results of Mie calculations of thermal radiation absorption inside large spherical droplets illuminated from a hemisphere are presented. Simple approximations for the angular and radial dependencies of the absorbed radiation power are suggested. These approximations are generalisations of the approximations suggested earlier by the authors for the case of symmetric illumination of droplets. They predict the results close to those which follow from the Mie calculations. Results of approximate calculations for a typical diesel fuel droplet at the periphery of the spray are presented. As in the case of symmetrical droplet illumination, an increased absorption of thermal radiation in the central area of the droplet is predicted. Also, at the illuminated side of the droplet, the absorption of radiation in a thin layer near the surface of the droplet is predicted, as in the case of symmetrical droplet illumination. Absorption of radiation in the central area of the droplet is related to the contribution of radiation in the spectral ranges of semi-transparency. The maximum of radiation absorption near the droplet surface is linked to the contribution of radiation in the vicinity of the diesel fuel absorption peak (λ≈3.4 μm).