Numerical study of global rainbow technique: sensitivity to non-sphericity of droplets

The measurement of droplet temperature and size distribution in sprays is a difficult task. To reach this aim, the global rainbow technique (GRT) has been developed on the assumption that the synthetic rainbow created by a large number of droplets is insensitive to the non-sphericity of droplets if the droplets’ orientations were sufficiently random. In order to test this assumption, numerical as well as experimental analyses of GRT are carried out by our team. As a companion to the work done in experiments, the objective of this work is to quantify the sensitivity of the GRT to the non-sphericity of droplets from a numerical aspect. Light scattering properties around the rainbow angle are investigated by using the Null-field method within a T-matrix formulation, both for a single spheroid in an arbitrary orientation and for an ensemble of spheroids in random orientations illuminated by a plane wave. Refractive index and size distribution of droplets are extracted from simulated global rainbow signals so as to quantify the sensitivity of the GRT to the non-sphericity. Exemplifying results are compiled and presented. Additionally, comparisons between the Null-field method and the generalized Lorenz-Mie theory for spheroids are also provided in this paper.