Sedimentation analysis of columnar ice crystals in viscous flow regimes

Abstract

The sedimentation process of columnar ice crystals was evaluated using data obtained by the lattice Boltzmann method. The data used correspond to columnar ice crystals with maximum dimension less than 100 μm and aspect ratios between 1 and 3. The terminal velocity was computed for different ice-crystal bulk densities and for three falling orientations. The analysis corresponds to ice crystals falling in viscous flow regimes, where theoretical formulations overestimate the terminal velocity. Different characteristic lengths of columnar ice crystals and different theoretical proposals for the sedimentation process were tested in order to find the best representation of the data. Characteristic lengths reported in the literature do not represent the sedimentation process for all the falling orientations used in this study. Thus, it was not possible to obtain a unique relation between the Best and Reynolds numbers. In particular, columnar ice crystals falling with their longer dimension parallel to the vertical direction show a large dispersion that it does not seem possible to reduce. The theoretical and semi-empirical formulations of the terminal velocity evaluated show large deviations in the computed velocity, with a strong dependence on ice-crystal aspect ratio. The dispersion observed seems to be intrinsically related to the dimensionless variables used to parametrize the terminal velocity. To derive a unique scale law that could represent the sedimentation process of ice crystals, geometric, kinematic, and dynamic similarities are required. However, these conditions are not fulfilled in the sedimentation process.