Modeling ice crystal growth using the lattice Boltzmann method

Abstract

Given the multitude of growth habits, pronounced sensitivity to ambient conditions and wide range of scales involved, snowflake crystals are particularly challenging systems to simulate. Only a few models are able to reproduce the diversity observed regarding snowflake morphology. It is particularly difficult to perform reliable numerical simulations of snow crystals. Here, we present a modified phase-field model that describes vapor-ice phase transition through anisotropic surface tension, surface diffusion, condensation, and water molecule depletion rate. The present work focuses on the development and validation of such a coupled flow/species/phase solver in two spatial dimensions based on the lattice Boltzmann method. It is first shown that the model is able to correctly capture species and phase growth coupling. Furthermore, through a study of crystal growth subject to ventilation effects, it is shown that the model correctly captures hydrodynamics-induced asymmetrical growth. The validated solver is then used to model snowflake growth under different ambient conditions with respect to humidity and temperature in the plate-growth regime section of the Nakaya diagram. The resulting crystal habits are compared to both numerical and experimental reference data available in the literature. The overall agreement with experimental data shows that the proposed algorithm correctly captures both the crystal shape and the onset of primary and secondary branching instabilities. As a final part of the study, the effects of forced convection on snowflake growth are studied. It is shown, in agreement with observations in the literature, that under such conditions the crystal exhibits nonsymmetrical growth. The non-uniform humidity around the crystal due to forced convection can even result in the coexistence of different growth modes on different sides of the same crystal.