Numerical analysis of frazil ice formation in turbulent convection

Abstract

We study the first steps of ice formation in fresh water turbulent convection (frazil ice regime). We explore the sensitivity of the ice formation process to the set of non-dimensional parameters governing the system. We model the mixture of ice crystals and water as a two-phase medium composed of water and ice particles of fixed diameter. We use the Boussinesq approximation and we integrate numerically the set of equation making use of a numerical code based on second order finite difference. A dynamic LES model for the subgrid scales is used. We show that the ice particle rise velocity and the ice concentration source term coefficient significantly affect the frazil ice dynamics. The maximum of ice production is obtained in those situations where the rise velocity is of the same order of magnitude of a characteristic velocity of the thermal downwelling plumes. We develop a simple model which captures the trend of the growth rate as a function of the relevant parameters. Finally, we explore the nonlinear regime and we show that the parameter which plays a key role in fixing the concentration value at the statistically steady state is the heat exchange source term coefficient.