A lattice Boltzmann model for liquid-vapor-solid flow with thermal phase change

Abstract

On the basis of phase-field theory, we develop a simple lattice Boltzmann (LB) model for liquid-vapor-solid flow with thermal phase change, which is able to deal with large fluid density contrasts. The conservative Allen-Cahn equation and Navier-Stokes equations are modified to take into account the phase change effects based on the Stefan boundary condition. Three distribution functions are used in the model, one of which is to track the interface among the fluids, one is employed for the fluid hydrodynamics, and the other one is utilized to solve the heat equation. The LB evolution equations are incorporated with proper source terms such that the modified interface tracking equation and hydrodynamic equations can be derived exactly. The proposed model for phase change is much simpler than the previous phase-field LB models. Combining with particle dynamics algorithms, the present model can further simulate liquid-vapor-solid systems with phase change. Several numerical tests, including the one-dimensional Stefan problem and droplet evaporation, have been performed to test the accuracy and stability of the present model, and the results obtained by this approach are in good agreement with the theory. Evaporation of a droplet wetting on a particle is simulated, it is found the fluid-solid interaction associated with the interface can be captured. Finally, as an application, the motion and growth of a rising vapor bubble with a particle through a superheated liquid is investigated.