A Unified Numerical Framework for Turbulent Convection and Phase-Change Dynamics in Coupled Fluid-Porous Systems

Abstract

This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is established based on the Darcy-Brinkman equation, the advection-diffusion equations for heat and solute, and a phase field equation describing the evolution of porous medium. Phase-changing process and relevant influences are incorporated as corresponding source terms. A numerical method is then developed to solve the governing equations. Several different types of model problems are simulated with the numerical method. For the incompressible flows inside a coupled fluid-porous-medium system, the channel turbulence over a porous substrate and the thermal convection in a two-layer system are simulated. For the phase-changing flows, the one-dimensional Stefan problem and the two-dimensional flow of pure water freezing are tested. The results agree with the existing simulations. Finally, the full solver is used to simulate the growth of mushy ice during seawater freezing, which can successfully reproduce the experimental results at the exactly same conditions. Therefore, the developed framework provides a versatile and reliable tool for studying complex multiphase, multi-component transport phenomena in fluid-porous-medium systems involving solid-liquid phase change.