An efficient tracking method of evaporative and flat free surfaces for turbulent convection

Abstract

In this paper, we present a tracking algorithm of evaporative and flat free surfaces on collocated grids. This algorithm combines the ghost-fluid method with a flux-interpolation technique and is well suited for the numerical treatment of gas–liquid flows involving turbulent convection, mixing, and phase change via evaporation across a free surface. Further, it can accurately take into account the jumps in the values of the various flow quantities across the free surface and the time-dependent interaction between the two phases. The efficiency of the proposed algorithm is illustrated via numerical tests. The first test involves Couette flow above a liquid at rest; our numerical predictions for the evaporative mass flux compares very favorably with the analytical solution. The second test involves 2D simulations and grid-convergence study of free convection with evaporation in a system comprising a column of water and a layer of air above it. Cases at different Rayleigh numbers are considered and our numerical predictions are compared with experimental data and with earlier single-phase simulations based on approximate evaporation models. Further, we present and discuss results from 3D numerical simulations involving evaporation across the free surface, turbulent convection below it (liquid side) and free convection with mixing above it (gas side). Our numerical results are in good agreement with experiments and show that the algorithm provides accurate predictions of the evaporative mass flux and is robust enough to handle the descent of the free surface and simultaneously resolve the emerging turbulent structures.