Rayleigh–Bénard convection driven by free-surface evaporation

Abstract

A novel approach to account for mass loss due to evaporation in rectangular pool geometries is introduced. In this method, the free surface is approximated by a free-slip upper boundary, and its descent is distributed proportionally across all cells by re-meshing the grid at each time step. This approach prevents changes in the field at the boundaries while distributing the discretization error along the height. Although this remeshing process appears straightforward, it requires a modification in the temporal discretization of the various equations. Stefan’s problem and its analytical solution are used to demonstrate the validity of the method.

The method, which incorporates mass transfer across the interface, is integrated with the model proposed by Hay et al. (2021) which addresses the local heat exchanges occurring at the interface. Direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in water pools driven by evaporation at the free surface are carried out using this dynamic and inhomogeneous evaporation model. The predicted evaporative and convective heat transfers are used to apply a non-zero Neumann condition for the temperature while the predicted evaporative mass flux is used to dynamically remesh the computational domain. Simulations of Rayleigh–Bénard convection driven by evaporation are run until a 10% initial height lost is reached. The rate of height decrease, flow topology, relationship between Rayleigh and Nusselt numbers and turbulence statistics are analyzed, taking into account the unsteady aspect of the flow.