Turbulent thermal convection driven by free-surface evaporation in cuboidal domains of different aspect ratios

Abstract

In this paper, we present simulations of turbulent thermal convection driven by free-surface evaporation above and by a heated wall below. A novel algorithm is proposed for predicting evaporation rates at a free surface, which we then validate against experimental data. At the top of a cuboidal domain, a shear-free boundary condition acts as an approximation of the free surface. We first focus on a domain of aspect ratio Γ = 1, where a fully resolved direct numerical simulation is carried out at a moderate Rayleigh number, Ra = 1.2 × 107, and we compare flow statistics with a Large-Eddy Simulation (LES) on a coarse grid. Both the fully resolved simulation and the LES predict well the time- and area-averaged evaporation rate and free surface temperature when compared with the experimental data. Next, we carry out a series of LES with an increasing lower wall temperature and, consequently, Ra. We then validate the evaporation model by comparing LES predictions of the time- and area-averaged mass flux and temperature at the upper boundary against the experimental measurements. The aspect ratio of the domain is then reduced, and we show, for the first time, the transition to a dual-roll state of the large-scale circulation (LSC) at the aspect ratio of Γ = 1/4 in a cuboidal domain. The temperature and velocity distributions at the free surface are impacted by the state of the LSC. However, we find that the water-side turbulence and aspect ratio play a negligible role on the evaporation rate above, in accordance with experimental observations.