Turbulent natural convection in an air–water system with evaporation across the free surface

Abstract

In this paper we report on direct numerical simulations of turbulent convection in a cuboidal pool that contains liquid water in the lower part and air in the upper one. The bottom wall is uniformly heated and natural convection is established in both phases, accompanied by water evaporation across the free surface of the water. The descent of the free surface due to evaporation is computed via a newly developed tracking algorithm based on the ghost-fluid method. We present results for three different cases which correspond to different pool heights. In all of them, the natural convection in the water lies in the soft-turbulence regime. Whereas in the gas, it lies in the laminar, transitional and soft-turbulence regimes, respectively. Our analysis focuses on the characteristics of the convective patterns in the two phases and the statistics of the various flow quantities of interest. According to our simulations, the flow in the water is organized in a single-roll Large-Scale Circulation (LSC). In the gas, it is organized in single or dual-roll LSCs, depending on the aspect ratio of the pool. Interestingly, the impingement points of the LSCs of the two phases at the free surface remain very close to one another, which is attributed to the continuity of the shear stresses across the free surface. Further, after the initial transient period, both the free-surface temperature and the evaporative mass flux are stabilized and remain almost constant, but they exhibit small-scale fluctuations in time due to turbulence. Also, the transport of water vapor in air has similar properties as the heat transport, and the ratio between the Sherwood and Nusselt numbers is very close to the Lewis number for air.