Bénard–Marangoni Convection in an Open Cavity with Liquids at Low Prandtl Numbers

Abstract

Bénard–Marangoni convection in an open cavity has attracted much attention in the past century. In most of the previous works, liquids with Prandtl numbers larger than unity were used to study in this issue. However, the Bénard–Marangoni convection with liquids at Prandtl numbers lower than unity is still unclear. In this study, Bénard–Marangoni convection in an open cavity with liquids at Prandtl numbers lower than unity in zero-gravity conditions is investigated to reveal the bifurcations of the flow and quantify the heat and mass transfer. Three-dimensional direct numerical simulation is conducted by the finite-volume method with a SIMPLE scheme for the pressure–velocity coupling. The bottom boundary is nonslip and isothermal heated. The top boundary is assumed to be flat, cooled by air and opposed by the Marangoni stress. Numerical simulation is conducted for a wide range of Marangoni numbers (Ma) from 5.0 × 101 to 4.0 × 104 and different Prandtl numbers (Pr) of 0.011, 0.029, and 0.063. Generally, for small Ma, the liquid metal in the cavity is dominated by conduction, and there is no convection. The critical Marangoni number for liquids with Prandtl numbers lower than unity equals those with Prandtl numbers larger than unity, but the cells are different. As Ma increases further, the cells pattern becomes irregular and the structure of the top surface of the cells becomes finer. The thermal boundary layer becomes thinner, and the column of velocity magnitudes in the middle slice of the fluid is denser, indicating a stronger convection with higher Marangoni numbers. A new scaling is found for the area-weighted mean velocity magnitude at the top boundary of um~Ma Pr−2/3, which means the mass transfer may be enhanced by high Marangoni numbers and low Prandtl numbers. The Nusselt number is approximately constant for Ma ≤ 400 but increases slowly for Ma > 400, indicating that the heat transfer may be enhanced by increasing the Marangoni number.