Direct numerical simulation of Rayleigh-Bénard-Marangoni convection of cold water near its density maximum in a cylindrical pool

In order to understand the influence of Marangoni effect on Rayleigh-Bénard convection, a series of three-dimensional numerical simulations of Rayleigh-Bénard- Marangoni convection of cold water near its maximum density in a cylindrical pool heated from below and with a free surface at the top were carried out by using the finite volume approach. Results show that the flow pattern is strongly influenced by the Rayleigh number, as well as by the Biot number. When the Biot number is small, the critical Rayleigh number for the onset of convection is low due to the strong Marangoni effect on the free surface. As the Biot number increases, the Marangoni effect becomes weaker. Therefore, the critical Rayleigh number becomes much larger and more flow patterns can be observed at different density inversion parameters. Furthermore, the average Nusselt number is influenced by the Rayleigh number, the Biot number and the density inversion parameter. Specifically, the average Nusselt number increases with the increase of the Rayleigh number and the decrease of the density inversion parameter. Meanwhile, as the Biot number goes up, the average Nusselt number increases at first and then decreases. In addition, there exists a sudden increase of the Nusselt number when the flow pattern transits from a relative stable state to a violent state, which means the flow pattern can also influence the heat transfer ability.