Free convection in a differentially heated square cavity filled with low-Prandtl-number materials: Numerical studies using transition shear stress transport model

Abstract

Computing the flow field under free convection in a cavity becomes particularly challenging for low-Prandtl-number (Pr) fluids typically encountered for liquid metals. The objective of the present study is to investigate the natural convection process in a differentially heated square cavity employing the transition shear stress transport (SST) model for the Prandtl number Pr∈[0.001,0.1] and the Rayleigh number Ra∈[104,1010]. The mean flow field is visualized through streamlines, isotherms, non-dimensional velocity, and temperature profiles, turbulence intensity, contours of intermittency (γ) times, the production of turbulent kinetic energy (Pκ), and distribution of skin friction coefficient and the Nusselt number (Nu). The transition SST model can capture the mean flow field and thermal transport over the entire parametric regime successfully. An average Nusselt number (Nu¯) on the hot wall is found to scale with a certain power (n) of the Boussinesq number (Bo), the product of Ra and Pr. The value of n is 0.18 for Ra up to 106 and 0.25 for higher Ra.