Numerical simulations for natural convection with high Rayleigh number in a tall rectangular cavity

To generalize heat transfer technology of natural convection with high Rayleigh number, it is necessary to extensively investigate the characteristics of fluid flow and heat transfer by natural convection. For a tall rectangular cavity of an aspect ratio 4, direct numerical simulations are carried out without any artificial perturbations on the flow field, and the distributions of averaged physical quantities such as temperature, mainstream velocity, vorticity and local Nusselt number are analyzed. The results show that: 1) Starting under quiescent and isothermal flow conditions, the flow can be driven to turbulence without any artificial perturbations, which saves computational resources; 2) As Rayleigh numbers up to 10¹⁰, the distributions of temperature, mainstream velocity, vorticity and local Nusselt numbers for natural convection in the tall cavity are endowed with the similar features of those in boundary-layer flow on a heated vertical plate; and 3) With Prandtl number in range of 0.71-500 and local Rayleigh number of magnitudes 10⁷-10⁸, heat transfer on the isothermal surfaces of tall cavity already presents the characteristics of turbulent flow.