Numerical solutions for double diffusive convection in an enclosure

Abstract

A numerical study is made of double-diffusive convection in a rectangular cavity with combined horizontal temperature and concentration gradients. Numerical solutions to the governing full time-dependent Navier-Stokes equations at large thermal ($R_t$) and solutal ($R_s$) Rayleigh numbers are acquired. The essential details of flow, temperature and concentration fields are described for a large value of the Lewis number. The time evolutions of these fields are portrayed. The vertical profiles of the velocity, temperatures, solute, and the local Nussselt number are constructed, delineating the influence of solutal buoyancy effect relative to the thermal effect. The present paper is consist of four parts according to the boundary conditions at the bounding walls. In the First, the fluid is initally at rest with a pre-existing stably stratified solutal gradient. The motion is initiated by abruptly raising the temperature at one vertical sidewall. Far-reaching analyese are made of the numerical results over a wide rage of the solutal Rayleigh numbers $R_s$ using the thermal Rayleigh number, $R_t=10^7$. The categorization of the basic character of the flow into the supercritical ($Ra > Ra_c$)and subcritical regimes ($Ra < Ra_c$), which is based on experimental obervations, is satisfactorily verified by the numerical results. The present numerical simulatios are also supportive of the prior observations, which illustrated the qualitative difference in the time-dependent patterns of the formation of the layered structure in the supercritical and subcirtical regimes. By assessing the present numerical results, the previous estimate of the value of $Ra_c\cong1.5\times10^4$ has been found to be reasonably accurate. Secondly, the fluid is initially at rest with a pre-existing vertical solute gradient as the same way in the first part. However, both a horizontal temperature gradient and a vertical solute gradient are externally applied on the cavity boundaries and maintain...