Lattice Boltzmann simulations of the double-diffusive natural convection and oscillation characteristics in an enclosure with Soret and Dufour effects

Abstract

Abstract Lattice Boltzmann method (LBM) is used for examining the double-diffusive natural convection around a heated cylinder in a square enclosure with Soret and Dufour effects. The inner heated cylinder is positioned at the square enclosure center with high temperature and concentration. Four surrounding walls are rigid non-slip surfaces with low temperature and concentration. The distributions of velocity, temperature, and concentration are solved by three independent lattice Bhatnagar–Gross–Krook (LBGK) equations combined into a coupled equation through the Boussinesq approximation. The Soret and Dufour effects are involved in the equilibrium distribution functions of C i e q and T i e q , respectively. The influences of Soret number Sr (0.0≤Sr\u202f≤\u202f0.8) and Dufour number Df (0.0≤Df\u202f≤\u202f0.8) combined with buoyancy ratio Br (−10\u202f≤\u202fBr\u202f≤\u202f10) on double-diffusive natural convection are investigated numerically. Results are presented in terms of streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers. Furthermore, time history and phase space trajectory are used to investigate the effects of Soret and Dufour numbers on unsteady flow characteristics at a high Rayleigh number (Ra\u202f=\u202f5\u202f×\u202f106). Results indicate that heat and mass transfers are weakened with simultaneous increasing Df and Sr and the flow stability can be enhanced.