Numerical Study of the non-Boussinesq Effects in Rayleigh-Bénard Convection

The Rayleigh-Bénard convection of supercritical fluid was studied numerically using the variable property-based lattice Boltzmann flux solver (VPLBFS) proposed by the present author. The variable property solution (VPS) in which the total variation in fluid properties was taken into account was obtained. In addition, both the constant property solution (CPS) based on the well-established Boussinesq approximation and the solution based on the partial Boussinesq approximation, denoted by the PBA solution, were reconstructed by using simplified versions of the VPLBFS. The non-Boussinesq effects on the Rayleigh-Bénard convection of supercritical fluid were analyzed through the comparisons of the three solutions. The non-Boussinesq effects under various temperature difference conditions were discussed. Results indicate that non-Boussinesq effects have a notable suppression of the Rayleigh-Bénard convection, which demonstrates the necessity of considering the total variation in fluid properties in the study about thermal flow problems.