Lattice Boltzmann simulations of Rayleigh–Bénard convection with compressibility-induced non-Oberbeck–Boussinesq effects

To analyse compressibility-induced non-Oberbeck–Boussinesq (NOB-II) effects, we present a lattice Boltzmann (LB) model capable of simulating supercritical fluids. The LB model is validated using analytical solutions and experimental data. Using this model, we conduct two-dimensional laminar LB simulations of Rayleigh–Bénard convection (RBC) in supercritical fluids. Our results reveal that the ratio of the adiabatic temperature difference to the total temperature difference, $\alpha$ , effectively indicates the intensity of NOB-II effects. We find that, NOB-II effects do not break the symmetry of the temperature, density or momentum fields. However, due to density differences between the upper and lower regions, NOB-II effects break the velocity symmetry. Moreover, we report for the first time the density inversion phenomenon in RBC, wherein convection can still occur when the bottom fluid is denser than the top fluid. The condition for density inversion is given as $\alpha \gt (c_p - c_v)/{c_p}$ , where $c_p$ and $c_v$ are the specific heat capacities at constant pressure and volume, respectively. This inversion is attributed to the coupling effect of a significant pressure gradient and fluid compressibility. Our results also show that for a given Rayleigh number, NOB-II effects have no impact on the Reynolds number. However, as $\alpha$ approaches 1, the Nusselt number decreases linearly towards 1, indicating significant heat transfer deterioration (HTD). The mechanism underlying HTD is attributed to the compression work term in the energy equation, which absorbs heat from the hot plume in central region, diminishing its capacity to transfer heat from the bottom to the top plate.