Particle-resolved multiphase Rayleigh-Bénard convection

Numerical simulations of Rayleigh-Bénard convection with suspended particles are described. The Rayleigh number is ${10}^7$ and the Prandtl number unity. The particles have a finite size and are individually resolved by the physalis method which combines a regular Cartesian grid with a local spectral method around each particle. Two cells are considered, a cubic one with up to 3000 particles and a quasi-two-dimensional one with aspect ratio 2 with up to 1000 particles. In both cases the maximum volume fraction is about 20%. Emphasis is placed on the key role played by particle "dunes" in the resuspension of particles after they have fallen to the ground. Dunes are structures formed on the bottom of the cell by the nearly horizontal fluid velocity field which pushes particles from the foot of the descending plume to that of the ascending one. Without this mechanism which, by its very nature, cannot be captured by point-particle models, very few particles, if any, would be resuspended. Bigger dunes, formed by more or heavier particles, are more effective than smaller ones in causing particle resuspension provided the total number and mass of particles is not too large. A small number of particles produces a modest improvement on the Nusselt number, but the effectiveness of particles as heat carriers is soon overshadowed by the weight they add to the mixture which slows down the circulation. The efficiency with which particles extract gravitational energy from the fluid reaches 20%, far higher than previous estimates in the literature which place it below 1%.