Assessing Eulerian–Lagrangian simulations of dense solid-liquid suspensions settling under gravity

Abstract

We study dense solid-liquid suspensions through numerical simulations. The liquid flow is solved by the lattice-Boltzmann method on a fixed (Eulerian), cubic, uniform grid. Spherical solid particles are tracked through that grid. Our main interest is in cases where the grid spacing and the particle diameter have the same order of magnitude (d/Δ=O(1)). Critical issues then are the mapping operations that relate properties on the grid and properties of the particles, e.g. the local solids volume fraction seen by a particle, or the distribution of solid-to-liquid hydrodynamic forces over grid points adjacent to a particle. For assessing the mapping operations we compare results for particles settling under gravity in fully periodic, three-dimensional domains of simulations with d/Δ=O(1) to much higher resolved simulations (d/Δ=O(10)) that do not require mapping. Comparisons are made in terms of average slip velocities as well as in terms of liquid and fluid velocity fluctuation levels. Solids volume fractions are in the range 0.3 to 0.5, Reynolds numbers are of order 0.1 to 10.