Fully Resolved Numerical Simulation of Free Convection of Falling Spherical Particles in Sedimentation Transports Using Immersed Boundary Method

Abstract

In this research, the direct numerical simulations are applied to study the sedimentation of spherical particles in an unsteady thermal condition in a viscous flow. The immersed boundary method is used to fully resolve the hydrodynamic interactions of solid–fluid phases, and a volume of fluid approach is employed to account the heat transfer both inside and outside the solid particles. The Boussinesq approximation is used to consider the density variation of the fluid. The behavior of particles is examined under different thermal conductivity ratios ($k_{\mathrm{r}}$) ranging between 0.1 to 10 and various Grashof numbers (Gr) up to 5000. The results indicate that for the Grashof and Galilean (Ga) numbers less than 5000 and 50, respectively, the threshold of $k_{\mathrm{r}}$ to solve the energy equation inside the particles is $k_{\mathrm{r}}=0.1,$ and for the thermal conductivity ratio higher than this value, the heating/cooling of the particles is fast enough to assume that the temperature over the solid particle changes uniformly. Furthermore, we investigate the well-known drafting–kissing–tumbling (DKT) phenomenon for a pair of spherical particles in an enclosed space at different $k_{\mathrm{r}}$ and Gr numbers. It is observed that the DKT motion of two particles with varied temperature is proceeded with any values of $k_{\mathrm{r}}$ and Grashof number; however, the natural convection delays this process.