Direct numerical simulation of coupled heat and mass transfer in fluid‐solid systems

Abstract

In this paper, an efficient ghost-cell based immersed boundary method is introduced to perform direct numerical simulation (DNS) of particulate flows. The fluid-solid coupling is achieved by implicit incorporation of the boundary conditions into the discretized momentum, thermal and species conservation equations of the fluid phase. Taking the advantage of a second order quadratic interpolation scheme, different boundary conditions could be realized consistently in our ghost-cell based immersed boundary method. The heat and mass transport in a fluid-particle system is coupled through the solid temperature, which offers a dynamic boundary condition for the fluid thermal equation. The present simulations are performed for three different fluidsolid systems. The first one is the unsteady mass and heat diffusion in a large pool of quiescent fluid. The solution of the solid temperature development obtained from DNS is compared with the “exact” solution obtained from a standard second-order finite difference technique. Following that, we consider a stationary sphere under forced convection. The steady state temperature of the particle can be calculated from the fluidsolid mass and heat transfer rates, which are obtained from the well-known empirical Ranz-Marshall and Frössling correlations. The last simulation case is an in-line array of three spheres, the so-called three-bead reactor. The computed adiabatic temperature rise obtained from DNS shows good agreement with the value calculated from the overall species conversion ratio of the reactor.