A penalization method for the simulation of weakly compressible reacting gas-particle flows with general boundary conditions

Abstract

In this paper, the Brinkman penalization method is extended to the weakly compressible formulation of the Navier–Stokes equations to study gas-particle flows with reactions and coupled heat and mass transfer. The weakly compressible approximation removes the acoustic modes from the solution while allowing a variable density. The Brinkman volume penalization method describes the solid phase as a porous medium with a vanishing permeability. The method is validated with literature benchmarks for a fixed or moving particle. Various reaction scenarios are then investigated. First, the capability of the method to deal with intra-particle diffusion and reaction is evaluated. The impact on the conversion of the particle Reynolds number based on the slip velocity is assessed, for a range of Reynolds numbers encountered in fluidization. Next, surface reactions are focused on, with infinite or finite rate. A Dirichlet-type condition is imposed on the particle surface to treat an infinite reaction rate and a high solid thermal conductivity while a finite-rate surface reaction requires Neumann and Robin surface conditions for the temperature and species mass fractions. The impact of density changes induced by heat release and molecular weight changes is assessed in these different cases. It is shown that the combination of the weakly compressible approximation and the penalization method allows to treat the presence of the solid phase and reactions in an efficient manner and to take into account the effects of compressibility in commonly encountered situations in reaction engineering.