Homogenization and fingering instability of a microgravity smoldering combustion problem with radiative heat transfer
Abstract The present study concerns the homogenization and fingering instability of a microgravity smoldering combustion problem with radiative heat transfer. The major premise of the homogenization procedure is the slow exothermic fuel oxidation of a reactive porous medium at the pore level. The porous medium consists of ϵ -periodically distributed cells, with ϵ a suitable scale parameter. A nonlinear reaction rate of Arrhenius type accounts for the relationship between the reactants and the heat that sustains the smoldering process. At the gas–solid interface, the balance of thermal fluxes is given by the heat production rate due to the reaction and the radiative heat losses at the interface. Since the size of the inclusions is small with respect to ϵ , we derive a kinetic model for fuel conversion in the region occupied by the solid inclusions and hence complete the description of a single-step chemical kinetics. The derived macroscopic model shows a close correspondence to a previous phenomenological reaction-diffusion model, within a suitable choice of parameters. We perform numerical simulations on the microscopic and homogenized models in order to verify the efficiency of the homogenization process in the slow smoldering regime. We show that the results of the macroscopic model capture the distinct fingering states reminiscent of microgravity smoldering combustion. We also show qualitative results that confirm the close relationship between the radiative heat losses and the characteristic length scales of the instability.