A universal model of opposed flow combustion of solid fuel over an inert porous medium

Abstract

In this study, a universal model is developed to examine the behavior of combustion wave observed in porous solid matters (e.g., smoldering, self-propagating high-temperature synthesis (SHS), diesel particulate filter (DPF) regeneration process). Analytical expressions of the combustion characters of solid combustible (e.g., diesel particulate matters trapped in a DPF) deposited over an inert porous medium are obtained employing large activation energy asymptotic taking into account the sensible transport processes; namely, heat transfer between the porous medium and gas phases, radiation heat transfer from the porous medium, heat loss from the porous medium to the environment, mass transfer of oxygen from the gas stream to the surface of solid fuel and the effective diffusion in modeling the species diffusion. Then it has been validated that the present model is applicable and adaptable for predicting the characteristics of smoldering combustion and thus SHS process. As a result, the features of combustion wave of the present phenomena would be useful to other processes. From practical point of view and for deep understanding of the behavior of combustion wave of these processes, we investigate the effects of various physical parameters over a wide range of conditions. We observe that the moving speed of the reaction front increases with the increase of porosity of the porous medium, mass transfer coefficient and initial fuel mass fraction; while it decreases owing to the increase of heat transfer rate from the porous medium to the gas, heat loss to the environment and radiative heat transfer. Furthermore, the results reveal that extinction tends to occur due to lower porosity of the porous medium, higher radiative heat transfer from the porous medium, higher heat transfer rate from the porous medium to the gas and higher heat losses from the porous medium to the environment. Even the observed near-extinction behavior in reaction front speed versus heat loss diagram is found to be similar what we got in gaseous premixed flame propagating through the porous medium. An extinction limit diagram has been presented as a function of radiation-conduction parameter and the gas flow velocity. In addition to, the impact of radiation and the combined effect of the inclusion of Knudsen diffusion and tortuosity are demonstrated in terms of the spatial temperature and species profiles to examine how these two parameters modify the reaction front structure. Furthermore, the governing equations have been solved numerically and it is observed that asymptotic analysis gives a good agreement with the numerical solution.