Direct simulation vs volume-averaged treatment of adiabatic, premixed flame in a porous medium

For the case of flame thickness being of the order of the pore linear dimension, the flame structure and speed in adiabatic, premixed methane-air combustion in porous media are examined. The local, volume-averaged conservation equations that assume a local thermal equilibrium between the solid and the gas phases (i.e. the single-medium treatment) or allow for a thermal nonequilibrium (i.e. the two-medium treatment) are used along with the direct application of the pointwise conservation equation to a two-dimensional porous medium model (ordered arrangement of discrete or connected square cylinders). The effective properties of the porous medium in the volume-averaged treatments, including the interfacial Nusselt number, are found by applying the local volume-averaging principles. The results show that, although significant variations of the temperature and species concentrations occur over a pore, the flame structure, thickness, speed, and excess temperature (i.e. local gas temperature in excess of the adiabatic temperature) are fairly well predicted by the two-medium model (the single-medium treatment is unable to predict the local excess temperature). However, the volume-averaged treatments are unable to predict the pore-level, local high temperature region in the gas phase (which can be up to 40% above the adiabatic temperature), and the pore-level variation in the flame speed with respect to the flame location in the pore (which can vary by up to 20%). Other shortcomings of the volume-averaged treatments are also revealed through a parametric examination involving the pore-geometry variables, solid to gas conductivity ratio, equivalence ratio, porosity, and flame location within the pore.