Effects of gas-solid nonequilibrium in filtration combustion
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To determine the effects of gas-solid nonequilibrium on forced filtration combustion (FC) waves, a two-temperature model is employed, with separate temperature fields for the solid and gas particles. We consider heterogeneous (solid/gas) combustion in a porous sample with a prescribed gas flux at the inlet. If the reaction is initiated at the inlet (outlet) of the sample and the combustion wave travels in the direction of (opposite to ) gas filtration it is referred to as coflow (counterflow) FC. We determine the effects of gas-solid nonequilibrium on various aspects of forced FC waves. First, we consider coflow FC waves, in which case the gas infiltrating through the hot product region significantly enhances the propagation of the combustion wave. For a relatively small gas flux, the infiltrating gas delivers heat from hot product to the combustion layer, thus increasing the combustion temperature and, hence, the combustion rate. Propagation of such waves is controlled by conduction of the heat released in the reaction to the preheat zone. Conductively driven coflow FC waves have been studied extensively using one-temperature models, which assume a very large rate of interphase heat exchange between the solid and the gas, so that thermal equilibrium is attained almost immediately. However, if the gas flux is sufficiently large, the phases do not have sufficient time to equilibrate and, hence, the underlying assumption of one-temperature models is no longer valid. One-temperature models are only appropriate for describing slowly propagating coflow FC waves in which the time of contact between the solid particles and the gas is sufficiently large for rapid thermal equilibrium to occur. However, not all coflow FC waves are slowly propagating. There can also be rapidly propagating coflow FC waves, in which case a two-temperature model, with the solid and the gas attaining distinct temperatures, is more appropriate. For a relatively large gas flux, an alternative mechanism of enhancement occurs in the combustion temperature is increased as a result of increasing the effective initial temperature of the unurned solid ahead of the reaction zone. Propagation of such waves is controlled by convection of heat stored in the product to the preheat zone. Convectively driven coflow FC waves depend on a pronounced temperature difference between the phases and, therefore, cannot be described by a one-temperature model. We employ a two-temperature model to study coflow FC waves. The two-temperature model must also account for the fact that the oxidizer concentration at the surface of the solid particles, where the reaction occurs, may be significantly less than the average oxidizer concentration in the gas stream. Effects of gas-solid nonequilibrium are determined by the interphase heat transfer rate, as well as the rate of oxidizer diffusion to the solid particle surface. In the appropriate limits, the model can describe both conductive and convective coflow FC waves. We determine steady solutions in each of the limits and compare and contrast the structures, the combustion characteristics, and the parameter dependences of the two modes of propagation. Transition between conductive and convective steady-traveling coflow FC waves is discussed. We determine how gas-solid nonequilibrium affects such features as the wave velocity, the extinction limit, net gas production or consumption in the reaction, and the ability of the wave to accumulate energy near the reaction site. The results of our analyses are verified by numerical computations of the time-dependent problem. Next, we consider the effects of gas-solid nonequilibrium on counterflow FC waves, in which case the solid near the reaction site loses heat to the cool infiltrating gas. Counterflow FC waves are necessarly driven by conduction because the convective mechanism relies on the gas to deliver heat to, rather than carry heat away from, the unburned solid fuel. It is known from one-temperature-model analyses that extinction of steady-traveling waves will occur if the gas influx is sufficiently large. However, when the gas flux is sufficiently large to cause extinction, the two phases may not have sufficient time to attain thermal equilibrium, in which case a two-temperature model is required. Though only conductively driven counterflow FC waves are possible, we find that thermal nonequilibrium has a significant effect on the intrinsic extinction limit and the combustion characteristics.