Rapid, upward buoyant filtration combustion waves driven by convection

Abstract

A two-temperature model is employed to analyze upward buoyant filtration combustion (BFC) waves. We consider heterogeneous (solid/gas) combustion in a porous sample open to gas flow only at the top and the bottom. The reaction is initiated at the bottom of the sample and the combustion wave travels in the direction of gas filtration. There is a localized region of high temperature either ahead of or behind (depending on certain parameters) the combustion layer. Hot gas contained within this region rises due to gravity induced buoyant forces, thus drawing cool fresh gas containing oxidizer in through the bottom of the sample. We focus on the reaction leading structure, in which the reaction occurs at the leading edge of the heated portion of the sample. 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 the hot product region to the reaction zone, thus increasing the maximum burning temperature, and hence, the combustion rate. This is referred to as the superadiabatic effect. The propagation of such waves is controlled by the diffusion of heat released in the reaction to the preheat zone. Diffusively driven BFC waves have been studied extensively using one-temperature models. One-temperature models 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 solid and the gas do not have sufficient time to equilibrate, and hence, the underlying assumption of one-temperature models is no longer valid. That is, one-temperature models are only appropriate for describing slowly propagating BFC waves in which the time of contact between the solid and the gas is sufficiently large for rapid thermal equilibrium to occur. However, not all BFC waves are slowly propagating. There can also be rapidly propagating BFC 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 that the maximum combustion temperature is increased as a result of increasing the effective initial temperature of the solid. The propagation of such waves is controlled by the convection of heat stored in the product to the preheat zone. Convectively driven BFC waves depend on a pronounced temperature difference between the solid and the gas, and therefore, cannot be described with a one-temperature model. We employ a two-temperature model to study upward propagating BFC waves. In the appropriate limits, we consider both diffusively and convectively driven BFC waves, with the main interest lying in the latter, which requires that a two-temperature model be used. We analyze both modes of propagation and compare and contrast the results. The filtration of gas may be driven by various mechanisms. A process that is simpler than, yet similar to upward BFC, is forced forward FC, in which the incoming gas flux is fixed by an external source. In BFC, gas flux is induced by the combustion process and must be determined, whereas in forced forward filtration combustion (FC), the hydrodynamic description is reduced to prescribing the gas flux at the inlet of the sample. By comparing and contrasting convective upward BFC waves and convective forced forward FC waves, we determine the effects of a buoyancy driven gas flux, as opposed to a fixed gas flux, on convective FC waves.