Maximal energy accumulation in a superadiabatic filtration combustion wave

Abstract

The ability of energy to be concentrated in the front of a coflow (forward) filtration combustion (FC) wave in a porous solid is analyzed. Combustion is due to the exothermic reaction between the fuel in the porous solid and oxidizer contained in the gas flowing through the solid. Coflow filtration refers to the fact that the gaseous oxidizer flows to the reaction site through the product region, so that energy accumulation occurs due to the recovery of heat stored in the product. The gas flowing through the burned region transfers heat from the product region to the reaction site, and, even more importantly to the unburned fuel region. This results, primarily in preheating the fresh mixture, and consequently in strong overheating of the reaction zone where the temperature far exceeds the thermodynamic combustion temperature. This is the superadiabatic effect. The paper focuses on the mode of FC wave propagation corresponding to the most pronounced superadiabatic effect. We show that for this case, in the absence of heat losses, the temperature grows as l where l is the distance traveled by the reaction front. The ratio l T / l, where l T is the width of the high temperature zone into which the energy is gathered, decreases as l −1/2, showing that the efficiency of energy accumulation increases as the wave propagates. In addition, it was previously shown that there exist both reaction leading and reaction trailing traveling wave (TW) structures, which occur when a parameter δ, which is proportional to the ratio of the specific heats of the gas and solid and to the ratio of the initial concentrations of the solid fuel and the gaseous oxidizer, is greater than or less than 1, respectively. The case δ = 1 which separates the two structures corresponds to the most pronounced superadiabatic effect, and to a combustion temperature T b which is infinite. Thus, the TW analysis breaks down when δ = 1, indicating that TW solutions are no longer possible. For this case (δ = 1) we therefore investigate the full time-dependent problem to determine the structure of the FC wave, to determine whether T b actually becomes infinite and if so, its rate of approach to infinity. Though the combustion temperature in a FC wave experiment is, in fact, bounded, the ratio ( T b − T 0)/ q may be extremely large. Here, q, which characterizes the effect of the caloricity of the medium, is small when either the amount of fuel in the solid or the heat release in the reaction, is small. Thus, for any given q, no matter how small, FC wave propagation can always be realized by enhancing the energy accumulation. Heat losses to the environment bound the temperature growth at a level depending on the rate of heat exchange with the environment and the rate of incoming gas flux. Increasing the heat loss above the critical level causes extinction. The extinction limit may be overcome by increasing the gas influx.