Counterflow combustion waves in short samples of metal powders at natural filtration of oxygen

Combustion of a porous solid fuel is considered. An exothermic reaction takes place between the fuel and a gaseous oxidiser which is delivered to the reaction zone by filtration through the pores in the sample from an open end toward which the combustion wave propagates (counterflow filtration). The gas reacts with the solid fuel to form a solid product. The gas filtration is due to the pressure difference between the ambient pressure at the open end and the pressure in the reaction zone where the gas is being consumed (referred to as natural filtration). A 1D mathematical model based on equations describing conservation of energy, gas mass, solid reactant mass, and gas momentum, as well as an equation of state, and appropriate boundary and initial conditions is formulated and analytically studied taking advantage of the separation of length scales in the process. When the reaction zone is sufficiently far from the open end, the combustion wave propagates at a constant speed and has a time-independent structure, while when the reaction is close to the open end (closer than the filtration length), the structure of the combustion wave and its speed become time dependent. Both cases are discussed in the paper though the main emphasis is on short samples, in which the combustion wave is affected by the gas flow from the open end during the entire propagation process. A specific example of interest involves magnesium as the solid fuel and oxygen as the gaseous oxidiser.