Critical phenomena in the cellular mode of filtration combustion in the presence of heat loss

Critical conditions for combustion failure due to heat loss to the environment are examined. The process of filtration combustion is considered under conditions where a cellular structure of the front is realized, because the planar combustion front loses its stability and splits into separate cells of exothermic chemical conversion, which propagate in self-sustained mode. The size and structure of the cells of chemical interaction depend nonlinearly on the governing parameters, including the rate of heat loss to the environment. Within the framework of a mathematical model of filtration combustion, the steady-state dynamics of the combustion process and the structure of the cell of exothermic chemical reaction of a powder mixture with a gaseous reagent with the formation of solid products are simulated. The specifics of the evolution of the cell before combustion failure as a function of the heat loss rate are studied.