Modeling of heat and mass transfer in heat-shielding composite materials based on the universal law of binder decomposition

A physical and mathematical model of heat and mass transfer under phase transformations during the high-temperature, aerodynamic heating of high-speed aircraft is constructed in this work based on the identified law of the decomposition of binders of most heat-shielding composite materials. The mathematical model includes a description of the occurrence and advancement of the binder-decomposition zone (pyrolysis) limited by two moving boundaries of phase transformations, the heat transfer and filtration of pyrolysis gases in the porous coke residue, their injection into the gasdynamic boundary layer, and the distribution of the temperature and density of the composite material in the zone pyrolysis. The mathematical model and analytical method for the solution of the nonlinear heat and mass transfer problem allow the Stefan-type problem to be reduced to the solution of the transcendental equation with respect to the mass velocity of the pyrolysis zone. The results were obtained for temperature fields with allowance for the filtration in the porous residue and the pressure distribution of pyrolysis gases and for temperature fields in the pyrolysis zone that were not affected by binder decomposition, as well as the distribution of pyrolysis gas density in the pyrolysis zone.