Modeling of Stefan-type problems under conditions of thermal decomposition of binders in thermal protection composite materials

This study addresses the complex problem of heat and mass transfer modeling in thermal protection composite materials subjected to heating of high intensity. The study examines the process of binder thermal decomposition, which results in the formation of a gaseous phase and a porous coke residue, followed by gas filtration through this residue and its injection into the gas-dynamic boundary layer. A Stefan-type problem with two moving boundaries defining the decomposition zone is formulated and solved analytically. The velocity of this zone is determined from the heat flux balance. To describe gas generation within the decomposition zone, an approach based on a modified Arrhenius law is proposed. Its parameters are identified using the composite material's reference data (decomposition onset and completion temperatures and densities), thereby eliminating the need for complex, hard-to-formulate full chemical kinetics.
Analytical solutions for temperature fields in all three regions are obtained: the porous coke residue, the active decomposition zone, and the virgin material. Distributions of the composite material density and the gas phase density in the decomposition zone, as well as filtration flow characteristics, are determined. Analysis of the results demonstrates that the temperature distribution in the decomposition zone is essentially nonlinear, while the density distributions are close to linear. The results of this work enable the assessment of mass-dimensional characteristics of thermal protection systems for high-speed aircraft structural elements at the design stage.