Modeling of Heat and Mass Transfer in Heat-Shielding Composite Materials Based on the Universal Law of Binder Decomposit
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AND MASS TRANSFER AND PHYSICAL GASDYNAMICS
Modeling of Heat and Mass Transfer in Heat-Shielding Composite Materials Based on the Universal Law of Binder Decomposition V. F. Formalev* Moscow Aviation Institute (National Research University), Moscow, Russia *e-mail: [email protected] Received December 4, 2019; revised December 16, 2019; accepted March 10, 2020
Abstract—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. DOI: 10.1134/S0018151X20030050
INTRODUCTION Heat-shielding composite materials (CMs) under the conditions of the aerodynamic heating of supersonic and hypersonic aircraft undergo phase transformations, namely, the decomposition of binders (pyrolysis) of CMs with the formation of a gas component and a porous residue through which pyrolysis gases are filtered and injected into the high-temperature boundary layer, mass ablation from the outer boundary of the aircraft under the action of high temperatures and shear stresses in the boundary layer, and various heterogeneous and homogeneous chemical reactions inside the CMs. In the design of thermal protection made from heat-insulating CMs, it is primarily necessary to determine the mass decomposition rate of the binder CMs with allowance for the endothermic effect, the mass and linear velocities of the pyrolysis zone, and the mass and linear velocities of gas filtration through the porous residue, (with allowance for convective cooling), as well as the thermal effect blowing into the temperature boundary layer. All of these processes occur under the influence of high temperatures and heat fluxes from the boundary layer to the body in parallel with heat and mass transfer inside the CM. A specific physico-mathematical model of the decomposition of binders has been developed for each heat-shielding CM. It takes into account their chemica
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