Modeling the Thermal Expansion Boundary Layer During the Combustion of Energetic Materials

An approach is presented for modeling the thermal expansion boundary layer in energetic materials such as solid propellants and explosives during their combustion. A thermodynamically consistent system of conservation laws is presented that describes the thermo-elastic solid with a temperature dependent thermal expansion coefficient in order to study the role of thermal expansion in heat transfer and deformation in a thin layer adjacent to the combustion zone. It is shown that the thermal expansion can produce an effect that absorbs energy near the burning surface and can significantly reduce the temperature in a small layer. The analysis given here is also relevant to the technologically important problem of laser ablation of materials, but the the discussion is focused on application to propellant combustion. Nomenclature: k thermal conductivity μ, λ elastic coefficients ρ density E Tensor of deformation ρ0 reference density F Deformation gradient m mass flux H Displacement gradient α thermal expansion ψ Helmholtz free energy coefficient B Left Cauchy-Green tensor Ey Young’s modulus ε internal energy K bulk modulus η entropy n coordinate in the ρ density moving frame f ′ displacement gradient u speed of a material Vf speed of the regressing particle in the lab. frame (flame) front ν Poisson’s ratio T temperature σ stress Ts decomposition surface temperature ps Chamber (surface) pressure T0 ambient reference temperature Tm melt temperature ∗Corresponding author: D. Scott Stewart, Theoretical and Applied Mechanics, University of Illinois, 216 Talbot Laboratory, 104 S. Wright St., Urbana, IL 61081, USA (FAX: 217-244-5707, email: [email protected])