Burning rate of homogeneous energetic materials with thermal expansion and varying thermal properties in the condensed phase

We present a study of the one-dimensional flame structure of combusting solid propellants that focuses on the effects of thermal expansion and variable thermal properties in the condensed phase. A nonlinear heat equation is derived for a burning thermo-elastic solid with temperature-dependent specific heat, thermal expansion, and thermal conductivity coefficients. It is solved for different modelling approximations both analytically and numerically. Explicit expressions are derived for the regression rate of the propellant surface as functions of surface temperature and thermal expansion parameters. A simple one-step reaction model of the gas phase is used to study the full structure of propellent flame and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance. Results are displayed for HMX and compared with experimental data and numerical simulation with fair success.