Modeling the thermo-mechanical structure of energetic material flames

The small-scale flame structure of combusting homogeneous energetic material is investigated with focus on the thermal expansion, variable thermal properties in the condensed phase, and effects introduced by small curvature of the burning surface.; 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 modeling approximations both analytically and numerically. Explicit expressions are obtained for the regression rate of the burning 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 the flame front and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance.; The small curvature limit is studied to determine curvature effects on deflagration of a curved surface of a homogeneous energetic material. Under the assumption of quasi-steady deflagration, a method of matched asymptotics is employed to derive first-order curvature corrections to the burning rate and surface temperature. The problem of a spherical particle deflagration is solved, both by asymptotics and by numerics, under the assumption of solid phase-controlled burning.; A numerical method is derived, as a result of extensive study and testing of various surface-tracking algorithms, to simulate combustion of energetic material in a fully coupled formulation with high activation energy in the solid phase for linear and spherically symmetric cases. This method is used to verify the assumption of quasi-steadiness of the energetic material deflagration.; The problem of efficiently computing the stable burn-back of a solid rocket motor when the motor is in the quasi-steady burning regime of operation is considered. Through the use of a straightforward two-timing multi-scale asymptotic analysis, the reduced description of the quasi-steady burning regime for a model problem is developed that is extensible to a full three-dimensional rocket. Advanced time-integration strategies developed for the airspace industry are adopted to the solid rocket motor grain burning to compute a series of realizations of steady flows as the grain burns back to near completion.