Hot-Spot modelling of propellant regression. Part 2

In a previous work a simple one-dimensional model to study theoretically various effects in energetic materials was presented [1]. The model solves the heat and mass transport equation coupled with a reaction kinetic involving the strong non-linear Arrhenius-term of the chemical reaction rate constant. The energetic material is ignited by a heat impulse modeled as a Gaussian function. It is called a Hot-Spot. Other applications and a 3-dimensional version with applications to thermite reactions were presented in different works [2-4]. In this work the model is expanded with material parameters dependent on position, a phase transition and a new chemical reaction scheme with convective heat feedback to the unburned material. With the space-dependent material parameters the model takes into account the different thermal conductivity, density and heat capacity of the energetic material and the gas phase of the burned material. The phase transition models the melting of the energetic material. The chemical reaction scheme is modelled by a 1st or 2nd order reaction. It takes place in the gas-phase of vaporized material and radiates the energy partly back to the energetic material. Also different other heat losses can be modeled. Here the numerical procedure for solving these two coupled differential equations with different source terms is described. Therefore the method of the 1-dimensional Green`s function is used. The one-dimensional solution of the problem could be a simplification for many 3-dimensional problems because of the symmetry. With this model, parameter studies could be performed to investigate the influence of the different parameters. As a simple model the combustion of an energetic material with different chemical reaction schemes are presented and compared. It supplements the previous work. First examples of a study vary different parameters, like the material parameters, phase transition enthalpies, the chemical reaction scheme and heat of reaction. The influence of the different parameters is investigated by the burning rate.