Numerical simulations applying to the analysis of thermal explosion of organic gel fuel in a hot gas

In this work we investigate theoretically and numerically the nature of the evolution of a hot gas mixture containing organic gel fuel droplets of different radii with oscillatory evaporation within the context of thermal explosion theory. The polydisperse spray is modeled using a probability density function (PDF). In this paper we take into account the time evolution of the size distribution due to the evaporation process by using the kinetic equation. This new model is in the form of singular perturbed system (SPS) of highly nonlinear of ordinary differential equations. This SPS form of the model and the non-dimensionalization of the equations enable us first to apply the methods of integral manifolds (MIM) and second to identify the parameters that play a major role in determining the dynamical regimes of the considered system. Our analytical and numerical simulations results that based on the MIM show that the dynamical behavior is different than that found with the conventional liquid droplets. An explicit expression of the critical condition for thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory.