Boundary conditions in problems of studying the stability of a plane stationary detonation wave

Abstract

The research’s problems of a plane stationary detonation wave’s stability are considered. It is shown that the boundary conditions for the two-front model allow estimating the main parameters of the internal structure of gas detonation. Such a model can serve as the basis for development of mathematical support and software for an intellectual decision support system for the problems of explosion-proof and explosion protection. An attempt has been made to systematize the problem of setting boundary conditions in studies of the stability of a detonation wave in order to further create a decision support system (DSS) on problems of explosion safety and explosion protection. The following models of a plane stationary detonation wave were considered, which the stability problem is stated for: 1) the Chapman-Jouget detonation model is the simplest model where the shock-detonation front is modeled by a direct shock wave, and all chemical transformations are assumed to occur instantaneously, directly at the front; 2) a two-front (single-stage, square-wave) model based on the assumption that chemical transformations also occur instantaneously, not on the leading shock front, but in a plane (called the instantaneous combustion front), which is separated from the leading shock front by the induction zone; 3) a multistage model that approximates the continuous distribution of parameters behind the leading shock front piecewise constant function; 4) a model with a continuous distribution of parameters behind the leading shock front, which most accurately reflects the real physical processes in a stationary detonation wave. These models are fundamentally different in boundary conditions, which small pertur-bations in the region separating the regions of the initial combustible medium and detona-tion products satisfy. The advantages and disadvantages of the models described above are both assessed from the standpoint of the correctness of the physical analysis of the detonation process and from the point of view of applicability for the mathematical support of DSS on problems of explosion safety and explosion protection. It is shown that the boundary conditions for the two-front model allow to estimate the main parameters of the internal structure of the gas detonation. Such model can be as the basis for the development of mathematical support and software of DSS for problems of explosion safety and explosion protection