On thermal explosion of a cool spray in a hot gas

The effect of a flammable spray on thermal explosion in a preheated combustible gas mixture is investigated using a simplified model that contains the essentials of the basic physical processes at work. The study represents a re-examination of the question of the ignition of a spray of droplets from the viewpoint of an explosion problem, in which the droplets are taken to be a source of endothermicity. Use is made of various methods for the qualitative analysis of systems of differential equations in order to examine the dynamics of the system. Possible types of dynamical behavior of the system are looked into and parametric regions of their existence are determined analytically. Peculiarities of these dynamical regimes are investigated, and their dependence on the physical system parameters are analyzed. In particular, analytical formulas are developed for ignition delay times by exploiting the sensitivity of the process to the chemical activation energy. A qualitative comparison of predicted ignition times with independent experimental measurements from the literature yields good order of magnitude agreement.