Transition of deflagration to detonation and estimation of the detonation induction distance

Abstract

Deflagration-to-detonation transition is interesting both for explosion safety and for the pulse detonation engine designing. Such engines are energetically favorable at flight Mach numbers exceeding 3. But transition from subsonic combustion to detonation is not investigated enough at present, and that is a serious difficulty both to the explosion safety problem solution and to engineering of detonation engines (both aeroengines and rocket engines). The aim of the study is investigation of mathematical laws for the mentioned transition. A mathematical model for deflagration-to-detonation transition that is based on the solution of the flame stability problem is offered. This model amplifies modern theory of combustion and explosion and turbulence theory. Theoretical estimates for the detonation induction distance and for the detonation wave formation time are made. It is proved that the detonation induction distance for a slow-burning mixture is greater than for a fast-burning one. The obtained results make it possible to improve mathematical support of the automated control systems for the dangerously explosive objects and the detonation engine designing