An Elementary Model for Autoignition of Free Round Turbulent Jets
This paper is concerned with the study of autoignition of fully developed free round turbulent jets consisting of oxidizing and chemically reacting components. We derive an elementary, still experimentally feasible, model for autoignition of such jets and present analysis of this model. The derivation of the model is based on the well-established experimental fact that the fully developed free round turbulent jets, in a first approximation, have the shape of a conical frustum. Moreover, the velocity as well as concentration fields within such jets, prior to autoignition, assume self-similar profiles and can be viewed as prescribed. Using these facts as well as the appropriately modified Semenov--Frank-Kamenetskii theory of thermal explosion we derive an equation that describes the initial stage of evolution of the temperature field within the jet. We provide detailed analysis of the model that results in a sharp condition for autoignition of free round turbulent jets in terms of principal physical and geo...