A geometric approach to the modelling of critical phenomena for a spray combustion model

Samara National Research University, 34, Moskovskoye shosse, Samara 443086, Russia

^* Corresponding author: shchepakina@yahoo.com

Abstract

The paper is devoted to the modelling of the critical phenomena in multiscale combustion models. Such models are usually described by singularly perturbed systems of differential equations to reflect the significant distinction in characteristic relaxation times of different physicochemical processes. The paper proposes an approach for modelling of critical phenomena on the basis of the geometric asymptotic method of invariant manifolds. The critical phenomenon means as a sharp change in the dynamics of the process under consideration. As an illustration of this approach a dynamic model of fuel spray ignition and combustion is considered. The realizability conditions for the critical regime is obtained in the form of the asymptotic expression for the control parameter. The main feature of the critical regime is that during it the temperature of the combustible mixture can reach a high value within the framework of a safe process. It is shown that the critical regime plays the role of a watershed between the slow combustion regimes and the thermal explosion.