Delay time for fine particle ignition within gas with fluctuating temperature

Abstract

The Pontryagin equation was applied to calculating the average time for the random process escaping the assign interval: this gives the average delay time for waiting of particle ignition moment in a turbulent flow of gas. A direct numerical simulation method was developed for gas temperature fluctuations with assigned autocorrelation function and particle temperature fluctuations due to exothermal chemical reaction. The method was based on numerical solution of a system of stochastic differential equations. Results of direct simulation were validated through comparing with the analytical solution available for particles without exothermal reaction. Analytical calculations and results of direct numerical simulation for the delay time of particle ignition are in agreement.