Investigation of scalar dissipation rate fluctuations in non-premixed turbulent combustion using a stochastic approach

Turbulent fluctuations of the scalar dissipation rate are well known to have a strong impact on ignition and extinction in non-premixed combustion. In the present study the influence of stochastic fluctuations of the scalar dissipation rate on the solution of the flamelet equations is investigated. A one-step irreversible reaction is assumed. The system can thereby be described by the solution of the temperature equation. By modelling the diffusion terms in the flamelet equation this can be written as an ordinary stochastic differential equation (SDE). In addition, an SDE is derived for the scalar dissipation rate. From these two equations, a Fokker–Planck equation can be obtained describing the joint probability of temperature and the scalar dissipation rate. The equation is analysed and integrated numerically using a fourth-order Runge–Kutta scheme. The influence of the main parameters, which are the Damköhler number, the Zeldovich number, the heat release parameter and the variance of the scalar dissipation rate fluctuations, are discussed.