Investigation of Scalar Dissipation Rate Fluctuations in Non-Premixed Turbulent Combustion Using a Stochastic Approach

摘要

Turbulent °uctuations of the scalar dissipation rate are well knownrnto have strong impact on ignition and extinction in non-premixed combustion.rnIn the present study the in°uence of stochastic °uctuationsrnof the scalar dissipation rate on the solution of the °amelet equationsrnis investigated. By assuming a one-step irreversible reaction the systemrncan be described by the solution of the temperature equation.rnBy modeling the di?usion terms in the °amelet equation this can bernwritten as a ordinary stochastic di?erential equation (SDE). In additionrnan SDE is derived for the scalar dissipation rate. From these twornequations a Fokker-Planck equation can be obtained describing thernjoint probability of temperature and the scalar dissipation rate. Thernequation is analyzed and numerically integrated using a fourth orderrnRunge-Kutta scheme. The in°uence of the main parameter, whichrnare the Damk?ohler number, the Zeldovich number, the heat releasernparameter, and the variance of the scalar dissipation rate °uctuationrnare discussed.