Modelling of unclosed nonlinear terms in a pdf closure for turbulent flames

Abstract

Turbulent combustion modelling based on the probability density function (pdf) approach has proven to offer certain significant advantages over other solution methods. In the pdf formulation, important nonlinear terms appearing in the mathematical description of the flow are closed. The most prominent examples are in the case of the joint velocity-scalar pdf, the effects of chemical reactions and mean pressure gradient. Established models used in Monte Carlo particle pdf modelling to approximate the unclosed terms in the pdf equation are briefly reviewed. The models for the molecular mixing of scalars, viscous dissipation of momentum, and fluctuating pressure gradient perform well in constant density flows. However, modifications of these models are necessary if variable-density combusting flows are to be modelled accurately. This problem is here examined with particular reference to the flamelet regime of combustion, where the effects of combustion-induced acceleration of a fluid may be quantified. Simple approximations which result in a stochastic model for the effect of volume generation in flamelets are proposed.