A Generalized Conditional Scalar Dissipation-Mixture Fraction Joint PDF for Flamelet Modeling of Non-Premixed Flames

Abstract

One problem in flamelet modeling of turbulent non-premixed flames is that of formulating a scalar dissipation rate-mixture fraction joint probability density function (pdf). While the individual flamelet calculation provides a conditional scalar dissipation rate, the turbulent flame calculation provides a marginal scalar dissipation rate. Thus, linking the laminar and turbulent flame calculations through the joint pdf is not straightforward, and, for simplicity, it is often assumed that the marginal and conditional probability densities are equal. The present paper assesses the validity of this assumption and examines its consequences in a numerical example. A conditional, scalar dissipation rate-mixture fraction joint pdf is developed which is based upon numerical solutions of the laminar counterflow diffusion flame and functional relationships among the scalar dissipation rate, the conditional scalar dissipation rate, and the mixture fraction. Interestingly, the result, when applied to a turbulent non-premixed flame, results in predictions of NO concentration which are not significantly different. The analysis also suggests experiments which may provide insight into flamelet structure, thereby assessing the validity of the idealized, underlying laminar counterflow configuration used in the flamelet modeling of non-premixed flames.