Conceptual Limitations of the Probability Density Function Method for Modeling Turbulent Premixed Combustion and Closed-Form Description of Chemical Reactions’ Effects

In this paper, we critically analyzed possibilities of probability density function (PDF) methods for the closed-form description of combustion chemical effects in turbulent premixed flames. We came to the conclusion that the concept of a closed-form description of chemical effects in the classical modeling strategy in the PDF method based on the use of reaction-independent mixing models is not applicable to turbulent flames. The reason for this is the strong dependence of mixing on the combustion reactions due to the thin-reaction-zone nature of turbulent combustion confirmed in recent optical studies and direct numerical simulations. In this case, the chemical effect is caused by coupled reaction–diffusion processes that take place in thin zones of instantaneous combustion. We considered possible alternative modeling strategies in the PDF method that would allow the chemical effects to be described in a closed form and came to the conclusion that this is possible only in a hypothetical case where instantaneous combustion occurs in reaction zones identical to the reaction zone of the undisturbed laminar flame. For turbulent combustion in the laminar flamelet regime, we use an inverse modeling strategy where the model PDF directly contains the characteristics of the laminar flame. For turbulent combustion in the distributed preheat zone regime, we offer an original joint direct/inverse modeling strategy. For turbulent combustion in the thickened flamelet regime, we combine the joint direct/inverse and inverse modeling strategies correspondingly for simulation of the thickened flamelet structure and for the determination of the global characteristics of the turbulent flame.