An SMLD Joint PDF Model for Turbulent Non-Premixed Combustion Using the Flamelet Progress-Variable Approach

This paper provides an improved flamelet/progress variable (FPV) model for the simulation of turbulent combustion, employing the statistically most likely distribution (SMLD) approach for the joint probability density function (PDF) of the mixture fraction, Z, and of the progress parameter, Λ. Steady-state FPV models are built presuming the functional shape of the joint PDF of Z and Λ in order to evaluate Favre-averages of thermodynamic quantities. The mixture fraction is widely assumed to behave as a passive scalar with a mono-modal behaviour modelled by a β-distribution. Moreover, under the hypothesis that Z and Λ are statistically independent, the joint PDF coincides with the product of the two marginal PDFs. In this work we discuss these two constitutive hypotheses. The proposed model evaluates the most probable joint distribution of Z and Λ, relaxing some crucial assumption on their statistical behaviour. This provides a more general model in the context of FPV approach and an effective tool to verify the adequateness of widely used hypotheses. The model is validated versus experimental data of well-known test cases, namely, the Sandia flames. The results are also compared with those obtained by the standard FPV approach, analysing the role of the PDF functional form on turbulent combustion simulations.

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