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This paper provides an extension of the standard flamelet progress variable(FPV) approach for turbulent combustion, applying the statistically most likelydistribution (SMLD) framework to the joint PDF of the mixture fraction, Z, andthe progress variable, C. In this way one does not need to make any assumptionabout the statistical correlation between Z and C and about the behaviour ofthe mixture fraction, as required in previous FPV models. In fact, forstate-of-the-art models, with the assumption of very-fast-chemistry,Z is widelyaccepted to behave as a passive scalar characterized by a $\beta$-distributionfunction. Instead, the model proposed here, evaluates the most probable jointdistribution of Z and C without any assumption on their behaviour and providesan effective tool to verify the adequateness of widely used hypotheses, such astheir statistical independence. The model is validated versus three well-knowntest cases, namely, the Sandia flames. The results are compared with thoseobtained by the standard FPV approach, analysing the role of the PDF functionalform on turbulent combustion simulations.

An extended SMLD approach for presumed probability density function in flamelet combustion model