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

TL;DR

This paper extends the flamelet progress variable approach by applying the SMLD framework to jointly model the PDF of mixture fraction and progress variable, removing assumptions about their correlation and behavior, validated on Sandia flames.

Contribution

It introduces a novel SMLD-based joint PDF model for turbulent combustion that does not rely on traditional assumptions, enhancing accuracy and validation capabilities.

Findings

The SMLD approach accurately predicts flame behavior in Sandia tests.

The model reveals potential correlations between mixture fraction and progress variable.

Comparison shows improved performance over standard FPV models.

Abstract

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