Probability Density Function Characterization for Conditional Source-term Estimation in High-Pressure Combustion

Abstract

The present study investigates the long-standing issue in the accurate simulations of high-pressure (high-p) combustion, namely: the modeling of turbulence-chemistry - thermodynamic interaction. This issue is addressed through an a posteriori study of a Direct Numerical Simulation (DNS) database representing high-p turbulent combustion. The DNS database is described in Bellan (2017) and consists of simulations of a temporal mixing layer in which a single-step chemical reaction occurs. That study indicates that when the single-conditioned Conditional Source-term Estimate (CSE) approach is used based on a beta probability distribution function (PDF) representing the mixture fraction, the turbulent reaction rate is significantly over-predicted; the inaccuracy of the model is here traced to the large variance about the conditional mean due to the non-linearity in the real-gas equation of state. It is shown that by doubly-conditioning the source-term using as conditioning variables the mixture fraction and a characteristic thermodynamic variable, the chemical source-term estimation is considerably improved for all test cases in the DNS database. The rationale directing the choice of the PDF and the reason for the Double-Conditioned Source-term Estimate approach success are explained.