Modeling of the Turbulent Reaction Rate in High-Pressure Flows

Abstract

The modeling of turbulence-chemistry-thermodynamic interaction is addressed through an a priori study pf a Direct Numerical Simulation (DNS) database representing high-p turbulent combustion. The DNS database consists of simulations of a temporal mixing layer in which a single-step chemical reaction occurs; the results are presented here for a single DNS realization. The potential of the single-conditioned Conditional Source-term Estimate (CSE) approach to model the filtered turbulent reaction rate needed for conducting Large Eddy Simulation (LES) is examined. Evaluations conducted with the mixture fraction as a conditioning variable at two filter widths and with the probability distribution function (PDF) extracted from the DNS database representing the mixture fraction, show that the deviation between the model and template is large and substantially increases with filter width. To address this deviation, the Double-conditioned Source-term Estimate (DCSE) approach is explored with two different second conditioning variables, the first conditioning variable being still the mixture fraction; several filter widths are considered. The first choice of the second conditioning variable is a normalized process variable based on the CO_2 mass fraction and the second choice of the second conditioning variable is a normalized temperature. With each second conditional variable, the DCSE results represent a substantial improvement over CSE, by as much as an order of magnitude when measured by the relative error from the filtered reaction rate. A quantitative test based on a root mean square identifies the reason for the DCSE success compared to CSE, the DCSE is able to reduce the departure of the fluctuations of the modeled reaction rate from the filtered reaction rate over the entire range of the filtered reaction rate values. Comparing the DCSE results obtained with the two second conditioning variables, it appears that the normalized process variable based on the CO_2 mass fraction as the second conditioning variable is more successful than the normalized temperature in modeling the filtered reaction rate over its entire range.