The modeling of the turbulent reaction rate under high-pressure conditions: A priori evaluation of the Conditional Source-term Estimation concept

Abstract

With the goal of obtaining an accurate model of the turbulent reaction rate for Large Eddy Simulations (LESs), the modeling of turbulence-chemistry-thermodynamic interaction is addressed through an a priori study of a Direct Numerical Simulation (DNS) database representing high-pressure turbulent combustion. The DNS database consists of simulations of a temporal mixing layer in which a single-step chemical reaction occurs. The potential of the single-conditioned Conditional Source-term Estimation (CSE) approach to model the filtered turbulent reaction rate needed for conducting LES is examined. Evaluations conducted with the mixture fraction as a conditioning variable at two filter widths and with the probability density function (PDF) extracted from the DNS database that represents 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 CSE (DCSE) approach is explored with two different second conditioning variables, the first conditioning variable still being the mixture fraction; four filter widths are considered. The first choice of the second conditioning variable is a normalized progress variable based on the CO2 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 DNS-extracted filtered reaction rate. A quantitative test based on a root mean square identifies the reason for the DCSE success compared to CSE: unlike in CSE, the DCSE is able to substantially reduce the fluctuations of the modeled reaction rate from the filtered reaction rate over the entire range of the filtered reaction rate values, and particularly at the larger reaction rate values for which the DCSE model has higher fidelity. The results are shown to be equally favorable for the two conditioning variables. Consideration of DNS realizations at higher free-stream pressure or larger Reynolds number shows that the results are essentially equally successful at other pressure or Reynolds number values.