Modeling of Progress Variable Variance Transport in Head-On Quenching of Turbulent Premixed Flames: A Direct Numerical Simulation Analysis

Abstract

The statistical behavior of the transport of reaction progress variable variance (Formula presented.) has been analyzed using three-dimensional direct numerical simulation (DNS) data for different values of Damköhler, Karlovitz, and global Lewis numbers in the context of head-on quenching of turbulent premixed flames by an inert isothermal wall. It has been found that reaction rate contribution to the variance (Formula presented.) transport acts as a leading order source, whereas the molecular dissipation term remains as the leading order sink for all cases considered here. However, all of the terms of the variance (Formula presented.) transport equation decay significantly in the near-wall region once the quenching starts. The existing models for the turbulent transport, reaction, and dissipation contributions to the variance (Formula presented.) transport do not adequately capture the near-wall behavior. The wall effects on the unclosed terms of the variance (Formula presented.) transport equation have been analyzed using explicitly Reynolds averaged DNS data and the existing closures of the unclosed terms have been modified to account for the near-wall effects. A-priori DNS analysis suggests that the proposed modifications to the existing closures for the unclosed terms of the variance (Formula presented.) transport equation provide satisfactory predictions both away from and near to the wall.