Statistical Behavior of Scalar Dissipation Rate in Head-On Quenching of Turbulent Premixed Flames: A Direct Numerical Simulation Analysis

The statistical behavior of the scalar dissipation rate (SDR) and its transport in the context of Reynolds averaged Navier Stokes (RANS) simulations has been analyzed for head-on quenching of turbulent premixed flames using a three-dimensional simplified chemistry based direct numerical simulations (DNS) database. The flame quenching statistics have been analyzed in terms of wall Peclet number Pe (i.e., non-dimensional distance of the flame in the wall normal direction) and non-dimensional wall heat flux magnitude phi. It has been found that flame wrinkling induces fluctuations of wall heat flux in turbulent cases and the magnitude of the maximum wall heat flux increases with increasing root-mean-square turbulent velocity u'. The closure of mean reaction rate using the SDR of reaction progress variable in the near wall region has been assessed based on a priori analysis of DNS data. It has been demonstrated that the existing SDR-based reaction rate closure does not work satisfactorily near the wall. A modification to this existing closure has been proposed, which is found to satisfactorily predict the mean reaction rate of reaction progress variable (omega) over bar in the near wall region and approaches the existing closure away from the wall. The wall effects on the unclosed terms of the SDR transport equation have been analyzed and the order of magnitude estimates of the leading order contributors to the SDR transport have been utilized to modify an existing algebraic SDR closure to account for the near wall effects. A priori DNS analysis suggests that the proposed modification to the aforementioned SDR closure provides satisfactory prediction both away from and near to the wall.