Turbulent kinetic energy transport in head-on quenching of turbulent premixed flames in the context of Reynolds Averaged Navier Stokes simulations

This paper investigates the statistical behaviour of the turbulent kinetic energy transport for moderate values of turbulent Renolds number Ret in turbulent premixed flames by using Direct Numerical Simulation (DNS) data in the case of head-on quenching by an isothermal inert wall for different Lewis numbers (i.e. Le=0.8-1.2). The magnitudes of turbulent kinetic energy and the terms of its transport equation have been found to increase with a reduction in global Lewis number. The magnitudes of all the terms except the viscous dissipation rate drops sharply near the wall whereas the magnitude of viscous dissipation rate exhibits a sharp increase in the near-wall region. The statistical behaviours of the terms arising from turbulent transport, pressure fluctuation transport, mean pressure gradient, pressure dilatation and viscous dissipation have been analysed by explicit Reynolds averaging of DNS data. It has been found that the viscous dissipation term acts as a major sink for all cases and all locations. The mean pressure gradient acts as the leading order source for all cases. However, the magnitudes of the mean pressure gradient, pressure dilatation and transport terms diminish with increasing Lewis number. Moreover, turbulent flux of kinetic energy has been found to exhibit counter-gradient transport and its extent diminishes with increasing Lewis number as a result of the weakening of flame normal acceleration. Detailed physical explanations have been provided for the observed behaviour of the turbulent kinetic energy transport. Existing models for the unclosed terms have been modified for accurate prediction of the corresponding terms extracted from DNS data especially in the near-wall region.