Effects of buoyancy on turbulent scalar flux closure for turbulent premixed flames in the context of Reynolds Averaged Navier–Stokes simulations

The effects of body force on the statistical behaviour of turbulent scalar flux and its closure in the context of Reynolds Averaged Navier–Stokes simulations have been studied using Direct Numerical Simulations (DNS) of statistically planar turbulent premixed flames under different turbulence intensities and Froude numbers. An increase in body force magnitude in the case of unstable density stratification has been found to augment flame wrinkling, burning rate and gradient transport in comparison to a case without body force but with statistically similar unburned gas turbulence. By contrast, an increase in body force magnitude in the case of stable stratification reduces the flame wrinkling, burning rate and gradient transport in comparison to the flame without body force subjected to statistically similar unburned gas turbulence. Based on a-priori DNS analysis, an algebraic closure for turbulent scalar flux has been identified where the Froude number effects are explicitly accounted for. The body force has been found to have significant influence on the statistical behaviours and magnitudes of the terms of the scalar flux transport equation and this effect is particularly strong for the mean pressure gradient term in the scalar flux transport equation. Based on a detailed a priori DNS analysis, suitable model expressions have been identified for the turbulent transport, pressure gradient, dissipation and reaction rate-velocity correlation terms of the scalar flux transport equation by incorporating the effects of body force (e.g. Froude number effects) for improved model performance.