The impact of dilatation, scrambling, and pressure transport in turbulent premixed flames

Premixed turbulent flames feature strong interactions between chemical reactions and turbulence that affect scalar and turbulence statistics. The focus of the present work is on clarifying the impact of pressure dilatation/flamelet scrambling effects with a comprehensive second-moment closure used for evaluation purposes. Model extensions that take into account flamelet orientation and molecular diffusion are derived. Isothermal pressure transport is included with an additional variable density contribution derived for the flamelet regime of combustion. Full closure is assessed by comparisons with Direct Numerical Simulations (DNSs) of statistically 'steady' fully developed premixed turbulent planar flames at different expansion ratios. Subsequently, the prediction of lean premixed turbulent methane-air flames featuring fractal grid generated turbulence in an opposed jet geometry is considered. The overall agreement shows that 'dilatation' effects contribute to counter-gradient transport and can also increase the turbulent kinetic energy significantly. Levels of anisotropy are broadly consistent with the DNS data and key aspects of opposed jet flames are well predicted. However, it is also shown that complications arise due to interactions between the imposed pressure gradient and combustion and that redistribution is affected along with the scalar flux at the leading edge. The latter is strongly affected by the reaction rate closure and, potentially, by pressure transport. Overall, the derived models offer significant improvements and can readily be applied to the modelling of premixed turbulent flames at practical rates of heat release.