A new analysis of the modeling of pressure fluctuations effects in premixed turbulent flames and its validation based on DNS data

The modeling of transport in premixed turbulent flames is considered. In this context of second order modeling of momentum and scalar turbulent fluxes, special attention is paid to the closure of pressure fluctuating terms responsible for counter-gradient diffusion and flame generated turbulence effects. Based on a relatively general form of the PDF made of a series of delta functions, a new modeling proposal for these terms is introduced. The resulting model for the pressure terms takes into account (i) a nonreactive part that represents density changes, (ii) a reactive part directly related to mean chemical rate and (iii) an isotropization part which is a generalisation of the "return-to-isotropy" model for constant density flows. The model is tested using a three-dimensional compressible Direct Numerical Simulation database of a statistically steady planar turbulent premixed flame. A good agreement is found between the model expressions and the pressure fluctuating terms evaluated from DNS.