A second-order model for turbulent reactive flows with variable equivalence ratiol

A new theory for Reynolds stresses and turbulent scalar flux of both passive and reactive scalar is developed to describe turbulent reactive flows with partially premixed reactants. Starting points of the present study are based on i) an earlier analysis of the joint scalar PDF in partially premixed situations made by Libby and Williams (2000), and ii) a recent work carried out by Domingo and Bray (2000) dealing with the modeling of pressure fluctuating terms. Concerning the first point, the LW-P approach using a discrete PDF, made of four Dirac delta functions, is used in conjunction with the recent scalar dissipation closure proposed by Mura et al. (2007). Concerning the second point, special attention is paid to the closure of pressure fluctuating terms responsible for counter-gradient diffusion and flame generated turbulence effects. A new model for these terms valid in the case of partially premixed situations is proposed. This model takes different contributions into account, namely (i) a nonreactive part representing density changes closed by using conditional mean equations of motion, (ii) a reactive part, directly related to the mean chemical rate and (iii) an isotropization part which is a generalization of the return-to-isotropy model for constant density flows. Using this new closure, calculations are performed in the case of a confined turbulent partially premixed flame stabilized behind the plane sudden expansion of a 2-D channel.