A MULTI-DIRAC PRESUMED PDF MODEL FOR TURBULENT REACTIVE FLOWS WITH VARIABLE EQUIVALENCE RATIO

Abstract

The present paper is devoted to the numerical modeling of turbulent reactive flows in situations where reactants are not ideally premixed. In this case, the description of the local thermochemistry requires at least two variables. Here, we chose the mixture fraction ξ to describe the local composition of fresh mixture and the fuel mass fraction Y f to evaluate the progress of the chemical reaction. The numerical model is based on the earlier analysis made by Libby and Williams (2000 Libby , P.A. and Williams , F.A. ( 2000 ) Presumed PDF analysis of partially premixed turbulent combustion . Combust. Sci. Technol. , 161 , 351 – 390 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), an analysis that led eventually to the LW-P model (Ribert et al. 2004 Ribert , G. , Champion , M. , and Plion , P. ( 2004 ) Modelling turbulent reactive flows with variable equivalence ratio: application to the calculation of a reactive shear layer . Combust. Sci. Technol. , 176 , 907 – 923 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) based on a two-scalar (Y f , ξ) Probability Density Function (PDF) involving two Dirac delta functions. In the present contribution, a generalization of the LW-P model to four delta function PDF is proposed, one which allows the cross-correlation between the two scalars to behave as predicted by the experiments. The model is applied to the calculation of a turbulent reactive flow of propane and air stabilized by a sudden expansion of a 2-D channel (Besson et al. 2001 Besson , M. ( 2001 ) Etude expérimentale d'une zone de combustion en écoulement turbulent stabilisé en aval d'un élargissement brusque symétrique. PhD Thesis, University of Poitiers . [Google Scholar]). Results obtained using either a two Dirac delta function PDF or a four Dirac delta function PDF are compared with available experimental data. The closure problem raised by the mean scalar dissipation term is also discussed.