Modelling of parallel competitive reactions in isotropic homogeneous turbulence using a filtered density approach for large eddy simulations

A methodology termed the filtered density function (FDF) has been implemented for a large eddy simulation of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function of the subgrid scale scalar quantities. A transport equation for the FDF is used in which the effects of chemical reactions appear in closed form. Colucci et al. (1998) developed and implemented the scheme for a single reaction, and demonstrated that results obtained from direct numerical simulations could be well reproduced. We used the FDF approach to implement a parallel, competitive reaction scheme in a large eddy simulation of an isotropic, homogeneous turbulent flow. The mixing intensity was varied over five orders of magnitude (by adjusting the Damköhler number Da), and for each case the yield of the slow reaction was determined. The relative yield approached in the extreme cases of very intense mixing (Da≪ 1) and very poor mixing (Da≫ 1) the theoretical values 0.0 and 0.5, respectively. Over a range of about one order of magnitude around Da=l, an intermediate mixing intensity exist in which the predicted yield was in between 0.0-0.5. This indicates that the sensitivity for mixing intensity is (at least qualitatively) well predicted by the FDF model.