Parametric sensitivities of the generalized binomial Langevin–multiple mapping conditioning model

Abstract

The binomial Langevin model (BLM) predicts mixture fraction statistics including higher moments excellently, but imposing boundedness for the large scalar spaces typically associated with chemically reacting flows becomes intractable. This central difficulty can be removed by using the mixture fraction as the reference variable in a generalized multiple mapping conditioning (MMC) approach. The resulting probabilistic BLM–MMC formulation has several free parameters that impact the turbulence–chemistry interactions in complex flows: the dissipation timescale ratio, the locality in selecting pairs of particles for mixing, and the fraction of particles mixed per time step. The impact of parametric variations on the behavior of the BLM–MMC model is investigated for a complex flow featuring auto-ignition to determine model sensitivities and identify optimal values. It is shown that only the mixture fraction rms is sensitive to the dissipation timescale ratio with the expected behavior of an increased ratio leading to a reduction in rms. Controlling locality by increasing the maximum possible distance between paired particles in reference space has a similar impact. Increasing the fraction of particles mixed only affects reacting scalars by advancing ignition. The modified Curl's model is used for the mixing process and the specified amount of mixing principally controls the local extinction and reignition behavior. It is further shown that the standard value of the dissipation timescale ratio is satisfactory; the amount of mixing should be half that specified by Curl's model; and the distance between particle pairs in reference space should be proportional to the diffusion length scale.