A stochastic micromixing model based on the turbulent diffusion length scale

Abstract

A new micromixing model to close probability density function (pdf) models is proposed. The model is based on the proposition that each computational timestep, stochastic particles move within the scalar space (on average) by a distance equal to the turbulent diffusion length scale. At each timestep, the model evaluates the distance in scalar space between all particles. During the timestep, a discrete pdf is computed for the distance between unmixed particles and the cumulative integral for the mean calculated. A filter is applied to retain the lower portion of the distance domain so that the cumulative integral is equal to the average diffusion length required to decrease the scalar variance. A sample (a pair of particles) is chosen from this filtered part of the domain and the particles mixed using Modified Curl’s model. The complete interparticle-distance pdf is re-evaluated for each pair to ensure that there is sufficient capacity to mix to meet the variance decay requirements. Preliminary tests show that this model obeys several fundamental properties required of micromixing models, including conservation, correct decay of variance and relaxation to Gaussian pdf.