A Lagrangian stochastic model for particle trajectories in non-Gaussian turbulent flows

Abstract

A Lagrangian stochastic model, a generalization of the Langevin equation to inhomogeneous flows, is developed for the simulation of particle trajectories within inhomogeneous turbulent flows. For homogeneous flows the model yields a Gaussian distribution of velocity and is exactly consistent with Thomson's well-mixed condition. For inhomogeneous flows: the model takes explicit account of the non-Gaussian distribution of velocity; Thomson's well-mixed condition is satisfied approximately to second order; whilst third- and higher-order moments of the velocity distribution are determined by the modelled dynamics. The model is shown to predict mean particle concentrations within a three-dimensional inhomogeneous turbulent flow (a ventilating air flow) in accord with experimental findings. These predictions are contrasted with those obtained using Thomson's model which exactly satisfies the well-mixed condition for inhomogeneous Gaussian turbulence. The results support the view that third- and higher-order moments of velocity are of secondary importance in determining particle dispersion in highly inhomogeneous turbulent flows when compared to the effects of strong mean-streamline straining and large gradients in Reynolds-stress.