A CRW Model for Free Shear Flows

Abstract

Computational models that are used to simulate particle diffusion in turbulence employing a stochastic Lagrangian particle methodology can fall into several categories. These can be arranged from the least computationally intensive to the most computationally intensive as: discontinuous random walk (DRW) models, continuous random walk (CRW) models, and stochastic differential equation (SDE) methods. The first two models are characterized by having a Reynolds-Averaged Navier-Stokes (RANS) solution for the continuous phase and computing the trajectory of a large number of particles in the flow to obtain mean particle diffusion information. Both the DRW and CRW models include an eddy–particle interaction model that computes the length and time scales of an eddy from the gas-phase RANS solution. These scales, along with a random number generator, are used to simulate the chaotic effect of the turbulence on the particles. The CRW model correlates the turbulence statistics in time and utilizes a Markov chain to correlate the velocity fluctuations with the ones from the previous time step. The chapter validates and evaluates the CRW methodology for homogeneous and inhomogeneous turbulence through comparison with detailed experimental data. The CRW model is used to study long time particle diffusion in isotropic turbulence, and understand the influences of particle Stokes number and eddy Froude number on particle diffusion.