A Lagrangian particle random walk model for hybrid RANS/LES turbulent flows

A continuous random walk (CRW) turbulent diffusion model was adapted for Lagrangian particles within gas flowfields simulated by hybrid RANS/LES methodologies. The methodology was designed to model all the particle diffusion in RANS regions and model only the sub-grid diffusion in LES regions. In the RANS approach, the mean flowfield and the turbulent time- and length-scales are obtained with a k–ω (Menter SST) turbulence model. These values are used with a discrete stochastic equation to compute instantaneous gas velocity along an individual particle trajectory. Experimental results for turbulent diffusion of particles in a homogeneous wake flow were first used to calibrate the RANS model. The stochastic diffusion model was then extended to utilize the Nichols–Nelson k–ω hybrid RANS/LES turbulence model in the unsteady three-dimensional wake of a cylinder. In particular, the flow at a Mach number of 0.1 and Reynolds number (ReD) of 800 was computed with a 5th-order upwind-biased scheme. The discrete stochastic equation was used to compute sub-grid fluctuations, which could be added to the resolved velocity field, and specifically took into account combined effects of particle inertia and non-homogeneous turbulence. The combination of resolved diffusion and sub-grid diffusion compared quite reasonably with diffusion based on Direct Numerical Simulation of the Navier–Stokes equations. The results indicate that eddy-crossing effects and inertia-based drift corrections can be critical, even when most of the kinetic energy is captured with the resolved-scales of an LES approach.