In this study, the accuracy of the discrete random walk (DRW) stochastic model in generating the instantaneous velocity fluctuations as seen by micro- and nano-particles in inhomogeneous turbulent flows were examined. Particular attention was given to the effects of the non-uniform normal RMS velocity fluctuations and turbulence time scale on the DRW model predictions. The trajectories of randomly injected point-particles with diameters ranging from 10 nm to 30 μm in a duct were evaluated using an in-house Matlab particle tracking code. The particle equation of motion included the drag and Brownian forces. The fully developed mean velocity and RMS fluctuation velocity profiles were exported from the RANS (v2f) simulations and were used for the particle dispersion and transport analysis. It was assumed that the particle-laden flow is sufficiently dilute so that the particle-particle collisions and the two-way coupling effects of particles on the flow could be ignored.
To incorporate the instantaneous turbulence velocity fluctuations effects on particle dispersion, the Conventional-DRW model (in the absence of drift corrections), which was originally developed for homogenous turbulent flows, was first used. It was shown that the Conventional-DRW model leads to superfluous migration of fluid-point particles toward the wall and erroneous particle deposition rate. The Modified-DRW model with an appropriate velocity gradient drift correction term was also tested. It was found that the predicted concentration profiles of tracer particles still are not uniform. It was hypothesized that the reason for this erroneous prediction is due to the inhomogeneous turbulence time macroscale in the channel flow. A new drift correction term as a function of gradients of both RMS fluctuation velocity and the turbulence time macroscale was proposed. It was shown that the new Improved-DRW model with the velocity and time scale drift corrections leads to uniform distributions for fluid-point particles and reasonable concentration profiles for finite-size particles. It was shown that the predicted deposition velocities of different size particles by the proposed Improved-DRW model are in good agreement with the available experimental data as well as the predictions of the empirical models and earlier DNS results.