Accuracy of the CRW Models for Prediction of the Deposition and Dispersion of Particles in Inhomogeneous Turbulent Channel Flows

Abstract

Abstract The accuracy of the continuous random walk (CRW) stochastic model for prediction of dispersion and deposition of suspended particles in inhomogeneous turbulent channel flows was explored. The Reynolds-averaged Navier-Stokes (RANS) equations in conjunction with the Reynolds Stress Transport model was used to evaluate the mean flow and RMS velocity fluctuation characteristics of a fully developed turbulent channel flow at shear Reynolds number of 219. Then, spherical particles with diameters ranging from 10 nm to 30 μm and dimensionless relaxation times of 10−4 to 50 (in wall units) were uniformly introduced into the channel and their trajectories were evaluated by using the equation of particle motion including the Stokes drag and Brownian excitation. The particle laden flow was assumed to be sufficiently dilute so that the particle-particle collisions and the effects of particles on the flow could be ignored. To incorporate the effects of turbulence velocity fluctuations on particle motions, first, the Conventional-CRW stochastic model, which was originally proposed for homogenous turbulent flows, was used. The particles were tracked for the duration of 10,000 wall units of time and the deposition of particles on the walls was evaluated. By conducting ensemble averaging, the steady-state concentration profiles and deposition velocity of the particles were calculated. Comparison of the predicted results with the direct numerical simulation (DNS) and experimental data suggests that the deposition velocity was overestimated. In addition, unrealistic accumulation of fluid-point particles in the near-wall regions, and overestimation of the turbophoresis effects on finite-size particles were also observed. The poor agreement of the concentration profiles and deposition velocities resulting from the conventional (homogenous flow) CRW model with the experimental and the DNS data pointed to the lack of accuracy of the Conventional-CRW model in generating instantaneous fluid velocity fluctuations seen by ultrafine and finite-size particles in inhomogeneous turbulent flows. Then, the normalized Langevin equation with a drift correction term that was suggested by Bocksell and Loth [1] was used as an improved CRW model for applications to inhomogeneous flows. The simulations for the same range of particle sizes were repeated and the corresponding concentration profiles and the deposition velocity were evaluated. It was shown that the improved CRW model led to a reasonable uniform concentration profile for the ultrafine particles and the predicted concentration profiles of finite-size particles quantitatively matched with the DNS data. In addition, the evaluated deposition velocities from the improved CRW model were also in a good agreement with the experimental data and empirical model predictions.