Direct numerical simulation of particle deposition onto a free-slip and no-slip surface

Abstract

We consider here the direct numerical simulation (DNS) of channel flow with two different surfaces: a no-slip, fixed wall and on the opposite side a free-slip, free surface. The simulated velocity field agrees well with the experimental data for a free-surface flow obtained by Komori et al. [Int. J. Heat Mass Transf. 25, 513 (1982)]. The DNS is used to simulate particle trajectories, which are computed with a dynamic particle equation in which only the drag force given by the Stokes law is taken into account. For the particle time scale, nondimensionalized in terms of the fixed-wall friction velocity and the kinematic viscosity, we use the values τ+=5 and τ+=15. A statistically stationary condition is studied that is obtained by the introduction of a uniform distribution of particles at the beginning of the channel and by continuous removal through deposition at the two walls. The steady-state concentration distribution is nonuniform across the channel width, primarily due to the process whereby particles are trapped close to the surface. Moreover, we find that the wall–normal concentration profiles are self-similar. The deposition on both the no-slip and the free-slip wall can be described by a constant deposition coefficient, with for τ+=5 the larger value on the free-slip wall and for τ+=15 the opposite, i.e., the larger value over the no-slip wall. To study the deposition process in more detail we consider the cross channel particle fluxes and velocity statistics that are conditioned on deposition events. By means of instantaneous near-wall particle distributions we also consider the patterns of particles and their accumulation in certain areas of the flow. For a no-slip surface the well-known result that particles tend to collect in the low-speed streaks is confirmed. The patterns of particles near the free-slip surface are completely different, which can be explained in terms of the different types of coherent structures that are present near this surface.