Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels

Abstract

The motion of small particles in the wall region of turbulent channel flows has been investigated using direct numerical simulation. It is assumed that the particle concentration is low enough to allow the use of one-way coupling in the calculations, i.e. the fluid moves the particles but there is no feedback from the particles on the fluid motion. The velocity of the fluid is calculated by using a pseudospectral, direct solution of the Navier-Stokes equations. The calculations indicate that particles tend to segregate into the low-speed regions of the fluid motion near the wall. The segregation tendency depends on the time constant of the particle made non-dimensional with the wall shear velocity and kinematic viscosity. For very small and very large time constants, the particles are distributed more uniformly. For intermediate time constants (of the order 3), the segregation into the low-speed fluid regions is the highest. The finding that segregation occurs for a range of particle time constants is supported by experimental results. The findings regarding the more uniform distributions, however, still remain to be verified against experimental data which is not yet available. For horizontal channel flows, it is also found that particles are resuspended by ejections (of portions of the low-speed streaks) from the wall and are, therefore, primarily associated with low-speed fluid. The smaller particles are flung further upwards and, as they fall back towards the wall, they tend to be accelerated close to the fluid velocity. The larger particles have greater inertia and, consequently, accelerate to lower velocities giving higher relative velocities. This velocity difference, as a function of wall-normal distance, follows the same trend as in experiments but is always somewhat smaller in the calculations. This appears to be due to the Reynolds number for the numerical simulation being smaller than that in the experiment. It is concluded that the average particle velocity depends not only on the wall variables for scaling, but also on outer variables associated with the mean fluid velocity and fluid depth in the channel. This is because fluid depth in combination with the wall shear velocity determines how much time a particle, of a given size and density, spends in the outer flow and, hence, how close it gets to the local fluid velocity.