Turbulent channel flow past a moving array of spheres

We have performed a particle-resolved direct numerical simulation of a turbulent channel flow past a moving dilute array of spherical particles. The flow shares important features with dilute vertical gas solid flow at high Stokes number, such as significant attenuation of the turbulence kinetic energy (TKE) at low particle volume fraction. The flow has been simulated by means of an overset grid method, using spherical grids around each particle overset on a background non-uniform Cartesian grid. The main focus of the present paper is on the TKE budget, which is analysed both in the fixed channel frame of reference and in the moving particle frame of reference. The overall (domain-integrated) TKE and turbulence production due to mean shear are reduced compared to unladen flow. In the fixed frame, the interfacial term, which represents production due to relative (slip) velocity, accounts for approximately 40% of the total turbulence production in the channel. As a consequence, the total turbulence production and the overall turbulence dissipation rate remain approximately the same as in the unladen flow. However, a comparison with laminar flow past the same particle configuration reveals that significant parts of various fixed-frame statistics are due to non-turbulent structures, spatial variations that are steady in the moving particle frame. In order to obtain a clearer picture of the modification of the true turbulence and in order to reveal the rich three-dimensional (3-D) statistical structure of turbulence interacting with particles, time averaging in the moving frame of reference of the particle is used to extract the fluctuations entirely due to true turbulence. In the moving frame, the turbulence production is positive near the sides and in the wake, but negative in a region near the front of the particle. The turbulence dissipation rate and even more the dissipation rate of the 3-D mean flow attain very large values on a large part of the particle surface, up to approximately 400 and 4000 times the local turbulence dissipation rate of the unladen flow, respectively. Very close to the particle, viscous diffusion is the dominant transport term, but somewhat further away, in particular near the front and sides of the particle, pressure diffusion and also convection provide large and positive transport contributions to the moving-frame budget. A radial analysis shows that the regions around the particles draw energy from the regions further away via the surprising dominance of the pressure diffusion flux over a large range of radii. Spectra show that (very) far away from the particles all scales of the (true) turbulence are reduced. Near the particles enhancement of small scale turbulence is observed, for the streamwise component of the velocity fluctuation more than for the other components. The most important reason for turbulence reduction and anisotropy increase appears to be particle-induced non-uniformity of the mean driving force of the flow.