On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification

Abstract

The modification of decaying homogeneous turbulence due to its interaction with dispersed small solid particles (d/η<1), at a volumetric loading ratio φv≤5×10−4, is studied using direct numerical simulation. The results show that the particles increase the fluid turbulence energy at high wave numbers. This increase of energy is accompanied by an increase of the viscous dissipation rate, and, hence, an increase in the rate of energy transfer T(k) from the large-scale motion. Thus, depending on the conditions at particle injection, the fluid turbulence kinetic energy may increase initially. But, in the absence of external sources (shear or buoyancy), the turbulence energy eventually decays faster than in the particle-free turbulence. In gravitational environment, particles transfer their momentum to the small-scale motion but in an anisotropic manner. The pressure-strain correlation acts to remove this anisotropy by transferring energy from the direction of gravity to the other two directions, but at the same wave number, i.e., to the small-scale motion in directions normal to gravity. This input of energy in the two directions with lowest energy content causes a reverse cascade. This reverse cascade tends to build up the energy level at lower wave numbers, thus reducing the decay rate of energy as compared to that of either the particle-free turbulence or the zero-gravity particle-laden flow.