The rapid distortion of two-way coupled particle-laden turbulence

In this study, we address the modification of sheared turbulence by dispersed inertial particles. The preferential sampling of the straining regions of the flow by inertial particles in turbulence leads to an inhomogeneous distribution of particles. The strong gravitational loading exerted by the highly concentrated regions results in anisotropic alteration of turbulence at small scales in the direction of gravity. These effects are investigated in a rapid distortion theory (RDT) extended for two-way coupled particle-laden flows. To make the analysis tractable, we assume that particles have small but non-zero inertia. In the classical results for single-phase flows, the RDT assumption of fast shearing compared to the turbulence time scales leads to the distortion and shear-induced production of turbulence. In particle-laden turbulence, the coupling between the two phases under rapid shearing induces number density fluctuations that convert gravitational potential energy to turbulent kinetic energy and modulate the turbulence spectrum in a manner that increases with mass loading. Turbulence statistics obtained from RDT are compared with Euler-Lagrange simulations of homogeneously sheared particle-laden turbulence.