Statistical description of turbulent particle-laden flows in the very dilute regime using the anisotropic Gaussian moment method

Abstract

The present work aims at investigating the ability of a Kinetic-Based Moment Method (KBMM) to reproduce the statistics of turbulent particle-laden flows using the Anisotropic Gaussian (AG) closure. This method is the simplest KBMM member that can account for Particle Trajectory Crossing (PTC) properly with a well-posed mathematical structure Vié et al. (2015). In order to validate this model further, we investigate here 3D turbulent flows that are more representative of the mixing processes, which occurs in realistic applications. The chosen configuration is a 3D statistically-stationary Homogeneous Isotropic Turbulence (HIT) loaded with particles in a very dilute regime. The analysis focuses on the description of the first three lowest order moments of the particulate flow: the number density, the Eulerian velocity and the internal energy. A thorough numerical study on a large range of particle inertia allows us to show that the AG closure extends the ability of the Eulerian models to correctly reproduce the particle dynamics up to a Stokes number based on the Eulerian turbulence macro-scale equal to one, but also highlights the necessity of high-order numerical schemes to reach mesh convergence, especially for the number density field.