Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.