Development of an algebraic-closure-based moment method for unsteady Eulerian simulations of particle-laden turbulent flows in very dilute regime

Abstract

International audienceAn algebraic-closure-based moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersed-phase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are low-order moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the second-order moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different algebraic closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particle-laden turbulent planar jet. Several million-particle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with Eulerian-Lagrangian DNSs and properly represent all crucial trends extracted from such simulations

Point-Particle DNS and LES of Particle-Laden Turbulent flow - a state-of-the-art review

“…An Euler-Euler LES method has been proposed by Moreau et al [74], where the algebraic-closure-based moment method has been used to derive the LES model. Euler-Euler DNS has recently been applied by Masi et al [67], who used a similar idea to make Euler-Euler DNS suitable for turbulence with mean shear and particles with larger Stokes numbers. The algebraic-closure-based moment method is based on the mesoscopic Eulerian formalism [38], in which the particle velocity field is partitioned in two contributions.…”

A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

“…Lagrangian methods are also applied to the simulation of charged particles in plasmas, the reader being referred to Birdsall and Langdon's monograph [12]. In the case of particle-laden flows, DSMC is considered as a reference method to solve the transport operator and is used to validate velocity closures [29,72,91]. It is also a well established approach in mechanical engineering problems such as gas turbines [87,60], solar concentrators [96], and chemical engineering risers [17].…”

Particle-laden flows forced by the disperse phase: Comparison between Lagrangian and Eulerian simulations

“…Eulerian particle methods have been explored as an alternative to the Lagrangian particle tracking method [9,14,15,22,27,28,8,24,47]. The goal of such methods is to solve the statistics of the disperse phase, i.e.…”