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

Masi, Enrica and Simonin, Olivier and Riber, Eleonore and Sierra Sánchez, Patricia and Gicquel, Laurent Y.M. Development of an algebraic-closure-based moment method for unsteady Eulerian simulations of particle-laden turbulent flows in very dilute regime. (2014) International Journal of Multiphase Flow, 58. 257-278. ISSN 0301-9322

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Official URL: http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.10.001

Abstract

An 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.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at International Journal of Multiphase Flow website : http://www.sciencedirect.com/science/journal/03019322
HAL Id:hal-01010316
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Funders:
European Community through the TIMECOP-AE project (Project # AST5-CT-2006- 030828)
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Deposited On:19 Jun 2014 07:04

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