Comptes Rendus
no. 9
A lattice method for the Eulerian simulation of heavy particle suspensions
[Méthode sur réseau pour la simulation eulérienne de suspensions de particules lourdes]
François Laenen1 ; Giorgio Krstulovic1 ; Jérémie Bec1 
1 Laboratoire Joseph-Louis-Lagrange, Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, bd de l'Observatoire, 06300 Nice, France
Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 672-683.

La modélisation de particules solides dispersées dans un fluide reste actuellement un défi numérique, surtout lorsqu'il y a une grande séparation d'échelles entre le couplage et l'écoulement, comme par exemple dans l'atmosphère ou les écoulements industriels à grand nombre de Reynolds. Une méthode numérique est ici présentée dans le but de simuler la dynamique de particules lourdes diffusives dans des écoulements turbulents. L'approche est basée sur la distribution des particules dans l'espace des phases positions–vitesses. La discrétisation en vitesses s'inspire de la méthode de Boltzmann sur réseau et est choisie de telle manière à ce qu'elle corresponde à des déplacements discrets entre deux pas de temps. Pour chaque position spatiale, l'évolution temporelle de la quantité de mouvement est résolue par une approche de volumes finis. La méthode proposée est testée pour des particules soumises à un frottement visqueux de Stokes, avec des écoulements aléatoires en une dimension, et avec des solutions de l'équation de Navier–Stokes incompressible forcée en deux dimensions. Les résultats montrent un bon accord entre les simulations lagrangiennes et eulériennes pour reproduire les concentrations préférentielles et la dispersion des vitesses des particules. De plus, la méthode proposée, contrairement à des descriptions hydrodynamiques des suspensions, permet de résoudre le croisement de trajectoires et la formation de caustiques, ce qui montre sa pertinence aux grands nombres de Stokes pour les situations où les détails des processus de collision sont importants.

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase–space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier–Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial clustering and the dispersion in particle velocities. In particular, the proposed method, in contrast to hydrodynamical Eulerian descriptions of the dispersed phase, is able to reproduce fine particle kinetic phenomena, such as caustic formation or trajectory crossings. This indicates the suitability of this approach at large Stokes numbers for situations where details of collision processes are important.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.05.004
Keywords: Disperse flows, Particles in turbulence, Eulerian modeling, Lattice methods
Mot clés : Écoulements dispersés, Particules en turbulence, Modélisation eulérienne, Méthodes sur réseau

François Laenen 1 ; Giorgio Krstulovic 1 ; Jérémie Bec 1

1 Laboratoire Joseph-Louis-Lagrange, Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, bd de l'Observatoire, 06300 Nice, France 
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François Laenen; Giorgio Krstulovic; Jérémie Bec. A lattice method for the Eulerian simulation of heavy particle suspensions. Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 672-683. doi : 10.1016/j.crme.2016.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.05.004/

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