1051
A Coupled Analysis of Fluid-Particle Interactions in Granular Soils
Analyse couplée des interactions fluide-particules dans les sols granulaires
Zhao J., Shan T.
Department of Civil & Environmental Engineering, Hong Kong University of Science & Technology, Hong Kong
ABSTRACT: Fluid-particle interaction is important to a variety of geotechnical applications. Particle-scale simulation may help to
provide key microscopic information towards better understanding of the behavior of granular soils. This paper presents a coupled
Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) approach to simulate the fluid-particle interactions in
soils. The granular particle system is modeled by solving the Newton’s equation of motion by DEM and the fluid (may comprise of
both water and air) flow is simulated by solving the locally averaged Navier-Stokes equation with CFD. The coupling is considered
by exchanging such interaction forces as drag force, buoyancy force and virtual mass force between the DEM and CFD computations.
The numerical tool has been benchmarked by two classic geomechanics problems for which analytical solutions are available, the
single particle settling problem and the one-dimensional consolidation problem. In both cases good comparisons are observed. It has
been further applied to the prediction of sand heap formation in water through hopper flow. It is found the pressure dip of vertical
stress profile underneath the sand pile appears to be moderately reduced by the presence of water, as compared to the dry case.
Characteristics of force chain network in the former case become less heterogeneous.
RÉSUMÉ : L'interaction fluide-particules est de première importance dans un grand nombre d'applications géotechniques. Des
simulations à l'échelle de la particule semblent être un moyen pertinent d'améliorer notre connaissance du comportement
microscopique des matériaux granulaires. L'article présente une approche couplant Mécanique des Fluides et Modélisation Discrète
(CFD-DEM) afin de simuler les interactions fluide-particules dans les sols. Le système granulaire est simulé par résolution des
équations du mouvement de Newton par Méthode des Eléments Discrets, et l'écoulement du fluide (gaz et/ou liquide) est simulé par
résolution de l'équation de Navier-Stokes moyennée localement. Le couplage CFD-DEM est réalisé par l'intermédiaire des forces
d'interaction telles que trainée, poussée d'Archimède, et masse virtuelle. L'outil numérique a été validé sur deux problèmes
géotechniques classiques pour lesquels les solutions analytiques sont connues : la chute libre d'une particule unique dans un fluide, et
la consolidation unidirectionnelle. Il a ensuite été appliqué à la prédiction de la formation d'un tas de sable dans l'eau après
écoulement en trémie. Il apparaît que le déficit de contrainte verticale au centre de la base du tas de sable est modérément réduit en
présence d'eau en comparaison avec le cas du sable sec. Il semble également que la présence d'eau homogénéise le réseau des chaînes
de forces.
KEYWORDS: Fluid-particle interactions, granular media, coupled CFD-DEM modeling, sand pile, anisotropy.
1 INTRODUCTION
Granular media exist in frequent form of two-phase system with
stationary or moving fluids in the pores. The interactions
between the fluid phase and the granular particles may play a
key role in affecting the overall behavior of the material, which
may sometimes work favorably for us, such as in sand
production of oil reservoir, but on other occasions may cause
generate adverse consequences, such as in the case of
internal/surface erosion of embankments and debris flow and
slope failures. Conventional approaches considering the
coupling between fluid and granular particles have been mainly
based on continuum mechanics and mostly phenomenological
in nature. They cannot fully account for the microscopic origin
of fluid-particle interaction and their impact on the macroscopic
behavior of granular media, and have difficulties in dealing with
the dynamic interactions between fluid phase and particles as
well. This paper presents a micromechanical approach to
investigate the coupling behavior in granular materials. In
particular, a coupled Computational Fluid Dynamics and
Discrete Element Method (CFD-DEM) approach will be
developed to consider the coupling. Some interaction forces
typical in relevant geomechanics applications are considered in
the coupled numerical schemes. The numerical tool will be
benchmarked by some classic problems before being applied to
the prediction of sandpiling in water.
2 APPROACH AND FORMULATION
The coupled CFD-DEM approach typically solves the following
system of equations governing the motions of both particles in
the DEM system and the fluid cells in the CFD system
1
1
d
d
d
d
0
c
i
c
i
n
p
c
f
g
i
i
ij
i
i
j
n
i
i
ij
j
f
f
f
f
f
p
f
f
f
f
f
m
t
I
t
n
n
n
p
t
n
n
t
n
U F F F
ω M
U
U U
U
f
g
U
(1)
where the first two equations express the Newton’s law of
motion which govern the translational and rotational motions of
a granular particle
i
(Cundall and Strack, 1979), while the last
two equations are the Navier-Stokes equation and the continuity
equation governing the fluid flow which is locally averaged
over a specific fluid cell (Anderson and Jackson, 1967). The
variables involved in Eq. (1) are explained as follows:
U
p
i
= the
translational velocity of the considered particle;
i
= the
