1047
Particulate Modeling of Sand Slurry Flow Retardation
Modélisation par les milieux granulaires de l’effet de retard de l'écoulement des boues résiduelles
Tomac I., Gutierrez M.
Colorado School of Mines, Golden, CO, USA
ABSTRACT: The focus of this study is on the flow of dense sand slurries within a narrow channel, with a volumetric particle
concentration greater than 0.1 and a ratio of channel width and particle radius less than 10. In sand slurry flow processes in narrow
channels, clogging and velocity retardation often occur and are governed by the sand concentration and slurry flow rate. A numerical
model developed in this study permits an improved understanding of the conditions which lead to particle clogging in sand slurry flow
within narrow channels. The used numerical model couples the discrete element method (DEM) with computational fluid dynamics
(CFD)to study this flow process. A user-defined contact model was developed to capture the non-linear collision of submerged
particles and walls. A damping effect, formulated using the theory of lubrication associated with a thin fluid layer between particles is
associated with the contact model. Lubrication is observed to enhance the formation of particle packs in the slurry flow, and decreases
the kinetic energy of particle collisions.
RÉSUMÉ : Cette étude considère l’écoulement des boues de sable dense dans un canal étroit, avec une concentration en particules
volumétrique supérieur à 0,1 et un rapport de largeur de canal moins de 10 rayon des particules. Dans les processus d’écoulement de
boue de sable dans des chenaux étroits, le colmatage et le retard de la vitesse se produisent souvent et sont régis par la concentration
en sable et le débit de la pâte. Un modèle numérique développé dans cette étude permet une meilleure compréhension des conditions
qui conduisent à des particules le colmatage de l’écoulement de boue dans les chenaux étroits. Le modèle établi un couplage entre la
méthode des éléments discrets et les méthodes numériques de la dynamique des fluides pour étudier ce processus. Un modèle de
contact pouvant être défini par l'utilisateur a été mis au point pour représenter la collision non linéaire des particules immergées et les
murs. Un effet d'amortissement, formulée en utilisant la théorie de lubrification associée à une couche mince de fluide entre les
particules, est associé au modèle de contact. On observe que la lubrification d'améliore la formation des paquets de particules dans
l'écoulement de suspension, et diminue l'énergie cinétique des collisions de particules.
KEYWORDS: sand, lubrication, discrete element model, computational fluid mechanics, dense phase flow
1 INTRODUCTION
Sand and other particulate material submerged in water and
subjected to a fluid driven transport can be found in many
geotechnical problems. For example, the stability of sand drains
often fails under the increase groundwater pressure during the
stabilization of excavation pit bottoms or consolidation process.
Failure of dams and embankments can be caused by formation
of localized fluid channels - pipes caused by seepage within the
embankment body that carry out material and water (Fig. 1).
Another potential application of the results from this study is
the prediction of grouting effectiveness. A discrete element
study is performed to better understand the sand-water slurry
flow in narrow channels from a micro-mechanical point of
view.
1
3
v
d
r
c
D v
Figure 1. Piping in embankment caused by seepage
The motivation for the micro-mechanical approach comes from
the multi-phase theory, which explains that at higher sand
concentrations, the flow is assumed to be in category of dense
phase flows, in which the particle interaction forces dominate
over the fluid drag forces in the slurry behavior.
2 METHODOLOGY
Discrete element method coupled with computational fluid
dynamics (CFD-DEM) in two dimensions is used with the
commercialy available Particle Flow Code (PFC
2D
) (Itasca
Consulting Group, Inc. 2008a). Two-way particle fluid coupling
is used to model a dense phase flow of medium coarse sand and
water. Fluid motion is averaged over each fluid grid element,
while particle motion is tracked individually. In the dense phase
flow, particle–particle collisions dominate over the fluid drag
force, because there is no sufficient time to respond to the local
fluid dynamic forces before the next collision occurs. Dense
flow is described with the relation (Crowe et al., 2011):
(1)
where
v
=fluid response time and
c
=particle response time,
d
=bulk density of the dispersed phase (sand),
D
=particle
diameter,
v
r
=relative particle velocity,
=fluid dynamic
viscosity.
In order to account for collision forces with more accuracy,
a new discrete element contact model is developed for particle –
particle collisions suspended in the fluid, and it is based on the
elasto-hydro-dynamic theory equation that incorporates a
lubrication force at particle-particle impact (Davis et al., 1986).
2.1 Continuum fluid dynamics and discrete element model
The Discrete Element Method defines a system of particles that
are represented by finite spherical or disc spaces (Cundall and
Strack, 1979). The motion of each particle is solved using the
explicit finite difference scheme. The calculation cycle in DEM
is a time-stepping algorithm that consists of repeated
applications of the law of motion to each particle, the force-
displacement law to each contact, and the constant updating of
