(237s) Multifluid Modelling Approaches for the Numerical Investigation of Liquid-Solid Suspensions: Limitations and Challenges

Multifluid modelling
approaches for the numerical investigation of liquid-solid suspensions:
limitations and challenges

Rashid Jamshidi, Giovanni Meridiano, Panagiota Angeli, Luca
Mazzei*

Department
of Chemical Engineering, University College London, Torrington Pl, London WC1E 7JE,
UK

*l.mazzei@ucl.ac.uk, angeli@ucl.ac.uk,  r.jamshidi@ucl.ac.uk, giovanni.meridiano.17@ucl.ac.uk

The Eulerian-Eulerian and mixture modelling approaches, which regard all
the phases in multiphase flows as interpenetrating continua, have been used
extensively for modelling liquid-solid suspensions. In this talk, we address the
problem of closure that these models pose for the effective stress tensors of
the phases. Our interest is in the applicability of the constitutive equations
for the effective stresses for the simulation of suspensions of identical
spherical particles in Newtonian liquids. We show that for such suspensions some
of the widely used closures suggested in the literature are not able to
reproduce important experimental observations.  

In experiments, researchers have observed three important phenomena,
which are common to almost all suspensions. The first one is a monotonic increase
in the viscosity of a suspension with the solid concentration. This has been detected
for all ranges of solid concentration. The second phenomenon is that of
particle migration. A substantial amount of experimental work has shown that in
dense suspensions solid particles migrate from regions of high concentration
and/or shear to regions of low concentration and/or shear. The third phenomenon
is the change of the rheology of a suspension of particles dispersed in a
Newtonian interstitial liquid from Newtonian to non-Newtonian. This change in
the rheology occurs at different values of particle concentration, the value
being system-dependent. We explain that the deficiency of the closures in
replicating the aforementioned phenomena is because the closures disregard some
essential physical mechanisms that occur in such suspensions. We report and
discuss these mechanisms.

We use Computational Fluid
Dynamics (CFD) to investigate the effect of different constitutive equations
for the effective stress tensors in the Eulerian-Eulerian and mixture modelling
approaches on predicting three different suspension flows. In the first case,
the simulation results of a laminar flow in a horizontal pipe of a dilute
suspension of particles are compared to experimental data obtained from the
literature. We show that the mixture model coupled with a suitable experimental
constitutive relation for the mixture rheology yields the most accurate
prediction of the pressure drop. In the second case, we simulate the laminar
flow of a dense particle suspension through an abrupt expansion. Our goal is to
compare the recirculation length of the vortex after the expansion obtained
using CFD with that observed experimentally. We show that the concentration
profile in the upstream tube, which develops owing to shear-induced particle migration,
significantly affects the flow pattern downstream of the expansion. We
demonstrate that the migration of particles should be considered using a suitable
closure for the effective stress tensor of the solid phase; by doing so, one
can capture this sophisticated flow pattern by means of CFD. Finally, we
implement the multiphase model to a lab-scale stirred tank configuration, which
we use for dispersing particles in a liquid mixture. We observe good agreement
between the torque values obtained numerically and experimentally.