2731
Simulating Flotation Cells Using Smoothed Particle
Hydrodynamics (SPH)
Stephen J. Neethling, Diego Mesa, Jorge Avalos Patino, Pablo R. Brito-Parada
Advanced Mineral Processing Research Group, Department of Earth Science and Engineering, Imperial College London
ABSTRACT: A new simulator, based on a smoothed particle hydrodynamics (SPH) framework, has been
developed for modelling flotation cells. This simulator incorporates liquid, solid and gas motion models,
with full coupling between phases, including granular pressure so that high solids contents can be modelled.
Bubble-particle attachment models are implemented including multiple particle types combining different
sizes, densities and levels of hydrophobicity. The semi-Lagrangian approach virtually eliminates the numerical
diffusion that commonly arises in traditional Eulerian-Eulerian simulations. This simulator is demonstrated
using both novel fluidised bed flotation cells, as well as more traditional mechanical cells, where the impeller is
explicitly modelled as a moving component.
INTRODUCTION
Flotation is a complex multiphase system, with strong cou-
pling interactions between all the phases. The simulation
of these systems becomes even more challenging due to
the presence of a rapidly spinning impeller in mechanical
flotation cells. Traditionally, the simulation of these cells
involves using an Eulerian-Eulerian model for the cou-
pling between the fluid and the various discrete phases,
within either a finite volume or finite element frame-
work. However, there are two significant drawbacks to this
approach. The first is related to the inclusion of the impeller
itself, as the presence of a mesh requires solutions such as a
frozen rotor approach, sliding meshes, or dynamic re-mesh-
ing, all of which lead to inaccurate solutions, significant
artefacts, or high computational costs. The second draw-
back is the significant numerical diffusion resulting from
the disparity between the large velocities of the fluid and
the comparatively small relative velocities of the particles
and bubbles with respect to the fluid. To tackle these chal-
lenges, a novel framework for flotation simulation based
on smoothed particle hydrodynamics (SPH) is presented,
which eliminates or significantly ameliorates the aforemen-
tioned challenges.
In this paper, we describe recent developments in the
Imperial College SPH simulator, a parallel SPH simula-
tor capable of utilising hundreds or thousands of cores for
simulating large problems at high resolution (Neethling &
Barker, 2016). The most significant of these developments
is the implementation of a continuum model to include the
discrete phase behaviour. This method makes use of a semi-
Lagrangian approach in which the SPH reference frame
moves at a momentum-averaged velocity. Consequently,
the discrete phase momentum and continuity equations
only need to account for the motion of these phases rela-
tive to the reference frame, with the continuous/solution
phase motion being obtained by difference. Since the dis-
crete phase motion relative to the reference frame will be
small compared to the reference frame motion, the numeri-
cal dispersion that can smear out and obscure the details
of the particle and bubble behaviour in more traditional
simulators is virtually eliminated.
Simulating Flotation Cells Using Smoothed Particle
Hydrodynamics (SPH)
Stephen J. Neethling, Diego Mesa, Jorge Avalos Patino, Pablo R. Brito-Parada
Advanced Mineral Processing Research Group, Department of Earth Science and Engineering, Imperial College London
ABSTRACT: A new simulator, based on a smoothed particle hydrodynamics (SPH) framework, has been
developed for modelling flotation cells. This simulator incorporates liquid, solid and gas motion models,
with full coupling between phases, including granular pressure so that high solids contents can be modelled.
Bubble-particle attachment models are implemented including multiple particle types combining different
sizes, densities and levels of hydrophobicity. The semi-Lagrangian approach virtually eliminates the numerical
diffusion that commonly arises in traditional Eulerian-Eulerian simulations. This simulator is demonstrated
using both novel fluidised bed flotation cells, as well as more traditional mechanical cells, where the impeller is
explicitly modelled as a moving component.
INTRODUCTION
Flotation is a complex multiphase system, with strong cou-
pling interactions between all the phases. The simulation
of these systems becomes even more challenging due to
the presence of a rapidly spinning impeller in mechanical
flotation cells. Traditionally, the simulation of these cells
involves using an Eulerian-Eulerian model for the cou-
pling between the fluid and the various discrete phases,
within either a finite volume or finite element frame-
work. However, there are two significant drawbacks to this
approach. The first is related to the inclusion of the impeller
itself, as the presence of a mesh requires solutions such as a
frozen rotor approach, sliding meshes, or dynamic re-mesh-
ing, all of which lead to inaccurate solutions, significant
artefacts, or high computational costs. The second draw-
back is the significant numerical diffusion resulting from
the disparity between the large velocities of the fluid and
the comparatively small relative velocities of the particles
and bubbles with respect to the fluid. To tackle these chal-
lenges, a novel framework for flotation simulation based
on smoothed particle hydrodynamics (SPH) is presented,
which eliminates or significantly ameliorates the aforemen-
tioned challenges.
In this paper, we describe recent developments in the
Imperial College SPH simulator, a parallel SPH simula-
tor capable of utilising hundreds or thousands of cores for
simulating large problems at high resolution (Neethling &
Barker, 2016). The most significant of these developments
is the implementation of a continuum model to include the
discrete phase behaviour. This method makes use of a semi-
Lagrangian approach in which the SPH reference frame
moves at a momentum-averaged velocity. Consequently,
the discrete phase momentum and continuity equations
only need to account for the motion of these phases rela-
tive to the reference frame, with the continuous/solution
phase motion being obtained by difference. Since the dis-
crete phase motion relative to the reference frame will be
small compared to the reference frame motion, the numeri-
cal dispersion that can smear out and obscure the details
of the particle and bubble behaviour in more traditional
simulators is virtually eliminated.