2734 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
turbulent interactions (Abrahamson, 1975) multiplied by
the probabilities that these interacting bubbles and par-
ticles will actually collide and subsequently attach to one
another. Both of these probabilities are based on the models
of (Yoon &Luttrell, 1989).
The detachment process is modelled by considering
the rate at which the bubble particle aggregates will inter-
act with turbulent eddies based on the model of (Koh &
Schwarz, 2005) followed by the probability that the inter-
action will result in detachment, with this probability pre-
dicted using a modified version of the model of Schulze
(Schulze et al., 1989).
These attachment and detachment processes results in
a net attachment rate that not only transfers mass between
the unattached classes and the bubble-particle aggregates,
but also transfers momentum, thus influencing both the
momentum and continuity of the system.
EXAMPLE SIMULATIONS
The modelling framework allows for complex and moving
system geometries to be modelled. The meshless Lagrangian
nature of the SPH method means that components such as
spinning impellers can be directly modelled without prob-
lems with mesh quality or the introduction of the artefacts
associated with sliding meshes or similar techniques used to
allow moving components in Eulerian-Eulerian reference
frames. In these simulations, the only meshes required are
the 2D meshes associated with boundaries of the domain.
The simulator accepts CAD files for these geometries,
allowing complex designs to be readily simulated.
The simulator is also designed to be run in parallel on
high performance computing clusters, allowing for high
resolution simulations
Laboratory Scale Flotation Cell
The first example simulations are based on a laboratory
scales cell used with our laboratory, including for PEPT
experiments (Mesa et al., 2022). The cell has a volume of
4 litres, with air being introduced into the cell via a porous
plate on the bottom of the cell below the impeller. In these
simulation 3 different particle size classes are simulated,
with a hydrophilic and a hydrophobic class for each size.
The simulator can handle an arbitrary number of classes
based on size, density and hydrophobicity (characterised
by means of an attachment induction time), but the com-
putational cost increases with the number of classes sim-
ulated. In addition to the particle classes, a single bubble
class was used (multiple bubble size classes can be simu-
lated, each potentially able to form multiple different types
of bubble-particle aggregates, but again at the expense of
computational cost).
As this a dynamic simulation, Figure 1 shows a snap-
shot of the results once the flow has reached steady state
(after 16 seconds of real time has passed). Note that the
solids content, especially the floatable material, will not
achieve a true steady state as this is a simulation of a batch
flotation experiment. The attached solids towards the edge
of the cell move upwards, but some of the attached solids
are swept towards the centre of the cell and recirculated
through the impeller as there are regions of the cell where
the aggregates are not able to rise fast enough to counter the
downward velocity of the liquid in the centre of the cell.
This is especially true of some of the highly loaded bubble-
particle aggregates.
In addition to simulation with a standard laboratory
flotation cell, further simulations were carried out in which
a funnel insert was placed within the cell. The aim of these
inserts was to create a quiescent zone below the froth and
thereby both reduce entrainment and improve froth stabil-
ity. As these simulations do not include a true froth phase
the aim of these simulations is to investigate the impact
that these inserts have on hydrodynamics of these systems.
Once again a snapshot of the results are presented at 16
seconds of real time. It can be seen that the inclusion of
the granular pressure means that solids can accumulate on
the top of the funnel and air on the underside without the
concentrations becoming unphysically high and thus caus-
ing simulation and data interpretation problems (Figure 2).
Simulating Fluidised Bed Flotation Cells.
There is increasing interest in fluidised bed flotation cells
for the flotation of coarse material. The advantage of these
cells are the relatively quiescent flow and therefore lower
rates of particle detachment, a major contribution to par-
ticle losses for coarser particles. In this paper we will present
result from the simulation of the laboratory and pilot scale
CoarseAir ™ cell produced by FLSmidth.
Laboratory Scale CoarseAir™ Cell
Because SPH can readily handle free surfaces, we were able
to simulate the startup process so that it matched what was
done experimentally. This was important as the flotation
kinetics are quite fast and what happens during startup can
have a big impact on the flotation trends. In these experi-
ments the approximately 10 litre laboratory scale cell was
started with 2.5 litres of water within it. The fresh feed, tail-
ings recycle and fluidisation (including the air) were then
simultaneously started. This simulation was carried out
turbulent interactions (Abrahamson, 1975) multiplied by
the probabilities that these interacting bubbles and par-
ticles will actually collide and subsequently attach to one
another. Both of these probabilities are based on the models
of (Yoon &Luttrell, 1989).
The detachment process is modelled by considering
the rate at which the bubble particle aggregates will inter-
act with turbulent eddies based on the model of (Koh &
Schwarz, 2005) followed by the probability that the inter-
action will result in detachment, with this probability pre-
dicted using a modified version of the model of Schulze
(Schulze et al., 1989).
These attachment and detachment processes results in
a net attachment rate that not only transfers mass between
the unattached classes and the bubble-particle aggregates,
but also transfers momentum, thus influencing both the
momentum and continuity of the system.
EXAMPLE SIMULATIONS
The modelling framework allows for complex and moving
system geometries to be modelled. The meshless Lagrangian
nature of the SPH method means that components such as
spinning impellers can be directly modelled without prob-
lems with mesh quality or the introduction of the artefacts
associated with sliding meshes or similar techniques used to
allow moving components in Eulerian-Eulerian reference
frames. In these simulations, the only meshes required are
the 2D meshes associated with boundaries of the domain.
The simulator accepts CAD files for these geometries,
allowing complex designs to be readily simulated.
The simulator is also designed to be run in parallel on
high performance computing clusters, allowing for high
resolution simulations
Laboratory Scale Flotation Cell
The first example simulations are based on a laboratory
scales cell used with our laboratory, including for PEPT
experiments (Mesa et al., 2022). The cell has a volume of
4 litres, with air being introduced into the cell via a porous
plate on the bottom of the cell below the impeller. In these
simulation 3 different particle size classes are simulated,
with a hydrophilic and a hydrophobic class for each size.
The simulator can handle an arbitrary number of classes
based on size, density and hydrophobicity (characterised
by means of an attachment induction time), but the com-
putational cost increases with the number of classes sim-
ulated. In addition to the particle classes, a single bubble
class was used (multiple bubble size classes can be simu-
lated, each potentially able to form multiple different types
of bubble-particle aggregates, but again at the expense of
computational cost).
As this a dynamic simulation, Figure 1 shows a snap-
shot of the results once the flow has reached steady state
(after 16 seconds of real time has passed). Note that the
solids content, especially the floatable material, will not
achieve a true steady state as this is a simulation of a batch
flotation experiment. The attached solids towards the edge
of the cell move upwards, but some of the attached solids
are swept towards the centre of the cell and recirculated
through the impeller as there are regions of the cell where
the aggregates are not able to rise fast enough to counter the
downward velocity of the liquid in the centre of the cell.
This is especially true of some of the highly loaded bubble-
particle aggregates.
In addition to simulation with a standard laboratory
flotation cell, further simulations were carried out in which
a funnel insert was placed within the cell. The aim of these
inserts was to create a quiescent zone below the froth and
thereby both reduce entrainment and improve froth stabil-
ity. As these simulations do not include a true froth phase
the aim of these simulations is to investigate the impact
that these inserts have on hydrodynamics of these systems.
Once again a snapshot of the results are presented at 16
seconds of real time. It can be seen that the inclusion of
the granular pressure means that solids can accumulate on
the top of the funnel and air on the underside without the
concentrations becoming unphysically high and thus caus-
ing simulation and data interpretation problems (Figure 2).
Simulating Fluidised Bed Flotation Cells.
There is increasing interest in fluidised bed flotation cells
for the flotation of coarse material. The advantage of these
cells are the relatively quiescent flow and therefore lower
rates of particle detachment, a major contribution to par-
ticle losses for coarser particles. In this paper we will present
result from the simulation of the laboratory and pilot scale
CoarseAir ™ cell produced by FLSmidth.
Laboratory Scale CoarseAir™ Cell
Because SPH can readily handle free surfaces, we were able
to simulate the startup process so that it matched what was
done experimentally. This was important as the flotation
kinetics are quite fast and what happens during startup can
have a big impact on the flotation trends. In these experi-
ments the approximately 10 litre laboratory scale cell was
started with 2.5 litres of water within it. The fresh feed, tail-
ings recycle and fluidisation (including the air) were then
simultaneously started. This simulation was carried out