XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3839
to computational inefficiency and numerical divergence
(Monaghan, 1992).
The present study innovatively investigates the influ-
ence of slurry viscosity on tumbling mill performance by
coupling SPH with DEM simulations. Such an approach
comprehensively explores the interplay between solid par-
ticles and fluid within mills, providing insights into particle
collisions and comminution efficiency.
Validation of simulations at the mesoscale is con-
ducted using Positron Emission Particle Tracking (PEPT),
a nuclear imaging technique offering kinematic data (solids
fraction, velocity) at millisecond temporal and millime-
tre spatial resolution. Averaging these Lagrangian outputs
using representative voxel elements yields a continuum
description of the data.
The experimental setup involves a 460mm rotat-
ing drum filled with 10mm glass beads at 50% filling. To
simulate a slurry, a water-glycerol mixture is introduced,
minimally filling voids between beads. Mesoscopic statisti-
cal comparison of simulated DEM kinematic data (veloc-
ity, solids fraction) against measured PEPT data guides the
tuning of simulations (friction, averaging length, etc.) until
acceptable statistical agreement is achieved. This kinematic
validation instills confidence in DEM dynamic outputs,
providing insights into tuning DEM systems for realistic
outputs.
COMPUTATIONAL AND
EXPERIMENTAL METHODS
DEM
The ANSYS-ROCKY framework was employed to simulate
glass beads in this study due to its GPU-friendly nature,
providing a significant advantage over traditional CPU-
based computation. The utilisation of multiple cores on
GPUs (approximately 10,000 on GPUs vs. about 10 on
CPU) significantly accelerates simulation times, a crucial
factor in coupled simulations.
The DEM methodology utilised in this work involves
simulating particles as soft spheres capable of overlapping,
with the degree of overlap being proportional to the energy
dissipated in each collision. For a more comprehensive
understanding of the methodology, readers are referred to
Moodley and Govender (2022).
In the context of the rotating drum particle simula-
tions with relatively large particles (10 mm) in a wet batch
environment, the relevance of gravity and inter-particle
contact is complemented by the induction of lubrication
forces from the glycerol-water mixture. The total contact
force acting on a particle is decomposed into normal and
tangential components with respect to the contact plane.
For the normal component of the contact force,
the linear spring dashpot contact model (Cundall and
Strack, 1979) is employed, described by the equation
F K S C S˙
n nl n n n =+,where K
nl is the normal contact stiff-
ness, C
n is the normal damping coefficient, S
n is the con-
tact normal overlap, and (S˙
n )is the time derivative of the
contact normal overlap, representing velocity.
The tangential component of the contact force is
described by the Linear-spring Coulomb limit model,
which incorporates both elastic and frictional forces. The
elastic component at time t is given by F F K S
,e
t t t =-
x x x x
-
where F t t
x
-is the tangential force at the previous time, S
x is the tangential relative displacement during the calcula-
tion timestep (10–7s in this work), and K
x is the tangential
stiffness. The friction component introduces the Coulomb
limit, ensuring that the tangential force does not exceed
n
t nF ,where n is the friction coefficient and F
n
t is the con-
tact normal force at time t. This limit represents the point
at which surface contact initiates shearing, leading to the
sliding of particles over one another.
SPH
Traditional CFD methods rely on fixed meshes and aver-
age fluid behaviour at specific points within this mesh.
Typically, finer meshes are required around corners and
sharp points, while coarser meshes suffice around flat sur-
faces with negligible gradients. However, the unique nature
of the current rotating drum system, comprising solid (glass
beads), liquid (glycerol-water mixture), and gas phases (air
constituting the remaining 50% filling), poses challenges
for CFD convergence at interfaces with significant gradi-
ents ie. along free surface and cataracting region.
In response, Smoothed Particle Hydrodynamics (SPH),
a mesh-free numerical scheme, is introduced. SPH employs
small elements (smaller than DEM counterparts) to create
a point-wise grid from which properties are averaged. These
elements interact similarly to DEM counterparts, utilis-
ing a spring-dashpot model. Unlike DEM, SPH properties
are not computed at discrete points but are interpolated
between points using a specific kernel mediation scheme.
The grid formed by these elements is dynamic, constantly
changing due to interactions among the elements them-
selves (One-way coupling) and reaction forces from DEM
particles (Two-way coupling). The two-way coupling is
achieved by replacing each DEM particle by a representa-
tive number of SPH elements such that they occupy the
same volume (Potapov and Campbell, 2001). In doing so,
these SPH elements now have an associated artificial mass,
density and velocity thereby being able to satisfy the no-
slip boundary condition at the particle surface. In other
to computational inefficiency and numerical divergence
(Monaghan, 1992).
The present study innovatively investigates the influ-
ence of slurry viscosity on tumbling mill performance by
coupling SPH with DEM simulations. Such an approach
comprehensively explores the interplay between solid par-
ticles and fluid within mills, providing insights into particle
collisions and comminution efficiency.
Validation of simulations at the mesoscale is con-
ducted using Positron Emission Particle Tracking (PEPT),
a nuclear imaging technique offering kinematic data (solids
fraction, velocity) at millisecond temporal and millime-
tre spatial resolution. Averaging these Lagrangian outputs
using representative voxel elements yields a continuum
description of the data.
The experimental setup involves a 460mm rotat-
ing drum filled with 10mm glass beads at 50% filling. To
simulate a slurry, a water-glycerol mixture is introduced,
minimally filling voids between beads. Mesoscopic statisti-
cal comparison of simulated DEM kinematic data (veloc-
ity, solids fraction) against measured PEPT data guides the
tuning of simulations (friction, averaging length, etc.) until
acceptable statistical agreement is achieved. This kinematic
validation instills confidence in DEM dynamic outputs,
providing insights into tuning DEM systems for realistic
outputs.
COMPUTATIONAL AND
EXPERIMENTAL METHODS
DEM
The ANSYS-ROCKY framework was employed to simulate
glass beads in this study due to its GPU-friendly nature,
providing a significant advantage over traditional CPU-
based computation. The utilisation of multiple cores on
GPUs (approximately 10,000 on GPUs vs. about 10 on
CPU) significantly accelerates simulation times, a crucial
factor in coupled simulations.
The DEM methodology utilised in this work involves
simulating particles as soft spheres capable of overlapping,
with the degree of overlap being proportional to the energy
dissipated in each collision. For a more comprehensive
understanding of the methodology, readers are referred to
Moodley and Govender (2022).
In the context of the rotating drum particle simula-
tions with relatively large particles (10 mm) in a wet batch
environment, the relevance of gravity and inter-particle
contact is complemented by the induction of lubrication
forces from the glycerol-water mixture. The total contact
force acting on a particle is decomposed into normal and
tangential components with respect to the contact plane.
For the normal component of the contact force,
the linear spring dashpot contact model (Cundall and
Strack, 1979) is employed, described by the equation
F K S C S˙
n nl n n n =+,where K
nl is the normal contact stiff-
ness, C
n is the normal damping coefficient, S
n is the con-
tact normal overlap, and (S˙
n )is the time derivative of the
contact normal overlap, representing velocity.
The tangential component of the contact force is
described by the Linear-spring Coulomb limit model,
which incorporates both elastic and frictional forces. The
elastic component at time t is given by F F K S
,e
t t t =-
x x x x
-
where F t t
x
-is the tangential force at the previous time, S
x is the tangential relative displacement during the calcula-
tion timestep (10–7s in this work), and K
x is the tangential
stiffness. The friction component introduces the Coulomb
limit, ensuring that the tangential force does not exceed
n
t nF ,where n is the friction coefficient and F
n
t is the con-
tact normal force at time t. This limit represents the point
at which surface contact initiates shearing, leading to the
sliding of particles over one another.
SPH
Traditional CFD methods rely on fixed meshes and aver-
age fluid behaviour at specific points within this mesh.
Typically, finer meshes are required around corners and
sharp points, while coarser meshes suffice around flat sur-
faces with negligible gradients. However, the unique nature
of the current rotating drum system, comprising solid (glass
beads), liquid (glycerol-water mixture), and gas phases (air
constituting the remaining 50% filling), poses challenges
for CFD convergence at interfaces with significant gradi-
ents ie. along free surface and cataracting region.
In response, Smoothed Particle Hydrodynamics (SPH),
a mesh-free numerical scheme, is introduced. SPH employs
small elements (smaller than DEM counterparts) to create
a point-wise grid from which properties are averaged. These
elements interact similarly to DEM counterparts, utilis-
ing a spring-dashpot model. Unlike DEM, SPH properties
are not computed at discrete points but are interpolated
between points using a specific kernel mediation scheme.
The grid formed by these elements is dynamic, constantly
changing due to interactions among the elements them-
selves (One-way coupling) and reaction forces from DEM
particles (Two-way coupling). The two-way coupling is
achieved by replacing each DEM particle by a representa-
tive number of SPH elements such that they occupy the
same volume (Potapov and Campbell, 2001). In doing so,
these SPH elements now have an associated artificial mass,
density and velocity thereby being able to satisfy the no-
slip boundary condition at the particle surface. In other