XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 1143
Particle Shape Effects During the Particle Discharge
from the Hopper
The particle shape effects found to be significant during the
discharge of the spherical and cubic shaped particles. The
spherical particles exhibited smooth discharge flow than
the cubes having sphericity 0.81. The experimental mass
discharge %from the hopper with time for the spherical
and cubic-shaped particles data displayed that the discharge
is faster in case of spheres as the spheres moved around at
ease when compared with the cubes. At around 6.4 s, all
the spherical particles from the hopper exited the set-up,
while cubes took around 7.6 s to empty the hopper. The
cubes also had a greater number of sharp edges than the
spheres, leading to the observation of more interlocking
behaviours. The particle–particle contact, which was point-
wise in spheres, could involve vertices, corners, and edges
in the case of the cubes producing more hinderance to the
particle flow behaviour. From the DEM simulation results,
the same behaviour was validated. The cube discharge was
well represented using the polyhedral-based DEM because
of the accurate shape representation of the cubes using that
method. The multi-sphere DEM discharge of the cube
showed distinct funnel flow behaviour similar to the spheri-
cal particle discharge. Understanding the proper flow pat-
tern inside the hopper with the true particle shapes would
help in proper designing of the hoppers in mineral indus-
tries in-terms of stable discharge of the particles from the
hoppers. The parameters like hopper width, length of the
orifice opening and the hopper angle should be fine-tuned
in accordance to the particle shape and size to have the con-
trolled withdrawal of the particles from the hopper.
A few deviations were observed which were mainly
from the experimental set-ups. The friction between the
particles and the walls is comparatively higher and non-
uniform during the experiments because of the surface
roughness created due to the repetitive performance of the
experiments. This led to deviations from the desired flow
fields. Other factors, like the expansion or constriction of
the hopper material, were also found to affect the experi-
mental conditions. The simulations showed the ideal behav-
ioural conditions of the material discharge from the hopper
without the restrictions imposed during the experiments.
CONCLUSIONS
The hopper discharge study is very effective to understand
the behaviour of granular materials, especially in mineral
industries. In the present study, the influence of particle
shape during the particles discharge from the hopper was
analyzed with spheres and cubes. The flow pattern was
smooth for the spherical particles, while for cubes there
were few flow deformities. The cubes were having less
sphericity and more sharp edges than the spheres leading
to easy interlocking amongst them. The non-uniformity of
the particle shape led to arching of the particles near the
discharge outlet of the hopper. This also produced over-
all slower discharge of the cubic particles than the spheres.
These factors generally pose problems during the experi-
mental hopper discharge of the non-spherical particles.
This has been encountered in the literature and additional
set-ups or vibrations were used to counter it (Yang and
Hsiau, 2001 Khalid and Zhou, 2021).
The experimental results were also validated against the
results from the DEM simulations which accounted the
shape of the cube using the multi-sphere and polyhedral
based DEM approach. The spherical DEM results agreed
well with the experiments in terms of the mass discharge
rate and the velocity contours. The spherical DEM showed
average deviation of 3.78% when the mass discharge %was
compared. For the cubes, the polyhedral DEM matched
the experimental simulations, but the multi-sphere DEM
showed faster discharge profiles because of the smooth-
edges in the description of the particle shape. Also, the
polyhedral DEM produced slowest discharge rate as the
contact between these particles is complex to identify and
to model. When comparing the mass discharge %,the
polyhedral DEM showed an average deviation of 10.76%
and the multi-sphere DEM showed 19.21% deviation.
The flow pattern of the polyhedral DEM was similar to
the experiments, but the multi-sphere DEM showed flow
pattern more similar to the spheres than the cubes. This
showed that the representation of the particles with sharp
edges is well demonstrated using the polyhedral DEM,
while multi-sphere DEM would produce better results for
particles with smooth edges. The experimental difficulties,
like the loss of a few cubic particles before arching, slightly
rougher edges of the particles and the hopper walls made
some impact while obtaining data. In contrast, the simu-
lation results showed the ideal flow behaviour of spheres
and cubes from the hopper. The study shall be extended
to include different particle shapes and the effect of these
shapes on the particle discharge profile from the hopper.
ACKNOWLEDGMENTS
The authors would like to acknowledge Prime Minister’s
Research Fellowship (PMRF) (2002214-2022) and Indian
Institute of Technology Hyderabad for the funding and
encouragement in this research work. The authors would
also like to thank Dr. Vikrant Verma from Indian Institute
of Technology Delhi for his insightful feedbacks in the
research work.
Particle Shape Effects During the Particle Discharge
from the Hopper
The particle shape effects found to be significant during the
discharge of the spherical and cubic shaped particles. The
spherical particles exhibited smooth discharge flow than
the cubes having sphericity 0.81. The experimental mass
discharge %from the hopper with time for the spherical
and cubic-shaped particles data displayed that the discharge
is faster in case of spheres as the spheres moved around at
ease when compared with the cubes. At around 6.4 s, all
the spherical particles from the hopper exited the set-up,
while cubes took around 7.6 s to empty the hopper. The
cubes also had a greater number of sharp edges than the
spheres, leading to the observation of more interlocking
behaviours. The particle–particle contact, which was point-
wise in spheres, could involve vertices, corners, and edges
in the case of the cubes producing more hinderance to the
particle flow behaviour. From the DEM simulation results,
the same behaviour was validated. The cube discharge was
well represented using the polyhedral-based DEM because
of the accurate shape representation of the cubes using that
method. The multi-sphere DEM discharge of the cube
showed distinct funnel flow behaviour similar to the spheri-
cal particle discharge. Understanding the proper flow pat-
tern inside the hopper with the true particle shapes would
help in proper designing of the hoppers in mineral indus-
tries in-terms of stable discharge of the particles from the
hoppers. The parameters like hopper width, length of the
orifice opening and the hopper angle should be fine-tuned
in accordance to the particle shape and size to have the con-
trolled withdrawal of the particles from the hopper.
A few deviations were observed which were mainly
from the experimental set-ups. The friction between the
particles and the walls is comparatively higher and non-
uniform during the experiments because of the surface
roughness created due to the repetitive performance of the
experiments. This led to deviations from the desired flow
fields. Other factors, like the expansion or constriction of
the hopper material, were also found to affect the experi-
mental conditions. The simulations showed the ideal behav-
ioural conditions of the material discharge from the hopper
without the restrictions imposed during the experiments.
CONCLUSIONS
The hopper discharge study is very effective to understand
the behaviour of granular materials, especially in mineral
industries. In the present study, the influence of particle
shape during the particles discharge from the hopper was
analyzed with spheres and cubes. The flow pattern was
smooth for the spherical particles, while for cubes there
were few flow deformities. The cubes were having less
sphericity and more sharp edges than the spheres leading
to easy interlocking amongst them. The non-uniformity of
the particle shape led to arching of the particles near the
discharge outlet of the hopper. This also produced over-
all slower discharge of the cubic particles than the spheres.
These factors generally pose problems during the experi-
mental hopper discharge of the non-spherical particles.
This has been encountered in the literature and additional
set-ups or vibrations were used to counter it (Yang and
Hsiau, 2001 Khalid and Zhou, 2021).
The experimental results were also validated against the
results from the DEM simulations which accounted the
shape of the cube using the multi-sphere and polyhedral
based DEM approach. The spherical DEM results agreed
well with the experiments in terms of the mass discharge
rate and the velocity contours. The spherical DEM showed
average deviation of 3.78% when the mass discharge %was
compared. For the cubes, the polyhedral DEM matched
the experimental simulations, but the multi-sphere DEM
showed faster discharge profiles because of the smooth-
edges in the description of the particle shape. Also, the
polyhedral DEM produced slowest discharge rate as the
contact between these particles is complex to identify and
to model. When comparing the mass discharge %,the
polyhedral DEM showed an average deviation of 10.76%
and the multi-sphere DEM showed 19.21% deviation.
The flow pattern of the polyhedral DEM was similar to
the experiments, but the multi-sphere DEM showed flow
pattern more similar to the spheres than the cubes. This
showed that the representation of the particles with sharp
edges is well demonstrated using the polyhedral DEM,
while multi-sphere DEM would produce better results for
particles with smooth edges. The experimental difficulties,
like the loss of a few cubic particles before arching, slightly
rougher edges of the particles and the hopper walls made
some impact while obtaining data. In contrast, the simu-
lation results showed the ideal flow behaviour of spheres
and cubes from the hopper. The study shall be extended
to include different particle shapes and the effect of these
shapes on the particle discharge profile from the hopper.
ACKNOWLEDGMENTS
The authors would like to acknowledge Prime Minister’s
Research Fellowship (PMRF) (2002214-2022) and Indian
Institute of Technology Hyderabad for the funding and
encouragement in this research work. The authors would
also like to thank Dr. Vikrant Verma from Indian Institute
of Technology Delhi for his insightful feedbacks in the
research work.