XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 1135
walls. The knowledge of the flowability of these particles
is essential as they affect the storage and transport of the
particles (Zatloukal and Šklubalová 2012). Hopper designs
are based on their applications and mostly under spheri-
cal shape calculations. The flow pattern and the discharge
rate of solids influence these designs. Understanding the
pressure distribution on the walls of the hopper during the
charge, storage, and discharge of the solids is critical for
their design.
The proper design is required to have smooth par-
ticle dynamics without flow rate fluctuations, solidifica-
tion, plugging, funnel flow, bridging, rat-holing, etc., The
particles in motion may cause arch formation above the
hopper aperture and cause clogging, restricting the parti-
cle flow within the hoppers when dealing particularly the
mineral ore particles. The variables influencing the arch-
ing are polydispersity of the particles’ size, shape, density,
cohesion, orifice geometry, hopper width, driving force,
and height of the particle bed. The probability of the arch
formation increases when the opening size decreases due to
constraint flow (Pascot et al., 2020). Börzsönyi et al., 2017
used X-ray tomography and optical methods to study the
flow and clogging of particles in a 3D hopper. Their X-ray
tomograms provided information on the bulk filling of
the hopper and the particle orientation. Hafez et al., 2021
investigated the discharge and the clogging behaviour of
spherical, elongated, faceted, and non-convex particles and
highlighted the interlocking behaviour of the cubes and
3D crosses. They also identified that the particle-particle
interactions define the geometry of clogging domes. The
average discharge volume before clogging depends on the
orifice-to-particle size ratio and initial solidity (Hafez et al.,
2021). One phenomenon used to control the flow inside
the hopper in industries is the forced vibration of the hop-
per walls (Kumar et al., 2020). The factors like frequency
and amplitude of the vibrations, hopper size and geometry,
and particle size need to be optimal to avoid segregation
of the mixture. The flow fields of the hoppers are modified
by using the inserts, which improve the flow from funnel
flow type to mass flow type during the discharge (Yang and
Hsiau 2001). Khalid and Zhou 2021 studied the effect of
providing an obstacle above the exit and applying a heli-
cal texture to the arching. Various types of hopper geom-
etries proposed in the literature include cylindrical with flat
bottom (Liu et al., 2013, Börzsönyi et al., 2017, Hilton
and Cleary 2011) conical (Ahn et al., 2007, Kumar et al.,
2018, Kumar et al., 2020), wedged (Tao, Zhong and Jin,
2014 Lattanzi and Stickel, 2020 Chen et al., 2023) eccen-
tric, tilted and hopper with inserts (Huang et al., 2021).
Huang et al., 2021 also found that curved hoppers can
increase the flow rate by 100%. They found that the criti-
cal prefill level is slightly higher for the optimised curved
hopper than the corresponding conical hopper. Höhner,
Wirtz, and Scherer 2012 studied the granular flow in six
different hopper geometries. They used the polyhedral and
multisphere-based DEM to study the particle shape. The
Höhner, Wirtz, and Scherer 2012 studies suggested that the
angular particles predicted core (funnel) flow with particle
movement mainly in the centre of the hopper, while spheres
and clustered particles predicted mass flow behaviour with
significant movement reaching far to the side walls of the
hopper. The increase in the hopper angle signified the
increased mass flow rate for all shapes. Smaller orifice sizes
favoured bridging inside the hopper when filled with highly
angular polyhedral particles. Ahn et al., 2007 studied the
effect of the hopper angle (angle with the perpendicular
line) on the discharge coefficient and found that an angle
greater than 45o showed little effect. In contrast, for an
angle less than 45o, the discharge coefficient increased with
decreasing angle of the hopper.
The interaction of the particles with the other particles
and the environment has been extensively studied using
experiments and modelling/simulation studies. A quali-
tative insight into particles’ velocity profile and flow pat-
tern has been obtained by tracking the deformation of the
particle layers during the discharge. (Norouzi et al., 2016).
Computationally, the Discrete Element Model (DEM) is
a powerful lagrangian tool to predict the flow behaviour
of particles with dry, cohesive, and non-spherical nature.
DEM tracks the motion of the individual particles and cal-
culates the contact force between them when they interact
with the other particles. (Cundall and Strack 1979)Discrete
Element Method (DEM) has been widely used in recent
years to investigate the flow behavior of granular systems
with spherical shaped particles. The discrete element tech-
nique is based on the principle of modeling phenomena
at the microscopic level and investigating how these phe-
nomena affect the motion of the entire media at the macro-
scopic level. The DEM model is used to track the collisions
between the particles with each other and with the walls
by using appropriate contact force calculations. The par-
ticle motion is then obtained by solving for the equation
of the motion. The non-spherical representation in DEM
can be carried out in three ways: the multisphere (Favier,
Abbaspour-Fard, and Kremmer 2001), polyhedral (Fraige,
Langston, and Chen 2008 Cundall 1988 Govender et al.,
2018 Mack et al., 2011) and superquadric (Williams and
Pentland 1992) approaches. The application and compu-
tational resources available determine the preferred par-
ticle shape representation method. Each method incurs a
walls. The knowledge of the flowability of these particles
is essential as they affect the storage and transport of the
particles (Zatloukal and Šklubalová 2012). Hopper designs
are based on their applications and mostly under spheri-
cal shape calculations. The flow pattern and the discharge
rate of solids influence these designs. Understanding the
pressure distribution on the walls of the hopper during the
charge, storage, and discharge of the solids is critical for
their design.
The proper design is required to have smooth par-
ticle dynamics without flow rate fluctuations, solidifica-
tion, plugging, funnel flow, bridging, rat-holing, etc., The
particles in motion may cause arch formation above the
hopper aperture and cause clogging, restricting the parti-
cle flow within the hoppers when dealing particularly the
mineral ore particles. The variables influencing the arch-
ing are polydispersity of the particles’ size, shape, density,
cohesion, orifice geometry, hopper width, driving force,
and height of the particle bed. The probability of the arch
formation increases when the opening size decreases due to
constraint flow (Pascot et al., 2020). Börzsönyi et al., 2017
used X-ray tomography and optical methods to study the
flow and clogging of particles in a 3D hopper. Their X-ray
tomograms provided information on the bulk filling of
the hopper and the particle orientation. Hafez et al., 2021
investigated the discharge and the clogging behaviour of
spherical, elongated, faceted, and non-convex particles and
highlighted the interlocking behaviour of the cubes and
3D crosses. They also identified that the particle-particle
interactions define the geometry of clogging domes. The
average discharge volume before clogging depends on the
orifice-to-particle size ratio and initial solidity (Hafez et al.,
2021). One phenomenon used to control the flow inside
the hopper in industries is the forced vibration of the hop-
per walls (Kumar et al., 2020). The factors like frequency
and amplitude of the vibrations, hopper size and geometry,
and particle size need to be optimal to avoid segregation
of the mixture. The flow fields of the hoppers are modified
by using the inserts, which improve the flow from funnel
flow type to mass flow type during the discharge (Yang and
Hsiau 2001). Khalid and Zhou 2021 studied the effect of
providing an obstacle above the exit and applying a heli-
cal texture to the arching. Various types of hopper geom-
etries proposed in the literature include cylindrical with flat
bottom (Liu et al., 2013, Börzsönyi et al., 2017, Hilton
and Cleary 2011) conical (Ahn et al., 2007, Kumar et al.,
2018, Kumar et al., 2020), wedged (Tao, Zhong and Jin,
2014 Lattanzi and Stickel, 2020 Chen et al., 2023) eccen-
tric, tilted and hopper with inserts (Huang et al., 2021).
Huang et al., 2021 also found that curved hoppers can
increase the flow rate by 100%. They found that the criti-
cal prefill level is slightly higher for the optimised curved
hopper than the corresponding conical hopper. Höhner,
Wirtz, and Scherer 2012 studied the granular flow in six
different hopper geometries. They used the polyhedral and
multisphere-based DEM to study the particle shape. The
Höhner, Wirtz, and Scherer 2012 studies suggested that the
angular particles predicted core (funnel) flow with particle
movement mainly in the centre of the hopper, while spheres
and clustered particles predicted mass flow behaviour with
significant movement reaching far to the side walls of the
hopper. The increase in the hopper angle signified the
increased mass flow rate for all shapes. Smaller orifice sizes
favoured bridging inside the hopper when filled with highly
angular polyhedral particles. Ahn et al., 2007 studied the
effect of the hopper angle (angle with the perpendicular
line) on the discharge coefficient and found that an angle
greater than 45o showed little effect. In contrast, for an
angle less than 45o, the discharge coefficient increased with
decreasing angle of the hopper.
The interaction of the particles with the other particles
and the environment has been extensively studied using
experiments and modelling/simulation studies. A quali-
tative insight into particles’ velocity profile and flow pat-
tern has been obtained by tracking the deformation of the
particle layers during the discharge. (Norouzi et al., 2016).
Computationally, the Discrete Element Model (DEM) is
a powerful lagrangian tool to predict the flow behaviour
of particles with dry, cohesive, and non-spherical nature.
DEM tracks the motion of the individual particles and cal-
culates the contact force between them when they interact
with the other particles. (Cundall and Strack 1979)Discrete
Element Method (DEM) has been widely used in recent
years to investigate the flow behavior of granular systems
with spherical shaped particles. The discrete element tech-
nique is based on the principle of modeling phenomena
at the microscopic level and investigating how these phe-
nomena affect the motion of the entire media at the macro-
scopic level. The DEM model is used to track the collisions
between the particles with each other and with the walls
by using appropriate contact force calculations. The par-
ticle motion is then obtained by solving for the equation
of the motion. The non-spherical representation in DEM
can be carried out in three ways: the multisphere (Favier,
Abbaspour-Fard, and Kremmer 2001), polyhedral (Fraige,
Langston, and Chen 2008 Cundall 1988 Govender et al.,
2018 Mack et al., 2011) and superquadric (Williams and
Pentland 1992) approaches. The application and compu-
tational resources available determine the preferred par-
ticle shape representation method. Each method incurs a