The particle generator capability enables a modeling approach in which the
discrete element method considers particles only after entering a region of
interest. This approach can simplify model set-up and improve computational
efficiency. Characteristics of this capability include:
particles are generated at an inlet that can vary in shape over time,
generated particles can have random sizes based on a user-specified
probability density function,
multiple species of particles can be generated simultaneously by a
single generator, and
the net mass flow rate and particle speeds at the inlet can be specified
with time dependence.
Applications
How you use the particle generator will depend on the process being
analyzed. Two broad usage categories are as follows:
Model creation
In many applications the particle generator can be used to fill part of a
domain with particles to establish initial conditions for subsequent studies.
Figure 1
shows an example where two particle generators are filling a drum mixer with
two different batches of particles prior to performing a mixing simulation. The
sequence of images show the start and end of the particle generation phase.
Continuous
generation
In another type of application a particle generator can be used to inject a
continuous stream of particles into the domain while an event of interest
involving particles that have been introduced is underway.
Figure 2
shows the use of a particle generator in a sorting analysis. In this
application a particle generator is continuously feeding random sized particles
to a screen sorter assembly while the analysis is in progress.
Defining a Particle Generator
To define a particle generator, you specify a name for the generator, the type of particle to be
generated, and the maximum number of particles that may be generated during the analysis.
You must define an inlet surface, the list of particle species that will be generated, and
the size distribution for each species.
In many processes the number and speed of the particles being introduced
into the domain are not constant during the analysis. You must define the
time-dependent mass flow rate per unit inlet area and the particle speed at the
generator inlet to control the rate of injection of particles of each species
through the inlet. These specifications allow the possibility of turning the
particle generator on or off during the analysis.
Inlet Surface
The inlet surface can be thought of as an opening through which the
particles are injected into the domain. It is important that no other model
feature is positioned in front of the generator inlet to obstruct the flow of
particles. An element-based surface must be defined for the inlet surface.
Using surface elements is appropriate in most applications. Care should be
taken with respect to the positive surface normal direction at the inlet
because the initial particle velocity will be in this direction. A complex
inlet geometry as shown in
Figure 3
may have several facets. In this example the normal direction to the inlet
surface is out of the page.
The size and shape of the inlet surface can be modified during an analysis
by adjusting the nodal positions of the inlet surface. The inlet surface can
expand, collapse, and translate as well as undergo rigid body motions.
Figure 4
shows the inlet surface of four different generators being subjected to
different deformation and motion.
Particle Species
In many applications several different types of particles interact with each
other. For example, sand, cement, and aggregate particles are mixed together to
prepare a batch of concrete. A particle generator can be used to generate one
or more species of particles as shown in
Figure 5,
where the two colors represent the two species of particles that have been
simultaneously generated by a particle generator. An element set name is
associated with each species in the mixture. This is analogous to a regular
DEM analysis where the particles are grouped
into element sets.
Particle Size Distribution
Statistical distributions are commonly used to specify the particle sizes.
Statistical distributions are defined by analytical or user-specified piecewise
linear tabular probability density functions
(PDF). The particle generator supports the
following different types of probability density functions: uniform, normal,
log-normal, and piecewise linear. The normal and log-normal
PDFs have well-known analytical forms that
depend on the mean and standard deviation of the random deviate. In some cases
the particle size distribution may be obtained from sieving particle samples in
the field. These data are usually in the form of a table of size ranges and the
percentages of particles that fall within those size ranges (a histogram). The
piecewise linear PDF can be used for such
data. See
Probability Density Function
for further details on the usage of probability density functions.
Mass Flow Rate
The rate of generation of particles is governed by the specified mass flow
rate per unit area at the inlet, the area of the inlet, and the ability of the
generator to insert a particle of a given size. The time varying mass flow rate
per unit inlet area, ,
has the units .
For a multiple species particle generator the total mass flow rate per unit
inlet area is the sum of the mass flow rates per unit inlet area of the
individual species:
The time varying mass flow rate per unit inlet area for each species must be
provided in the form of an amplitude table (Amplitude Curves).
Particle Speed
For a given particle generator, particles of all species are introduced into
the domain through the inlet with a specified flow speed. The flow direction of
the particles is along the normal to the inlet facet. Particles generated from
different facets in the inlet surface will all have the same flow speed;
however, depending on the facet normal direction, they may have different
velocities. The time varying particle flow speed must be provided in the form
of an amplitude table (Amplitude Curves).
Local Coordinate System for Inlet Faces
The current coordinates of the nodes of each facet in the inlet surface are
used to define a plane (a generation plane) where particles will be generated.
Figure 6
shows the local directions of the generation plane. The first local direction,
,
is defined by the longest facet edge, while ,
the third local direction, is normal to the facet. The normal to the facet is
obtained from the cross-product of the diagonal vectors (the vector joining
nodes 2 and 4 and the vector joining nodes 1 and 3; see
Figure 6
for local node numbers). The second in-plane direction is
.
The plane of generation is positioned
in front of the inlet facet, where
is the smallest particle radius for the generator.
The in-plane particle coordinates of a particle are generated randomly
according to a uniform random distribution. The generated in-plane coordinates
are acceptable if the particle can be placed at that location ensuring that it
does not overlap with previously generated particles and also does not
intersect the boundaries defined by the facet edges.
Assigning Properties to Particles
Particles of different species will have different size distribution,
density, and contact properties. To assign a density and size distribution for
a particle species, the corresponding element set name is specified on a
section definition for the PD3D elements. The element set name is also used to define a surface
that is referred to under the contact specifications. This way of assigning
particle properties and contact properties for generated particles is no
different from what is done for user-defined sets of discrete particles. See
Discrete Element Method
for details on how to assign properties to PD3D elements and how to set up contact definitions for a
DEM analysis.
Particle Size Rejection
Abaqus/Explicit
discards particle sizes that are outside the specified minimum and maximum
range for the PDF. For normal and log-normal
type PDFs this leads to a truncated
distribution, as explained in
Probability Density Function.
Keep this in mind when comparing the generated particle size distribution to
the target PDF.
A generated particle size is discarded if it is too large to fit through the
current inlet geometry. It is possible that the generator may fail to place a
particle in the randomly generated location in the generation plane if there is
not sufficient room to accommodate the newly generated particle size. If this
happens, the generator will generate another random location and attempt to
place the particle there. By default, 15 such attempts will be made, after
which the particle size is discarded and another particle size is randomly
generated and the process is repeated. You can modify the default number of
attempts to place a generated particle size.
If particle sizes are rejected because of either of the above reasons, the
generated size distribution cannot be guaranteed to match the specified size
distribution.
Figure 7
shows a comparison of generated and specified piecewise linear particle size
distributions for a specific problem where 14608 particles were generated at a
constant mass flow rate and with constant particle speed through an inlet of
fixed geometry. The overall agreement of the generated particle size
distribution is good even though the generator was unable to insert some
particles into the domain.
Mass Balance for Continuous Generation
At any increment, k, corresponding to the end of
increment time, ,
and time increment size, ,
the specified mass of particles of species, i, to be
generated is
where
is the current inlet facet area. Due to the discrete nature of the time
increment and particle sizes, the particle generator will not be able to match
the specified mass exactly for the species for the given increment. The
particle generator, therefore, maintains a mass balance for each species. For a
given species a negative mass balance indicates that for that species the mass
of particles generated was higher than what was required. The excess mass
balance for species, i, from the previous increment
is taken into account while computing the target mass to be generated in the
current increment:
The mass balance for species i for the current
increment is
where
is the actual mass of the particles generated in increment
k. The particle generator tries to match the specified
mass flow rate per unit inlet area as closely as possible. If the target mass
for a species is negative because of a high negative mass balance, no particles
will be generated for that species until the target mass becomes positive
again.
Figure 8
shows a comparison of generated and specified mass flow rate for a specific
problem where the specified mass flow rate per unit inlet area does not vary
with time and the inlet geometry is fixed.
Inlet Blocking
The flow speed, ,
and mass flow rate per unit inlet area, ,
are related as follows:
where
is the particle density and
is the solid fraction. The solid fraction is the ratio of the volume of
particles to the volume of the region they occupy. This relation suggests that
the packing of particles ahead of the inlet increases for a given mass flow
rate per unit inlet area as the flow speed is reduced. If this happens, the
particle generator will take many more attempts to insert a particle.
Therefore, a meaningful specification of flow speed for a given mass flow rate
per unit inlet area is crucial for the efficiency of the particle generator. It
is also important that no other model feature is positioned in front of the
generator inlet to obstruct the flow of particles.
Automatic Halting of Particle Generator
A particle generator will permanently halt after generating the maximum
number of particles. Since it may be difficult to make an accurate estimation
of the total number of particles that need to be generated during an analysis,
overestimating the maximum number of particles will ensure that a particle
generator will not run out of particles. However, grossly overestimating the
maximum number of particles will lead to larger memory requirements for the
analysis.
The particle generator will temporarily halt for an increment if the region
near the inlet has a high volume fraction of particles. This helps avoid
performance degradation due to an excessive number of failed attempts to insert
a new particle when the inlet is becoming clogged with existing particles. The
default threshold for a temporary halt to the generator is a particle volume
fraction of 0.4 over a volume that extends
in front of the inlet surface, where
is the maximum particle radius for the generator. You can modify the default
value of the solid fraction used for halting the generator.
It is possible that the current inlet geometry and the particle size
distribution is such that the particle generator repeatedly exhausts the 15
attempts to insert a particle of a given size. If 10 such cycles of 15 attempts
each have been unsuccessful in a given increment, the generator will
temporarily halt generation. You can modify the default value of 10 cycles
prior to halting particle generation.
Initial Conditions
Initial conditions should not be applied to nodes of particle species.
Boundary Conditions
Boundary conditions can be applied to the nodes of the inlet facet to
expand, shrink, or move the inlet facets of a generator.
Loads
The element set name for a species can be used to apply loads such as
gravity or body loads.
Elements
The particle generator generates PD3D elements only.
Constraints
Constraints such as multi-point constraint type BEAM can be applied to the nodes of inlet facets to facilitate the
application of rigid body motion to the inlet facet of a generator.
Interactions
Contact interactions between particle species are specified similar to
user-defined PD3D elements. You must not include the inlet facets in the contact
domain.
Output
Output is available for the element sets and node sets generated by the
particle generator.
Limitations
The following limitations apply to analyses involving the particle
generator:
Only PD3D elements can be generated.
It is not possible to generate clusters of PD3D elements.
Input File Template
The following example illustrates a particle generator
with two particle species: