New software speeds design tasks as varied as
modelling the flow of real particles or counting the number of
beans to be packed in a jar. Tom Shelley reports
Reducing particles to patterns of pixels or voxels allows
realistic modelling of many real world problems, from designing
packaging for loose groceries to complex segregation effects,
which occur when particles of different shapes and densities are
shaken.
The name of the software is DigiPac, developed by Dr Xiaodong Jia
and colleagues in the Institute for Particle and Engineering at
Leeds University. Its approach is derived from image processing
and is based on reducing each shape to a pattern of whole pixels,
or picture elements, or in 3D, voxels, or volume elements, moving
on a square lattice. The shapes are allowed to move randomly, one
lattice grid at a time. Diagonal moves are composed of two/three
orthogonal moves. The consequent use of integers or whole numbers
avoids the need for floating point calculations and greatly
reduces computation time. Rounding off to integers introduces
initial errors, but such errors can be greatly reduced by using
finer resolutions. The area ratio error incurred by representing
a circle by 76 pixels on a 10 x 10 grid is 3.2% or 0.6% by
representing a circle by 316 pixels on a 20 x 20 grid. During the
packing process, translational movements do not incur rounding
errors and special measures are taken to minimise errors arising
from rotations.
The shapes can be simple or complex, derived from scanning in
real world particles. In 2D, they may be scanned in using a
simple image scanner. But in 3D they require the use of either 3D
x-ray microtomography, if they are inside something else, or a 3D
optical scanner. This contrasts with previously available
software only able to cope with spheres or other simple
geometrical shapes such as ellipses, spheroids and cylinders.
Dr Jia says that the key to modelling their behaviour is to apply
"very simple rules for each pixel or voxel." For
example, if studying coating behaviour, there can be a rule that
causes small particles to move towards big particles. Stickiness
and cohesiveness can be simulated using probabilities, which may
not represent a strict reproduction of physical behaviour but
result in particle behaving at least qualitatively in a realistic
way.
Particles
in a coating can take any form
2D simulations take minutes to accomplish on a PC, sufficient to
demonstrate effects and behaviour. But more realistic 3D
simulations take hours. However, the 2D simulations are often
good enough to permit study of real world effects, even if 3D
simulation is necessary to verify them more quantitatively.
The simplest task in 2D or 3D is to model the packing of
particles in a container. Particles can be of many different
shapes, and quite large. It is also possible to model their
behaviour as they fall through a hopper, and/or build a heap. In
the simplest model of dog bone shaped particles, which does not
take rebounding or particle rotation into account, one might find
a packing density of, say, 0.39. This approach is known as a
'rain' model. But with a 50% rebounding probability with
rotation, this rises to 0.6. Boundary conditions can either be
periodical or solid walls. In theory, with solid walls, the
software could be used to study how more commuters could be
packed into trains, by digitising a range of humans and train
interiors, and applying whatever rules the train companies care
to apply.
With periodical boundary conditions, a particle moves out of one
side and comes in from the opposite side at the same time. This
allows bulk properties to be predicted by a small sample. The
width of the simulation box should be at least ten times bigger
than that of the largest particle. With solid walls, in
containers of particles or on trains, the packing is usually less
dense near the wall than in the central part.
As well as studying assemblages of loose particles, it is also
possible to study the effects of reinforcing particles and
chopped fibres of different sizes and shapes, in chopped fibre
reinforced plastics and metal matrix composites. It may well be
that a combination of sizes and shapes could achieve greater
strengths than single sized, chopped fibre lengths, but hitherto,
there has been no computer tool available to model this.
Compaction, force distribution and strength of both loose
assemblages and composites can all be deduced.
If a bed of particles is vibrated, it is possible to study size
segregation effects, and how size distribution and shape affect
these. This is very important in studying the behaviour of
building materials, such as concrete and asphalt, which initially
consist of heterogeneous mixtures of particles of different
densities, size and shape. Segregation can, of course, lead to
fairly disastrous results in the end product, be it building or
road.
By imposing a rule that reduces surface area in order to minimise
surface energy, it is possible to model sintering. By studying
the particle pixels or voxels in contact with each other, it is
possible to model thermal conductivity. Simulations then show how
some areas of particles tend to get heated more than others. And
by studying pixels or voxels representing the gaps in between, it
is possible to model gas and liquid permeability, simulating both
pressure distributions and flow rates.
The initial research was supported by EPSRC, the Keyworth
Institute and the White Rose Faraday Packaging Partnership. Now
the team is looking for consultancy and support for research
projects. Licensing of software for use by clients for their own
investigations may follow later. And work is in hand to extend
modelling capabilities to include deformable shapes, and to
verify predictions.
(More information from www.particles.leeds.ac.uk
and X.Jia@leeds.ac.uk )
Design Pointers
* New modelling method allows the more realistic simulation of
the behaviour of particles of different sizes and shapes.
* Packing, flow, heat transfer, permeability and compaction can
all be simulated
* It may now be possible to use to tool to discover new types of
composite reinforcement which could not previously be
investigated other than by an excessively long trial and error
process
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