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geometric description of the die is usually in the form of a
computer-aided design (CAD) file. This file is parsed by
the mesh generator (such as FEMAP) to produce the
surface mesh of the die and volume meshes for the die
volume and for the liquid metal. The nodes of the mesh
become the positions of the SPH boundary particles. For
the surface meshes, the boundary normals are calculated.
For all particles, masses are calculated, material properties
and other state variables are set to give the complete initial
set-up for SPH simulation. The boundary normals are
required for computing the boundary force described
above. If it is required, the mesh generator will also
produce a volume mesh in the selected region of the 3D
object. The nodes of the volume mesh are positions of the
initial fluid particles. Boundary Conditions
To simulate confined fluid flow, such as die filling in high
pressure die casting, it is necessary to prevent the fluid
penetrating the physical boundary. One approach that has
proved to be flexible and applicable to many problems is
to replace the boundaries by boundary particles, which
interact with the fluid by forces that are dependent on the
orthogonal distance of the particle from the boundary.
Arbitrary boundary surfaces can be readily represented by
boundary particles. They have a further advantage that it
is easy to simulate the motion of boundary particles.
To work with boundary particles, it is necessary to find a
way to ensure the fluid particles feel a continuous
boundary when two straight/curved boundaries are joined
at edges or corners. If the boundary force is not
continuous then nearby particle motions are unphysical
and generally catastrophic for the simulation. The present
implementation of the normal boundary force is described
in Monaghan (1995) and involves the use of a repulsive
Leonard-Jones potential force field that connects the
adjacent boundary particles and repels the fluid particles.
As fluid particles approach the boundary, the repulsive
force rises rapidly and prevents them from penetrating.
This approach is very flexible allowing arbitrary, smoothly
varying boundary shapes. In the tangential direction, the
particles are included in the summation for the shear force
to give non-slip boundary conditions for the walls. Details
are contained in Cleary and Monaghan (1993). NUMERICAL RESULTS
In this section, SPH simulations of two dies are presented.
The two dies are the C-shaped mould (see Figure 1) and a
die cast object (see Figure 3) chosen to exhibit typical
features of cast objects.
The C-shaped mould is
geometrically simple, enabling its initial set-up to be built
The simple geometry also allows any
programming problem that is associated with the geometry
to be identified relatively more readily. Furthermore, it
allows easier capture of “clean” experimental images from
water analogue modelling. The second die shown in
Figure 3 is more representative of industrial and
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This note was uploaded on 10/30/2013 for the course ENG 101 taught by Professor Cheng,m. during the Fall '13 term at Nevada State College.
- Fall '13