Smoothed Particle Hydrodynamics - Application
Validation study of HPDC in a circular disc with core
High pressure die casting (HPDC) is an important industrial process by
which very complex shaped castings with excellent surface finishes can be
produced in high volumes and at low cost. Smoothed particle hydrodynamics
(SPH), being a Lagrangrian method, is well suited to modelling
momentum-dominated flows involving droplet formation, splashing and free
surfaces, such as occur in HPDC. A preliminary validation of the
application of SPH to HPDC has been undertaken by comparing SPH
predictions with those obtained both from an independent numerical
simulation and from a water-analogue experiment for a relatively simple
geometry.
The geometry considered is a die with a circular cross-section and a
circular core. The diameter of the disc and core are 140 mm and 45 mm,
respectively. The thickness of the mould (in the vertical direction) is 2
mm and water flows through the gate of width 45 mm at a velocity of 18.0
m/s.
The SPH predictions are compared with the corresponding numerical
and experimental results of Schmid and Klein [1]. The numerical
simulations of Schmid & Klein were performed using RIPPLE, a computer
program developed by Kothe and co-workers at Los Alamos National
Laboratory. RIPPLE uses the volume of fluid (VOF) method. It is capable of
simulating transient, two-dimensional flows of incompressible fluid
involving free surfaces with or without surface tension. Surface tension
is modelled as a volume force derived from the continuum-surface-force
model so that surface tension effects at the free surface as well as
wall-adhesion effects are modelled. RIPPLE uses finite difference
discretization on an Eulerian, rectilinear mesh in Cartesian or
cylindrical geometry. A two-step projection method is used to solve for
the incompressible flow. The Poisson pressure equation is solved via an
incomplete Cholesky conjugate gradient technique. The method of
partial-cell treatment is used to handle obstacles and curved interior
boundaries interior to the mesh.
As seen in the plots below, the SPH simulations and the VOF simulations
of Schmid and Klein both produce very good agreement with the experiment.
Both capture the essential nature of the flow. However, there are several
smaller scale flow features that our SPH simulations are better able to
capture than could be done with the VOF technique employed by Schmid and
Klein.
As observed in the above plots, for both the VOF and SPH results the
wide jet enters the die, strikes the core and splits into two jets. These
jets strike the outside of the die and each split into two jets with one
travelling in each direction around the outside of the die. The first of
the above times shows flow when the two branches of the fluid near the top
are approaching each other. The SPH simulation better captures the smooth
edges of the incoming jet and of the two branches after splitting at the
core. The SPH solution is particularly better at capturing the shape of
the four sub-branches travelling around the outside of the die. In both
the upper and lower pair of branches their leading edges of the jets have
reached very similar points on the outside of the die and they have
similar thicknesses meaning that the correct amount of material is in the
correct locations. In contrast, the VOF captures the upper two branches
reasonably well, but fails to predict the lower two branches. This is a
well known difficulty with VOF schemes in resolving small scale features.
At 11.76 ms, the upper two branches have merged to produce a vertical
downward jet that strikes the core from above. The superior predictions
ofthe SPH method are most evident at this time. These include:
- The shape and smoothness of the two main jets after the first impact
of the jet with the core.
- The shapes of both the upper and lower voids.
- The thin films around the outside of the bottom voids are well
predicted including their diminishing thickness as the gate is
approached.
- The shape of the merged jet and particularly the shapes of the void
to either side. Note also that the asymmetric buckling of this jet to
the left is reproduced. The VOF solution enforces a symmetric flow
pattern by using only half of the mesh and symmetric boundary
conditions whereas the SPH solution predicts a symmetric pattern for
the first two impacts of the jets with the die but predicts an
asymmetric one for the final impact of the downward jet. We note that
the direction of the jet's deflection is coincidental. In both the
experiment and the SPH simulation the direction is determined by
perturbations in each system. These can be either small asymmetries in
the geometrical configuration or disturbances from upstream in the
flow.
At 16.17 ms, when the filling is complete the VOF predictions have
improved and are quite close to the experiment and the SPH result. The SPH
prediction of the lower void shapes is better. The VOF again predicts long
narrow voids instead of more rounded ones. The upper voids are very
similar for all three cases.
More details concerning this validation study can be found in [2].
Download QuickTime
animation (1.2 MB)
References
[1] M. Schmid and F. Klein, Fluid flow in die cavities
- experimental and numerical simulation, NADCA 18. International Die
Casting Congress and Exposition (Indianapolis, 1995) pp. 93-99. (See also Markus
Schmid's Homepage.)
[2] J. Ha and P.W. Cleary, Comparison of SPH
simulations of high pressure die casting with the experiments and VOF
simulations of Schmid and Klein, submitted to International Journal
of Cast Metals Research (1999).
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