Smoothed Particle Hydrodynamics - Application
Validation study of HPDC in an S-shaped cavity
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 an S-shaped cavity with a series of curved
and right-angled bends. 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 8.7 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.
Unfortunately, as seen from the plots below, the experimental
photographs for this configuration are not entirely clear, making
interpretation and comparison somewhat difficult. In particular there are
some structures which could be either reflections off the front of the die
or stationary trapped air bubbles.
Despite this problem, both the VOF and SPH numerical solutions are
close to experiment. At 7.15 ms, both numerical solutions are very close
to each other and to the experiment, even in the fine details. At 25.03 ms
both simulations again do quite well, with the SPH capturing some fine
details better than the VOF. However, for this time there are some
features where the VOF performs slightly better. The VOF has some
artifacts at this time, including the separation from the first right
angle corner occurring erroneously just past the corner and the presence
of unusual "bubbles" in the filled curved entry region. The VOF
under-predicts the size of the semi-circular void on the vertical face
past the first corner, while the SPH solution over-predicts the size of
the void. The actual void seems to be mid-way between the two numerical
solutions. The void near the lower curved region is not predicted by
either the SPH or the VOF. Both methods slightly under-predict the void
width in the first horizontal section. The VOF solution predicts the shape
of the jet as it smoothly turns into the second vertical section better
than the SPH. However the SPH is able to predict the somewhat fragmented
nature of the free surface in this vertical section.
At 39.34 ms, both solutions are again similar and are reasonably close
to the experiment, but the details of the SPH solution are slightly
better. In particular SPH predicts a void beside the first vertical wall
of the die, whereas the VOF void has vanished by this stage. As occurred
for the earlier time, the SPH void is a little too large. There are also
two bubbles near the bottom wall of the first horizontal section of the
die in the experiment. The SPH solution has a void corresponding to the
left most of these bubbles. The SPH prediction of the separation point at
the corner of the second vertical section and the shape of the free
surface as the fluid rounds the corner into the second horizontal section
is quite a bit closer to the experiment than is the VOF solution in that
region. Near the tip of the jet both methods have material approximately
in the correct positions. The SPH simulation perhaps has slightly too
little fluid in this region, whereas the VOF predicts a little too much.
Both methods correctly predict the distance travelled in the die.
At 53.64 ms, the recirculation bubble on the first vertical section has
disappeared. This is correctly predicted by both methods. The separation
bubble at the second vertical section has again prematurely vanished in
the VOF solution, but is well predicted by the SPH. There appears to be
some sort of void structure in the first horizontal section. Both methods
predict small amounts of voidage here. The larger bubble is likely to
result from entrained air gathering in this region and cannot be predicted
by these models. The SPH solution again captures the shape of the
separation void around the third vertical section and of the free surface
in the final horizontal section. The fluid behaviour at the end of the die
is difficult to determine from the photograph of the experiment, but both
methods again predict the correct progress of the front of the jet.
More details concerning this validation study can be found in [2].
Download QuickTime
animation (0.63 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).
|
To
top