Smoothed Particle Hydrodynamics - Application
Validation study of HPDC in a plate die
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
plate die.
The geometry considered is a thin flat plate, 150 mm high, 100 mm wide
and 2 mm thick. Water flows through a gate of width 45 mm at the bottom of
the plate. The Reynolds number for the flow is Re = 1.29x106,
based on the gate velocity of 8.6 m/s and the height of the plate.
The SPH predictions are compared with the corresponding numerical and
experimental results of Schmid & 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 generally compare well with the experimental results.
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.
At the first time shown above, the shape of the SPH jet is much closer
to the experiment. The front of the jet is curved in a similar way and is
broader than the jet behind. The sides of the jet are also not straight.
These differences do not result from the choice of method but rather from
the choice of initial conditions. In our SPH solution, we include a
reasonable length of tube to the mould and we start the simulation with
the fluid several jet diameters from the entrance to the mould. Viscous
interaction with the walls produces a velocity distribution within the jet
that is neither constant (as used by Schmid and Klein) nor parabolic, but
rather somewhere in between. This is particularly important for predicting
the shape of the initial material in the jet. The interaction of the jet
front with the walls creates a pair of oppositely rotating eddies at the
front. Once the jet has entered the cavity, recirculating fluid in these
eddies distorts the front of the jet giving it a rounded shape that
increases as the jet moves further into the cavity. This demonstrates how
critical it is to use correct initial conditions for the fluid velocity.
In die casting simulations this essentially means that a reasonable amount
of the die casting machine before the entry to the die cavity must be
simulated in order to correctly prescribe the initial velocity
distribution. Some small differences still remain in the shape of the
early jet, but to obtain a closer result requires more knowledge about the
inlet geometry and the way in which the fluid was accelerated.
The experimental results at 26.63 ms show that the fluid travelling
down along the left side walls of the cavity is of fairly uniform
thickness, except near the tip where there appears to be a reasonable
amount of fragmented fluid. The jet on the right is more fragmented. The
SPH results demonstrate both these features (constant thickness of the jet
and fragmentation) while the simulations of Schmid and Klein show tapered
side jets that narrow towards there tip. In both the SPH case and the
experiment there are hints of the main jet narrowing marginally half way
up the die cavity. The curvature of the U-shaped free surface is closer to
the experiment in the SPH solution than for the VOF. In particular there
should be more curvature as the fluid turns and enters the downward side
jet and less curvature where the fluid in the main jet starts to broaden
out. The VOF solutions have the curvatures the opposite way around. Both
numerical schemes underpredict the distance that the U-shaped free
surfaces have moved from the top wall of the cavity. Similarly, the SPH
solution does not capture the structure of the side jets as they start at
around 23 ms. We suspect that this is due to some three dimensionality of
the flow, where the fluid flows preferentially along the upper and lower
horizontal surfaces of the die.
The largest differences between the SPH and VOF solutions occurs late
in the filling process. At 33.73 ms, the upward jet in the experiment has
become pinched and is narrower than the gate width. The VOF simulations
predict very long narrow voids on either side of the upward jet with
little sign of this pinching. The SPH solution does predict the narrowing
of the jet by about the correct amount and better captures the rounded
shape of the voids.
Overall, both numerical solutions are very good, but the SPH solution
captures a range of the fine detail better than does the VOF, particularly
at later times in the filling process.
More details concerning this validation study can be found in [2].
Download QuickTime
animation (0.76 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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