Smoothed Particle Hydrodynamics - Application
Validation study of HPDC in a C-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 C-shaped cavity, 50 mm long and 20.9 mm
high. The mould is connected to the shot sleeve by a gate of width 2.9 mm
(this is the length scale used in defining the Reynolds number, Re). The
width of the vertical sections is 4 mm and the width of the connecting
horizontal section is 4.9 mm.
The experiments were performed by V. Ahuja at CSIRO Manufacturing
Science and Technology. The experimental apparatus is shown schematically
in the figure below. The water flow re-circulates in the loop on the lower
left, until the 3-way valve is electro-pnuematically switched to re-direct
the flow into the mould cavity (top center). The desired gate velocity is
set approximately by using the flow meter. The apparatus is designed so
that the pressure drop in the re-circulation circuit and in the cavity
filling line are similar. The timing unit allows synchronisation of valve
switching and triggering the video camera. The video footage was captured
using an Olympus Encore high speed video camera. The 240x210 pixel video
images were recorded at 1000 frames per second using a shutter speed of 50
us. The transparent acrylic mould was forward lit and the water seeded
with white neutrally bouyant particles to show the flow. The captured
footage was down loaded to a VCR and then digitised. The actual values of
gate velocity were measured by tracing a particle or bubble in the
digitised images.
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Schematic diagram of the experimental apparatus |
On the left-hand-side figures below are shown stills for six different
times throughout the filling process. They are taken from the video
recording of the experiment whose gate velocity was measured as 0.62 m/s.
For the SPH simulations, 150 particles were used across the 20.9 mm
height of the mould, giving rise to a total of 29,613 particles. These
results were checked for convergence using 250 particles across. The fluid
was assumed to have a density of 1000 kg/m3, corresponding to
water. The Reynolds number of the flow at the gate is 1798, so the flow
either is in or near the turbulent regime. To account for this, the SPH
simulations were performed using a value of 0.005 kg/m/s for the dynamic
viscosity, this being 5 times that of water. Computations have also been
made using dynamic viscosity values of 0.001 and 0.01 kg/m/s to study the
influence of viscosity on the predicted flow.
On the right-hand-side of the above figures are shown six snap shots of
the flow of water into the die predicted using the 2D SPH method at the
same times as the experimental shots. Comparison of these figures shows
that the essential features of the flow are the same for both the
experiment and SPH calculation. The SPH results capture the filling
process in the left vertical section of the mould and the first right
angle bend rather well. In particular, the shape of the jet, its
trajectory along the right vertical wall, the shape and size of the void
in the left part of the vertical section and the spreading of the jet to
left and right after contact with the top of the mould in both experiment
and SPH calculation are quite similar. Experimental results have not yet
been obtained for flow beyond the left half of the die.
The comparisons between the SPH calculations and experiment in the
horizontal section for 46 ms and 67 ms are slightly less favourable. The
differences may be due to a range of processes not present or fully
captured in the simulations. These include the effects of air pressure
slowing the fluid and causing the jet to become more rounded, turbulence
increasing the effective viscosity and increasing three dimensionality of
the real flow producing a two-dimensional projection of the fluid that
covers a larger area of the mould than expected. The relative
contributions are presently unknown. Overall, the comparison shows that
the SPH simulations capture most of the flow features.
More details concerning this validation study can be found in [1].
Reference
[1] J. Ha, V. Ahuja and P.W. Cleary, Comparison of SPH
simulations of high pressure die filling with the experiment,
Proceedings of the 13th Australasian Fluid Mechanics Conference,
Melbourne, 901-904 (1998).
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