Numerical simulations have been found to be very useful in many areas
which lead many researchers attempting to implement them into die casting
process.
Considerable research work has been carried out on the problem of
solidification
including fluid flow which is known also as Stefan problems
[#!solid:review!#].
Minaie et al in one of the pioneered work poro:minaie use this
knowledge and simulated the filling and the solidification of the cavity
using finite difference method.
Hu et al poro:jia used the finite element method to improve
the grid problem and to account for atomization of the liquid metal.
The atomization model in the last model was based on the mass transfer
coefficient.
Clearly, this model is in waiting to be replaced by a realistic model
to describe the mass transfer^{}.
The Enthalpy method was further exploded by Swaminathan and Voller
solid:enthalpy and others to study the filling and
solidification problem.

While numerical simulation looks very promising, all the methods (finite
difference, finite elements, or boundary elements etc) ^{} suffer from several
major drawbacks that prevent from them yielding reasonable results.

- There is no theory (model) that explains the heat transfer between the
mold walls and the liquid metal.
The lubricant sprayed on the mold change the characteristic of the heat
transfer.
The difference in the density between the liquid phase and solid phase
creates a gap during the solidification process between the mold and the
ingate
which depends on the geometry.
For example, Osborne et al poro:magma showed that a commercial
software
(MAGMA) required fiddling with the heat transfer coefficient to get
the numerical simulation match the experimental results
^{}. - As it was mentioned earlier,
it is not clear when the liquid metal flows as a spray and when
it flows as continuous liquid.
Experimental work has demonstrated that the flow, for large part of the
filling
time, is atomized [#!poro:genickthesis!#].
- The pressure in the mold cavity
in all the commercial codes are calculated
without taking into account the resistance to the air flow out.
Thus, built-up pressure in the cavity is poorly estimated
and therefore the characteristic
flow of the liquid metal in the mold cavity is poorly estimated as well.
- The flow in all the simulations is assumed to be turbulent flow.
However, time and space are required to achieved a fully turbulent flow.
For example, if the flow at the entrance to a pipe with the typical
conditions in die casting is laminar (actually it is a plug flow) it will
take
a runner with a length of about 10[m] to achieved fully developed flow.
With this in mind, clearly some part of the flow is laminar.
Additionally, the solidification process is faster compared to the
dissipation process in the initial stage
so it is also a factor
in changing the flow from a turbulent (in case the flow is turbulent)
to a laminar flow.
- The liquid metal velocity at the entrance to the runner is assumed in the
numerical
simulation and not calculated.
In reality this velocity has to be calculated utilizing diagram.
- If turbulence is exist in the flow field, what is the model that describes
it
adequately?
Clearly, model such are based on isentropic homogeneous
with mild change in the properties cannot describes situations
where the flow changes into two-phase flow (solid-liquid flow) etc.
- The heat extracted from the die is done by cooling liquid (oil or water).
In most models (all the commercial models) the mechanism is assumed to be
by ``regular cooling''.
In actuality, some part of the heat is removed by boiling heat transfer.
- The governing equations in all the numerical models, I am aware of,
neglecting the dissipation term in during the solidification.
The dissipation term is the most import term in that case.

One wonders how, with unknown flow pattern (or correct flow pattern), unrealistic pressure in the mold, wrong heat removal mechanism (cooling method), erroneous governing equation in the solidification phase, and inappropriate heat transfer coefficient, a simulation could produce any realistic results. Clearly, much work is need to be done in these areas before any realistic results should be expected from any numerical simulation. Furthermore, to demonstrate this point, there are numerical studies that assume that the flow is turbulent, continuous, no air exist (or no air leaving the cavity) and proves with their experiments that their model simulate ``reality'' [#!poro:ekkSolidification!#]. On the other hand, other numerical studies assumed that the flow does not have any effect on the solidification and of course have their experiments to back this claim [#!poro:davey97!#]. Clearly, this contradiction suggest several options:

- Both of the them are right and the model itself does not matter.
- One is right and the other one is wrong.
- Both of them are wrong.

Another example of such study is
the model of the flow in the shot sleeve by Backer and Sant from EKK [#!poro:ekk!#].
The researchers assumed that the flow is turbulent and they justified
it because they calculated an found a ``jet'' with extreme
velocity.
Unfortunately, all the experimental evidence demonstrate that there is no
such jet [#!jump:madsen!#].
It seems that this jet is results from the ``poor'' boundary and initial
conditions^{}.
In the presentation, the researchers also stated that results they obtained
for laminar and turbulent flow were
the same^{}while a simple analysis can demonstrate the difference is very large.
Also, one can wonder how liquid with zero velocity to be turbulent.
With these results one can wonder if the code is of any value or the
implementation is at fault.

The bizarre belief that the numerical simulations are a panacea
to the all the design problem is very popular in the die casting industry.
I am convinced that any model has to describes the physical situation in
order to be useful.
I cannot see experimental evidence supporting wrong models
as a real evidence^{}.
I would like to see numerical calculations that produce realistic results
based on the real physics understanding.
Until that point come, I will suggest to be suspicious about any
numerical model
and its supporting evidence.^{}

copyright Dec , 2006

The pdf version is also available here