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# 1.5 Numerical Simulations

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.
The third research we mentioned here is an example where the calculations can be shown to be totally wrong and yet the researchers have experimental proofs to back them up. Viswanathan et al poro:viswanathan studied a noble process in which the liquid metal is poured into the cavity and direct pressure is applied to the cavity. In their calculations the authors assumed that metal enter to the cavity and fill the whole entrance (gate) to the cavity. Based on this assumption their model predict defects in certain geometry. Now lets look at this model a bit more in critical examination. The assumption of no air flow out by the authors (was ``explained'' to me privately that air amount is small and therefore not important) is very critical as will be shown here. The volumetric air flow rate into the cavity has to be on average equal to liquid metal flow rate (conservation of volume for constant density). Hence, air velocity has to be approximately infinite to achieve zero vent area. Conversely, if the assumption that the air flows in same velocity as the liquid entering the cavity, liquid metal flow area is a half what is assume in the researchers model. In realty, the flow of the liquid metal is in the two phase region and in this case it is like turning a bottle full of water over and liquid inside flows as ``blobs'' . In this case the whole calculations do not have much to do with reality since the velocity is not continuous and different from the calculated.

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 samewhile 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.

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Genick Bar-Meir ||| www.potto.org
copyright Dec , 2006

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