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Next: 1.6 ``Integral'' Models Up: 1. Introduction Previous: 1.4 Historical Background

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.

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:

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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