Modeling filters in the future: the standard method of modeling filtration devices is good, but the ability to model actual filters in the future will be better.

Pressure drop characteristics are currently the industry-accepted standard approach to computationally modeling filtration devices. The approach involves globally modeling the filtration device as if it were a boundary condition, and many studies have shown this approach to be generally accurate with respect to flow velocity profiles and fill time predictions. However, this fact has not been explicitly proven for foam filtration devices due to the complexity and long computational time involved in modeling such filters for use in computer simulation.

A new approach can be employed to obtain an actual 3-D model of a foam filtration device. The results of simulations comparing the flow velocities and pressure profiles of an actual 3-D filter model to the pressure drop approximation show agreement in modeling the global flow characteristics of the filter. But dramatic flow velocity profile differences between the two approaches are shown just before and after the filter. Therefore, pressure drop is not accurate in situations where these flow fields must be analyzed.

It is not practical, at the moment, for the average computer simulation user to conduct simulations with actual 3-D foam filtration models due to the computer requirements and extensive run times. However, this article proves that it is possible to model a complex foam filter and that the flow results in and around the filter are more accurate than with a pressure-drop approximation.

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Pressure Drop on the Rise

Mold filling simulation software was developed decades ago and continues to become more sophisticated every year. However, the modeling of molten metal flow through filtration devices is in its relative infancy.

Over a decade ago, researchers began studying the permeability of foam filters and the possibility of mathematically modeling these types of filtration devices using well established, porous media predictive methods. This led to the discovery that an equation using permeability coefficients could be used to mathematically simulate molten metal flow through filtration devices. This calculation method is often referred to simply as the "pressure drop" method.

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Pressure Drop Limitations

Use of pressure drop acts as a simple boundary condition within the mold filling algorithm, and while it can provide reasonably accurate filling results, it cannot provide detailed flow information directly before and after the filter itself. Only modeling an actual filter structure in the gating system allows for analysis of these flow characteristics.

The accuracy and limitations of using the pressure drop method to simulate the flow through an actual reticulated foam filter were evaluated using several different filter types and porosities. However, this article will concentrate on a 2 x 2-in. (50 x 50-mm) square, 0.9 in. (22 mm) thick, 10-ppi foam filter used for iron casting applications as a representative example.

Several hundred filters were sampled from the production facility and tested for pressure drop using a water modeling device. The results were plotted, and an average filter curve was determined. From these results, a single filter with the average pressure drop characteristics was chosen as the filter to evaluate.

This exact filter then was used to create the complex 3-D model. This procedure ensured that the filter structural model and the resultant pressure drop data were for the identical filter structure, thus allowing direct comparison of individual simulations run with the 3-D filter model and the pressure drop data.

For this study, the 3-D electronic models were generated using detailed, advanced scanning techniques (Fig. 1), and this significant development made possible the simulation of flow through the actual foam filter geometry. For the actual metal casting, a 2-on configuration was used with a single filter and insulating/exothermic feeding systems.

100-70-03 ductile iron at a pouring temperature of 2,552F (1,400C) was used for all simulations, and the mold was modeled as high pressure molding sand. A 31.36-mbar pressure constraint (based on the ladle configuration and pouring procedure) resulted in a predicted fill time of approximately 12 seconds. The actual castings were poured at 2,552F and filled in 11-12 seconds, thus confirming the predicted results.

A mesh size of 20 million elements properly captured the reticulated foam filter geometry details, and both configurations were initially meshed in this fashion. This was overly conservative for the pressure drop configuration, and an adequate mesh for this case would be an order of magnitude lower in number of elements. Simulation accuracy was preserved, and only computational run time was adversely affected by this approach.

Collecting the Results

The filling simulation using the pressure drop data ran to completion in 100 hours using a personal computer. The filling simulation using the actual filter model, the same mesh and the same workstation ran very slowly and reached 10% filled after 200 hours of run time. It was estimated that running to completion would take several months. However, this same simulation ran to 40% filled in 24 hours using a cluster network, even after being re-meshed to an even finer 30 million element model.

The results for the pressure drop simulation and the identical results for the filter model simulation were contrasted and compared from the start of filling to 40% filled. At 2% filled, the molten metal was just beginning to enter the filter. At this point, the pressure drop and actual filter flow velocity results were similar, with both showing some priming at the bottom of the filter (Fig. 2).

Things began to change at 5% filled. The flow was not fully established through the filter, but already differences between the uniformity of flow through the different filter models appeared (Fig. 3). The actual filter was more realistic and less uniform just after the filter, and there was flatter, faster distribution of flow into the runner bar.

At 10% filled, the flow through the filter was fully established, and the differences in models were clear. The actual filter model configuration showed much less flow uniformity just before and after the filter, as compared to the pressure drop boundary condition model.

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Fig. 4 further supports this point with a filling pressure comparison. The pressure profiles were similar downstream of the filter, with the actual filter model showing pressures 1-2% lower than the pressure drop model. This close comparison was evidence that the pressure drop velocity dependent data curve properly reflected the pressure changes in the flow stream due to the presence of the filter.

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However, significantly different flow results appeared in close proximity to the filter itself. Because the pressure drop data was treated as a boundary condition within the mold filling algorithm, the flow results just after the filter should have been uniform (Fig. 5). In reality, flow streamlines coincided with filter exit holes and shear planes between the various streamlines, as shown in the actual 3-D model simulation. Ultimately, these shear planes mixed into a continuous, uniform flow field, but this took place some distance downstream of the filter.

In Fig. 6, the flow direction of the filter exit just as the area was reduced for the runner bar is towards the reader. At the exit, the pressure drop boundary condition showed a continuous, uniform flow field. The actual filter displayed the more realistic flow stream discontinuities one would expect from a porous media. Fig. 7 is the same view comparing the filling pressure results.

Here, the pressure field just behind the filter was similar for the two filter models, but again the actual filter showed slightly lower pressure results than the pressure drop method. In Fig. 7, the pressure differences were less than 1% between the two filter models. The velocity and pressure comparisons and resultant conclusions remained consistent as the filling process progressed toward completion.

One exception occurred shortly after the metal flow filled the ingate and began to fill the casting, as shown in Fig. 8 at 12% filled. The model of the actual filter decreased the flow energy slightly more than the pressure drop boundary condition and resulted in less splashing and turbulence when the metal first contacted the casting sidewall. Beyond this point, the basic flow comparisons and conclusions were again similar to the results at lower fill percentages as the filling process progressed toward completion.

At 20% filled, the flow profiles into the casting cavity were very similar between the two models, and the predicted fill times were within 1% at 2.531 and 2.554 seconds. Again, there appeared to be slightly less flow energy in the actual filter model simulation. These same points were consistent at 40% filled, the last data point analyzed.

Differences in flow velocity could be seen in the runner bar, but the flow in the casting cavity was essentially the same for the two filter modeling techniques. The predicted fill time was 5.058 seconds for the pressure drop model compared to 5.102 seconds for the actual filter model. Based on these comparisons, it was evident that pressure drop data yielded reasonable predicted fill time and general flow results because it captured the global effect of the filter on the flow in a gating system. The flow velocity profile for the pressure drop configuration in Fig. 6 was similar to the area averaged in the actual filter flow results, which was supported by the relatively minor pressure differences seen in Fig. 7.

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For situations where a more detailed flow analysis in and around the filter is required, or when filtration efficiency predictions are required, the actual filter must be modeled, and the computational time will be substantial. This may not be practical at this time unless one employs computer cluster technology.

In the near future, with advances in computational capability, it will become practical to model actual foam filtration devices, and mold filling simulations will become more accurate as a result. This will allow new analyses of filtration efficiency, filter priming, inclusion entrapment and a host of advancements in filtration technology.

For more Information

"Metal Flow Through a Filter System," 2002 AFS Transactions (02-020).

Anthony Midea, Foseco Metallurgical Inc., Cleveland, Ohio Luciano Oliveira, Foseco Industrial e Comercial Ltda, Sao Paulo, Brazil

Anthony Midea is product development and technical group manager for Foseco Metallurgical, Cleveland, Ohio, and Luciano Oliveira is project manager for Foseco Industrial e Comercial Ltda, Sad Paulo, Brazil.