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# Casting Processes with Changing Geometry

This is a condensed version of a paper prepared by Drs. Michael Barkhudarov and Gengsheng Wei. Read the full article, including a detailed description of the mathematical model and additional examples of GMO applications for casting problems.

## Introduction

In recent years casting modeling has become an accepted and even required part of the design process. Modern simulation tools are capable of modeling flow, thermal and structural aspects of the many casting processes. In these cases most of the modeling work involves fixed geometry of the mold. However, there are casting practices that involve moving parts directly in contact with liquid metal. Metal handling before and during pouring involves moving furnaces and ladles, in high pressure die casting a plunger propels metal into the die cavity, in centrifugal and tilt pour castings the molds move, and in squeeze casting pieces of the die move together to form the metal into a shape.

FLOW-3D’s new model, called General Moving Object (GMO), provides a robust and accurate way to simulate three-dimensional motion of arbitrary shapes in a fixed computational grid. Multiple moving objects can exist in the same domain and each of them can have a different type of translational and rotational motion, either prescribed or dynamically coupled with metal flow [1]. This fixed-mesh GMO method has advantages over the moving and deforming mesh methods because of its efficiency and flexibility. The shape and the motion of each moving object are not restricted in their complexity.

Potential applications of the GMO method exist not only in casting, but in many other engineering problems, such as civil engineering and seakeeping. Two examples of the application of the new GMO model to the simulation casting processes are shown below. In each case the motion of the moving part of the geometry is prescribed as if controlled by a programmable machine.

Figure 1. The simulated pouring sequence of
a liquid aluminum alloy from a ladle into
a sand mold using the prescribed-motion GMO
model. Color represents volume fraction of the
entrained air with the scale going from
0.0 (blue) to 8.0 % air by volume (red).

## Pouring out of a Ladle

This example employs both translational and rotational time-dependent prescribed motion to simulate the process of pouring liquid metal from a ladle into a sand mold. The ability to model the handling of metal before it gets into the mold is an important extension of the general filling simulation capability. Even though significant metal damage through oxidation and air entrainment can occur during this early stage of the casting process, it is usually left out of the conventional filling analysis, and replaced by a fixed flow rate at the top of the pouring basin. The new model allows engineers to investigate this highly transient and turbulent stage, and, combined with heat transfer, air entrainment and defect tracking models, the quality of the filling process can be evaluated in more detail.

The metal is initially placed into a vertically oriented ladle, which then moves horizontally to a location above the pouring basin and stops. After stopping, the ladle tilts forward 60 degrees, then recovers and moves back to the initial position—all in the time span of 10 seconds. An animation from the results of the simulation is shown in Fig. 1. The color represents the amount of entrained air in the metal, measured by the fraction of the air volume in the air/metal mixture. The entrainment of air is modeled in terms of a competition between turbulent, surface tension and gravity forces [7].

Most of the entrainment of air occurs in the sprue where the free falling liquid metal jet mixes with the metal already in the sprue. This is where the speed of the metal is the highest, and the level of turbulence is also the highest. In addition, the footprint of the jet moves in and around the top of the sprue, adding even more turbulence and variability to the flow in the basin and sprue. If one needs to minimize the metal damage at this point during filling, these aspects of the flow must be investigated closely.

Figure 2. Flow in the shot sleeve during
the slow shot and fast shot stages of
the filling process. Color represents metal
velocity with the scale going from 0.0 (blue)
to 10 m/sec (red).

## Simulating Shot Sleeves

In this example we use a linear, one-dimensional, time-dependent prescribed motion of a cylindrical plunger, 0.06 m in diameter, to simulate the process of pushing metal in the shot sleeve into a cavity during high pressure die casting. As with pouring from a ladle, proper handling of metal in the shot sleeve in the cold chamber process is critical to ensure a good quality casting. The speed of the plunger must be carefully programmed to avoid the entrainment of air by overturning surface waves. The speed of the plunger can be defined as an arbitrary function of time.

The shot sleeve is initially half filled by liquid metal. The motion of the plunger is divided into a slow stage, 0.6 second long, with a velocity of 0.2 m/s, and a fast stage, with the velocity of 2 m/s. The transition between the two stages is linear and occurs over a time interval of 0.05 second. The flow results are shown in Fig. 2, with metal colored by the velocity magnitude. A shallow wave is sent ahead of the plunger during the slow shot stage. Before the wave reaches the end of the sleeve, the plunger accelerates generating a much larger wave.

Pouring into a shot sleeve from a metal transfer cup could also be added to the shot sleeve model for a more detailed description of metal flow. The pouring process may result in a significant residual metal flow in the shot sleeve before the plunger starts moving.

## Conclusions

The GMO model can be applied to simulate a wide range of casting processes that involve moving geometry such as pouring operations, shot sleeves, centrifugal and squeeze casting. Combined with the heat transfer and air and oxide film entrainment models, it can yield detailed insights into these processes and allows engineers to extend their knowledge and understanding of the complex interactions between various process parameters.

1. Wei, G., “A Fixed-Mesh Method for General Moving Objects in Fluid Flow,” Modern Physics Letters B, Vol. 19, Nos. 28-29, 1719-1722, 2005.

2. C. W. Hirt and J. M. Sicilian, “A Porosity Technique for the Definition of Obstacles in Rectangular Cell Meshes,” Proc. Fourth International Conf. Ship Hydro., National Academic of Science, Washington, DC, Sept. 1985.

3. H. Goldstein, P. Charles and J. Safko, Classical Mechanics (Boston, MA, Addison Wesley and Company, 2002).

4. FLOW-3D Theory Manual, (Flow Science Inc., 2006).

5. C. W. Hirt and B. D. Nichols, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Computational Physics, 39 (1981), 201-225.