M. Barkhudarov, Flow Science Inc., Santa Fe, New Mexico; S. Mascetti, XC Engineering, Italy; R. Pirovano, XC Engineering, Italy Abstract High pressure die casting is one of the most complex processes in the foundry world due to the wide range of physical phenomena and process parameters that control the outcome. A particular challenge is achieving optimal conditions in the shot sleeve from which metal is injected into the die cavity. The speed of the plunger in a horizontal shot sleeve must be carefully controlled to avoid unnecessary entrainment of air in the metal and, at the same time, minimize heat losses in the sleeve.  The paper presents a general solution for the flow of metal in a shot sleeve, based on the shallow water approximation of the interaction of the moving plunger and liquid metal. The derived analytical solution allows engineers to precisely control the behavior of metal in the shot sleeve during the slow-shot stage of the high pressure die casting process, minimizing the risk of air entrainment. Results are validated with three-dimensional numerical modeling of the process. Coupled with parametric optimization, the numerical model can improve the process conditions predicted by the analytical model. Introduction The speed of the plunger in a horizontal shot sleeve must be carefully controlled to avoid unnecessary entrainment of air in the metal and at the same time minimize heat losses in the sleeve. If the plunger moves too fast, large waves are created on the surface of the liquid metal that may overturn and entrain air into the metal, which will then be carried into the die cavity. A plunger moving too slow results in waves reflecting from the opposite end of the shot sleeve. The reflected waves prevent proper expulsion of air into the die cavity. In either case, the outcome is excessive porosity in the final casting. Moreover, a slow plunger increases also oxidation of the free surface of liquid metal, and the heat losses because of the long contact time with the mold walls. In this article two approaches are used to limit these effects: a general solution for the plunger speed as a function of time and a full-physics, three-dimensional CFD optimization. Mathematical model The dynamics of waves in a horizontal shot sleeve can be analyzed by drawing an analogy with flow in an open channel. A detailed analysis is possible by modeling the flow of metal in a rectangular shot sleeve of length L and height H (justified for initial fill fractions in the range of 40-60% [1]) using the shallow water approximation [3]. In this approximation the flow in the vertical direction is neglected in comparison with the horizontal velocity component. The flow is modeled in two dimensions, with the x axis directed along the direction of motion of the plunger, and the z axis pointing upwards. If viscous forces are omitted, then the flow has only one velocity component, u, along the length of the channel. The plunger speed in the positive x direction is given by dX/dt=X’(t), where X(t) defines the position of the plunger at time t>0.  At the moving surface of the plunger, the velocity is defined as . As the plunger moves along the length of the channel it sends waves traveling forward along the metal surface. Each wave is associated with a small segment of the metal free surface and the column of metal directly below it (Fig. 1). The location, metal speed and depth in a wave that separates from the surface of the plunger at time t=tp are given by [3]: (1) Where According to Eq. (1), the metal speed, u, and depth, h, in each wave are constant and depend only on the time of the wave separation from the plunger, tp. They both increase with the speed of the plunger X’. Therefore, the first conclusion is that to maintain a monotonic slope of the metal surface in the direction away from the plunger, the latter must not decelerate. If this condition is not satisfied, then there will be waves sloped in both directions. When they reflect off the end of the sleeve and travel back towards the plunger, it creates unfavorable conditions for the evacuation of air from the sleeve and into the die cavity. Figure 1: Schematic representation of the flow in a shot sleeve and the coordinate system. Controlling the Waves Once a wave detaches from the plunger it travels at a constant speed given by (2) If the plunger accelerates, then each successive wave will move faster than the waves generated earlier. This will lead to a steepening of the surface slope as the waves travel further down the channel, and can potentialy result in overturning. If the speed of the plunger can be controlled as to limit the wave steepening during the slow shot stage, then the overturning can be avoided. Figure 2: The illustration for calculation of the slope of the metal’s free surface. Let us analyze the evolution … [Lire plus...]