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 … [Read more...]

## Optimisation of the shape of a toilet

The design of sanitary ware not only follows aesthetic criteria but must also be subject to strict regulations that govern its proper functioning. Among these, a sanitary fixture must guarantee a good and effective cleaning of the internal surfaces, making sure that during the drainage phase the water properly removes most of the dirt. This study aims to analyze possible alternative forms for both the water inlet and the toilet bowl itself, which maximize the surface area of the interior of the toilet wetted by water. The variables involved are potentially multiple and interconnected: manually exploring all possible values can be a very long and complex work, as well as understanding the effects on the target set. For this reason we have chosen to use an optimization software that responds to this need: interfacing with the most disparate software you are able to automate the work, analyze the influence of multiple parameters and understand the link between them and the performance you want to improve. The software chosen is IMPROVEit, which thanks to its simple interface allows you to easily perform both the setup phase and the processing of results. https://www.youtube.com/watch?v=7KoQHw1VQfk&feature=youtu.be The software is able to internally modify the shape of STL geometries on the basis of parameters set by the user, launch fluid dynamic simulations interfacing with the CFD software FLOW-3D® using the modified geometries, extract the results of the software and process them with appropriate mathematical nodes or invoking Excel to obtain the quantity to be optimized. FLOW-3D® has been chosen for its excellent capabilities, in terms of speed and accuracy, in the calculation of transient and free surface flows. Three geometric parameters were chosen to vary, so as not to complicate the problem too much: the direction of the inlet, the outlet section of the inlet and the slope of the front part of the sanitary, playing with the curvature present here. Optimisation can certainly be complicated with more time available. The objective is to maximize the wetted surface of the inside of the sanitaryware, calculated as the integral area covered by liquid during the entire discharge time divided by the discharge time itself. Moreover, it has been imposed the constraint that the water must not escape from the upper part of the sanitary, even in small quantities, to discard those solutions that while washing the surface cause unwanted splashes. The fluid dynamics simulation was set up by initializing the water in the tank upstream of the toilet and setting as boundary conditions the exit from the exhaust pipe and the atmospheric pressure of the air. In this way, the water flow is free to enter freely and naturally into the sanitaryware. The simulation is stopped when the tank is completely empty. IMPROVEit has the advantage that it does not require knowledge in the field of optimization to be used, as it is able to independently choose the best strategy to achieve the goal. It only requires you to define a budget, which is the time you want to devote to optimization, because the strategy chosen is such as to seek optimal solutions around the end of this period. Since each calculation cycle (variation of the geometries, fluid dynamics simulation and elaboration of the outputs) lasts approximately 40 minutes, a budget of 25 cycles has been chosen, in order to have the result in little more than a day. Considering that there are 3 variables at play and that the problem is complex, it can be considered a rather challenging case for the optimization software. Nevertheless, IMPROVEit has already been able to propose solutions that increase the surface area of the toilet wetted by water by up to 35%. Moreover, by analysing the panorama of the solutions found, it is possible to better understand the influence of the various factors. It can be seen, in fact, as larger outlet diameters premino because they allow a greater leakage of mass in the unit of time, despite a reduced throttle leads to higher speeds. The direction of the inlet that gives the best results, however, is aligned with the horizontal plane, while the shape of the sanitary has more varied effects, without highlighting such a clear trend. … [Read more...]