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...]

## A new frontier in the simulation of gas defects

Thanks to their high reliability, efficiency and precision, process simulation software is increasingly used on a daily basis: many of the defects commonly found in foundry parts are already successfully grasped by existing numerical models and can therefore be prevented. These technologies are rapidly evolving and, thanks to the increasing availability of computing power, you are now able to simulate very complex problems by dividing the domain with millions of cells. Despite this, some important physical aspects have dimensions that remain much smaller than the size of the grid cell: in the modeling of these phenomena are introduced the main approximations, not being able to simulate them directly. Among the numerical challenges that propose the "sub-grid" models - those that involve precisely physical phenomena with a characteristic length smaller than the cell size - one of the largest is to accurately and effectively simulate the smallest air bubbles that remain embedded within the metal. THE SOFTWARE FLOW-3D® CAST The aim is therefore to show the current solutions available for the simulation and analysis of air incorporation and to propose an innovative solution able to overcome the limits of traditional methods. This was done using FLOW-3D® CAST software, one of the most accurate software for modelling a wide range of foundry processes. Its peculiarities are the ability to interpret with great accuracy the geometries of the piece through the FAVOR algorithm, despite the use of a structured grid, and the absolute precision in modeling the movement of the fluid alloy during the filling phase, using the TruVOF algorithm. In addition, the software has numerous numerical models able to simulate all the physics and particularities characterizing the foundry processes, from the thermal cycle of preheating to the final extraction of the piece from the mould. Thanks to this it is possible to carry out simulations with a high precision in determining the position of the defects related to the filling phase. Furthermore, FLOW-3D® CAST has a partially open-source code that can be easily customised: allowing the creation of new numerical models or the improvement of existing ones, the software adapts perfectly to the purpose of this work. NUMERICAL MODELS TO SIMULATE AIR ENTRAPMENT Within FLOW-3D® CAST there are different approaches to simulate air incorporation, of increasing complexity. The simplest approximation is to completely ignore the influence of air on the metal, except for a condition of constant and uniform pressure imposed on the exposed surface of the liquid alloy. With this approximation, the metal behaves as if a perfect vacuum had been created inside the mold, or similarly as if the air could be evacuated instantly from anywhere in the mold. The most complete modeling, on the other hand, consists in simulating also the dynamics of the air, calculating its speed at each point. Although it is possible to consider the complete and coupled fluid dynamics of metal and air simultaneously, in most cases this is not necessary. Due to the relatively small influence of air on the dense and viscous surface of the metal, it is possible to significantly reduce the calculation time by concentrating most of the resources on resolving the motion of the alloy. On the other hand, completely neglecting the influence of air does not allow to obtain realistic solutions to the problem, both in terms of filling dynamics and with regard to the identification of defects related to the presence of air. To obtain the best compromise between simulation speed and precision of the result, considering all the physical phenomena that have a significant influence during the filling phase of a die-casting process, within FLOW-3D® CAST it was decided not to calculate the complete dynamics of the air but to approximate its main contributions with two additional numerical models: In fact, air can be incorporated in the fluid because it is completely surrounded by it, in the form of compressible bubbles (bubble model), or trapped as a quantity dispersed by the effect of turbulence (air entrainment model). Air Entrainment model The air entrainment model [1] was developed in the 1990s to simulate the effect of turbulence on the surface of a moving liquid. During filling, in fact, the high speeds at which the fluid is found are sufficient to disturb the surface to the point of incorporating air in the form of microscopic bubbles. Every single air particle is much smaller than the calculation cell: for this reason the air is represented as a diffused quantity in the metal. Despite the fact that the individual bubbles, being microscopic, are not able by themselves to create a significant defect in the piece, their presence, at different concentrations, can affect the movement of the metal itself. The presence of air in the alloy, in fact, causes the density and local viscosity of the fluid to vary significantly. … [Read more...]

## A dam failure 3D-Shallow Water hybrid simulation on a real topography

The water and environmental simulation of the effect of a dam failure on a real extent topography was in the past a very hard goal because of the too many cells needed for the calculation. Since v11.0 of FLOW-3D® it is possible to use a hybrid approach, coupling a complete 3D simulation in the zone around the dam, where the splashing effects are more important, to a shallow water approach in the zone far away, having a solution to fast simulate such kind of situation. Moreover, since v11.1 of FLOW-3D®, it is possible to easily import raster file containing the topography with just one click, making the setup phase a matter of only some minutes. https://www.youtube.com/watch?v=Q7x55ohyDxA Video 1 : Overall view In the simulation a real topography of a lake with mountains has been used, the extension of the computational domain is around 5’000 km2, and a hypothetical large Dam has been created inside the topography. Using all the physical models described before, and the general moving object to simulate the dam failure in a 3D accurate way, it was possible to predict the effect of the failure, the affected zone and the submerged zone in the topography. The simulation lasts for more of 35 minutes of real time, simulating in a transient way the impact of the water on the topography up to the empty of the Dam. The resulting flow-rate across the broken dam is an interesting output of the simulation. All the post processing makes use of lot of Flow-Sight new features: moving camera, different realistic coloration for topography and water, fine tuning of light transparencies and reflections to make the visualization more realistic as possible, the use of textures to represent the surface of the dam, moving camera to follow the fluid path, different plots and viewports to show in one only visualization all the critical aspect of the simulation. https://www.youtube.com/watch?v=xsKx4L9QThI Video 2 : flow depth Video 1 represent an overall view of the water flow with realistic colors. The video 2 instead is a more “scientific analysis”: the water is colored with the fluid depth, using a 20-colors color scale in order to highlight the depth difference also in small portion of the scale; the terrain is colored with the elevation. Finally, a plot of the flow rate across a baffle positioned in correspondence of the dam wall is also reported. In the images a set of realistic rendering are saved, some of them with an evolution over time. … [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...]

## Sleeve filling and slow shot phase analysis with FLOW-3D Cast

High pressure Die Casting is a complex field of foundry. The liquid hot metal is generally poured into a shot sleeve for few seconds, until the desired volume is reached. Then, after a short waiting time, the plunger pushes the metal into the die cavity. First a slow shot phase is performed to avoid air entrainment in the sleeve, then a final high speed phase that fill the casting part in a very short amount of time. One of the targets of any producer is to find the best compromise between a fast process, to increase the productivity and to reduce the heat losses, and a slow filing and shot necessary to minimize the air entrainment. FLOW-3D Cast, due to its capabilities, is one of the best software to analyse this process. It can combine easily moving objects, mass sources, heat transfer and solidification, everything in fast and accurate simulations. Several studies were already done to determine the best plunger velocity curve, also coupling FLOW-3D Cast to numerical optimization software. The aim of the present simulation, instead, is to focus on the sleeve filling, underlining the possibility to control also this phase and the defects that could arise from a not-optimal solution. https://www.youtube.com/watch?v=cGQUmH8EHZ0 In the video both fluid and walls are coloured by temperature, with two different colour scales. The heat transfer coefficients have been artificially increased to emphasize the temperature change. Thanks to this fact, it is possible to notice that some drops of metal flow on the beginning of the runner system, solidifying and influencing the casting phase until they are melted again. It is possible also to notice the big waves generated when the filling is finished, and how this waves contribute to entrain some big air bubbles that are pushed into the casting part, generating defects. … [Read more...]