Short shots and industrial case studies: Understanding fluid flow and solidification in high pressure die casting

The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three dimensional fluid flow with significant free surface fragmentation and splashing. A simulation method that has proved particularly suited to modelling HPDC is Smoothed Particle Hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling more accurate prediction of fluid flows involving complex free surface motion. Three practical industrial case studies of SPH simulated HPDC flows are presented; aluminium casting of a differential cover (automotive), an electronic housing and zinc casting of a door lock plate. These show significant detail in the fragmented fluid free surfaces and allow us to understand the predisposition to create defects such as porosity in the castings. The validation of flow predictions coupled with heat transfer and solidification is an important area for such modelling. One powerful approach is to use short shots, where insufficient metal is used in the casting or the casting shot is halted part way through, to leave the die cavity only partially filled. The frozen partial castings capture significant detail about the order of fill and the flow structures occurring during different stages of filling. Validation can occur by matching experimental and simulated short shots. Here we explore the effect of die temperature, metal super-heat and volume fill on the short shots for the casting of a simple coaster. The bulk features of the final solid castings are found to be in good agreement with the predictions, but the fine details appear to depend on surface behaviour of the solidifying metals. This potentially has significant implications for modelling HPDC.     

Numerical modelling of solidification of castings made of two‐component alloys

The paper deals with a numerical modelling of equiaxed microstructure formation during the solidification of two‐component alloys. The basic enthalpy formulation was applied to model the solidification. The equiaxed grain size was dependent on the average cooling velocity at the moment when the liquid metal reaches the liquidus temperature. The experimentally determined dependence between grain radius and cooling velocity was used in the calculation of average grain radii distribution.     

Two-dimensional ultrasound Doppler velocimeter for velocity field measurements of liquid metal flows

We present a novel fluid flow measurement system based on the pulsed-wave ultrasound Doppler velocimetry being able to determine two-dimensional velocity fields. It applies for the measurement of unsteady liquid metal flows driven by electromagnetic forces concerning the research field of magnetohydrodynamics. The application of advanced processing techniques enable high data acquisition rates and concurrently a high spatial resolution facilitating to resolve transient liquid metal flow structures which could not been acquired so far. An experimental setup utilizing liquid metal in a cubic vessel exposed to a stationary rotating magnetic field was used to validate the reliability of the measurement system. The swirling fluid motion in its horizontal section could be resolved into a velocity field grid of 24 × 24 vectors while achieving frame rates of about 30 fps. Results from a further study driving liquid metal in a cylindrical vessel by a pulsed rotating magnetic field are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of coupled turbulent flow and solidification in a single belt caster with electromagnetic brake

A mathematical model has been developed to simulate turbulent fluid flow and solidification in the presence of a DC magnetic field in an extended nozzle for metal delivery to a single belt caster. This paper reports on predicted effects of DC magnetic field conditions in modifying flows and solidification behavior in the metal delivery system. It is shown that the application of a DC magnetic brake to the proposed system can result in a reasonably uniform feeding of melt onto the cooled moving belt. This, in turn, optimises the rate of even shell growth along the chilled substrate. In order to account for the effects of turbulence, a revised low-Reynolds k–ε turbulent model was employed. A Darcy-porosity approach was used to simulate fluid flow within the mushy solidification region. Simulations were carried out for plain carbon steel strip casting. The fully coupled transport equations were numerically solved using the finite volume method. The computed flow patterns were compared with those reported in the literature. The performance of the magnetic flow control device proposed in this work is evaluated and compared with flow modifications obtained by inserting a ceramic filter within the reservoir.     

Extension of SPH to predict feeding,freezing and defect creation in low pressure die casting

Low pressure die casting is used to manufacture complex metal components where there is a need for high structural integrity. In this process, liquid metal is fed from below into the die used to form the component under a positive pressure. Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian method that has specific advantages for modelling such material forming applications. This paper describes extensions to the SPH method for predicting shrinkage of the cooling metal, tracking of oxide formation, prediction of feeding, solidification front dynamics and finally direct prediction of the residual pressure distribution in the solidified metal and of cavity defect formation. These are demonstrated using a simple two dimensional example which contains the essential features of an engine block.     

A three-dimensional fluid flow model for puddle formation in the single-roll rapid solidification process

The single-roll rapid solidification process (SRRSP) is considered to be a process of perspective to produce a Fe-Si-B ribbon of amorphous microstructure and near net shape products such as thin strips of stainless steel. The condition of a melt puddle between the nozzle and rotating wheel in the single-roll rapid solidification process significantly affects the quality and dimensional uniformity of the products as well as the smoothness of the operation. The purpose of this study was to develop a three-dimensional fluid flow analysis system to model the formation of puddle and flow conditions of molten metal in the puddle for the single-roll rapid solidification processes which include the planar flow casting (PFC) process and the single-roll strip casting process. The model is based on a computational fluid dynamics technique called the SOLA-VOF scheme, which possesses the capability of treating transient fluid flow problems with the evolution of free boundaries. Furthermore, the SOLA-VOF scheme is extended from two dimensions to three dimensions. The simulated results reveal how the melt puddle is formed between the nozzle and the rotating substrate and its corresponding fluid flow behavior for the PFC process as well as the single-roll strip casting process. The test results also demonstrate that two-dimensional analysis cannot properly consider the actual flow condition in the puddle.     

Mathematical and physical modelling of steel flow and solidification in twin-roll/horizontal belt thin-strip casting machines

Near-net-shape casting technology is one of the most important research areas in the iron and steel industry today. Driving forces for the development of this technology include a reduction in the number of operations needed for conventionally produced strip. This is especially true of hot rolling operations. The consequent reduction in investment cost when considering new industrial facilities, makes near-net-shape casting operations extremely attractive from a commercial standpoint. Various processes for near-net-shape casting of steel are currently being developed around the world. Of these processes, twin-roll casting machines represent a major area of concentration. We believe that one of the main issues concerning the design of twin-roll casters is the metal delivery system and its effect on the homogeneity of solid shell formation, segregation and surface quality. In the present work, computational fluid dynamics has been used to study different metal delivery systems for twin-roll casting (TRC) and horizontal belt casting (HBC) operations. The METFLO code has been adapted to simulate three-dimensional turbulent fluid flows, heat transfer and solidification in these types of machines. The enthalpy–porosity technique was used to couple fluid flow and solidification phenomena. Two configurations for metal delivery system have been studied to date for TRC: one is a conventional tubular nozzle with horizontal outlets in the directions of the side dams; the other is a slot nozzle with a vertical inlet stream. These simulations have been applied to a pilot caster being studied in Canada, with a roll radius of 0.30 m, producing steel strips with thicknesses ranging from 4 to 7 mm, at relatively low roll speeds ranging between 4 and 12 m/min. Different positions and penetrations of the nozzles in the liquid pool have also been analysed. It has been shown that a tubular nozzle leads to the formation of a non-uniform solid shell along the roll width. In both configurations, a thicker solid shell is formed close to the roll edges, due to the presence of the side dams. In the case of HBC, computations have been made for an extended nozzle metal delivery system, and preliminary water modelling tests carried out to confirm the flow delivery concepts proposed. In addition, instantaneous heat flux measurements to simulated belt substrates have been performed for the horizontal casting of aluminum strip that show somewhat similar characteristics to those measured for steel in the pilot TRC, in terms of transient peaks and decays.     

Transient thermal model for the hot chamber injection system in the pressure die casting process

This paper describes a three-dimensional numerical model that is used to predict the transient thermal behaviour of the metal injection system of a hot chamber pressure die casting machine. The behaviour of the injection system is considered in conjunction with that of the die. The Boundary Element Method (BEM) is used to model the transient thermal behaviour of the injection system elements and the die blocks. A perturbation approach is adopted. By adopting this approach, only those surfaces over which a significant transient variation in temperature occurs need be considered. The model assumes that a corresponding steady-state analysis has first been performed so that time-averaged thermal information is available. A finite element based technique is used to model the phase change of the liquid metal in the die cavity and in the injection system. At injection the nozzle and die are assumed to be instantly filled with liquid metal, however, a procedure is presented that attempts to model the heat transfer associated with the flow through the nozzle, gate, and runner regions during injection. Model predictions are compared against thermocouple readings and thermal images obtained from experimental tests. Good agreement is obtained between predicted and measured temperatures. The transient thermal behaviour of an existing hot chamber injection system is investigated in detail and recommendations for improved performance are made. In an attempt to improve the solidification pattern of the casting and the thermal behaviour of the injection system, a redesign of the experimental die is considered. The numerical predictions indicate that the redesign will have a beneficial effect on the solidification pattern of the casting, and on the performance of the injection system.     

Finite element analysis of multi-particle impact on erosion in abrasive water jet machining of titanium alloy

Abrasive water jets (AWJs) are finding growing applications for machining a wide range of difficult-to-machine materials such as titanium alloys, stainless steel, metal matrix and fibre reinforced composites, etc. Current applications of AWJs include machining of Titanium alloys for aircraft components and bio-medical implants to removal of aircraft engine coatings. This paper presents the application of an elasto-plastic model based explicit finite element analysis (FEA) to model the erosion behaviour in abrasive water jet machining (AWJM). The novelty of this work includes FE modelling of the effect of multiple (twenty) particle impact on erosion of Grade 5 Titanium alloy (Ti-6Al-4V). The influence of abrasive particle impact angle and velocity on the crater sphericity and depth, and erosion rate has been investigated. The FE model has been validated for stainless steel and yields largely improved results. Further, the same FEA approach has been extended to model the multi-particle impact erosion behaviour of Titanium alloy.     

Modelling and Simulation of solidification processes in polymer melt flows

This work deals with the modelling and simulation of solidification processes in polymer melt flows. Two models describing the latent heat and the rheological behaviour were implemented in a finite volume code. The models are empirical and their parameters are identified using experimental results obtained from investigations with a rotational rheometer and a differential scanning calorimetry. First results of the simulation of a solidifying channel flow are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modelling of melt-conditioned direct-chill casting

Melt conditioned direct-chill (MC-DC) casting is a novel technology which combines direct-chill (DC) casting with a high shear device directly immersed in the sump for in situ microstructural control. A numerical model of melt-conditioned direct-chill casting (MC-DC) is presented in this paper. This model is based on a finite volume continuum model using a moving reference frame (MRF) to enforce fluid rotation inside the rotor-stator region and is numerically stable within the range of processing conditions. The boundary conditions for the heat transfer include the effects of the hot-top, the aluminium mould, and the direct chill. This model is applied to the casting of two alloys: aluminium-based A6060 and magnesium-based AZ31. Results show that MC-DC casting modifies the temperature profile in the sump, resulting in a larger temperature gradient at the solidification front and a shorter local solidification time. The increased heat extraction rate due to forced convection in the sump is expected to contribute to a finer, more uniform grain structure in the as-cast billet.     

An asymptotic approach to solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys

The modelling of macrosegregation in the continuous casting of alloys normally requires resource-intensive computational fluid dynamics (CFD). By contrast, here we develop an asymptotic framework for the case when macrosegregation is driven by solidification shrinkage; as a first step, a binary alloy is considered. Systematic asymptotic analysis of the steady-state two-dimensional mass, momentum, heat and solute conservation equations in terms of the shrinkage parameter indicates that the overall problem can be reduced to a hierarchy of decoupled problems: a leading-order problem that is non-linear, and a sequence of linear problems, with the actual macrosegregation of the solute then being determined by means of one-dimensional quadrature. A numerical method that solves this sequence is then developed and implemented, and yields realistic macrosegregation profiles at low computational cost.     

Modelling confined multi-material heat and mass flows using SPH

Many applications in mineral and metal processing involve complex flows of multiple liquids and gases coupled with heat transfer. The motion of the surfaces of the liquids can involve sloshing, splashing and fragmentation. Substantially differing material properties are common. The flows are frequently complicated by other physical effects. Smoothed particle hydrodynamics (SPH) is a computational modelling technique that is ideally suited to such difficult flows. The Lagrangian framework means that momentum dominated flows and flows with complicated material interface behaviours are handled easily and naturally. To be able to model complex multi-physics flows, many aspects of SPH need to be explored. In this paper we describe developments that allow conductive and convective heat transfer to be modelled accurately for a sequence of idealised test problems.     

Functional gradient evaluation in the optimal control of a complex dynamical system

The gradient of the cost functional in a discrete optimal control problem for metal solidification in metal casting is exactly calculated. In contrast to previous studies, the object under analysis has a complex geometric shape. The mathematical model for describing the solidification process is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. Formulas for exact gradient evaluation are derived using the fast automatic differentiation technique.     

3D SPH flow predictions and validation for high pressure die casting of automotive components

The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three-dimensional fluid flow with significant free surface fragmentation and splashing. A Lagrangian simulation technique that is particularly well suited to modelling HPDC is smoothed particle hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling the accurate prediction of fluid flows involving complex free surface motion.     

Choosing a cost functional and a difference scheme in the optimal control of metal solidification

The optimal control of solidification in metal casting is considered. The underlying mathematical model is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. The study is focused on choosing a cost functional in the optimal control of solidification and choosing a difference scheme for solving the direct problem. The results of the study are described and analyzed.     

考虑大变形的刚-柔耦合旋转智能结构动力学分析

基于Hamilton原理对带端部质量的刚柔耦合旋转智能结构建立了耦合的非线性动力学模型．根据一阶近似耦合（FOAC）模型理论,通过有限元方法,得到了系统的有限维模型．模型中考虑了轴向、横向位移和转动角度的非线性几何效应,以及压电材料和结构的大变形及离心刚化效应．在有限元模型的基础上,建立了3种实际系统模型方程,分别是无压电层的结构,有压电层开环状态和闭环状态．最后基于简化模型的仿真结果显示出有端部质量和没有端部质量的差异,智能结构梁在闭环和开环的差异,高速旋转梁的离心作用及结构外加电载荷的动力响应．     

Determination of functional gradient in an optimal control problem related to metal solidification

The gradient of the cost functional in the discrete optimal control problem of metal solidification in casting is exactly evaluated. The mathematical model describing the solidification process is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. Formulas determining exact gradient determination are derived using the fast automatic differentiation technique.     

Application of Smoothed Particle Hydrodynamics for modelling gated spillway flows

Computational models of spillways are important for evaluating and improving dam safety, optimising spillway design and updating operating conditions. Traditionally, scaled down physical models have been used for validation and to collect hydraulic data. Computational fluid dynamics (CFD) models however provide advantages in time, cost and resource reduction. CFD models also provide greater efficiency when evaluating a range of spillway designs or operating conditions. Within the present literature, most studies of computational spillway models utilise a mesh-based method. In this work we use the particle based method of Smoothed Particle Hydrodynamics (SPH) to model weir flow through a four bay, gated, spillway system. Advantages of SPH for such modelling include automatic representation of the free surface flow behaviour due to the Lagrangian nature of the method, and the ability to incorporate complex and dynamic boundary objects such as gate structures or debris. To validate the SPH model, the reservoir water depth simulated is compared with a related physical study. The effect of SPH resolution on the predicted water depth is evaluated. The change in reservoir water level with discharge rates for weir flow conditions is also investigated, with the difference in simulated and experimental water depths found to range from 0.16% to 11.48%. These results are the first quantitative validation of the SPH method to capture spillway flow in three dimensions. The agreement achieved demonstrates the capability of the SPH method for modelling spillway flows.