A computational model for defect prediction in shape castings based on the interaction of free surface flow, heat transfer, and solidification phenomena

High-integrity castings require sophisticated design and manufacturing procedures to ensure they are essentially macrodefect free. Unfortunately, an important class of such defects—macroporosity, misruns, and pipe shrinkage—are all functions of the interactions of free surface flow, heat transfer, and solidication in complex geometries. Because these defects arise as an interaction of the preceding continuum phenomena, genuinely predictive models of these defects must represent these interactions explicitly. This work describes an attempt to model the formation of macrodefects explicitly as a function of the interacting continuum phenomena in arbitrarily complex three-dimensional geometries. The computational approach exploits a compatible set of finite volume procedures extended to unstructured meshes. The implementation of the model is described together with its testing and a measure of validation. The model demonstrates the potential to predict reliably shrinkage macroporosity, misruns, and pipe shrinkage directly as a result of interactions among free-surface fluid flow, heat transfer, and solidification.

Liquid metal turbulent flow dynamics in a cylindrical container with free surface: experiment and numerical analysis

The liquid metal flow in induction crucible models is known to be unstable, turbulent and difficult to predict in the regime of medium frequencies when the electromagnetic skin-layer is of considerable extent. We present long term turbulent flow measurements by a permanent magnet incorporated potential difference velocity probe in a cylindrical container filled with eutectic melt In-Ga-Sn. The parallel numerical simulation of the long time scale development of the turbulent average flow is presented. The numerical flow model uses an implicit pseudo-spectral code and k-w turbulence model, which was recently developed for the transitional flow modelling. The results compare reasonably to the experiment and demonstrate the time development of the turbulent flow field and the turbulence energy.

Liquid metal turbulent flow dynamics in a cylindrical container with free surface: experiment and numerical analysis

The liquid metal flow in inducation crucible models is known to be higly unstable and turbutlen in the regim e of medium frequecies when the elctronmagnetic skin-layer is of considerable extent. We present long term turbulent flow measurements by a permanent magnet incorporated potential difference veolocity probe in a cylindirical container filled with eutecti mlt In-Ga-SN. The parallel numerical simulation of the long time scale development of the turbulen average flow is presented. The numerical lfow model uses a pseud-spectral code and k-w turbulence model, which was recently developed for the transitional flow modelling. The result compare reasonably to the experiment and demonstrate the time development of the turbulent flow field.

Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Computational modeling of mold filling and related free-surface flows in shape casting: an overview of the challenges involved

Accurate representation of the coupled effects between turbulent fluid flow with a free surface, heat transfer, solidification, and mold deformation has been shown to be necessary for the realistic prediction of several defects in castings and also for determining the final crystalline structure. A core component of the computational modeling of casting processes involves mold filling, which is the most computationally intensive aspect of casting simulation at the continuum level. Considering the complex geometries involved in shape casting, the evolution of the free surface, gas entrapment, and the entrainment of oxide layers into the casting make this a very challenging task in every respect. Despite well over 30 years of effort in developing algorithms, this is by no means a closed subject. In this article, we will review the full range of computational methods used, from unstructured finite-element (FE) and finite-volume (FV) methods through fully structured and block-structured approaches utilizing the cut-cell family of techniques to capture the geometric complexity inherent in shape casting. This discussion will include the challenges of generating rapid solutions on high-performance parallel cluster technology and how mold filling links in with the full spectrum of physics involved in shape casting. Finally, some indications as to novel techniques emerging now that can address genuinely arbitrarily complex geometries are briefly outlined and their advantages and disadvantages are discussed.

Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

The application of free-surface techniques to metal forming processes

In this paper the use of free-surface techniques, within the framework of a finite volume methodology, are investigated for the simulation of metal forming processes. In such processes, for example extrusion and forging, a workpiece is subjected to large scale deformation to create the product's shape. The use of Eulerian free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remmeshing. Two free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remesingh. Two free-surface techniques are compared by modelling a typical example of this type of process - non-Newtonian extrusion of an aluminium workpiece through a conical die.

Free surface and mesh control for the FV simulation of semi-levitation melting

Abstract not available

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

Investigation of wall-slip effect on lead-free solder paste and isotropic conductive adhesives

Wall-slip plays an important role in characterising the flow behaviour of solder paste materials. The wall slip arises due to the various attractive and repulsive forces acting between the solder particles and the walls of the measuring geometry.These interactions could lead to the presence of a thin solvent layer adjacent to the wall, which gives rise to slippage. The wall slip effect can play an important role in ensure successfulpaste release after the printing process. Wall-slip plays animportant role in characterising the flow behaviour of solderpastes and isotropic conductive adhesives. The study investigates the wall-slip formation in solder paste andisotropic conductive adhesives using flow visualisation technique. The slip distance was measured for parallel plate with different surface roughness in order to quantify the wallslip formations in these paste materials. An ink marker line was drawn between the parallel plate and the free surface of the sample. The parallel was rotated slowly at a constant shear rate of 0.05 sec-1 and the displacement of the ink marker was observed using a video microscope and image capturing software was utilised to capture the displacement of ink marker. From this study, it was found that the wall-slip effect was evident in all the paste materials. In addition, the different surface roughness of the parallel plates did not prevent the formation of wall-slip. This study has revealed that the wallslip effect could used to understand the flow behaviour of the paste in the stencil printing process.

Dynamics of an axisymmetric electromagnetic ‘crucible’ melting

Different industrial induction melting processes involve free surface and melt-solid interface of the liquid metal subject to dynamic change during the technological operation. Simulation of the liquid metal dynamics requires to solve the non-linear, coupled hydrodynamic-electromagnetic-heat transfer problem accounting for the time development of the liquid metal free boundary with a suitable turbulent viscosity model. The present paper describes a numerical solution method applicable for various axisymmetric induction melting processes, such as, crucible with free top surface, levitation, semi-levitation, cold crucible and similar melting techniques. The presented results in the cases of semi-levitation and crucible with free top surface meltings demonstrate oscillating transient behaviour of the free metal surface indicating the presence of gravity-inertial-electromagnetic waves which are coupled to the internal fluid flow generated by both the rotational and potential parts of the electromagnetic force.

Computational magnetohydrodynamics - Application

There are many processes, particularly in the nuclear and metals processing industries, where electromagnetic fields are used to influence the flow behaviour of a fluid. Procedures exploiting finite volume (FV) methods in both structured and unstructured meshes have recently been developed which enable this influence to be modelled in the context of conventional FV CFD codes. A range of problems have been tackled by the authors, including electromagnetic pumps and brakes, weirs and dams in steelmaking tundishes and interface effects in aluminium smelting cells. Two cases are presented here, which exemplify the application of the new procedures. The first case investigates the influence of electromagnetic fields on solidification front progression in a tin casting and the second case shows how the liquid metals free surface may be controlled through an externally imposed magnetic field in the semi-levitation casting process.