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.

Magnetic levitation fluid dynamics

This work is concerned with the accurate computation of flow in a rapidly deforming liquid metal droplet, suspended in an AC magnetic field. Intense flow motion due to the induced electromagnetic force distorts dynamically the droplet envelope, which is initially spherical. The relative positional change between the liquid metal surface and the surrounding coil means that fluid flow and magnetic field computations need to be closely coupled. A spectral technique is used to solve this problem, which is assumed axisymmetric. The computed results are compared against a physical experiment and "ideal sphere" analytic solutions. A comparison between the "magnetic pressure" approximation and the full electromagnetic force solutions, shows fundamental differences; the full electromagnetic force solution is necessary for accurate results in most practical applications of this technique. The physical reason for the fundamental discrepancy is the difference in the electromagnetic force representation: only the gradient part of the full force is accounted for in the "magnetic pressure" approximation. Figs 9, Refs 13.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

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.

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.

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.

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.

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.

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.

Simulation of 2-D metal cutting by means of a distributed algorithm

Temperature distributions involved in some metal-cutting or surface-milling processes may be obtained by solving a non-linear inverse problem. A two-level concept on parallelism is introduced to compute such temperature distribution. The primary level is based on a problem-partitioning concept driven by the nature and properties of the non-linear inverse problem. Such partitioning results to a coarse-grained parallel algorithm. A simplified 2-D metal-cutting process is used as an example to illustrate the concept. A secondary level exploitation of further parallel properties based on the concept of domain-data parallelism is explained and implemented using MPI. Some experiments were performed on a network of loosely coupled machines consist of SUN Sparc Classic workstations and a network of tightly coupled processors, namely the Origin 2000.

Computational modelling of metal extrusion and forging processes

The computational modelling of extrusion and forging processes is now well established. There are two main approaches: Lagrangian and Eulerian. The first has considerable complexities associated with remeshing, especially when the code is parallelised. The second approach means that the mould has to be assumed to be entirely rigid and this may not be the case. In this paper, a novel approach is described which utilises finite volume methods on unstructured meshes. This approach involves the solution of free surface non-Newtonian fluid flow equations in an Eulerian context to track the behaviour of the workpiece and its extrusion/forging, and the solution of the solid mechanics equations in the Lagrangian context to predict the deformation/stress behaviour of the die. Test cases for modelling extrusion and forging problems using this approach will be presented.

The development and validation of computational MHD techniques for the modelling of metal production processes

Magnetic fields are used in a number of processes related to the extraction of metals, production of alloys and the shaping of metal components. Computational techniques have an increasingly important role to play in the simulation of such processes, since it is often difficult or very costly to conduct experiments in the high temperature conditions encountered and the complex interaction of fluid flow, heat transfer and magnetic fields means simple analytic models are often far removed from reality. In this paper an overview of the computational activity at the University of Greenwich is given in this area, covering the past ten years. The overview is given from the point of view of the modeller and within the space limitations imposed by the format it covers the numerical methods used, attempts at validation against experiments or analytic procedures; it highlights successes, but also some failures. A broad range of models is covered in the review (and accompanying lecture), used to simulate (a) A-C field applications: induction melting, magnetic confinement and levitation, casting and (b) D-C field applications such as: arc welding and aluminium electroloysis. Most of these processes involve phase change of the metal (melting or solidification), the presence of a dynamic free surface and turbulent flow. These issues affect accuracy and need to be address by the modeller.

A mixed Eulerian-Lagrangian approach for metal extrusion

In this paper a mixed Eulerian-Lagrangian approach for the modelling metal extrusion processes is presented. The approach involves the solution of non-Newtonian fluid flow equations in an Eulerian context, using a free-surface algorithm to track the behaviour of the workpiece and its extrusion. The solid mechanics equations associated with the tools are solved in Lagangrian context. Thermal interactions between the workpiece are modelled and a fluid-structure interaction technique is employed to model the effect of the fluid traction load imposed by the workpiece on the tools. Two extrusion test cases are investigated and the results obtained show the potential of the model with regard to representing the physics of the process and the simulation time.

Dynamic model for metal cleanness evaluation by melting in a cold crucible

Melting of metallic samples in a cold crucible causes inclusions to concentrate on the surface owing to the action of the electromagnetic force in the skin layer. This process is dynamic, involving the melting stage, then quasi-stationary particle separation, and finally the solidification in the cold crucible. The proposed modeling technique is based on the pseudospectral solution method for coupled turbulent fluid flow, thermal and electromagnetic fields within the time varying fluid volume contained by the free surface, and partially the solid crucible wall. The model uses two methods for particle tracking: (1) a direct Lagrangian particle path computation and (2) a drifting concentration model. Lagrangian tracking is implemented for arbitrary unsteady flow. A specific numerical time integration scheme is implemented using implicit advancement that permits relatively large time-steps in the Lagrangian model. The drifting concentration model is based on a local equilibrium drift velocity assumption. Both methods are compared and demonstrated to give qualitatively similar results for stationary flow situations. The particular results presented are obtained for iron alloys. Small size particles of the order of 1 μm are shown to be less prone to separation by electromagnetic field action. In contrast, larger particles, 10 to 100 μm, are easily “trapped” by the electromagnetic field and stay on the sample surface at predetermined locations depending on their size and properties. The model allows optimization for melting power, geometry, and solidification rate.