Jan Bohacek

A Dynamic Mesh-Based Approach to Model Melting and Shape of an ESR Electrode

This paper presents a numerical method to investigate the shape of tip and melt rate of an electrode during electroslag remelting process. The interactions between flow, temperature, and electromagnetic fields are taken into account. A dynamic mesh-based approach is employed to model the dynamic formation of the shape of electrode tip. The effect of slag properties such as thermal and electrical conductivities on the melt rate and electrode immersion depth is discussed. The thermal conductivity of slag has a dominant influence on the heat transfer in the system, hence on melt rate of electrode. The melt rate decreases with increasing thermal conductivity of slag. The electrical conductivity of slag governs the electric current path that in turn influences flow and temperature fields. The melting of electrode is a quite unstable process due to the complex interaction between the melt rate, immersion depth, and shape of electrode tip. Therefore, a numerical adaptation of electrode position in the slag has been implemented in order to achieve steady state melting. In fact, the melt rate, immersion depth, and shape of electrode tip are interdependent parameters of process. The generated power in the system is found to be dependent on both immersion depth and shape of electrode tip. In other words, the same amount of power was generated for the systems where the shapes of tip and immersion depth were different. Furthermore, it was observed that the shape of electrode tip is very similar for the systems running with the same ratio of power generation to melt rate. Comparison between simulations and experimental results was made to verify the numerical model.

Shallow water model for horizontal centrifugal casting

A numerical model was proposed to simulate the solidification process of an outer shell of work roll made by the horizontal centrifugal casting technique. Shallow water model was adopted to solve the 2D average flow dynamics of melt spreading and the average temperature distribution inside the centrifugal casting mould by considering the centrifugal force, Coriolis force, viscous force due to zero velocity on the mould wall, gravity, and energy transport by the flow. Additionally, a 1D sub-model was implemented to consider the heat transfer in the radial direction from the solidifying shell to the mould. The solidification front was tracked by fulfilling the Stefan condition. Radiative and convective heat losses were included from both, the free liquid surface and the outer wall of the mould. Several cases were simulated with the following assumed initial conditions: constant height of the liquid metal (10, 20, and 30 mm), uniform temperature of the free liquid surface (1755 K). The simulation results have shown that while the solidification front remained rather flat, the free surface was disturbed by waves. The amplitude of waves increased with the liquid height. Free surface waves diminished as the solidification proceeded.

Process Simulation for the Metallurgical Industry: New Insights into Invisible Phenomena

In order to demonstrate how advanced process simulation can help to understand metallurgical process details and thus to improve industrial productivity, a number of examples are shown and discussed. The paper covers recent simulation results gained at the Chair of Simulation and Modeling of Metallurgical Processes, namely (i) the flow and shell formation in thin slap casting of steel, (ii) multiphase flow and magneto-hydrodynamic during Electro-Slag-Remelting, (iii) mold filling, surface wave dissipation and solidification during horizontal centrifugal casting of rolls, and (iv) forced and natural convection during electro-refining of copper in an industrial-size tankhouse cell.ZusammenfassungIn dieser Arbeit wird anhand von vier Beispielen gezeigt, wie fortschrittliche Prozesssimulationen helfen können, metallurgische Prozessdetails zu verstehen und somit die industrielle Produktivität zu erhöhen. Die Beispiele stammen aus laufenden Forschungsarbeiten des Lehrstuhls für Simulation und Modellierung metallurgischer Prozesse. Es werden i) Strömungen und Erstarrung beim Dünnbrammengießen von Stahl, ii) Mehrphasenströmung und Magnetohydrodynamik beim Elektroschlackeumschmelzen, iii) Formfüllung, Bewegung von Oberflächenwellen und Erstarrung beim horizontalen Schleuderguss von Großwalzen, und iv) erzwungene und natürliche Strömung in industriellen Aggregaten bei der Elektroraffinationselektrolyse von Kupfer behandelt.

Transient melting of an ESR electrode

Melting parameters of ESR process such as melt rate and immersion depth of electrode are of great importance. In this paper, a dynamic mesh based simulation framework is proposed to model melt rate and shape of electrode during the ESR process. Coupling interactions between turbulent flow, temperature, and electromagnetic fields are fully considered. The model is computationally efficient, and enables us to directly calculate melting parameters. Furthermore, dynamic change of electrode shape by melting can be captured. It is necessary to control the feeding velocity of electrode due to melting instabilities in the ESR process. As such, a numerical control is implemented based on the immersion depth of electrode to achieve the steady state in the simulation. Furthermore, the modeling result is evaluated against an experiment.

A (non-)hydrostatic free-surface numerical model for two-layer flows

A semi-implicit (non-)hydrostatic free-surface numerical model for two layer flows is derived from the Navier–Stokes equations by applying kinematic boundary conditions at moving interfaces and by decomposing the pressure into the hydrostatic and the hydrodynamic part. When the latter is ignored, the algorithm conveniently transforms into a solver for a hydrostatic flow. In addition, when the vertical grid spacing is larger than the layer depths, the algorithm naturally degenerates into a solver for the shallow water equations. In this paper, the presented numerical model is developed for the horizontal centrifugal casting, a metallurgical process, in which a liquid metal is poured into a horizontally rotating cylindrical mold. The centrifugal force pushes the liquid metal toward the mold wall resulting in a formation of a sleeve with a uniform thickness. The mold gradually extracts the sensible and the latent heat from the sleeve, which eventually becomes solid. Often a second layer of another material is introduced during the solidification of the first layer. The proposed free-surface model is therefore coupled with the heat advection-diffusion equation with a stiff latent heat source term representing the solidification. The numerical results show a good agreement with measurements of temperatures performed in the plant. A validation of the proposed model is also provided with the help of using other numerical techniques such as the approximate Riemann solver for the two layer shallow water equations and the volume of fluid method.

Free-surface flow in horizontally rotating cylinder: experiment and simulation

The horizontal centrifugal casting process targets on a liquid layer with a uniform thickness. To achieve this, the rotations of the mold have to be large enough so that the liquid can pick up the speed of the mold. In the present paper, an experiment was conducted using a laboratory plexi-glass mold with water as a working fluid. Starting with an initial volume fraction of liquid resting in the bottom of the mold, the mold rotations were gradually increased from 0 rpm to max rpm and a new position of the contact line was recorded. In addition, first critical rpm was recorded, at which the transition from the liquid pool to a uniform liquid layer occurred. While gradually going back from max rpm to 0 rpm, second critical rpm was recorded, at which the uniform liquid layer collapsed. The experiment was compared with the numerical simulation solving the modified shallow water equations using the Newton-Raphson method with the Wallington filter.

Modified Shallow Water Equations With Application for Horizontal Centrifugal Casting of Rolls

A numerical model based on the shallow water equations (SWE) was proposed to simulate the two-dimensional (2D) average flow dynamics of the liquid metal spreading inside a horizontally rotating mold. The SWE were modified to account for the forces, such as the centrifugal force, Coriolis force, shear force with the mold wall, and gravity. In addition, inherent vibrations caused by a poor roundness of the mold and the mold deformation due to temperature gradients were applied explicitly by perturbing the gravity and the axis bending, respectively. Several cases were studied with the following initial conditions: a constant average height of the liquid metal (5, 10, 20, 30, and 40mm) patched as a flat or a perturbed surface. The angular frequency X of the mold (11150‐3200) was 71.2 (or 30) rad/s. Results showed various wave patterns propagating on the free surface. In early stages, a single longitudinal wave moved around the circumference. As the time proceeded, it slowly diminished and waves traveled mainly in the axial direction. It was found that the mean amplitude of the oscillations grows with the increasing liquid height. [DOI: 10.1115/1.4030760]