Alexander Vakhrushev

Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold

The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The importance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the turbulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed.

Modeling of the flow-solidification interaction in thin slab casting

A key issue for modelling the thin slab casting (TSC) is to consider the evolution of the solid shell, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel shape (curvature) of the mould. Here an enthalpy-based mixture solidification model with consideration of turbulent flow (Prescott and Incropera, ASME HTD, vol. 280, 1994, pp. 59) is employed, and further enhanced to include the deforming solid shell. The solid velocity in the fully-solidified strand shell and partially-solidified mushy zone is estimated by solving the Laplaces equation. Primary goals of this work are to examine the sensitivity of the modelling result to different model implementation schemes, and to explore the importance of the deforming and moving solid shell in the solidification. Therefore, a 2D benchmark, to mimic the solidification and deformation behaviour of the thin slab casting, is firstly simulated and evaluated. An example of 3D TSC is also presented. Due to the limitation of the current computation resources additional numerical techniques like parallel computing and mesh adaptation are necessarily applied to ensure the calculation accuracy for the full-3D TSC.

Simulation of Crystal Sedimentation and Viscoplastic Behavior of Sedimented Equiaxed Mushy Zones

During solidification of castings, equiaxed crystals that is formed sink downwards, sediment and form a packed bed. The behavior of separated moving crystals can be described by a submerged object approach, whereas the viscoplastic behavior of a semi-solid slurry follows a volume-averaged viscoplastic constitutive equation. In this work, a two-phase Eulerian–Eulerian volume-averaging approach is used to combine both flow regimes. The transition happens at a certain solid volume fraction, the so-called coherency limit. Starting with a uniform distribution of crystals at rest, sedimentation and packing of crystals are described. In addition, the material density of the crystal is assumed to increase on cooling and thus the domain shrinks which is also accounted for in this report. It is demonstrated how sensitive the model is, on the considered crystal diameters and on the assumed value for the coherency limits.

Two-phase modelling of equiaxed crystal sedimentation and thermomechanic stress development in the sedimented packed bed

During many industrial solidification processes equiaxed crystals form, grow and move. When those crystals are small they are carried by the melt, whereas when getting larger they sediment. As long as the volume fraction of crystals is below the packing limit, they are able to move relatively free. Crystals being backed in a so called packed bed form a semi-solid slurry, which may behave like a visco-plastic material. In addition, cooling-induced density increase of both, liquid and solid phases might lead to shrinkage of the whole casting domain. So deformation happens and gaps between casting and mold occur. In the present work, a two-phase Eulerian-Eulerian volume averaging model for describing the motion of equiaxed crystals in the melt is combined with a similar two-phase model for describing the dynamic of the packed bed. As constitutive equation for the solid skeleton in the packed bed Norton-Hoff law is applied. Shrinkage induced by density changes in the liquid or the solid phase is explicitly taken into account and handled by remeshing the calculation domain accordantly.

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.

Influence of forced convection on solidification and remelting in the developing mushy zone

The mushy zone and solid shell formed during solidification of a continuous casting are mostly uneven, and this unevenness of shell growth might lead to surface defects or breakout. One known example is the unevenness of shell growth at the impingement point between the jet flow (coming from submerged entry nozzle) and the solidification front. This phenomenon is primarily understood as the local remelting caused by the superheat of the melt, which is continuously brought by the jet flow towards the solidification front. A recent study of the authors [Metall. Mater. Trans. B, 2014, in press] hinted that, in addition to the aforementioned superheat-induced local remelting (1), two other factors also affect the shell growth. They are (2) the advection of latent heat in the semi-solid mushy zone and (3) the enhanced dissipation rate of energy by turbulence in the bulk-mush transition region. This paper is going to perform a detailed numerical analysis to gain an insight into the flow-solidification interaction phenomena. Contributions of each of the above factors to the shell formation are compared.

Advanced Process Simulation of Solidification and Melting

At some stage in the production of every metal part or product, the metal material has been melted and solidified to form the primary or final shape as well as the as-cast structure. Quantitative prediction and control of solidification and melting has been, and remains, the most critical issue in the metallurgical industry. Example questions currently raised by the Austrian metallurgical industry, which is one of the key economic sectors of this country, are as follows: in thin-slab casting, how does the solid shell form and interact with turbulent flow? How can the electro-slag-remelting (ESR) process be better understood and controlled (stabilized)? How can metallurgical imperfections (macrosegregation, porosity, non-metallic inclusion, surface crack, etc.) in castings be predicted and minimized? Therefore, a Christian-Doppler laboratory—Advanced Process Simulation of Solidification and Melting was established in July 2011 with the final goal to address the questions mentioned above. This article reports on some progresses.ZusammenfassungSo gut wie jeder metallische Werkstoff wurde im Laufe seines Herstellprozesses ein- oder mehrmals er- bzw. umgeschmolzen und anschließend erstarrt. Dabei bildete sich ein Gussgefüge mit charakteristischen Gefügemerkmalen (Korngröße, Textur, Lunker, Poren, Seigerung, usw.), welche die Gebrauchseigenschaften des Produkts wesentlich beeinflussen. Quantitative Prognosen zur Kontrolle von Schmelz- und Erstarrungsvorgängen sind deshalb in der gesamten metallurgischen Industrie von entscheidender Bedeutung. Beispielsweise werden folgende Fragen von der österreichischen metallurgischen Industrie, welche als einer der ökonomischen Schlüsselsektoren des Landes gilt, aufgeworfen. Wie bildet sich die Strangschale von Strangguss im Kokillenbereich und wie interagiert diese mit der turbulenten Strömung? Wie kann der Elektro-Schlacke-Umschmelzen (ESU) Prozess besser verstanden und gesteuert (stabilisiert) werden? Wie können die metallurgisch unerwünschten Imperfektionen in den Gussteilen vorhergesagt und minimiert werden? Zur Klärung dieser Fragen wurde im Juli 2011 ein Christian Doppler Labor für Prozesssimulation von Erstarrungs- und Umschmelzvorgängen eingerichtet. Über diesbezügliche Forschungsfortschritte wird im Rahmen dieses Artikels berichtet.