In this work, we revisit a recent transient three-dimensional (3D) model for longitudinal electromagnetic stirring in the continuous casting of rectangular steel blooms. Whereas the earlier work was able to demonstrate accurate approximations to the solutions in two asymptotic limits, both of which gave economical alternatives to time-consuming 3D computations, here we show that the original governing equations can be manipulated to a form that allows for rapid computation even outside of these asymptotic limits. The resulting formulation requires the numerical solution of two steady-state complex Helmholtz-like equations in two dimensions that are coupled via a non-standard internal interface condition that is reminiscent of that occurring in the study of Marangoni convection; these equations are then solved numerically using the finite-element software Comsol Multiphysics. With this formulation, it is possible to compute the time-averaged Lorentz force components in a way that requires around four orders of magnitude less computational time than the fully 3D approach.

A recent three-dimensional (3D) model that revisited earlier theoretical work for longitudinal electromagnetic stirring in the continuous casting of steel blooms is analyzed further to explore how the bloom width interacts with the pole pitch of the stirrer to affect the magnetic flux density. Whereas the first work indicated the presence of a boundary layer in the steel near the interface with the stirrer, with all three components of the magnetic flux density vector being coupled to each other, in the analysis presented here we find that the component along the direction of the travelling wave decouples from those in the other two directions and can even be determined analytically in the form of a series solution. Moreover, it is found that the remaining two components can be found via a two-dimensional computation, but that it is not possible in general to determine these components without taking into account the surrounding air. The validity of the asymptotically reduced model solution is confirmed by comparing it with the results of 3D numerical computations. Moreover, the asymptotic approach provides a way to compute the time-averaged Lorentz force components that requires two orders of magnitude less computational time than the fully 3D approach.

Recent work highlighting an anomaly in the modelling of rotary electromagnetic stirring (EMS) in the continuous casting of round steel billets is extended to the case of longitudinal stirring for rectangular blooms. An earlier, still often-cited, model forms the basis of the current analysis, which uses asymptotic methods on the three-dimensional (3D) Maxwell equations and demonstrates how the earlier result for the components of the Lorentz force is but a particular case of a more general form. Time-dependent 3D computations using finite-element methods are also performed to verify the validity of the asymptotic analysis, and the relevance of the results to modulated EMS is noted.

This thesis deals with two topics of relevance to the continuous casting of steel,in view of their importance as regards the quality of the final solidified structure.The first concerns the precipitation of gas pores and inclusions in the interden-dritic region of the solidifying metal. Motivated by experimental results thatindicate the formation of pore-inclusion clusters in the final cast structure, a the-oretical model is developed to describe how thus might occur; the model makesuse of the basic principles of fluid mechanics and heat transfer, with asymptoticmethods then being used in order to obtain solutions. In particular, it is foundthat soluto-thermocapillary drift in a direction perpendicular to the direction ofcasting, as a consequence of the dependence of surface tension at the pore-metalinterface on temperature and sulphur concentration, could explain cluster forma-tion. The second is a theoretical study concerning longitudinal electromagneticstirring (EMS), which is often used in the continuous casting of blooms in order toimprove product quality. Via an analysis of the three-dimensional (3D) Maxwellequations for the components of the magnetic flux density, a flaw is found inthe way that the components of the stirring Lorentz force have previously beencalculated; this is corrected and the new results are confirmed by comparison ofsolutions obtained from asymptotic analysis and time-dependent 3D computa-tions using finite-element methods. The analysis identifies the importance of theproduct of the bloom width and the wave vector of the applied field as a keydimensionless parameter.

Avhandlingen fokuserar på två frågeställningar som är relevanta för stränggjut-ning av stål med avseende på deras betydelse för kvaliteten på den stelnadestrukturen. Den första frågeställningen fokuserar på bildningen av porer och in-neslutningar i interdendritiska områden i den stelnade metallen. Experimentellaresultat påvisade en bildning av klusters bestående av porer och inneslutning-ar, vilket motiverade en utveckling av en teoretisk modell som beskriver dettafenomen. Modellen bygger på grundläggande principer för fluidmekanik och vär-meöverföring i kombination med asymptotiska metoder för att erhålla en lösningtill problemet. Resultaten visar att soluto-termokapillära driftkrafter, som ver-kar i en riktning vinkelrät mot stelningsriktningen, kan förklara uppkomsten avklusterbildningen. Specifikt så beror dessa krafter av ytspänningen vid metall-porgränsskiktet, som i sin tur påverkas av temperaturen och svavelkoncentrationen imetallen. Den andra frågeställningen är en teoretisk studie fokuserad på longitu-dinell elektromagnetisk omrörning (EMS), vilken ofta används vid stränggjutningav blooms i syfte att öka kvaliteten av det gjutna ämnet. Genom att analysera detredimensionella Maxwellekvationerna för komponenterna tillhörande magnetiskaflödestätheten, så hittades en felaktighet med avseende på hur komponenterna förLorentzkrafter tidigare beräknats. Dessa felaktigheter har korrigerats och de nyapredikteringarna med modellen har verifierats både med asymptotiska lösningaroch tredimensionella beräkningar med användande av finita elementmetoder. Re-sultaten visar på betydelsen att ta hänsyn till bredden på blooms och det användafältet som dimensionslösa parametrar vid denna typ av simuleringar

A mathematical model is derived to predict the trajectories of pores and inclusions that are nucleated in the interdendritic region during the continuous casting of steel. Using basic fluid mechanics and heat transfer, scaling analysis, and asymptotic methods, the model accounts for the possible lateral drift of the pores as a result of the dependence of the surface tension on temperature and sulfur concentration. Moreover, the soluto–thermocapillary drift of such pores prior to final solidification, coupled to the fact that any inclusions present can only have a vertical trajectory, can help interpret recent experimental observations of pore-inclusion clusters in solidified steel castings.

The possibility of cluster formation during solidication of steel is explored to explain structures that are seen on the fracture surface of the steel. A hypothesis is built that postulates porosities provide favourable locations for inclusions to agglomerate and form clusters.  A thermodynamic model is constructed to describe precipitation of porosity and inclusions. Formation of inclusions follow a nucleation and growth mechanism. Porosities on the other hand are the product of pressure balance in the liquid.  Motion of pores and inclusions is analysed based on the drag force and  surface  stresses. Gradient of surface tension is also identied as a driving force which acts on the pore surface and would cause motion. It is shown that relative motion of pores and inclusions coupled with  the inclusion tendency to get attached on pore surface makes or a viable mechanism explaining agglomeration of inclusion particles to clusters

There is a relationship between pores and inclusions. Inclusions and pores are both formed during solidification inside the interdendritic melt. As hypothesis goes, porosity moves to absorb inclusions and form clusters. Focus of this paper is how solidified dendritic structure affects pore precipitation in austenitic stainless steel. Steel sample is a continuously cast bloom. Temperature profile and width of the mushy zone of the strand is modeled according to a constant temperature at the strands surface. Thermal analysis has been performed with differential thermal analysis (DTA) and differential scanning calorimeter (DSC). Primary dendrite arm spacing (PDAS) is measured with light optical microscopy (LOM) and scanning electron microscopy (SEM). PDAS is represented as the weight average of the distance between parallel sets of primary dendrite stems. Pressure field is calculated based on Darcy's law. Pore formation is described through segregation of the gas components and pressure field in the liquid.

Formation mechanism and clustering of TiN-Al2O3 inclusions precipitated during solidification of austenitic stainless steel is analyzed in this paper. Steel sample are taken from a continuously cast bloom. Clustering of inclusions was examined with a hypothesis that inclusions gather inside the pores. Precipitation of the inclusions occurs through segregation in the residual melt in the interdendritic area. Size and mean distance of the inclusion particles are calculated with mass balance. Impact fracture test in cryogenic temperature reveals clusters of inclusions inside pores on the fracture surface. Size and distribution of the inclusions are examined using light optical microscopy and scanning electron microscopy. Inclusion's composition is investigated with energy dispersive X-ray spectroscopy analysis. Differential thermal analysis and differential scanning calorimetry Tests determined the transformation temperatures. Results of the experiments are in good agreement with theoretical analysis.