Theoretical magnetohydrodynamic and solidification studies of continuous strip casting
Abstract: The continuous casting of steel strips has been under investigation and development for several decades. The aim of this development is to be able to cast steel strips in a thickness range from 1 to 10 mm. Today, there are basically two such methods: the single-belt caster and the twin-roll caster. The advantage of these methods in comparison with the more conventionally produced strips, produced from slab-casting and hot-rolling, is that there is considerable energy savings if a continuous strip casting process can be successfully developed. In this thesis we consider the fluid dynamics and solidification process of the single-belt caster. This technique is used in a pilot-plant at MEFOS in Luleå, and in laboratory scale casters at the Clausthal University and at the Division of Fluid Mechanics at Luleå University of Technology. In this process the liquid metal is fed onto a single endless horizontal belt that runs between two rollers. The underside of the belt is cooled by water. The demands of the strip casting process regarding the shape and surface conditions of the strip are higher the smaller the thickness of the strip. Critical factors for the surface and the shape of the strip are the flow and the solidification conditions of the liquid metal at the feeding point onto the conveyor belt. One condition to be satisfied in the design of the feeding system, is that the average relative velocity between the liquid and the belt should not be too large, in order to avoid strong hydraulic jumps and turbulence. There are many different techniques for feeding the liquid metal onto the conveyor belt. The feeding systems in use are basically driven by gravity or pressure. In our study we consider the feeding through a slit or down an inclined plane. This generates approximately flat jets, falling vertically or obliquely onto the belt, with a nearly two-dimensional spreading in the casting direction. An interesting concept in the control of many metallurgical flows is to use electromagnetic forces. It is well known that magnetic fields may brake and stabilize liquid metal flow. In this thesis we analyse how the fluid dynamic conditions of the single-belt casting process can be improved with the application of a transverse DC magnetic field. The main complexity in the analysis of this kind of flow is the unknown position of the free surface and the occurrence of a hydraulic jump. It is found that with a sufficiently large ratio of the belt velocity to jet velocity the hydraulic jump can be eliminated. In this case, however, the characteristic distance it takes to decelerate the liquid metal smoothly to its final state, of constant thickness and uniform velocity, is very long. With the application of the magnetic field, this braking distance can be decreased considerably. As an example, a braking length of 0.25 m is achieved with a magnetic field of about 0.2 Tesla. A uniform velocity profile is favourable for flow stability and for the solidification process. From the solidification point of view, a homogenous velocity distribution is favourable since this causes minimum macrosegregation of the solidified strip. In the final state of constant thickness and uniform velocity distribution, which can be reached in a short distance with the application of a magnetic field, one therefore has good control of the solidification and the solidification process can easily be analysed. In the stability analysis we find two types of instabilities associated with this kind of flow. These are the surface mode and the shear modes. The stabilization of these modes can be accomplished with a moderate magnetic field of the order of 0.1 Tesla. From the stability point of view the transverse magnetic field acts in two ways. First, the field modifies the velocity profile due to the braking action into a more favourable "relaxed" profile. This is the most important stabilizing effect for weak magnetic fields of the order of 0.1 Tesla. Secondly, there is a resistive damping effect, which is small for weak magnetic fields. For the case of a uniform velocity distribution this is the only damping mechanism of the field. Therefore, in order to get an appreciable damping of ordinary gravity waves a stronger magnetic field of the order 1 Tesla is necessary. If the braking action of such a strong transverse magnetic field is too violent, a longitudinal magnetic field may be of interest. A longitudinal field causes no braking of the flow, but the resistive damping is still operative. The quality of the solidified steel depends to a large extent upon the degree of control during solidification. The solidification issues are therefore of great importance. Single-belt castings are characterized by an asymmetrical solidification structure, where the dendrites grow from the heat-extracting boundary towards the free surface of the casting. The resulting structure is finer on the contact side, due to the higher heat transfer rate, and coarsens across the thickness of the strip. The solidification process is primarily controlled by the heat transfer. Heat flows from the liquid metal to the heat-extracting conveyor belt. When the liquid metal reaches fusion temperature it solidifies onto a growing shell of steady state shape that is continuously conveyed downstream. The main difficulty in the determination of the growth of the solidification front is the coupling between heat and fluid flow. For the case of constant material properties, the heat flow is coupled to the fluid flow in terms of advection and the fluid flow is coupled to the heat flow by the boundary conditions at the solidification front. In this study we derive analytical results for the initial solidification process of a pure liquid metal over a moving boundary with a finite heat transfer coefficient. For the case of zero superheat in the melt, the initial growth of the solidified metal is immediate and linear. On the other hand, by contrast, for a weakly superheated melt the initial solidification is delayed somewhat with an initially quadratic growth of the solidification front. Further downstream the growth of the solidifying interface tends to the ideal case with a square root growth. In this thesis we also present the fluid flow at the stagnation point of the feeding jet as well as the boundary layer flow over an ideal solidification front. These solutions are useful in the determination of the morphological instabilities of the solidifying interface.
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