Kurenkov, Oleksiy (2005)
Reconstruction and stability analysis of interfaces between electrically conducting fluids.
Technische Universität Ilmenau
Dissertation, Bibliographie

Kurzbeschreibung (Abstract)

The topic of this thesis is the linear stability analysis and reconstruction of an unstable aluminium-cryolite interface in an aluminium reduction cell with background flow and the reconstruction of the aluminum-cryolite interface. Two reconstruction problems are considered. In the first one the interface was reconstructed from the electric potential perturbation and in the second one from the magnetic field perturbation. Both perturbations resulted from the deviation of the aluminium-cryolite interface from its flat shape. The stability analysis of the aluminium reduction cell was performed on a simplified geometrical model. The propagation of gravitational waves in the infinite channel with insulating channel walls was observed. Homogeneous vertical electrical current and magnetic field were applied. Navier-Stokes equations were written in the shallow water approximation and then linearized. The stability thresholds are formed by the dimensionless velocity of the background flow and the MHD-parameter. Also the aspect ratio and the material parameter influence the stability limits. It is found that the Kelvin-Helmholtz instability and the MHD- instability do not influence each other. The reconstruction of the interface in aluminium reduction cells from electrical potential measurement contains two classes of different problems. The forward problem concerns with the calculation of the electrical potential in the fluids if the interface shape between aluminium and cryolite is known. The inverse problem concerns with the determination of the unknown interface from a known potential distribution. In order to solve the forward problem the governing equations are linearized and solved analytically. The inverse problem was solved using standard techniques such as singular value decomposition (SVD). The optimal solution, which shows a compromise between data error and solution error, was found using a L-curve criterion. A numerical experiment is performed in order to validate the presented reconstruction method, which shows the robustness of the method with respect to the measurement error. For the reconstruction of the interface from magnetic field the forward problem was solved. The geometry under consideration contains an infinitely long rod with insulating walls and arbitrary form of the cross-section. Two fluids with different electrical conductivities and densities are superimposed. The vertical homogeneous electrical current flows throw the interface. The perturbation of the magnetic field and perturbation of electrical current are computed. Two examples are computed, one for a cylindrical and another for a rectangular cross-sections.

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