Combined analytical and numerical solutions in liquid metal flows in a rectangular duct with uniform or non-uniform, strong magnetic fields
Ting, Aili
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https://hdl.handle.net/2142/22338
Description
Title
Combined analytical and numerical solutions in liquid metal flows in a rectangular duct with uniform or non-uniform, strong magnetic fields
Author(s)
Ting, Aili
Issue Date
1991
Doctoral Committee Chair(s)
Walker, John S.
Department of Study
Mechanical Science and Engineering
Discipline
Mechanical Science and Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Mechanical
Physics, Fluid and Plasma
Language
eng
Abstract
In order to model liquid-metal flows in self-cooled liquid-lithium blankets for magnetic-confinement fusion reactors, liquid metal flows in rectangular ducts with thin conducting walls have been treated by combining analytical methods and numerical solutions. An asymptotic method has been used in the linear stability analysis for the high-velocity side layers in an MHD duct flow with a uniform and very strong, transverse magnetic field. A composite core-side-layer approach, which combines the inviscid core region and the viscous side layer adjacent to the side wall as a whole region, but which ignores the Hartmann layers adjacent to the top and bottoms walls, has been employed for steady, two-dimensional and three-dimensional duct flow problems for any moderately strong, uniform or non-uniform magnetic fields. Spectral methods with the Chebyshev collocation method or Chebyshev-Fourier collocation method have been used successfully for the numerical solutions.
A linear stability analysis has been carried out to help understand the periodic flow observed in experiments conducted at Argonne National Lab. There are two independent eigenvalue problems. The first problem involves a disturbance vorticity which is perpendicular to the magnetic field, and these disturbances decay for all wave lengths and Reynolds numbers. The second problem involves a disturbance vorticity which is parallel to the magnetic field, and the critical Reynolds number is found. The critical disturbance involves a short axial scale and a large velocity in the direction perpendicular to the side wall. Therefore, the fluctuations produce excellent mixing inside the side layers and strongly enhance the heat transfer from the first wall, which faces the plasma, for the self-cooled liquid-lithium blankets in fusion reactors.
A planar magnetic field associated with arbitrary pole faces has been successfully calculated, as a by-product of our analysis. A fully developed MHD flow for the composite core-side-layer approach has been obtained for Hartmann numbers up to 6400. The steady, three-dimensional MHD duct flow with a gradually varying, transverse magnetic field and with a non-uniform planar magnetic field have been solved with the composite core-side-layer approach. The results show the important three-dimensional effects, which include axial currents, and transverse velocities, as well as spanwise and transverse variations of pressure, as a result of the interaction among the flow field, the electric field and the magnetic field.
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