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An analytical solution to electromagnetically coupled duct flow in MHD

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Title: An analytical solution to electromagnetically coupled duct flow in MHD
Authors: Bluck, MJ
Wolfendale, MJ
Item Type: Journal Article
Abstract: The flow of an electrically conducting fluid in an array of square ducts, separated by arbitrary thickness conducting walls, subject to an applied magnetic field is studied. The analytical solution presented here is valid for thick walls and is based on the homogeneous solution obtained by Shercliff (Math. Proc. Camb. Phil. Soc., vol. 49 (01), 1953, pp. 136-144). Arrangements of ducts arise in a number of applications, most notably in fusion blankets, where liquid metal is used both as coolant and for tritium generation purposes. Analytical solutions, such as those presented here, provide insight into the physics and important benchmarking and validation data for computational magnetohydrodynamics (MHD), as well as providing approximate flow parameters for 1D systems codes. It is well known that arrays of such ducts with conducting walls exhibit varying degrees of coupling, significantly affecting the flow. An important practical example is the so-called Madarame problem (Madarame et al., Fusion Technol., vol. 8, 1985, pp. 264-269). In this work analytical results are derived for the relevant hydrodynamic and magnetic parameters for a single duct with thick walls analogous to the Hunt II case. These results are then extended to an array of such ducts stacked in the direction of the applied magnetic field. It is seen that there is a significant coupling affect, resulting in modifications to pressure drop and velocity profile. In certain circumstances, counter-current flow can occur as a result of the MHD effects, even to the point where the mean flow is reversed. Such phenomena are likely to have significant detrimental effects on both heat and mass transfer in fusion applications. The dependence of this coupling on parameters such as conductivities, wall thickness and Hartmann number is studied.
Issue Date: 25-May-2015
Date of Acceptance: 27-Mar-2015
URI: http://hdl.handle.net/10044/1/21944
DOI: 10.1017/jfm.2015.202
ISSN: 0022-1120
Publisher: Cambridge University Press
Start Page: 595
End Page: 623
Journal / Book Title: Journal of Fluid Mechanics
Volume: 771
Issue: 1
Copyright Statement: © 2015 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
materials processing flows
mathematical foundations
MHD and electrohydrodynamics
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Online Publication Date: 2015-04-23
Appears in Collections:Mechanical Engineering
Faculty of Engineering

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