Elevator mode convection in flows with strong magnetic fields
Abstract
Instability modes in the form of axially uniform vertical jets, also called “elevator modes,” are known to be the solutions of thermal convection problems for vertically unbounded systems. Typically, their relevance to the actual flow state is limited by threedimensional breakdown caused by rapid growth of secondary instabilities. We consider a flow of a liquid metal in a vertical duct with a heated wall and strong transverse magnetic field and find elevator modes that are stable and, thus, not just relevant, but a dominant feature of the flow. We then explore the hypothesis suggested by recent experimental data that an analogous instability to modes of slow axial variation develops in finitelength ducts, where it causes largeamplitude fluctuations of temperature. The implications for liquid metal blankets for tokamak fusion reactors that potentially invalidate some of the currently pursued design concepts are discussed.
 Authors:
 Department of Mechanical Engineering, University of MichiganDearborn, 481281491 Michigan (United States)
 Publication Date:
 OSTI Identifier:
 22403226
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; CONVECTION; DUCTS; EXPERIMENTAL DATA; FLUCTUATIONS; HYPOTHESIS; INSTABILITY; LIQUID METALS; MAGNETIC FIELDS; MATHEMATICAL SOLUTIONS; THERMONUCLEAR REACTORS; THREEDIMENSIONAL CALCULATIONS; TOKAMAK DEVICES; WALLS
Citation Formats
Liu, Li, and Zikanov, Oleg, Email: zikanov@umich.edu. Elevator mode convection in flows with strong magnetic fields. United States: N. p., 2015.
Web. doi:10.1063/1.4916901.
Liu, Li, & Zikanov, Oleg, Email: zikanov@umich.edu. Elevator mode convection in flows with strong magnetic fields. United States. doi:10.1063/1.4916901.
Liu, Li, and Zikanov, Oleg, Email: zikanov@umich.edu. 2015.
"Elevator mode convection in flows with strong magnetic fields". United States.
doi:10.1063/1.4916901.
@article{osti_22403226,
title = {Elevator mode convection in flows with strong magnetic fields},
author = {Liu, Li and Zikanov, Oleg, Email: zikanov@umich.edu},
abstractNote = {Instability modes in the form of axially uniform vertical jets, also called “elevator modes,” are known to be the solutions of thermal convection problems for vertically unbounded systems. Typically, their relevance to the actual flow state is limited by threedimensional breakdown caused by rapid growth of secondary instabilities. We consider a flow of a liquid metal in a vertical duct with a heated wall and strong transverse magnetic field and find elevator modes that are stable and, thus, not just relevant, but a dominant feature of the flow. We then explore the hypothesis suggested by recent experimental data that an analogous instability to modes of slow axial variation develops in finitelength ducts, where it causes largeamplitude fluctuations of temperature. The implications for liquid metal blankets for tokamak fusion reactors that potentially invalidate some of the currently pursued design concepts are discussed.},
doi = {10.1063/1.4916901},
journal = {Physics of Fluids (1994)},
number = 4,
volume = 27,
place = {United States},
year = 2015,
month = 4
}

The general solution is obtained to the problem on the flow of a liquid in strong magnetic fields applied normally to the flow direction. A twodimensional mathematical model is used that takes into account the Hall effect, thermoelectric currents, and the magnitude of an induced magnetic field for the case where the terms including pressure in the expression for the velocity may be neglected.