Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels

We show that the full set of magnetohydrodynamic (MHD) equations, for resistive and viscous incompressible fluids, allows in cylindrical coordinates an exact reduction to a pair of coupled, nonlinear, ordinary differential equations (ODE) for two scalar potentials. The ODEs represent self-similar MH...

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Autores principales: Gnavi, G., Gratton, F.T.
Formato: JOUR
Materias:
Channel flow
Flow control
Liquid metals
Navier Stokes equations
Ordinary differential equations
Partial differential equations
Reynolds number
Divergent-convergent channels
Magnetohydrodynamic flows
Magnetohydrodynamics
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p99_Gnavi
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03928764_v21_n1_p99_Gnavi2023-10-03T15:33:56Z Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels Gnavi, G. Gratton, F.T. Channel flow Flow control Liquid metals Navier Stokes equations Ordinary differential equations Partial differential equations Reynolds number Divergent-convergent channels Magnetohydrodynamic flows Magnetohydrodynamics We show that the full set of magnetohydrodynamic (MHD) equations, for resistive and viscous incompressible fluids, allows in cylindrical coordinates an exact reduction to a pair of coupled, nonlinear, ordinary differential equations (ODE) for two scalar potentials. The ODEs represent self-similar MHD flows in channels, bounded by non-parallel plane walls, intersecting on the z-axis, akin to the Jeffery-Hamel flows of non-conducting fluids. We consider the case in which an external current, flows along the z-axis, and exerts a body force that controls the flow. Only one nonlinear ODE governs the solution in this case. Besides the Reynolds number (Re) and the angle of the walls, two other non dimensional parameters determine the solutions, the magnetic Reynolds number (Rm), and the Hartmann number (Ha). We give a preliminary study of the properties of the high resistivity regime, in which the Hartmann number becomes important. The main result is that for Ha larger than 2 the flow reversal near the walls, which is a typical feature of channels with Ha=0 and Re∼O(1) or larger, tends to disappear. Moderate values of Ha∼6 are sufficient to suppress flow reversal up to Re∼25 for angular widths of the channel as large as 240°. The configuration may be of interest for applications to flow control of liquid metals, and industrial treatment of molten metals. Fil:Gnavi, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gratton, F.T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p99_Gnavi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Channel flow
Flow control
Liquid metals
Navier Stokes equations
Ordinary differential equations
Partial differential equations
Reynolds number
Divergent-convergent channels
Magnetohydrodynamic flows
Magnetohydrodynamics
spellingShingle Channel flow
Flow control
Liquid metals
Navier Stokes equations
Ordinary differential equations
Partial differential equations
Reynolds number
Divergent-convergent channels
Magnetohydrodynamic flows
Magnetohydrodynamics
Gnavi, G.
Gratton, F.T.
Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
topic_facet Channel flow
Flow control
Liquid metals
Navier Stokes equations
Ordinary differential equations
Partial differential equations
Reynolds number
Divergent-convergent channels
Magnetohydrodynamic flows
Magnetohydrodynamics
description We show that the full set of magnetohydrodynamic (MHD) equations, for resistive and viscous incompressible fluids, allows in cylindrical coordinates an exact reduction to a pair of coupled, nonlinear, ordinary differential equations (ODE) for two scalar potentials. The ODEs represent self-similar MHD flows in channels, bounded by non-parallel plane walls, intersecting on the z-axis, akin to the Jeffery-Hamel flows of non-conducting fluids. We consider the case in which an external current, flows along the z-axis, and exerts a body force that controls the flow. Only one nonlinear ODE governs the solution in this case. Besides the Reynolds number (Re) and the angle of the walls, two other non dimensional parameters determine the solutions, the magnetic Reynolds number (Rm), and the Hartmann number (Ha). We give a preliminary study of the properties of the high resistivity regime, in which the Hartmann number becomes important. The main result is that for Ha larger than 2 the flow reversal near the walls, which is a typical feature of channels with Ha=0 and Re∼O(1) or larger, tends to disappear. Moderate values of Ha∼6 are sufficient to suppress flow reversal up to Re∼25 for angular widths of the channel as large as 240°. The configuration may be of interest for applications to flow control of liquid metals, and industrial treatment of molten metals.
format JOUR
author Gnavi, G.
Gratton, F.T.
author_facet Gnavi, G.
Gratton, F.T.
author_sort Gnavi, G.
title Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_short Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_full Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_fullStr Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_full_unstemmed Magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
title_sort magnetohydrodynamic flows of conducting liquids in divergent-convergent channels
url http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p99_Gnavi
work_keys_str_mv AT gnavig magnetohydrodynamicflowsofconductingliquidsindivergentconvergentchannels
AT grattonft magnetohydrodynamicflowsofconductingliquidsindivergentconvergentchannels
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