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Fluids
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Numerical Analysis of Magnetohydrodynamic Flows
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Numerical Analysis of Magnetohydrodynamic Flows

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (31 October 2019) | Viewed by 22673

Special Issue Editor

Dr. Toshio Tagawa

E-Mail Website
Guest Editor
Department of Aeronautics and Astronautics, Tokyo Metropolitan University, Tokyo 191-0065, Japan
Interests: computational fluid dynamics; magnetohydrodynamics; modeling of interfacial flows; thermal convection; thermocappilary convection; centrifugal force; taylor–couette flow; boundary layer; transition stability
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Magnetohydrodynamics (MHD) is a field of study combined by the fluid mechanics and electromagnetism. The flow of conducting materials are substantially influenced by the electromagnetic force, i.e., J x B force. This mechanism has been widely applied to various industries, such as steel-making processes, semiconductor crystal growth, liquid metal blankets in nuclear fusion reactors, electromagnetic pumps, electromagnetic levitation of drop, dynamo simulation of planets, and so on. Related to these processes, it is necessary to investigate fundamental MHD flows such as natural convection, free-surface, rotational flows, as well as the flows in ducts or pipes. Chandraskar studied the magnetohydordynamic stability for fundamental flows (Rayleigh-Bénard convection or Taylor-Couette flow) extensively owing to his mathematical ability without direct use of the numerical analysis. Nowadays, due to the developments of both the computational resources and its techniques, more complex MHD flows are now being investigated through numerical analyses. This Special Issue focuses on numerical techniques for analysing complex MHD flows, for instance, 1) the method of how to solve induction equations expressed by the magnetic field or the magnetic vector potential, 2) free-surface MHD flows, 3) stability analysis for MHD flows, 4) MHD flows caused by alternating magnetic fields (moving, rotating or oscillating magnetic field), and 5) high Hartmann number flows.

Dr. Toshio Tagawa
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

  • induction equation
  • Hartmann number
  • stability analysis
  • alternating magnetic field

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Published Papers (6 papers)

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Editorial

Jump to: Research

2 pages, 148 KiB  
Editorial
Numerical Analysis of Magnetohydrodynamic Flows
by Toshio Tagawa
Fluids 2020, 5(1), 23; https://doi.org/10.3390/fluids5010023 - 10 Feb 2020
Cited by 3 | Viewed by 2467
Abstract
Magnetohydrodynamics (MHD) is a field of study combined by the fluid mechanics and electromagnetism [...] Full article
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamic Flows)

Research

Jump to: Editorial

21 pages, 5193 KiB  
Article
Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field
by Toshio Tagawa
Fluids 2019, 4(4), 177; https://doi.org/10.3390/fluids4040177 - 1 Oct 2019
Cited by 8 | Viewed by 3860
Abstract
Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing [...] Read more.
Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing equations consisted of the continuity of mass, momentum equation, Ohm’s law, and conservation of electric charge. A set of linearized disturbance equations for the complex amplitude was decomposed into real and imaginary parts and solved numerically with a finite difference method using the highly simplified marker and cell (HSMAC) algorithm on a two-dimensional staggered mesh system. The difficulty of the complex eigenvalue problem was circumvented with a Newton—Raphson method during which its corresponding eigenfunction was simultaneously obtained by using an iterative procedure. The relation among the Reynolds number, the wavenumber, the growth rate, and the angular frequency was successfully obtained for a given value of the Hartmann number as well as for a direction of external uniform magnetic field. Full article
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamic Flows)
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23 pages, 7341 KiB  
Article
Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field
by Toshio Tagawa and Kewei Song
Fluids 2019, 4(2), 77; https://doi.org/10.3390/fluids4020077 - 21 Apr 2019
Cited by 8 | Viewed by 4319
Abstract
The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and [...] Read more.
The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of the basic flow for the case of an infinitely long cylinder depends on the number of pole-pairs and the Hartmann number. A set of linearized disturbance equations to obtain a neutral state was successfully solved using the highly simplified marker and cell (HSMAC) method together with a Newton–Raphson method. For various cases of the basic flow, depending on both the number of pole-pairs and the Hartmann number, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The linear stability analyses reveal that the critical Reynolds number takes its minimum at a certain value of the Hartmann number. On the other hand, the velocity profile for cases of a finite length cylinder having a no-slip condition at the flat walls generates the Bödewadt boundary layers and such flows need to be computed including the non-linear terms of the Navier-Stokes equation. Full article
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamic Flows)
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17 pages, 2249 KiB  
Article
Thermomagnetic Convection of Paramagnetic Gas in an Enclosure under No Gravity Condition
by Kewei Song, Shuai Wu, Toshio Tagawa, Weina Shi and Shuyun Zhao
Fluids 2019, 4(1), 49; https://doi.org/10.3390/fluids4010049 - 15 Mar 2019
Cited by 7 | Viewed by 3342
Abstract
The thermomagnetic convection of paramagnetic gaseous oxygen in an enclosure under a magnetic field was numerically studied to simulate the thermomagnetic convection in a space environment with no gravity. The magnetic field in the enclosure was non-uniform and was generated by a permanent [...] Read more.
The thermomagnetic convection of paramagnetic gaseous oxygen in an enclosure under a magnetic field was numerically studied to simulate the thermomagnetic convection in a space environment with no gravity. The magnetic field in the enclosure was non-uniform and was generated by a permanent magnet which had a high magnetic energy product. The magnet was placed at different locations along one of the adiabatic walls with magnetic poles perpendicular to the hot and cold walls of the enclosure. The heat transfer performance, flow field, and temperature field were studied with each location of the magnet. The results show that the thermomagnetic convection in the enclosure was obviously affected by the location of the magnet. There was an optimum magnet location in terms of the best heat transfer performance in the enclosure. The optimum magnet location changed slightly and moved toward the hot wall as the magnetic flux density increased. The value of the Nusselt number, defined as the ratio of convection to conduction, reached up to 2.54 in the studied range of parameters. By optimizing the magnet location, the convection was enhanced by up to 77% at the optimum magnet location. Full article
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamic Flows)
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28 pages, 14347 KiB  
Article
Extended Magnetohydrodynamic Simulations of Decaying, Homogeneous, Approximately-Isotropic and Incompressible Turbulence
by Hideaki Miura
Fluids 2019, 4(1), 46; https://doi.org/10.3390/fluids4010046 - 11 Mar 2019
Cited by 13 | Viewed by 3268
Abstract
Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence. Numerical results were compared among MHD, Hall MHD, and extended MHD models focusing on [...] Read more.
Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence. Numerical results were compared among MHD, Hall MHD, and extended MHD models focusing on differences of Hall and extended MHD turbulence from MHD turbulence at a fully relaxed state. Magnetic and kinetic energies, energy spectra, energy transfer, vorticity and current structures were studied. The Hall and gyro-viscous terms change the energy transfer in the equations of motions to be forward-transfer-dominant while the magnetic energy transfer remains backward-transfer-dominant. The gyro-viscosity works as a kind of hyper-diffusivity, attenuating the kinetic energy spectrum sharply at a high wave-number region. However, this term also induces high-vorticity events more frequently than MHD turbulence, making the turbulent field more intermittent. Vortices and currents were found to be transformed from sheet to tubular structures under the influences of the Hall and/or the gyro-viscous terms. These observations highlight features of fluid-dynamic aspect of turbulence in sub-ion-scales where turbulence is governed by the ion skin depth and ion Larmor radius. Full article
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamic Flows)
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21 pages, 10742 KiB  
Article
Identification of the Structures for Low Reynolds Number Flow in the Strong Magnetic Field
by Łukasz Pleskacz and Elzbieta Fornalik-Wajs
Fluids 2019, 4(1), 36; https://doi.org/10.3390/fluids4010036 - 25 Feb 2019
Cited by 6 | Viewed by 3353
Abstract
Thermomagnetic convection is still a phenomenon which generates interest among researchers. The authors decided to focus their attention on the magnetic field influence on forced convection and analyze the extended Graetz–Brinkman problem. A numerical model based on a commonly available solver implemented with [...] Read more.
Thermomagnetic convection is still a phenomenon which generates interest among researchers. The authors decided to focus their attention on the magnetic field influence on forced convection and analyze the extended Graetz–Brinkman problem. A numerical model based on a commonly available solver implemented with user-defined functions was used. The results exhibited the variety of possible flow structures depending on the dimensionless parameters, namely Prandtl and Reynolds numbers. Three flow structure classes were distinguished, and they provide a platform for further research. Full article
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamic Flows)
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