Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field
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 consis...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-10-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/4/4/177 |
| _version_ | 1811286167284350976 |
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| author | Toshio Tagawa |
| author_facet | Toshio Tagawa |
| author_sort | Toshio Tagawa |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T02:55:39Z |
| format | Article |
| id | doaj.art-26ae1c0b58a74e438db8247d6dbc2f0d |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-04-13T02:55:39Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-26ae1c0b58a74e438db8247d6dbc2f0d2022-12-22T03:05:40ZengMDPI AGFluids2311-55212019-10-014417710.3390/fluids4040177fluids4040177Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic FieldToshio Tagawa0Department of Aeronautics and Astronautics, Tokyo Metropolitan University, Hino, Tokyo 191-0065, JapanLinear 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.https://www.mdpi.com/2311-5521/4/4/177hartmann numberliquid metal flowlinear stabilitynewton—raphson methodhighly simplified marker and cell (hsmac) method |
| spellingShingle | Toshio Tagawa Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field Fluids hartmann number liquid metal flow linear stability newton—raphson method highly simplified marker and cell (hsmac) method |
| title | Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field |
| title_full | Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field |
| title_fullStr | Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field |
| title_full_unstemmed | Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field |
| title_short | Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field |
| title_sort | linear stability analysis of liquid metal flow in an insulating rectangular duct under external uniform magnetic field |
| topic | hartmann number liquid metal flow linear stability newton—raphson method highly simplified marker and cell (hsmac) method |
| url | https://www.mdpi.com/2311-5521/4/4/177 |
| work_keys_str_mv | AT toshiotagawa linearstabilityanalysisofliquidmetalflowinaninsulatingrectangularductunderexternaluniformmagneticfield |