The linear stability of a fully developed liquid–metal magnetohydrodynamic pipe flow subject to a transverse magnetic field is studied numerically. Because of the lack of axial symmetry in the mean velocity profile, we need to perform a BiGlobal stability analysis. For that purpose, we develop a two-dimensional complex eigenvalue solver relying on a Chebyshev–Fourier collocation method in physical space. By performing an extensive parametric study, we show that in contrast to the Hagen–Poiseuille flow known to be linearly stable for all Reynolds numbers, the magnetohydrodynamic pipe flow with transverse magnetic field is unstable to three-dimensional disturbances at sufficiently high values of the Hartmann number and wall conductance ratio. The instability observed in this regime is attributed to the presence of velocity overspeed in the so-called Roberts layers and the corresponding inflection points in the mean velocity profile. The nature and characteristics of the most unstable modes are investigated, and we show that they vary significantly depending on the wall conductance ratio. A major result of this paper is that the global critical Reynolds number for the magnetohydrodynamic pipe flow with transverse magnetic field is Re = 45 230, and it occurs for a perfectly conducting pipe wall and the Hartmann number Ha = 19.7.
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April 2023
Research Article|
April 17 2023
On the instability of the magnetohydrodynamic pipe flow subject to a transverse magnetic field
Y. Velizhanina
;
Y. Velizhanina
(Formal analysis, Investigation, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
Physique des Systèmes Dynamiques, Faculté des Sciences, Université Libre de Bruxelles
, Boulevard du Triomphe CP231, 1050 Ixelles, Belgium
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B. Knaepen
B. Knaepen
a)
(Formal analysis, Funding acquisition, Investigation, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
Physique des Systèmes Dynamiques, Faculté des Sciences, Université Libre de Bruxelles
, Boulevard du Triomphe CP231, 1050 Ixelles, Belgium
a)Author to whom correspondence should be addressed: [email protected]
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a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 35, 044112 (2023)
Article history
Received:
March 07 2023
Accepted:
March 29 2023
Citation
Y. Velizhanina, B. Knaepen; On the instability of the magnetohydrodynamic pipe flow subject to a transverse magnetic field. Physics of Fluids 1 April 2023; 35 (4): 044112. https://doi.org/10.1063/5.0149639
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