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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2016007441
pages 471-488

EFFECTS OF AXIAL MAGNETIC FIELD AND THERMAL CONVECTION ON A COUNTERROTATING VON KARMAN FLOW

Lyes Bordja
Faculte des Sciences et Technologie, Dept. Genie Mecanique, Universite Cheikh Larbi Tebessi, Tebessa-12002, Algeria
Emilia Crespo del Arco
Departamento de Fisica Fundamental, U.N.E.D., Apdo. Correos 60.141, 28080 Madrid, Spain
Eric Serre
Aix-Marseille Universite, CNRS, Ecole Centrale Marseille, Laboratoire M2P2, Marseille, France
Rachid Bessaih
L.E.A.P, Dept. Genie Mecanique, Universite Mentouri de Constantine, Route d'Ain El Bey, 25000 Constantine, Algeria

ABSTRACT

The effects of thermal convection and of a constant axial magnetic field on a von Karman flow driven by the exact counterrotation of two lids are investigated in a vertical cylinder of aspect ratio Γ(= height/radius) = 2 at a fixed Reynolds number Re(= Ω R2/v) = 300. Direct numerical simulations are performed when varying separately the Rayleigh and Hartmann numbers in the range [0, 1800] and [0, 20], respectively, in the limit of the Boussinesq approximation and of a small magnetic Reynolds numbers, Rem << 1. Without a magnetic field, the base flow symmetries of the von Karman flow are broken by thermal convection that becomes dominant in the range of Ra [500, 1000]. Three-dimensional solutions are characterized by the occurrence of a steady, m = 1, azimuthal mode exhibiting a cat's eye vortex in the circumferential plane. When increasing the Rayleigh number in the range [500, 1000], the vortex pulsates in an oscillatory manner, due to variations of the flow intensity. Otherwise, increasing the axial magnetic field intensity stabilizes the flow, and the oscillatory motion can be inhibited. Numerical solutions show that the critical Rayleigh number for transition increases linearly with the Hartmann number. Finally, results show that when varying the Rayleigh number, the structure of the electric potential can be strongly modified by thermal convection. Such an observation suggests new induction mechanisms in the case of small nonzero values of the magnetic Reynolds number.


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