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Numerical study of disk driven rotating MHD flow of a liquid metal in a cylindrical enclosure

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Summary

A numerical study of the steady laminar MHD flow driven by a rotating disk at the top of a cylinder filled with a liquid metal is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. The effect of an axial magnetic field on the flow is investigated for an aspect ratioH/R equal to 1. The magnetic Reynolds number is assumed to be small whereas the interaction parameter,N, is large compared to unity. This allows to derive asymptotic results for the flow solution which are found in good agreement with the numerical calculations. The effect of the top, botton and vertical walls conductivity on the flow is studied. Various combinations of these conductivities are considered. The results obtained showed that one can control the primary flow through a good choice of the electrical conductivity of both the disk and cylinder walls.

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Abbreviations

B :

Magnetic field

H :

Height of the cylinder

Ha:

Hartmann number

jz :

Axial electric current

N :

Interaction parameter

P :

Dimensionless pressure

R :

Radius of the cylinder

Re:

Reynolds number

R m :

Magnetic Reynolds number

r :

Dimensionless radius

V r :

Dimensionless radial velocity

V z :

Dimensionless axial velocity

V ϑ :

Dimensionless azimuthal velocity

Z :

Dimensionless height

ϱ:

Density of the fluid

v :

Kinematic viscosity

μ:

Dynamic viscosity

σ:

Electrical conductivity

Ω:

Angular velocity

φ:

Dimensionless electric potential

δ:

Thickness of the Ekman layer

Δ:

Laplacian operator

Δr :

Increment of the grid in the radial direction

ΔZ :

Increment of the grid in the axial direction

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Author notes

  1. R. Bessaih & M. Kadja

    Present address: Inst. de Génie Mécanique, Univ. de Constantine, Route d'Ain El. Bey, 25000, Constantine, Algeria

  2. Ph. Marty

    Present address: Lab des Ecoulements Géophysiques et Industriels, B.P. 53 X, 38041, Grenoble Cedex, France

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    1. R. Bessaih
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    2. Ph. Marty
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    3. M. Kadja
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    Bessaih, R., Marty, P. & Kadja, M. Numerical study of disk driven rotating MHD flow of a liquid metal in a cylindrical enclosure. Acta Mechanica 135, 153–167 (1999). https://doi.org/10.1007/BF01305749

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    • DOI: https://doi.org/10.1007/BF01305749

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