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Research Papers: Flows in Complex Systems

Three-Dimensional Flow in a Driven Cavity Subjected to an External Magnetic Field

[+] Author and Article Information
K. Jin

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61820
e-mail: kaijin2@illinois.edu

S. P. Vanka

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61820
e-mail: spvanka@illinois.edu

B. G. Thomas

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61820
e-mail: bgthomas@illinois.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 16, 2014; final manuscript received January 20, 2015; published online March 26, 2015. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 137(7), 071104 (Jul 01, 2015) (14 pages) Paper No: FE-14-1666; doi: 10.1115/1.4029731 History: Received November 16, 2014; Revised January 20, 2015; Online March 26, 2015

In this paper, we study the three-dimensional (3D) flow of an electrically conducting fluid in a cubic cavity with the top wall moving and subjected to an external magnetic field. The governing flow and electromagnetic field equations are integrated by a second-order space and time accurate numerical scheme, implemented on a graphics processing unit (GPU) with high parallel efficiency. Solutions for several Reynolds and Stuart numbers have been obtained on sufficiently fine grids to achieve grid independent solutions. As expected, the magnetic field significantly influences the circulation in the cavity and modifies the shape and locations of the primary and secondary eddies. The observed flow patterns are illustrated graphically as well as through selected line plots and tabulated data. With increasing magnetic field strength, the center of the primary eddy is seen to shift to the top right corner. Further, situations where the flow is unsteady in the absence of the magnetic field have become steady after a certain value of the magnetic interaction parameter.

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Figures

Grahic Jump Location
Fig. 1

Comparison of velocity profiles in symmetry plane of a lid-driven cube, Re = 1000

Grahic Jump Location
Fig. 2

Validation result of 2D cavity MHD flow at Re = 5000 and N = 5

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Fig. 3

Grid independency study, Re = 3200 and N = 0.25 in symmetry plane (z = 0.5)

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Fig. 4

The lid driven cavity with an external magnetic field

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Fig. 5

Velocity magnitude contour at Re = 400 and N = 0.0 on: (a) z = 0.05, (b) z = 0.1, (c) z = 0.3, and (d) z = 0.5

Grahic Jump Location
Fig. 6

Velocity magnitude contour at Re = 400 and N = 1.0 on: (a) z = 0.05, (b) z = 0.1, (c) z = 0.2, and (d) z = 0.5

Grahic Jump Location
Fig. 7

Velocity magnitude contour at Re = 400 and N = 2.0 on: (a) z = 0.05, (b) z = 0.1, (c) z = 0.3, and (d) z = 0.5

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Fig. 8

Streamlines in z = 0.5 plane, Re = 400 for different N

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Fig. 9

(a) u, (b) v, and (c) w velocities on spanwise centerline

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Fig. 10

Centerline velocities in z = 0.5 plane, Re = 400 for different magnetic fields

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Fig. 11

Streamlines in z = 0.5 plane, Re = 2000 for different N

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Fig. 12

Centerline velocity in z = 0.5 plane, Re = 2000

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Fig. 13

Velocity vector in middle x plane for Re = 2000

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Fig. 14

Streamlines in z = 0.5 plane, Re = 3200 for different N

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Fig. 15

Centerline velocity in z = 0.5 plane, Re = 3200

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Fig. 16

Velocity vector in middle x plane for Re = 3200

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Fig. 17

Streamlines in z = 0.5 plane, Re = 5000 for N = 0.25 and N = 0.50

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