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TECHNICAL PAPERS

Shear-Driven Flow in a Toroid of Square Cross Section

[+] Author and Article Information
J. A. C. Humphrey

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904

J. Cushner

Shen Milsom & Wilke, Inc., 417 Fifth Avenue, New York, NY 10016

M. Al-Shannag, J. Herrero, F. Giralt

Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain

J. Fluids Eng 125(1), 130-137 (Jan 22, 2003) (8 pages) doi:10.1115/1.1523066 History: Received August 30, 2001; Revised July 29, 2002; Online January 22, 2003
Copyright © 2003 by ASME
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References

Figures

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Wall-driven flows in enclosures of square cross section. (a) Two-dimensional flow in a plane enclosure, (b) three-dimensional flow in a parallelepiped. At sufficiently large Re, centrifugal instabilities trigger Goertler vortices in the parallelepiped where the two end walls fix the sense of rotation of the corner (“c”) vortices and, as a consequence, of the remaining (“G”) vortices. The sense of rotation of the vortices in the bottom half of the parallelepiped is shown projected on an x-z plane.
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(a) Top and side views of the idealized toroid (Configuration 1); (b) side view of the experimental configuration (Configuration 2); (c) view showing one (r-z) plane of the 360-deg calculation domain corresponding to Configuration 2. Note that g/D=0 for Configuration 1 and g/D≪1 for Configuration 2. The drawings are not to scale.
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Visualization of the instantaneous flow in a toroid with Reg=5000,δ=0.25, and g/D=0.015. Picture shows a z*-θ plane at r*=0.90 as seen through the curved outer side wall of the toroid.
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Visualization of the instantaneous flow in a toroid with Reg=5000,δ=0.25, and g/D=0.015. Pictures show views of r*-θ planes as seen through the top wall of the toroid over a sector of 18 deg: (a) z*=0.9; (b) 0.7; (c) 0.5; (d) 0.3; and (e) 0.1.
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Instantaneous distributions of the calculated circumferential velocity component at t*=856 in r*-θ planes of a toroid with Reg=1143,δ=0.51, and g/D=0.04: (a) z*=0.7; (b) 0.5 and (c) 0.1. Black and white areas denote regions of opposite velocity.
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Time records of the dimensionless circumferential velocity component at (a) z*=0.25,r*=0.5, and θ=0.22π (b) z*=0.5,r*=0.5, and θ=0.22π for the conditions of Fig. 5
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Instantaneous dimensionless velocity vectors at times t*=860 (a) and t*=865 (b) in the lower half of the z*-θ plane at r*=0.5 for the conditions of Fig. 5
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Instantaneous streamlines obtained from a full domain three-dimensional flow calculation in a toroid with Reg=1143,δ=0.51, and g/D=0.04. The wall jet flows from left to right at the top of the toroid thus inducing a clockwise circulation of the core flow. Results shown correspond to the maximum penetration depth in an oscillation cycle. The maximum penetration depth is p/D=0.079 and the minimum is p/D=0.076.

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