The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, this flow configuration represents a more general paradigm for fluid mechanics research.
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January 2003
Technical Papers
Shear-Driven Flow in a Toroid of Square Cross Section
J. A. C. Humphrey,
J. A. C. Humphrey
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904
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J. Cushner,
J. Cushner
Shen Milsom & Wilke, Inc., 417 Fifth Avenue, New York, NY 10016
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M. Al-Shannag,
M. Al-Shannag
Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain
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J. Herrero,
J. Herrero
Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain
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F. Giralt
F. Giralt
Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain
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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
Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain
J. Herrero
Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain
F. Giralt
Department of Chemical Engineering, University of Rovira I Virgili, 43006 Tarragona, Catalunya, Spain
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division August 30, 2001; revised manuscript received July 29, 2002. Associate Editor: J. S. Marshall.
J. Fluids Eng. Jan 2003, 125(1): 130-137 (8 pages)
Published Online: January 22, 2003
Article history
Received:
August 30, 2001
Revised:
July 29, 2002
Online:
January 22, 2003
Citation
Humphrey, J. A. C., Cushner, J., Al-Shannag , M., Herrero , J., and Giralt , F. (January 22, 2003). "Shear-Driven Flow in a Toroid of Square Cross Section ." ASME. J. Fluids Eng. January 2003; 125(1): 130–137. https://doi.org/10.1115/1.1523066
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