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Physics of Fluids / Volume 16 / Issue 10 / ARTICLES

Phys. Fluids 16, 3614 (2004); http://dx.doi.org/10.1063/1.1779567 (13 pages)

The flow in a cylindrical container with a rotating end wall at small but finite Reynolds number

Benson K. Muite

School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544

(Received 21 October 2003; accepted 16 June 2004; published online 20 August 2004)

Similarity solutions of the first kind are intermediate asymptotic solutions for the Stokes flow field and for the first-order inertial correction to the Stokes flow field in small aspect ratio geometries with both no-slip and free-slip boundary conditions opposite the rotating end wall. These results differ from the semi-infinite cylindrical container, where similarity solutions of the second kind are intermediate asymptotic representations of the Stokes and first-order flow fields. Lanczos factors are used to show that for Reynolds numbers less than 1, the boundary discontinuity has a limited influence on the flow field with a no-slip boundary condition opposite the rotating end wall but the boundary discontinuity is important in determining the flow field with a free-slip boundary condition opposite the rotating end wall.

© 2004 American Institute of Physics

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KEYWORDS and PACS

Keywords

confined flow, rotational flow, numerical analysis, flow simulation, slip flow

PACS

  • 47.60.-i

    Flow phenomena in quasi-one-dimensional systems

  • 47.11.-j

    Computational methods in fluid dynamics

  • 47.32.-y

    Vortex dynamics; rotating fluids

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1779567

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    Y. Ventikos, "The effect of imperfections on the emergence of three-dimensionality in stationary vortex breakdown bubbles," Phys. Fluids 14, L13 (2002)PHFLE6000014000003000L13000001.

    A. H. Hirsa, J. M. Lopez, and R. Miraghaie, "Symmetry breaking to a rotating wave in a lid-driven cylinder with a free surface: Experimental observation," Phys. Fluids 14, L29 (2002)PHFLE6000014000006000L29000001.

    C. P. Hills, "Eddies induced in cylindrical containers by a rotating end-wall," Phys. Fluids 13, 2279 (2001)PHFLE6000013000008002279000001.


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