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On rotating disk flow

Published online by Cambridge University Press:  21 April 2006

John F. Brady  and
Louis Durlofsky
John F. Brady
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA.
Louis Durlofsky
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The relationship of the axisymmetric flow between large but finite coaxial rotating disks to the von Kármán similarity solution is studied. By means of a combined asymptotic – numerical analysis, the flow between finite disks of arbitrarily large aspect ratio, where the aspect ratio is defined as the ratio of the disk radii to the gap width separating the disks, is examined for two different end conditions: a ‘closed’ end (shrouded disks) and an ‘open’ end (unshrouded or free disks). Complete velocity and pressure fields in the flow domain between the finite rotating disks, subject to both end conditions, are determined for Reynolds number (based on gap width) up to 500 and disk rotation ratios between 0 and – 1. It is shown that the finite-disk and similarity solutions generally coincide over increasingly smaller portions of the flow domain with increasing Reynolds number for both end conditions. In some parameter ranges, the finite-disk solution may not be of similarity form even near the axis of rotation. It is also seen that the type of end condition may determine which of the multiple similarity solutions the finite-disk flow resembles, and that temporally unstable similarity solutions may qualitatively describe steady finite-disk flows over a portion of the flow domain. The asymptotic – numerical method employed has potential application to related rotating-disk problems as well as to a broad class of problems involving flow in regions of large aspect ratio.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 363 - 394
Copyright
© 1987 Cambridge University Press

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