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Nonlinear spiral waves in rotating pipe flow

Published online by Cambridge University Press:  21 April 2006

N. Toplosky  and
T. R. Akylas
N. Toplosky
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Present address: Naval Underwater Systems Center, New London, CT 06320, USA.
T. R. Akylas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A numerical investigation of finite-amplitude, non-axisymmetric disturbances, in the form of travelling spiral waves, is made in pipe flow with superimposed solid-body rotation. Rotating pipe flow is found to be supercritically unstable both in the rapid and slow-rotation regimes. Earlier weakly nonlinear calculations, suggesting subcritical instability in the slow-rotation limit, are shown to be in error. Bifurcating neutral waves are calculated for various axial and azimuthal Reynolds numbers and wavenumbers. For fixed axial mean pressure gradient, the axial mean flow induced by these waves gives rise to a significant flux defect, in certain cases as large as 40-50% of the undisturbed mass flux; the possible relevance of this finding to the phenomenon of vortex breakdown is pointed out. In non-rotating pipe flow, no neutral disturbances in the assumed form of spiral waves are found for moderate Reynolds numbers; this indicates that previous conjectures, regarding a possible connection between nonlinear spiral waves in slowly rotating pipe flow and the asymptotic neutral states of Smith & Bodonyi (1982) in non-rotating pipe flow, are not valid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 39 - 54
Copyright
© 1988 Cambridge University Press

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