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Oscillatory flow in curved pipes. Part 2. The fully developed case

Published online by Cambridge University Press:  19 April 2006

T. Mullin  and
C. A. Greated
T. Mullin
Affiliation:
Department of Physics, University of Edinburgh Present address: Mathematical Institute, University of Oxford.
C. A. Greated
Affiliation:
Department of Physics, University of Edinburgh
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Abstract

A theoretical and experimental investigation of oscillatory flow in curved pipes is presented. The equations for fully developed laminar flow are found to depend on an amplitude parameter G and a frequency parameter α. Initially the Navier–Stokes equations are expanded in terms of G and the resulting linearized equations are solved numerically using finite Hankel integral transforms. A further expansion is used for the case α → 0 and closed-form solutions are presented.

Laser-Doppler anemometry has been used to obtain velocity information in oscillatory air flow in small-diameter curved glass tubes. Using this technique, low-Reynolds-number experiments were carried out and comparison between theory and experiments is presented.

For α [les ] 1 the velocity distributions found are essentially those for steady flow, while for α [ges ] 11·0 the results are not at variance with earlier work. It is for the transition stage between these two regimes that unexpected behaviour is recorded, but a satisfactory explanation is found in terms of general trends within the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 2 , 29 May 1980 , pp. 397 - 416
Copyright
© 1980 Cambridge University Press

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