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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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References

Bertelsen, A. F. 1974 An investigation of the oscillating viscous flow in a curved pipe with special emphasis on low Reynolds number secondary steady streaming effects. Univ. of Bergen, Norway, Rep. no. 67.MGoogle Scholar
Bertelsen, A. F. 1975 An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow. J. Fluid Mech. 70, 519–527.Google Scholar
Blennerhasset, P. J. 1976 Secondary motion and diffusion in unsteady flow in a curved pipe. Ph.D. thesis, Imperial College, London.
Collins, W. M. & Dennis, S. C. R. 1975 The steady motion of a viscous fluid in a curved tube. Quart. J. Mech. Appl. Math. 28, 133–156.Google Scholar
Dean, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. 5 (7), 673–695.Google Scholar
Lyne, W. H. 1970 Unsteady viscous flow in a curved pipe. J. Fluid Mech. 45, 13–31.Google Scholar
McConalogue, D. J. & Srivastava, R. S. 1968 Motion of a fluid in a curved tube. Proc. Roy. Soc. A 37–53.Google Scholar
Mullin, T. 1978 Oscillatory flow in curved tubes. Ph.D. thesis, University of Edinburgh.
Mullin, T. & Greated, C. A. 1980 Oscillatory flow in curved pipes. Part 1. The developing- flow case. J. Fluid Mech. 98, 383–395.Google Scholar
Munsen, B. R. 1975 Experimental results for oscillating flow in a curved pipe. Phys. Fluids 18, 1607–1609.Google Scholar
Munsen, B. R. 1976 Secondary flows in a slowly oscillating torus. Phys. Fluids 19, 1823–1825.Google Scholar
Sexl, T. 1930 Über den von E. G. Richardson entdeckten ‘Annulareffeckt’. Z. Phys. 61, 349–362.Google Scholar
Smith, F. T. 1975 Pulsatile flow in curved pipes. J. Fluid Mech. 71, 15–42.Google Scholar
Sneddon, I. N. 1946 Finite Hankel transforms. Phil. Mag. 37 (1), 17–25.Google Scholar
Stroud, A. H. 1966 Gaussian Quadrature Formulae. Englewood Cliffs, New Jersey: Prentice-Hall.
Zalosh, R. G. 1970 Pulsating flow in a curved tube. Ph.D. thesis, North Eastern University, Boston.
Zalosh, R. G. & Nelson, W. G. 1973 Pulsating flow in a curved tube. J. Fluid Mech. 59, 693–705.Google Scholar