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Oscillatory flows in wavy-walled tubes

Published online by Cambridge University Press:  21 April 2006

M. E. Ralph
M. E. Ralph
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

The problem of oscillatory viscous flow in a tube with rigid sinusoidal walls of large amplitude is solved numerically, for Reynolds numbers up to 300 and Strouhal numbers in the range 10−4–1. Flow visualization photographs have confirmed qualitatively many of the predictions. Results analogous to those of Sobey (1980, 1983) for the two-dimensional problem have been obtained for regions of the parameter space studied in detail by that author. However, new flow structures are found in the previously neglected Strouhal number range of 0.02–0.1. These flows are characterized by significant interaction of flow events in successive half-cycles, due to the persistence of strong shed vortices. Bifurcation of the solution structure can then occur for Strouhal numbers between about 0.025 and 0.045, with the development of time-asymmetric flows: thus the velocity field at some instant of a positive-flow half-cycle may not be equal to minus the velocity field at the corresponding instant of a negative-flow half-cycle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 168 , July 1986 , pp. 515 - 540
Copyright
© 1986 Cambridge University Press

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References

Batchelor G. K.1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bellhouse B. J., Bellhouse F. H., Curl C. M., MacMillan T. I., Gunning A. J., Spratt E. H., MacMurray, S. B. & Nelems J. M.1973 A high efficiency membrane oxygenator and pulsatile pump and its application to animal trials. Trans. Am. Soc. Artif. Int. Organs 19, 72–79.Google Scholar
Bellhouse, B. J. & Snuggs T. A.1977 Augmented mass transfer in a membrane lung and a hemodialyser using vortex mixing INSERM-Euromech 92, 71, 371–384.Google Scholar
Cheng L. C., Clark, M. E. & Robertson J. M.1972 Numerical calculations of oscillatory flow in the vicinity of square wall obstacles in plane conduits. J. Biomech. 5, 467–484.Google Scholar
Cheng L. C., Robertson, J. M. & Clark M. E.1973 Numerical calculations of oscillatory non-uniform flow. II. Parametric study of pressure gradient and frequency with square wall obstacles. J. Biomech. 6, 521–538.Google Scholar
Daly B. J.1975 A numerical study of pulsatile flow through constricted arteries. Proc. 4th Intl Conf. on Num. Methods in Fluid Dyn. Lecture Notes in Physics, vol. 35, pp. 117–124. Springer.
Daly B. J.1976 A numerical study of pulsatile flow through stenosed canine femoral arteries. J. Biomech. 9, 465–475.Google Scholar
Gillani, N. V. & Swanson W. M.1976 Time-dependent laminar flow through a spherical cavity. J. Fluid Mech. 78, 99–127.Google Scholar
Hall P.1974 Unsteady viscous flow in a pipe of slowly varying cross-section. J. Fluid Mech. 64, 209–226.Google Scholar
Lyne W. H.1971 Unsteady viscous flow over a wavy wall. J. Fluid Mech. 50, 33–48.Google Scholar
O'Brien V.1975 Unsteady separation phenomena in a two-dimensional cavity. AIAA J. 13, 415–416.Google Scholar
Ralph M. E.1985 Flows in wavy-walled tubes. D.Phil. thesis, University of Oxford.
Roache P. J.1976 Computational Fluid Dynamics, 2nd edn. Hermosa.
Savvides, G. N. & Gerrard J. H.1984 Numerical analysis of the flow through a corrugated tube with the application to arterial prosthesis. J. Fluid Mech. 138, 129–160.Google Scholar
Sobey I. J.1980 On flow through furrowed channels. Part 1. Calculated flow patterns. J. Fluid Mech. 96, 1–26.Google Scholar
Sobey I. J.1982 Oscillatory flow at intermediate Reynolds number in asymmetric channels. J. Fluid Mech. 125, 359–373.Google Scholar
Sobey I. J.1983 The occurrence of separation in oscillatory flow. J. Fluid Mech. 134, 247–257.Google Scholar
Stephanoff K. D., Sobey, I. J. & Bellhouse B. J.1980 On flow through furrowed channels. Part 2. Observed flow patterns. J. Fluid Mech. 96, 27–32.Google Scholar