Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-20T05:14:25.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of time-periodic flows in a circular pipe

Published online by Cambridge University Press:  12 April 2006

W. H. Yang  and
Chia-Shun Yih
W. H. Yang
Affiliation:
Department of Applied Mechanics and Engineering Science, University of Michigan, Ann Arbor
Chia-Shun Yih
Affiliation:
Department of Applied Mechanics and Engineering Science, University of Michigan, Ann Arbor
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of time-periodic flows in a circular pipe is investigated. The disturbance is assumed to be axially symmetric and to have a small amplitude, so that the governing differential equation is linear. Calculations are carried out for the first ten modes for a range of values of the frequency of the primary motion, of the wavenumber of the disturbance, and of the Reynolds number of the primary flow. In the ranges of the parameters for which the calculations have been carried out, the flows are found to be stable and, as for Stokes flows (von Kerczek & Davis 1974), it is conjectured that the flows under study here are stable for all frequencies and all Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 3 , 27 September 1977 , pp. 497 - 505
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Davis, S. H. 1976 The stability of time-dependent flows. Ann. Rev. Fluid Mech. 8, 57–74.Google Scholar
Golub, G. 1973 Topics in Numerical Analysis (ed. J. Miller). Academic Press.
Grosch, C. E. & Salwen, H. 1968 The stability of steady and time-dependent plane Poiseuille flow. J. Fluid Mech. 34, 177–205.Google Scholar
Kerczek, C. Von & Davis, S. H. 1974 J. Fluid Mech. 62, 753–773.
Moler, C. B. & Stewart, G. W. 1973 An algorithm for the generalized eigenproblem. SIAM J. Numer. Anal. 10, 241–256.Google Scholar
Synge, J. L. 1938 Hydrodynamic stability. Semi-Centennial Publ., Am. Math. Soc. 2, 227–269.Google Scholar
Yih, C.-S. & Li, C.-H. 1972 Instability of unsteady flows or configurations. Part 2. Convective instability. J. Fluid Mech. 54, 143–152.Google Scholar