Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-27T11:57:45.266Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of secondary motion on axial transport in oscillatory tube flow

Published online by Cambridge University Press:  21 April 2006

T. J. Pedley  and
R. D. Kamm
T. J. Pedley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
R. D. Kamm
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In oscillatory flows through systems of branched or curved tubes, Taylor dispersion is modified both by the oscillation and by the induced secondary motions. As a model for this process, We examine axial transport in an annular region containing an oscillatory axial and steady secondary (circumferential) flow. Two complementary approaches are used: an asymptotic analysis for an annulus with a narrow gap (δ) and for large values of the secondary flow Peclet number (P); and a numerical solution for arbitrary values of δ and P. The results exhibit a form of resonance when the secondary-flow time equals the oscillation period, giving rise to a prominent maximum in the transport rate. This observation is consistent with preliminary numerical results for oscillatory flow in a curved tube, and can be explained physically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 347 - 367
Copyright
© 1988 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

Chatwin, P. C. 1975 On the longitudinal dispersion of passive contaminant in oscillatory flows in tubes. J. Fluid Mech. 71, 513–527.Google Scholar
Dean, W. R. 1928 The streamline motion of fluid in a curved pipe. Phil. Mag. S7 5, 673–695.Google Scholar
Drazen, J. H., Kamm, R. D. & Slutsky, A. S. 1984 High frequency ventilation. Physiol. Rev. 64, 505–543.Google Scholar
Erdogan, E. & Chatwin, P. C. 1967 The effects of curvature and buoyancy on the laminar dispersion of solute in a horizontal tube. J. Fluid Mech. 29, 465–484.Google Scholar
Janssen, L. A. M. 1976 Axial dispersion in laminar flow through coiled tubes. Chem. Engng Sci. 31, 215–218.Google Scholar
Johnson, M. & Kamm, R. D. 1986 Numerical studies of steady flow dispersion at low Dean number in a gently curving tube. J. Fluid Mech. 172, 329–345.Google Scholar
Joshi, C. H., Kamm, R. D., Drazen, J. M. & Slutsky, A. S. 1983 An experimental study of gas exchange in laminar oscillatory flow. J. Fluid Mech. 133, 245–254.Google Scholar
Leveque, M. A. 1928 Transmission de chaleur par convection. Ann. Mines 13, 201–362.Google Scholar
Lyne, W. H. 1971 Unsteady viscous flow in a curved pipe. J. Fluid Mech. 45, 13–31.Google Scholar
Nunge, R. L., Lin, T.-S. & Gill, W. N. 1972 Laminar dispersion incurved tubes and channels. J. Fluid Mech. 51, 363–383.Google Scholar
Olver, F. W. J. 1974 Asymptotics and Special Functions. Academic.
Rhines, P. B. & Young, W. R. 1983 How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133–145.Google Scholar
Schroter, R. C. & Sudlow, M. F. 1969 Flow patterns in models of the human bronchial airways. Respir. Physiol. 7, 341–355.Google Scholar
Sharp, K. 1987 Dispersion in a curved tube during oscillatory flow. Ph.D. dissertation, M. I. T.
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 2 20, 196–212.Google Scholar
Taylor G, I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube.. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Watson, E. J. 1983 Diffusion in oscillatory pipe flow. J. Fluid Mech. 133, 233–244.Google Scholar