Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T22:23:02.549Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical study of two-dimensional peristaltic flows

Published online by Cambridge University Press:  20 April 2006

S. Takabatake  and
K. Ayukawa
S. Takabatake
Affiliation:
Department of Mechanical Engineering, Ehime University, Matsuyama, Ehime 790, Japan
K. Ayukawa
Affiliation:
Department of Mechanical Engineering, Ehime University, Matsuyama, Ehime 790, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

The Navier–Stokes equations are solved numerically for two-dimensional peristaltic flows by using the finite-difference technique employing the upwind SOR method, and the velocity, pressure and stress fields for various peristaltic flows are obtained. The influences of the magnitudes of wave amplitude, wavelength and Reynolds number on the flow are investigated through numerical calculations, and the results are compared with those of the perturbation analysis. The paper is mainly concerned with elucidating the characteristics of the peristaltic flow at moderate Reynolds numbers where peristaltic pumping has a possibility of engineering application. As a result, it is found that the validity of the perturbation solutions by Jaffrin (1973) and Zien & Ostrach (1970) are restricted within a narrower range than that which they predicted, and that the reflux phenomenon in the flow does change the whole situation according to Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 439 - 465
Copyright
© 1982 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

Ayukawa, K., Kawai, T. & Kimura, M. 1981 Streamlines and path lines in peristaltic flows at high Reynolds numbers. Bull. Japan Soc. Mech. Engrs 24, 948–955.Google Scholar
Ayukawa, K. & Takabatake, S. 1982 Numerical analysis of two-dimensional peristaltic flows (1st report; Flow pattern). Bull. Japan Soc. Mech. Engrs 25 (to be published).Google Scholar
Brown, T. D. & Hung, T.-K. 1977 Computational and experimental investigations of two-dimensional nonlinear peristaltic flows. J. Fluid Mech. 83, 249–272.Google Scholar
Fung, Y. C. & Yih, C. S. 1968 Peristaltic transport. Trans. A.S.M.E., E, J. Appl. Mech. 35, 669–675.Google Scholar
Greenspan, D. 1968 Lectures on the Numerical Solution of Linear, Singular, and Nonlinear Differential Equations, pp. 122–147. Prentice-Hall.
Hanin, M. 1968 The flow through a channel due to transversely oscillating walls. Israel J. Tech. 6, 67–71.Google Scholar
Jaffrin, M. Y. 1973 Inertia and streamline curvature effects on peristaltic pumping. Int. J. Engng Sci. 11, 681–699.Google Scholar
Jaffrin, M. Y. & Shapiro, A. H. 1971 Peristaltic pumping. A. Rev. Fluid Mech. 3, 13–36.Google Scholar
Li, C. H. 1970 Peristaltic transport in circular cylindrical tubes. J. Biomech. 3, 513–523.Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics, 3-A-8. Hermosa.
Shapiro, A. H., Jaffrin, M. Y. & Weinberg, S. L. 1969 Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech. 37, 799–825.Google Scholar
Tong, P. & Vawter, D. 1972 An analysis of peristaltic pumping. Trans. A.S.M.E. E, J. Appl. Mech. 39, 857–862.Google Scholar
Weinberg, S. L., Eckstein, E. C. & Shapiro, A. H. 1971 An experimental study of peristaltic pumping. J. Fluid Mech. 49, 461–479.Google Scholar
Yin, F. & Fung, Y. C. 1969 Peristaltic waves in circular cylindrical tubes. Trans. A.S.M.E. E, J. Appl. Mech. 36, 579–587.Google Scholar
Yin, F. & Fung, Y. C. 1971 Comparison of theory and experiment in peristaltic transport. J. Fluid Mech. 47, 93–112.Google Scholar
Zien, T. F. & Ostrach, S. 1970 A long wave approximation to peristaltic motion. J. Biomech. 3, 63–75.Google Scholar