Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T15:17:20.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous eddies near a 90° and a 45° corner in flow through a curved tube of triangular cross-section

Published online by Cambridge University Press:  11 April 2006

W. M. Collins  and
S. C. R. Dennis
W. M. Collins
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical calculation is presented for the slow flow of a viscous fluid in a region bounded by a right-angled isosceles triangle. The particular flow considered is the secondary flow generated in the plane of a cross-section by the primary axial flow, under a constant pressure gradient, through a slightly curved tube of triangular cross-section. The flow is assumed to be at small Dean number so that the stream function of the secondary flow satisfies the biharmonic equation. The sequence of eddies of decreasing size and intensity first identified by Moffatt (1964a) is observed in each of the corners. Numerical details of a number of these eddies are given and their properties are found to be in excellent agreement with the theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 3 , 11 August 1976 , pp. 417 - 432
Copyright
© 1976 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

Allen, D. N. de G. & Dennis, S. C. R. 1951 Quart. J. Mech. Appl. Math. 4, 439.
Burggraf, O. R. 1966 J. Fluid Mech. 24, 113.
Cheng, K. C. & Akiyama, M. 1970 Int. J. Heat Mass Transfer. 13, 471.
Collins, W. M. & Dennis, S. C. R. 1975 Quart. J. Mech. Appl. Math. 28, 133.
Dean, W. R. 1927 Phil. Mag. 4, 208.
Dean, W. R. 1928 Phil. Mag. 5, 673.
Dean, W. R. & Montagnon, P. E. 1949 Proc. Camb. Phil. Soc. 45, 389.
Moffatt, H. K. 1964a J. Fluid Mech 18, 1.
Moffatt, H. K. 1964b Arch. Mech. Stosowanej. 14, 365.
Pan, F. & Acrivos, A. 1967 J. Fluid Mech. 28, 643.
Rayleigh, Lord 1920 Scientific Papers, vol. 6, p. 18. Cambridge University Press.
Smith, F. T. 1976 Proc. Roy. Soc. A 347, 345.
Smith, G. D. 1965 Numerical Solution of Partial Differential Equations. Oxford University Press.
Taylor, G. I. 1960 Aeronautics and Astronautics (ed. Hoff & Vincenti), p. 12. Pergamon.
Woods, L. C. 1954 Aero. Quart. 5, 176.