Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-07T09:54:49.013Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical solutions for steady symmetric viscous flow past a parabolic cylinder in a uniform stream

Published online by Cambridge University Press:  29 March 2006

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

Abstract

Numerical solutions are presented for steady two-dimensional symmetric flow past a parabolic cylinder in a uniform stream parallel to its axis. The solutions cover the range R = 0·25 to ∞, where R is the Reynolds number based on the nose radius of the cylinder. For large R, the calculated skin friction near the nose of the cylinder is compared with known theoretical results obtained from second-order boundary-layer theory. Some discrepancy is found to exist between the present calculations and the second-order theory. For small R, it is possible to obtain a reasonably consistent check with a recent theoretical prediction for the limit of the skin friction near the nose of the cylinder as R → 0.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 4 , 29 December 1971 , pp. 801 - 814
Copyright
© 1971 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

Burggraf, O. R. 1966 J. Fluid Mech. 24, 113.
Davis, R. T. 1967 J. Fluid Mech. 27, 691.
Davis, R. T. 1972 J. Fluid Mech. (to appear).
Dennis, S. C. R. & Chang, G. Z. 1069 Phys. Fluids Suppl. II, 12, II–88.
Fox, L. 1947 Proc. Roy. Soc. A 190, 31.
Goldstein, S. 1960 Lectures on Fluid Mechanics. Interscience.
Greenspan, D. 1968 In Lectures on the Numerical Solution of Linear, Singular and Nonlinear Differential Equations, chapter 10. Prentice Hall.
Imai, I. 1957 J. Aeron. Sci. 24, 155.
Kaplun, S. 1954 Z. angew. Math. Phys. 5, 111.
Kawaguti, M. 1961 J. Phys. Soc. Japan, 16, 2307.
Murray, J. D. 1965 J. Fluid Mech. 21, 337.
Schlichting, H. 1960 Boundary Layer Theory. McGraw-Hill.
Smith, A. M. O. & Clutter, D. W. 1963 Douglas Aircraft Corp. Engng. Papers, 1525, 1530. See also A.I.A.A. J. 1, 2062.
Spalding, D. B. 1967 Numerical Methods for Viscous Flows. AGARD Conference Proceedings no. 60.
Stewartson, K. 1957 J. Math. Phys. 36, 173.
Takami, H. & Keller, H. B. 1969 Phys. Fluids Suppl. II, 12, 11–51.
Van Dyke, M. 1962a J. Fluid Mech. 14, 161.
Van Dyke, M. 1962b J. Fluid Mech. 14, 481.
Van Dyke, M. 1964a J. Fluid Mech. 19, 145.
Van Dyke, M. 1964b Proc. Int. Hypersonics Symp. 1964. Cornell University Press.
Van Dyke, M. 1965 VII Symposium on Advanced Problems and Methods in Fluid Dynamics.Poland, Jarata 1965.
Varga, R. S. 1962 Matrix Iterative Analysis. Prentice-Hall.
Van De Vooren, A. I. & Dijkstra, D. 1970 J. Engng. Math. 4, 9.
Wachspress, E. L. 1966 Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics. Prentice-Hall.
Wang, R. S. 1965 Virginia Polytechnic Institute, M.S. thesis.
Yoshizawa, A. 1970 J. Phys. Soc. Japan, 28, 776.