Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-29T14:51:53.673Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculation of the steady flow past a sphere at low and moderate Reynolds numbers

Published online by Cambridge University Press:  29 March 2006

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

Abstract

The steady axially symmetric incompressible flow past a sphere is investigated for Reynolds numbers, based on the sphere diameter, in the range 0·1 to 40. The formulation is a semi-analytical one whereby the flow variables are expanded as series of Legendre functions, hence reducing the equations of motion to ordinary differential equations. The ordinary differential equations are solved by numerical methods. Only a finite number of these equations can be solved, corresponding to an approximation obtained by truncating the Legendre series at some stage. More terms of the series are required as R increases and the present calculations were terminated at R = 40. The calculated drag coefficient is compared with the results of previous investigations and with experimental data. The Reynolds number at which separation first occurs is estimated as 20·5.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 4 , 27 August 1971 , pp. 771 - 789
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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Beard, K. V. & Pruppacher, H. R. 1969 J. Atmos. Sci. 26, 1066.
Castleman, R. A. 1926 N.A.C.A. Tech. Note no. 231.
Chester, W. & Breach, D. R. 1969 J. Fluid Mech. 37, 751.
Dennis, S. C. R. & Chang, G. Z. 1969 Mathematics Research Center, University of Wisconsin. Technical Summary Report no. 859.
Dennis, S. C. R. & Walker, M. S. 1964 Aero. Res. Counc. no. 26, 105.
Goldstein, S. 1929 Proc. Roy. Soc. A, 123, 225.
Goldstein, S. 1938 Modern Developments in Fluid Dynamics. Oxford University Press.
Homann, F. 1936 N.A.C.A. Tech. Mem. no. 1334.
Hamielec, A. E., Hoffman, T. W. & Ross, L. L. 1967 A.I.Ch.E.J. 13, 212.
Jenson, V. G. 1959 Proc. Roy. Soc. A, 249, 346.
Kawaguti, M. 1950 Rep. Inst. Sci. Tokyo, 4, 154.
Le Clair, B. P., Hamielec, A. E. & Pruppacher, H. R. 1970 J. Atmos. Sci. 27, 308.
Lister, M. 1953 Ph.D. Thesis, London.
Maxworthy, T. 1965 J. Fluid Mech. 23, 369.
Oseen, C. W. 1910 Ark. f. Mat. Astr. og Fys. 6, 29.
Perry, J. 1950 (ed.) Chem. Engng Handbook, 3rd ed. New York: McGrow-Hill:
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 237.
Pruppacher, H. R., Le Clair, B. P. & Hamielec, A. E. 1970 J. Fluid Mech. 44, 781.
Pruppacher, H. R. & Steinberger, E. H. 1968 J. Appl. Phys. 39, 4129.
Rimon, Y. & Cheng, S. I. 1969 Phys. Fluids, 12, 949.
Rosser, J. B. 1967 Mathematics Research Center, University of Wisconsin, Technical Summary Report no. 797.
Rotenberg, M., Bivins, M., Metropolis, N. & Wooten, J. K. 1959 The 3-j and 6-j Symbols. Massachusetts Institute of Technology Press.
Schlichting, H. 1960 Boundary Layer Theory (4th ed.). New York: McGrow-Hill.
Shanks, D. 1955 J. Math. Phys. 34, 1.
Talman, J. D. 1968 Special Functions. New York: Benjamin.
Taneda, S. 1956 J. Phys. Soc. Japan, 11, 302.
Underwood, R. L. 1969 J. Fluid Mech. 37, 95.
Van Dyke, M. D. 1964a Proc. 11th Int. Cong. Appl. Mech., Munich, 1165–1169.
Van Dyke, M. D. 1964b Perturbation Methods in Fluid Mechanics. New York: Academic.
Van Dyke, M. D. 1965 Stanford University SUDAER no. 247.
Walker, J. D. A. 1968 M.Sc. Thesis, University of Western Ontario.