Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T00:33:01.267Z Has data issue: false hasContentIssue false
  • English
  • Français

Some relations between drag and flow pattern of viscous flow past a sphere and a cylinder at low and intermediate Reynolds numbers

Published online by Cambridge University Press:  29 March 2006

H. R. Pruppacher ,
B. P. Le Clair  and
A. E. Hamielec
H. R. Pruppacher
Affiliation:
Cloud Physics Laboratory, Department of Meteorology, University of California, Los Angeles
B. P. Le Clair
Affiliation:
Chemical Engineering Department, McMaster University, Hamilton, Canada
A. E. Hamielec
Affiliation:
Chemical Engineering Department, McMaster University, Hamilton, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

The results of a numerical evaluation of the Navier-Stokes equations of motion for the case of a viscous fluid streaming past a sphere are presented in terms of the length of the standing eddy behind the sphere and in terms of the angle of flow separation at the sphere. Emphasis was placed on calculating these quantities at Reynolds numbers between 20 and 40 where no reliable theoretical or experimental values are available. In support of these calculations, it is shown that the values for the drag on a sphere previously calculated by us from the Navier-Stokes equations of motion by the same numerical technique as that used for calculating the eddy length and angle of flow separation agree well with our recent, extensive drag measurements for a wide Reynolds number interval. Our results are used to make a comparison between drag and flow field as predicted by analytical solutions and numerical solutions to the Navier-Stokes equations of motion. Some limitations of the analytical solutions to predict correct values for the drag, and to describe the correct nature of the flow field, are pointed out. It is shown further that a plot of [(D/Ds) – 1] versus log NRe, where D is the actual drag on a sphere, Ds is the Stokes drag, and NRe is the Reynolds number, reveals that the variation of the drag on a sphere with Reynolds number follows well defined régimes, which correlate well with the régimes of the flow field around a sphere. A similar relationship between ‘drag-régime’ and flow field pattern is discussed for the case of viscous flow past a cylinder.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 4 , 16 December 1970 , pp. 781 - 790
Copyright
© 1970 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

Apelt, C. J. 1958 Aero. Res. Counc. R. & M. no. 3175.
Beard, K. V. & Pruppacher, H. R. 1969 J. atmos. Sci. 26, 106.
Carrier, G. 1953 Final Rep., Office of Naval Res. (Nonv.-653–00/1), Brown University. (Available under A.D. 16588.)
Chester, W. & Breach, D. R. 1969 J. Fluid Mech. 37, 75.
Dennis, S. C. R. & Shimshoni, M. 1964 Aero. Res. Counc., current paper no. 797.
Fage, A. 1934 Proc. Roy. Soc. A 144, 381.
Finn, R. K. 1953 J. appl. Phys. 24, 77.
Garner, F. H. & Grafton, R. W. 1954 Proc. Roy. Soc. A 224, 70.
Goldburg, A. & Florsheim, B. H. 1966 Phys. Fluids, 9, 45.
Goldstein, S. 1929 Proc. Roy. Soc. A 123, 216.
Hamielec, A. E., Hoffman, T. W. & Ross, L. L. 1967 A.I.Ch.E. J. 13, 21.
Hamielec, A. E. & Johnson, A. I. 1962 Can. J. Chem. Engng. 40, 4.
Hamielec, A. E., Storey, S. H. & Whitehead, J. M. 1962 Can. J. Chem. Engng. 41, 246.
Hamielec, A. E. & Raal, J. D. 1969 Phys. Fluids, 12, 11.
Homann, F. 1936 Forsch. Geb. Ing Wes. 7, 1.
Ingham, D. B. 1968 J. Fluid Mech. 31, 81.
Jayaweera, K. O. & Mason, B. J. 1965 J. Fluid Mech. 22, 70.
Jenson, V. G. 1959 Proc. Roy. Soc. A 249, 346.
Kawaguti, M. & Jain, P. 1966 J. Phys. Soc. Japan, 21, 2055.
Keller, H. B. & Takami, H. 1966 Proc. Adv. Symp. on Numerical Solutions of Non-Linear Differential Equations (ed. D. Greenspan), p. 115. New York: Wiley.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Le Clair, B. P., Hamielec, A. E. & Pruppacher, H. R. 1970 J. atmos. Sci. 27, 30.
Maxworthy, T. 1965 J. Fluid Mech. 23, 36.
Möller, W. 1938 Phys. Z. 39, 5.
Nisi, H. & Porter, A. W. 1923 Phil. Mag. B, 754.
Ockendon, J. R. 1968 J. Fluid Mech. 34, 22.
Oseen, W. 1927 Hydrodynamik. Leipzig: Akademische.
Perry, J. 1950 Chem. Eng. Handbook (3rd edn.), p. 1017. New York: McGraw-Hill.
Proudman, I. 1969 J. Fluid Mech. 37, 75.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 23.
Pruppacher, H. R. & Beard, K. V. 1970 Quart. J. Roy. Met. Soc. 96, 24.
Pruppacher, H. R. & Neiburger, M. 1968 Proc. Conf. Cloud Physics, Tokyo, p. 389.
Pruppacher, H. R. & Steinberger, E. H. 1968 J. appl. Phys. 39, 412.
Rhodes, J. M. 1967 Ph.D. Thesis, University of Tennesse.
Rimon, Y. & Cheng, S. I. 1969 Phys. Fluids, 12, 949.
Roshko, A. 1954 NACA Rep. 1191.
Son, J. S. & Hanratty, T. J. 1969 J. Fluid Mech. 35, 36.
Taneda, S. 1956a Rep. Res. Inst. appl. Mech. 6, 16, 99. Kyushu University.
Taneda, S. 1956b J. Phys. Soc. Japan, 11, 302.
Thom, A. 1933 Proc. Roy. Soc. A 141, 651.
Tritton, D. J. 1959 J. Fluid Mech. 6, 54.
Underwood, R. L. 1969 J. Fluid Mech. 37, 9.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.
Wieselsberger, G. 1922 Phys. Z. 22, 32.