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Flow past an impulsively started circular cylinder

Published online by Cambridge University Press:  29 March 2006

W. M. Collins  and
S. C. R. Dennis
W. M. Collins
Affiliation:
Department of Applied Mathematics, University of Western Ontario
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario
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Abstract

An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated for R = 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder for R = 500 is also found to be in reasonable agreement with experimental measurements for the case R = 560.

For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. For R > 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the case R = 500, but for higher Reynolds numbers, including the case R = ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 105 - 127
Copyright
© 1973 Cambridge University Press

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References

Belcher, R. J., Burggraf, O. R., Cooke, J. C., Robins, A. J. & Stewartson, K. 1972 Recent Research on Unsteady Boundary Layers, vol. 2 (ed. E. A. Eichelbrenner). Quebec: Laval University Press.
Blasius, H. 1908 Z. Math. Phys. 56, 1.
Collins, W. M. & Dennis, S. C. R. 1973 Quart. J. Mech. Appl. Math. 26, 53.
Dennis, S. C. R. & Chang, G. Z. 1969 Math. Res. Center, University of Wisconsin, Tech. Summary Rep. 859.
Dennis, S. C. R. & Chang, G. Z. 1970 J. Fluid Mech. 42, 471.
Dennis, S. C. R. & Staniforth, A. N. 1971 Lecture Notes in Physics 8, 343.
Goldstein, S. & Rosenhead, L. 1936 Proc. Comb. Phil. Soc. 32, 392.
Hirota, I. & Miyakoda, K. 1965 J. Met. Soc. Japan, Ser. II, 43, 30.
Honji, H. & Taneda, S. 1969 J. Phys. Soc. Japan, 27, 1668.
Honji, H. & Taneda, S. 1972 Rep. Res. Inst. Appl. Mech. Kyushu University, 19, 265.
Ingham, D. B. 1968 J. Fluid Mech. 31, 815.
Israeli, M. 1970 Studies in Appl. Math. 49, 327.
Israeli, M. 1972 Studies in Appl. Math. 51, 67.
Jain, P. C. & Rao, K. S. 1969 Phys. Fluids Suppl. II, 12, II-57.
Kawaguti, M. 1953 J. Phys. Soc. Japan, 8, 747.
Kawaguti, M. & Jain, P. C. 1966 J. Phys. Soc. Japan, 21, 2055.
Orszag, S. A. 1970 J. Atmos. Sci. 27, 890.
Orszag, S. A. 1971 Studies in Appl. Math. 50, 293.
Payne, R. B. 1958 J. Fluid Mech. 4, 81.
Proudman, I. & Johnson, K. 1962 J. Fluid Mech. 12, 161.
Robins, A. J. 1970 Ph.D. thesis, University of Bristol.
Rosser, J. B. 1967 Math. Res. Center, University of Wisconsin, Tech. Summary Rep. 797.
Schuh, H. 1953 Z. Flugwis. 1, 122.
Schwabe, M. 1935 Ing.-Arch. 6, 34.
Son, J. S. & Hanratty, T. J. 1969 J. Fluid Mech. 35, 369.
Takami, H. & Keller, H. B. 1969 Phys. Fluids Suppl. II, 12, II-51.
Taneda, S. 1972 Recent Research on Unsteady Boundary Layers, vol. 2 (ed. E. A. Eichelbrenner). Quebec: Laval University Press.
Thom, A. 1928 Aero. Res. Counc. R. & M. no. 1194.
Thoman, D. C. & Szewczyk, A. A. 1969 Phys. Fluids Suppl. II, 12, II-76.
Wang, C. Y. 1967 J. Math. Phys. 46, 195.
Watson, E. J. 1955 Proc. Roy. Soc. A 231, 104.
Wundt, H. 1955 Ing.-Arch. 23, 212.