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Symmetrical flow past a uniformly accelerated 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, London, Canada
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
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Abstract

The flow normal to an infinite circular cylinder which is uniformly accelerated from rest in a viscous fluid is considered. The flow is assumed to remain symmetrical about the direction of motion of the cylinder. Two types of solution are presented. In the first an expansion in powers of the time from the start of the motion is given which extends the results of boundary-layer theory by taking into account corrections for finite Reynolds numbers. Physical properties of the flow for small times and finite but large Reynolds numbers are calculated from this expansion. In the second method of solution the Navier-Stokes equations are integrated by an accurate procedure which is a logical extension of the solution in powers of the time. Results are obtained for R2 = 97·5, 5850, 122 × 103 and ∞, where R is the Reynolds number. This is defined as R = 2a(ab)½/v, where a is the radius of the cylinder, b the uniform acceleration and v the kinematic viscosity of the fluid. The methods are in good agreement for small times.

The numerical method of integration has been carried to moderate times and various flow properties have been calculated. The growth of the length of the separated wake behind the cylinder for R2 = 97·5, 5850 and 122 × 103 is compared with the results of recent experimental measurements. The agreement is only moderate for R2 = 97·5 but it improves greatly as R increases. The numerical integrations were continued in each case until the implicit method of integration failed to converge, which terminated the procedure. A secondary vortex appeared on the surface of the cylinder for the case R2 = 122 × 103.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 3 , 16 September 1974 , pp. 461 - 480
Copyright
© 1974 Cambridge University Press

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References

Blasius, H. 1908 Z. angew. Math. Phys. 56, 1.
Collins, W. M. & Dennis, S. C. R. 1973a Quart. J. Mech. Appl. Math. 26, 53.
Collins, W. M. & Dennis, S. C. R. 1973b J. Fluid Mech. 60, 105.
Goldstein, S. & Rosenhead, L. 1936 Proc. Camb. Phil. Soc. 32, 392.
Görtler, H. 1944 Ing.-Arch. 14, 286.
Görtler, H. 1948 Arch. Math. Karlsruhe, 1, 138.
Honji, H. & Taneda, S. 1972 Rep. Res. Inst. Appl. Mech., Kyushu University, 19, 265.
Israeli, M. 1970 Studies in Appl. Math. 49, 327.
Israeli, M. 1972 Studies in Appl. Math. 51, 67.
Orszag, S. A. 1970 J. Atmos. Sci. 27, 890.
Orszag, S. A. 1971 Studies in Appl. Math. 50, 293.
Taneda, S. 1972 Recent Research on Unsteady Bounday Layers, vol. 2 (ed E. A. Eichelbrenner), pp. 1165–1215. Quebec: Laval University Press.
Wang, C. Y. 1967 J. Math. Phys. 46, 195.
Watson, E. J. 1955 Proc. Roy. Soc. A, 231, 104.