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A numerical study of steady viscous flow past a circular cylinder

Published online by Cambridge University Press:  19 April 2006

Bengt Fornberg
Bengt Fornberg
Affiliation:
Department of Applied Mathematics, California Institute of Technology, Pasadena, California 91125, U.S.A.
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Abstract

Numerical solutions have been obtained for steady viscous flow past a circular cylinder at Reynolds numbers up to 300. A new technique is proposed for the boundary condition at large distances and an iteration scheme has been developed, based on Newton's method, which circumvents the numerical difficulties previously encountered around and beyond a Reynolds number of 100. Some new trends are observed in the solution shortly before a Reynolds number of 300. As vorticity starts to recirculate back from the end of the wake region, this region becomes wider and shorter. Other flow quantities like position of separation point, drag, pressure and vorticity distributions on the body surface appear to be quite unaffected by this reversal of trends.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 4 , 26 June 1980 , pp. 819 - 855
Copyright
© 1980 Cambridge University Press

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References

Allen, D. N. de G. & Southwell, R. V. 1955 Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quart. J. Mech. Appl. Math. 8, 129.Google Scholar
Batchelor, G. K. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388.Google Scholar
Brodetsky, S. 1923 Discontinuous fluid motion past circular and elliptic cylinders. Proc. Roy. Soc. A 102, 542.Google Scholar
Dennis, S. C. R. 1973 The numerical solution of the vorticity transport equation. Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mech., vol. 2 (ed. H. Cabannes & R. Tewam), Lecture notes in Physics, vol. 19, p. 120. Springer.
Dennis, S. C. R. 1976 A numerical method for calculating steady flow past a cylinder. Proc. 5th Int. Conf. on Numerical Methods in Fluid Dynamics (ed. A. I. van de Vooren & P. J. Zandbergen), Lecture notes in Physics, vol. 59, p. 165. Springer.
Dennis, S. C. R. & Chang, G. Z. 1970 Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 42, 471.Google Scholar
Gushchin, V. A. & Schennikov, V. V. 1974 A numerical method of solving the Navier-Stokes equations. Zh. vychist. Mat. mat. Fiz. 14, 512.Google Scholar
Hamielec, A. E. & Raal, J. D. 1969 Numerical studies of viscous flow around circular cylinders. Phys. Fluids 12, 11.Google Scholar
Helmholtz, H. v. 1868 Über discontinuirliche Flüssigkeits-Bewegungen, Phil. Mag. 36 (4), 337.Google Scholar
Imai, I. 1951 On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon's paradox. Proc. Roy. Soc. A 208, 487.Google Scholar
Ingham, D. B. 1968 Note on the numerical solution for unsteady viscous flow past a circular cylinder. J. Fluid Mech. 31, 815.Google Scholar
Jain, P. C. & Kawaguti, M. 1966 Numerical study of a viscous fluid past a circular cylinder. J. Phys. Soc. Japan 21, 2055.Google Scholar
Jain, P. C. & Sankara Rao, K. 1969 Numerical solution of unsteady viscous incompressible fluid flow past a circular cylinder. Phys. Fluids Suppl. II 57.Google Scholar
Kawaguti, M. 1953 Numerical solution of the Navier-Stokes equations for the flow around a circular cylinder at Reynolds number 40. J. Phys. Soc. Japan 8, 747.Google Scholar
Keller, H. B. & Takami, H. 1966 Numerical studies of viscous flow about cylinders. In Numerical Solutions of Nonlinear Differential Equations (ed. D. Greenspan), p. 115. Wiley.
Kirchhoff, G. 1869 Zur Theorie freier Flüssigkeits-Strahlen. J. reine angew. Math. 70, 289.Google Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meth. Appl. Mech. Engng 19, 59.Google Scholar
Nieuwstadt, F. & Keller, H. B. 1973 Viscous flow past circular cylinders. Comp. Fluids. 1, 59.Google Scholar
Patel, V. A. 1976 Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of series truncation. Comp. Fluids 4, 13.Google Scholar
Payne, R. B. 1958 Calculations of unsteady viscous flow past a circular cylinder. J. Fluid Mech. 4, 81.Google Scholar
Roache, P. J. 1976 Computational Fluid Dynamics Albuquerque: Hermosa.
Smith, F. T. 1979 Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag. J. Fluid Mech. 92, 171.Google Scholar
Son, J. S. & Hanratty, T. J. 1969 Numerical solution for the flow around a cylinder at Reynolds numbers of 40, 200 and 500. J. Fluid Mech. 35, 369.Google Scholar
Ta, P. L. 1975 Étude numérique de l’écoulement d'un fluide visqueux incompressible autour d'un cylindre fixe ou en rotation. Effet Magnus. J. Méc. 14, 109.Google Scholar
Takami, H. & Keller, H. B. 1969 Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder. Phys. Fluids Suppl. II51.Google Scholar
Thom, A. 1933 The flow past circular cylinders at low speeds. Proc. Roy. Soc. A 141, 651.Google Scholar
Thoman, D. C. & Szewczyk, A. A. 1969 Time dependent viscous flow over a circular cylinder. Phys. Fluids Suppl. II76.Google Scholar
Tuann, S.-Y. & Olson, M. D. 1978 Numerical studies of the flow around a circular cylinder by a finite element method. Comp. Fluids 6, 219.Google Scholar
Underwood, R. L. 1969 Calculations of incompressible flow past a circular cylinder at moderate Reynolds numbers. J. Fluid Mech. 37, 95.Google Scholar