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A finite-element study of the onset of vortex shedding in flow past variously shaped bodies

Published online by Cambridge University Press:  21 April 2006

C. P. Jackson
C. P. Jackson
Affiliation:
Theoretical Physics Division, Harwell Laboratory, Didcot OX11 0RA, UK
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Abstract

The onset of periodic behaviour in two-dimensional laminar flow past bodies of various shapes is examined by means of finite-element simulations. The transition from steady to periodic flow is marked by a Hopf bifurcation, which we locate by solving an appropriate extended set of steady-state equations. The bodies considered are a circular cylinder, triangular prisms of various shapes, and flat plates and elliptical cylinders aligned over a range of angles to the direction of flow. Our results for the circular cylinder are in good agreement with experimental observations and with the results of time-dependent calculations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 23 - 45
Copyright
© 1987 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Berger, E. & Wille, R. 1972 Periodic flow phenomena. Ann. Rev. Fluid Mech. 4, 313.Google Scholar
Braza, M., Chassaing, P. & Minh, H. Ha. 1987 A numerical study of the dynamics of different scale structures in the near wake of a circular cylinder in laminar to turbulent transition. In Numerical Methods in Laminar and Turbulent Flow. Pineridge (to appear.)
Coutanceau, M. & Bouard, R. 1977a Experimental determination of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1 Steady flow. J. Fluid Mech. 79, 231.Google Scholar
Coutanceau, M. & Bouard, R. 1977b Experimental determination of the viscous flow in the wake of a circular cylinder in uniform translation. Part 2 Unsteady flow. J. Fluid Mech. 79, 257.Google Scholar
Dyke, M. Van 1982 An Album of Fluid Motion. Parabolic Press.
Friehe, C. 1980 Vortex-shedding from cylinders at low Reynolds numbers. J. Fluid Mech. 100, 237.Google Scholar
Fromm, J. E. & Harlow, F. H. 1963 Numerical treatment of the problem of vortex street development. Phys. Fluids 6, 975.Google Scholar
Gaster, M. 1971 Vortex-shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749.Google Scholar
Gerrard, J. 1978 The wakes of cylindrical bluff bodies at low Reynolds numbers. Phil. Trans. R. Soc. Lond. A288, 351.Google Scholar
Gresho, P. M., Chan, S. T., Lee, R. L. & Upson, C. D. 1984 A modified finite-element method for solving the time-dependent incompressible Navier-Stokes equations. Part 2 Applications. Intl J. Numer. Meth. Fluids 4, 619.Google Scholar
Griewank, A. & Reddien, G. 1983 The calculation of Hopf points by a direct method. IMA J. Numer. Anal. 3, 295.Google Scholar
Hussain, A. K. M. F. & Ramjee, V. 1976 Periodic wake behind a circular cylinder at low Reynolds number. Aero Q. 27, 127.Google Scholar
Jackson, C. P. 1982 The TGSL finite-element subroutine library. Harwell Rep. AERE-R. 10713.Google Scholar
Jepson, A. D. 1981 Numerical Hopf bifurcation. Thesis part 2, California Institute of Technology, Pasadena, CA USA.
Kovasznay, L. S. G. 1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. R. Soc. Lond. A 198, 194.Google Scholar
Marsden, J. E. & McCracken, M. 1976 The Hopf bifurcation and its applications. Springer.
Mathis, C., Provansal, M. & Boyer, L. 1984 The Bénard-von Kármán instability: an experimental study near the threshold. J. Phys. Lett. Paris 45, L483.Google Scholar
Nishioka, M. & Sato, H. 1974 Measurements of velocity distribution in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 65, 97.Google Scholar
Nishioka, M. & Sato, H. 1978 Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers. J. Fluid Mech. 89, 49.Google Scholar
Perry, A., Chong, M. & Lim, T. 1982 The vortex shedding process behind two-dimensional bluff bodies. J. Fluid Mech. 116, 77.Google Scholar
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. no. 1191.Google Scholar
Thoman, D. A. & Szewczyk, A. A. 1969 Time-dependent viscous flow over a circular cylinder. Phys. Fluids, Supp. 2, p. 76.
Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547.Google Scholar
Tritton, D. J. 1971 A note on vortex streets behind circular cylinders at low Reynolds numbers. J. Fluid Mech. 45, 203.Google Scholar
Tritton, D. J. 1977 Physical Fluid Dynamics. Van Nostrand Reinhold.
Wilkinson, J. H. 1965 The Algebraic Eigenvalue Problem. Oxford University Press.
Zdravkovich, M. 1969 Smoke observations of a Kármán vortex street. J. Fluid Mech. 37, 491.Google Scholar