Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T02:39:08.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear perturbation of the vortex shedding from a circular cylinder

Published online by Cambridge University Press:  26 April 2006

Giancarlo Alfonsi  and
Aldo Giorgini
Giancarlo Alfonsi
Affiliation:
Istituto di Idraulica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Aldo Giorgini
Affiliation:
School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The influence of finite-amplitude perturbations on the unsteady vortex shedding past an impulsively started circular cylinder is investigated by means of a numerical model. The computational scheme is a mixed spectral–finite analytic technique, in which the fast-Fourier-transform algorithm is used for the evaluation of the nonlinear terms in the two-dimensional time-dependent Navier–Stokes equations in their stream function–vorticity transport form (the Helmholtz formulation) at Re = 1000. The vortex shedding is promoted by imposing at t = 0 a small rotational field to the initially irrotational flow. Attention is focused on the strength of the perturbation vortex, which affects the way in which the vortex shedding develops in time. The results of the simulations are presented by means of computer-generated drawings of absolute streamlines, relative streamlines and vorticity fields; it appears that, when the strength of the initial perturbation assumes the minimum value that has been tested, the vortex shedding phenomenon develops in a way different from that resulting from other numerical experiments of the same kind.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 267 - 291
Copyright
© 1991 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

Abernathy, F. H. & Kronauer, R. E., 1962 The formation of vortex streets. J. Fluid Mech. 13, 1.Google Scholar
Alfonsi, G.: 1988 Influence of finite amplitude perturbations on the vortex shedding past a circular cylinder. Ph.D. dissertation, Purdue University, Indiana.
Alfonsi, G. & Giorgini, A., 1987 Influence of perturbation amplitude on the wake behind a circular cylinder: numerical experiments at Re = 1000. Technical Rep. CE-HSE-87–7. School of Civil Engineering, Purdue University, West Lafayette, Indiana.
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. Q. J. Mech. Appl. Maths 8, 129.Google Scholar
Apelt, C. J.: 1958 The steady flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 44. Aero. Res. Counc. R. and M. 3175.Google Scholar
Aref, H.: 1986 The numerical experiment in fluid mechanics. J. Fluid Mech. 173, 15.Google Scholar
Avci, C. & Giorgini, A., 1985 Impulsively started flow past elliptic cylinders: a numerical study. Tech. Rep. CE-HSE-87–02. School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Badr, H. M. & Dennis, S. C. R. 1985 Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder. J. Fluid Mech. 158, 447.Google Scholar
Bairstow, L., Cave, B. M. & Lang, E. D., 1922 The two-dimensional slow motion of viscous fluids. Proc. R. Soc. Lond. A 100, 394.Google Scholar
Bairstow, L., Cave, B. M. & Lang, E. D., 1923 The resistance of a cylinder moving in a viscous fluid. Proc. R. Soc. Land. A 223, 383.Google Scholar
Bouard, R. & Coutanceau, M., 1980 The early stage of development of the wake behind an impulsively started cylinder for 40 Re 104. J. Fluid Mech. 101, 583.Google Scholar
Braza, M., Chassaing, P. & Ha Minh, H. 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973 Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105.Google Scholar
Cooley, J. W. & Tukey, J. W., 1965 An algorithm for the machine calculations of the complex Fourier series. Math. Comput. 19, 297.Google Scholar
Cowley, S. J.: 1983 Computer extension and analytic continuation of Blasius' expansion for impulsive flow past a circular cylinder. J. Fluid Mech. 135, 389.Google Scholar
Crane, R. L. & Klopfenstein, R. W., 1965 A predictor-corrector algorithm with an increased range of absolute stability. J. Assoc. Comput. Machinery 12, 227.Google Scholar
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
Eaton, B. E.: 1987 Analysis of laminar vortex shedding behind a circular cylinder by computer aided flow visualization. J. Fluid Mech. 180, 117.Google Scholar
Ece, M. C., Walker, J. D. A. & Doligalski, T. L. 1984 The boundary layer on an impulsively started rotating and translating cylinder. Phys. Fluids 27, 1077.Google Scholar
Ecer, A., Rout, R. K. & Ward, P., 1983 Investigation of solution of Navier—Stokes equations using a variational formulation. Intl J. Numer. Meth. Fluids 3, 23.Google Scholar
Fornberg, B.: 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819.Google Scholar
Gioegini, A.: 1968 Numerical Fourier analysis. Tech. Rep. 25. School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Giorgini, A. & Alfonsi, G., 1987 Influence of perturbation spread on the wake behind a circular cylinder: numerical experiments at Re = 1000. Tech. Rep. CE-HSE-87–8. School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Giorgini, A. & Rinaldo, A., 1982 A mixed discrete Fourier transform-quasi analytic algorithm for the solution of the Navier—Stokes equations: presentation of the method. Tech. Rep. CE-HSE-82–17. School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Giorgini, A. & Teavis, J. R., 1969 A short convolution. Tech. Rep. 2. Water Resources and Hydromechanics Laboratory, School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Hamidi, A. & Giorgini, A., 1985 Numerical solution of the Napier-Stokes equations: direct radial integration. Tech. Rep. CE-HSE-85–02. School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Hamielec, A. E. & Raal, J. D., 1969 Numerical studies of viscous flow around circular cylinders. Phys. Fluids 12, 11.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
Ingham, D. B.: 1983 Steady flow past a rotating cylinder. Comput. Fluids 11, 351.Google Scholar
Jackson, C. P.: 1987 A finite element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23.Google Scholar
Jain, P. C. & Rao, K. Sankara 1969 Numerical solution of unsteady viscous incompressible fluid flow past a circular cylinder. Phys. Fluids Suppl. 12, II 57.Google Scholar
Jordan, S. K. & Fromm, J. E., 1972 Oscillatory drag, lift and torque on a circular cylinder in a uniform flow. Phys. Fluids 15, 371.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
Kawaguti, M. & Jain, P. C., 1966 Numerical study of a viscous fluid past a circular cylinder. J. Phys. Soc. Japan 21, 2055.Google Scholar
Keller, H. B. & Takami, H., 1966 Numerical studies of viscous flows about cylinders. In Numerical Solutions of Nonlinear Differential Equations (ed. D. Greenspan). Wiley.
Lin, C. L., Pepper, D. W. & Lee, S. C., 1976 Numerical methods for separated flow solutions around a circular cylinder. AIAA J. 14, 900.Google Scholar
Nieuwstadt, F. & Keller, H. B., 1973 Viscous flow past circular cylinders. Comput. Fluids 1, 59.Google Scholar
Okajima, A., Takata, H. & Asanuma, T., 1975 Viscous flow around a rotationally oscillating circular cylinder. Institute of Space and Aeronautical Science, University of Tokyo Rep. 532.Google Scholar
Orszag, S. A.: 1971 Numerical simulation of incompressible flows within simple boundaries: accuracy. J. Fluid Mech. 49, 75.Google Scholar
Panikker, P. K. G. & Lavan, Z. 1975 Flow past impulsively started bodies using Green's function. J. Comput. Phys. 18, 46.Google Scholar
Patel, V. A.: 1976 Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of the series truncation. Comput. 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
Pravia, J. R. & Giorgini, A., 1985 A spectral finite analytic technique for the numerical integration of the Navier—Stokes equations: the impulsively started circular cylinder at Re = 3000. Tech. Rep. CE-HSE-85–15. School of Civil Engineering, Purdue University, Indiana.
Rinaldo, A. & Giorgini, A., 1984 A mixed algorithm for the calculation of rapidly varying fluid flows: the impulsively started circular cylinder. Intl J. Numer. Meth. Fluids 4, 949.Google Scholar
Roache, P. J.: 1976 Computational Fluid Dynamics. Hermosa.
Roshko, A.: 1953 On the development of turbulent wake from vortex streets. NACA Tech. Note 2913.Google Scholar
Roshko, A.: 1954 On the drag and shedding frequency of two-dimensional bluff bodies. NAGA Tech. Note 3169.Google Scholar
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
Smith, F. T.: 1981 Comparisons and comments concerning recent calculations for flow past a circular cylinder. J. Fluid Mech. 113, 407.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 Phuoc, Loc 1980 Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder. J. Fluid Mech. 100, 111.Google Scholar
Ta Phuoc, Loc & Bouard, R. 1985 Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualizations and measurements. J. Fluid Mech. 160, 93.Google Scholar
Takami, H. & Keller, H. B., 1969 Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder. Phys. Fluids Suppl. 12, II 51.Google Scholar
Tamada, K., Miura, H. & Miyagi, T., 1983 Low-Reynolds-number flow past a cylindrical body. J. Fluid Mech. 132, 445.Google Scholar
Thom, A.: 1932 Arithmetical solution of problems in steady viscous flow. Aero. Res. Comm. R. and M. 1475.Google Scholar
Thom, A.: 1933 The flow past circular cylinders at low speeds. Proc. R. Soc. Lond. A 141, 651.Google Scholar
Thoman, D. C. & Szewczyk, A. A., 1969 Time-dependent viscous flow over a circular cylinder. Phys. Fluids Suppl. 12, II 76.Google Scholar
Travis, J. R. & Giorgini, A., 1971 Numerical simulation of the Navier—Stokes equations in Fourier space. Tech. Rep. 30. Water Resources and Hydromechanics Laboratory, School of Civil Engineering, Purdue University, West Lafayette, Indiana.
Triantafyllou, G. S., Triantafyllou, M. S. & Chryssostomidis, C., 1986 On the formation of vortex streets behind stationary cylinders. J. Fluid Mech. 170, 461.Google Scholar
Tuann, S. Y. & Olson, M. D., 1978 Numerical studies of the flow around a circular cylinder by a finite element method. Comput. Fluids 6, 219.Google Scholar
Underwood, R. L.: 1969 Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers. J. Fluid Mech. 37, 95.Google Scholar
Wu, J. C. & Thompson, J. F., 1973 Numerical solutions of time-dependent incompressible Navier-Stokes equations using an integro-differential formulation. Comput. Fluids 1, 197.Google Scholar