Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T17:03:36.867Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method

Published online by Cambridge University Press:  26 April 2006

Chien-Cheng Chang and
Ruey-Ling Chern
Chien-Cheng Chang
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 10764, Taiwan, R.O.C.
Ruey-Ling Chern
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 10764, Taiwan, R.O.C.
Get accessRights & Permissions [Opens in a new window]

Abstract

Impulsively started flow around a circular cylinder at various Reynolds numbers is studied by a deterministic hybrid vortex method. The key feature of the method consists in solving the viscous vorticity equation by interlacing a finite-difference method for diffusion and a vortex-in-cell method for convection. The vorticity is updated along the surface of the cylinder to satisfy the no-slip condition. The present method is basically different from previous applications of vortex methods, which are primarily in the context of random vortex algorithms. The Reynolds numbers of the flows under investigation range from 300 to 106. Numerical results are compared with analytical solutions at small times, and compared with finite-difference solutions and flow visualization results at relatively long times. Satisfactory agreement is found in the evolutions of the separation angles, wake lengths, surface pressure and drag coefficients, streamline patterns, and some velocities on the axis of symmetry behind the circular cylinder. The present hybrid vortex method is highly stable and suffers from little numerical diffusivity, yielding convincing numerical results for unsteady vortical flows at moderately high Reynolds numbers.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991, pp. 243 - 263
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.)

Article purchase

Temporarily unavailable

References

Bar-Lev, M. & Yang, H. T. 1975 Initial flow field over an impulsively started circular cylinder. J. Fluid Mech. 72, 625–647.Google Scholar
Beale, J. T. & Majda, A. 1985 High order accurate vortex methods with explicit kernels. J. Comput. Phys. 58, 188–208.Google Scholar
Bouard, R. & Coutanceau, M. 1980 The early stage of development of the wake behind an impulsively started circular cylinder for 40 < Re < 104. J. Fluid Mech. 101, 583–607.Google Scholar
Cheer, A. Y. 1983 A study of incompressible 2-D vortex flow past a circular cylinder. SIAM J. Sci. Stat. Comput. 4, 685–705.Google Scholar
Cheer, A. Y. 1989 Unsteady separated wake behind an impulsively started cylinder in slightly viscous fluid. J. Fluid Mech. 201, 485–505.Google Scholar
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 785–796.Google Scholar
Chorin, A. J. 1978 Vortex sheet approximation of boundary layers. J. Comput. Phys. 27, 428–442.Google Scholar
Christiansen, J. P. 1973 Numerical simulation of hydrodynamics by the method of point vortices. J. Comput. Phys. 13, 363–379.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973a The initial flow past an impulsively started circular cylinder. Q.J. Mech. Appl. Maths 26, 53–72.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973b Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105–127.Google Scholar
Ghoniem, A. F., Chorin, A. J. & Oppenheim, A. K. 1982 Numerical modeling of turbulent flow in a combustion tunnel.. Phil. Trans. R. Soc. Lond. A 304, 303–325.Google Scholar
Graham, J. M. R. 1988 Computation of viscous separated flow using a particle method. In Numerical Methods for Fluid Dynamics, vol. 3, (ed. K. W. Morton & M. J. Baines), pp. 310–317. Oxford University Press.
Hald, O. H. 1979 The convergence of vortex methods II. SIAM J. Numer. Anal. 16, 726–755.Google Scholar
Honji, H. & Taneda, S. 1969 Unsteady flow past a circular cylinder. J. Phys. Soc. Japan 27, 1668–1677.Google Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comput. Phys. 37, 289–335.Google Scholar
Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex elements. Ann. Rev. Fluid Mech. 17, 523–559.Google Scholar
Panton, R. L. 1984 Incompressible Flow. Wiley.
Sarpkaya, T. 1989 Computational methods with vortices – the 1988 Freeman Scholar Lecture. Trans. ASME T: J. Fluids Engng 111, 5–52.Google Scholar
Sethian, J. A. 1984 Turbulent combustion in open and closed vessels. J. Comput. Phys. 54, 425–456.Google Scholar
Smith, P. A. & Stansby, P. K. 1988 Impulsively started flow around a circular cylinder by the vortex method. J. Fluid Mech. 194, 45–77.Google Scholar
Ta Phuoc Loc 1980 Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder. J. Fluid Mech. 100, 111–128.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 visualization and measurements. J. Fluid Mech. 160, 93–117.Google Scholar
Thoman, D. C. & Szewczyk, A. A. 1969 Time-dependent viscous flow over a circular cylinder. Phys. Fluids Suppl. 12 II, 76–86.Google Scholar
Tiemroth, E. C. 1986 Simulation of the viscous flow around a cylinder by the random vortex method. Ph.D. thesis. University of California, Berkeley.
Turitton, D. J. 1988 Physical Fluid Dynamics (2nd Edn). Oxford University Press.
Wang, C. Y. 1967 The flow past a circular cylinder which is started impulsively from rest. J. Maths & Phys. 46, 195–202.Google Scholar