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High-resolution simulations of the flow around an impulsively started cylinder using vortex methods

Published online by Cambridge University Press:  26 April 2006

P. Koumoutsakos  and
A. Leonard
P. Koumoutsakos
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA Present address: NASA Ames 202A-1, Moffett Field, CA 94035, USA.
A. Leonard
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 296 , 10 August 1995 , pp. 1 - 38
Copyright
© 1995 Cambridge University Press

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References

Anderson, C. R. & Reider, M. 1993 Investigation of the use of Prandtl/Navier—Stokes equation procedures for two-dimensional incompressible flows. CAM Rep. 93-02. Department of Mathematics, UCLA.
Bar-Lev, M. & Yang, H. T. 1975 Initial flow field over an impulsively started circular cylinder. J. Fluid Mech. 72, 625–647 (referred to herein as BY).Google Scholar
Barnes, J. E. & Hut, P. 1986 A hierarchical O(NlogN) force-calculation algorithm. Nature 324, 446–449.Google Scholar
Beale, J. T. 1986 On the accuracy of vortex methods at large times. Proc. Workshop on Comp. Fluid Dyn. and React. Gas Flows, IMA, University of Minnesota.
Blasius, H. 1908 Grenzchichten in Flüssigkeiten mit Kleiner Reibug. Z. Angew. Math. Phys. (Engl. transl.) NACA TM-1256 56, p. 1.Google Scholar
Bouard, R. & Coutanceau, M. 1980 The early stage of development of the wake behind an impulsively started cylinder for 40 [les ] Re [les ] 104. J. Fluid Mech. 101, 583–607 (referred to herein as BC).Google Scholar
Bryson, A. E. 1959 Symmetric vortex separation on circular cylinders and cones. Trans. ASME E: J. Appl. Mech. 11, 643.Google Scholar
Chang, C.C. & Chern, R. L. 1991 A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method. J. Fluid Mech. 233, 243–263 (referred to herein as CC).Google Scholar
Christiansen, J. P. 1973 Vortex methods for flow simulation. J. Comput. Phys. 13, 363.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973 The initial flow past an impulsively started circular cylinder. Q. J. Mech. Appl. Maths 26, 53–75 (referred to herein as CD).Google Scholar
Collins, W. M. & Dennis, S. C. R. 1973b Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105–127 (referred to herein as CD).Google Scholar
Degond, P. & Mas-Gallic, S. 1989 The weighted particle method for convection—diffusion equations, Part I: The case of an isotropic viscosity, Part II: The anisotropic case. Math. Comput. 53, 485–526.Google Scholar
Dennis, S. C. R. & Kocabiyik, S. 1991 An asymptotic matching condition for unsteady boundary-layer flows governed by the Navier—Stokes equations. IMA J. Appl. Maths 47, 81–98.Google Scholar
Doligaski, T. L., Smith, C. R. & Walker, J. D. A. 1994 Vortex interactions with walls. Ann. Rev. Fluid Mech. 26, 573–616.Google Scholar
Friedman, A. 1966 Partial Differential Equations of Parabolic Type. Prentice-Hall.
Greengard, L. & Rokhlin, V. 1987 A fast algorithm for particle simulations. J. Comput. Phys. 73, 325–348.Google Scholar
Koumoutsakos, P. 1993 Direct numerical simulations of unsteady separated flows using vortex methods. PhD thesis, California Institute of Technology.
Koumoutsakos, P. & Leonard, A. 1993 Improved boundary integral method for inviscid boundary condition applications. AIAA J. 31, 401–404.Google Scholar
Koumoutsakos, P., Leonard, A. & Pepin, F. 1994 Boundary conditions for viscous vortex methods. J. Comput. Phys. 113, 52.Google Scholar
Lecointe, Y. & Piquet, J. 1984 On the use of several compact methods for the study of the incompressible viscous flow around a circular cylinder. Computers Fluids 12, 255–280.Google Scholar
Lighthill, M. J. 1963 Introduction. In Boundary Layer Theory (ed. J. Rosenhead), pp. 54–61. Oxford University Press.
Payne, R. B. 1958 Calculation of viscous unsteady flows past a circular cylinder. J. Fluid Mech. 4, 81–86.Google Scholar
Prager, W. 1928 Die Druckverteilung an Körpern in ebener Potentialströmung. Physik. Z. 29, 865–869.Google Scholar
Prandtl, W. 1925 The magnus effect and windpowered ships. Wissenschaften 13, 93–108.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 (referred to herein as SS).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 (referred to herein as TL).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
Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547–567.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating boundary layer. J. Comput. Phys. 38, 125–140.Google Scholar
Wang, X. & Dalton, C. 1991 Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder. Intl J. Numer. Meth. Fluids 12, 383–400.Google Scholar
Wu, J. C. 1976 Numerical boundary conditions for viscous flow problems. AIAA J. 14, 1042–1049.Google Scholar
Wu, J.-Z., Wu, X., Ma, H. & Wu, J.-M. 1995 Dynamic vorticity condition: theory and numerical implementation. Intl J. Numer. Meth. Fluids (submitted).Google Scholar