On the use of several compact methods for the study of unsteady incompressible viscous flow round a circular cylinder

Abstract Fourth order accurate methods of mehrstellen type are compared to second order accurate methods for the solution of the unsteady incompressible Navier-Stokes equations in their vorticity stream function formulation. These methods are applied to the study of separated flow around a circular cylinder at several Reynolds numbers. The impulsively started cylinder at Re = 200 and 550, is considered without symmetry restrictions. The features illustrated include the bulge phenomenon at Re = 200, the occurrence of secondary vortices depending on the schemes used at Re = 550, and of twin secondary vortices at Re = 3000. The Karman vortex street is investigated at Re = 200 with a uniform flow in the far field and with superimposed motions of the cylinder. In this last case, a frequency analysis has allowed a critical examination of results pertaining to locked-in situations with respect to confinement effects.

[1]  D. Ingham.  Note on the numerical solution for unsteady viscous flow past a circular cylinder , 1968, Journal of Fluid Mechanics.

[2]  D. W. Pepper,et al.  Numerical Methods for Separated Flow Solutions around a Circular Cylinder , 1976 .

[3]  Separate Treatment of Attached and Detached Flow Regions in General Viscous Flows , 1981 .

[4]  S. Taneda,et al.  Unsteady Flow past a Circular Cylinder , 1969 .

[5]  R. F. Warming,et al.  Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative , 1980 .

[6]  M Israeli,et al.  Numerical Simulation of Viscous Incompressible Flows , 1974 .

[7]  Mitutosi Kawaguti,et al.  Numerical Study of a Viscous Fluid Flow past a Circular Cylinder , 1966 .

[8]  J. Wu.  Theory for Aerodynamic Force and Moment in Viscous Flows , 1981 .

[9]  A. Staniforth,et al.  A numerical method for calculating the initial flow past a cylinder in a viscous fluid , 1971 .

[10]  V. A. Patel.  Kármán vortex street behind a circular cylinder by the series truncation method , 1978 .

[11]  S. Dennis,et al.  THE INITIAL FLOW PAST AN IMPULSIVELY STARTED CIRCULAR CYLINDER , 1973 .

[12]  Richard Evelyn Donohue Bishop,et al.  The lift and drag forces on a circular cylinder in a flowing fluid , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  G. Koopmann,et al.  The vortex-excited lift and reaction forces on resonantly vibrating cylinders , 1977 .

[14]  E. Krause,et al.  Fourth order “mehrstellen”-integration for three-dimensional turbulent boundary layers , 1976 .

[15]  G. H. Koopmann,et al.  The vortex wakes of vibrating cylinders at low Reynolds numbers , 1967, Journal of Fluid Mechanics.

[16]  K. C. Wang.  On the Current Controversy about Unsteady Separation , 1981 .

[17]  J. F. Thompson,et al.  Numerical solutions of time-dependent incompressible Navier-Stokes equations using an integro-differential formulation , 1973 .

[18]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[19]  U. B. Mehta,et al.  Dynamic stall of an oscillating airfoil , 1978 .

[20]  Alan E. Berger,et al.  Generalized OCI schemes for boundary layer problems , 1980 .

[21]  S. Jordan,et al.  Oscillatory Drag, Lift, and Torque on a Circular Cylinder in a Uniform Flow , 1972 .

[22]  Ta Phuoc Loc.  Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder , 1980 .

[23]  Y. Adam,et al.  Highly accurate compact implicit methods and boundary conditions , 1977 .

[24]  Y. Tanida,et al.  Stability of a circular cylinder oscillating in uniform flow or in a wake , 1973, Journal of Fluid Mechanics.

[25]  Z. Lavan,et al.  Flow past impulsively started bodies using green's functions , 1975 .

[26]  M. Ciment,et al.  Review. The Operator Compact Implicit Method for Parabolic Equations , 1978 .

[27]  P. Jain,et al.  Shedding of vortices behind a circular cylinder , 1976 .

[28]  V. A. Patel.  Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of series truncation , 1976 .

[29]  R. B. Payne,et al.  Calculations of unsteady viscous flow past a circular cylinder , 1958, Journal of Fluid Mechanics.

[30]  Sadatoshi Taneda,et al.  Visual study of unsteady separated flows around bodies , 1976 .

[31]  T. Sarpkaya.  Vortex-Induced Oscillations: A Selective Review , 1979 .

[32]  T. J. Hanratty,et al.  Numerical solution for the flow around a cylinder at Reynolds numbers of 40, 200 and 500 , 1969, Journal of Fluid Mechanics.

[33]  D. Telionis.  Unsteady Viscous Flows , 1981 .

[34]  Malcolm L. Spaulding,et al.  Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream , 1982 .

[35]  F. Smith.  On the High Reynolds Number Theory of Laminar Flows , 1982 .

[36]  S. Dennis,et al.  Flow past an impulsively started circular cylinder , 1973, Journal of Fluid Mechanics.

[37]  R. Wille,et al.  Kármán Vortex Streets , 1960 .

[38]  L. Collatz.  The numerical treatment of differential equations , 1961 .

[39]  A. A. Szewczyk,et al.  Time‐Dependent Viscous Flow over a Circular Cylinder , 1969 .

[40]  Madeleine Coutanceau,et al.  The early stage of development of the wake behind an impulsively started cylinder for 40 < Re < 104 , 1980, Journal of Fluid Mechanics.

[41]  James Chen-yuan Wu,et al.  Unsteady viscous flow , 1975 .