Kármán Vortex Street behind a Circular Cylinder by the Series Truncation Method
Abstract
Semianalytical solutions of the NavierStokes equations are presented for twodimensional, viscous, and incompressible flow past a circular cylinder for Reynolds numbers 100, 200 and 500. The stream and vorticity functions are expanded in a finite Fourier series and then substituted in the NavierStokes equations. This leads to a system of coupled parabolic partial differential equations which are solved numerically. In order to excite the flow an asymmetric disturbance in the form of rotation at a constant angular velocity of a cylinder in clockwise and counterclockwise directions is introduced for a short time. This small disturbance very slowly triggers the start of vortex shedding. The flow pattern in the separated region, lift and separation angle oscillate with a definite pattern. The calculated drag, lift, pressure and vorticity distributions around the surface, separation angle and Strouhal number are compared with similar calculations and with available experimental data. Also, a comparison of the calculations has been made for Reynolds number 100 with N = 25 and N = 40.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 1978
 DOI:
 10.1016/00219991(78)90044X
 Bibcode:
 1978JCoPh..28...14P
 Keywords:

 Circular Cylinders;
 Computer Programs;
 Fourier Series;
 Karman Vortex Street;
 NavierStokes Equation;
 Two Dimensional Flow;
 Finite Difference Theory;
 Flow Distribution;
 Incompressible Flow;
 Parabolic Differential Equations;
 Reynolds Number;
 Truncation Errors;
 Viscous Flow;
 Vortex Streets;
 Vorticity;
 Fluid Mechanics and Heat Transfer