Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of series truncation

Abstract

Semi-analytic solutions of the Navier-Stokes equations are calculated for two-dimensional, symmetrical, viscous incompressible flow past a circular cylinder. The stream and vorticity functions are expanded in the finite Fourier series and then substituted in the Navier-Stokes equations. This led to a system of coupled parabolic partial differential equations which are solved numerically. More terms of the series are required as Reynolds number increases and the present calculations were terminated at Reynolds number 600 with 60 terms of Fourier series. The results are compared with similar calculations and experimental data for Reynolds numbers 60, 100, 200, 500, 550 and 600. At the termination of the calculations for Reynolds numbers 60 and 100, the separation angle, the wake length, the drag coefficient, and the vorticity distributions around the surface were very close to their steady-state values. A secondary vortex appeared on the surface of the cylinder in the case of Reynolds numbers 500, 550 and 600. The wake length, the drag coefficient and the separation angle differ slightly at a given instant in the case of Reynolds numbers 500, 550 and 600.