Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder

Abstract

The mechanism of the creation of secondary vortices behind an impulsively started circular cylinder is analysed in this paper by a higher order of accuracy numerical method. This is a combination of second-order and fourth-order compact finite difference schemes to resolve complete unsteady Navier–Stokes equations. The fourth-order compact scheme is used to calculate the Poisson equation of the stream function and the second-order alternating direction implicit scheme to resolve the vorticity transport equation.In particular, the growth of primary and secondary vortices with time is analysed for Reynolds numbers equal to 300, 550 and 1000. A single secondary vortex first appears at a Reynolds number equal to 300 on the surface of the cylinder. At R = 550, this creation is found numerically at dimensionless time t about 2·85, and this single secondary vortex is transformed into a pair of secondary vortices at t about 5. For R = 1000, two single vortices can be observed at t about 2·5, one near the separation point and another more important, easily identified in flow structure. These secondary vortices are transformed into a pair of secondary vortices at t about 4·5.A numerical analysis of the influence of the grid systems and the time step is also given. All numerical results presented here are compared with experimental visualizations. The comparison is found satisfactory.