Numerical Simulation of the Flow Around an Infinitely Long Circular Cylinder in the Transition Regime

Abstract.

The development of three-dimensional structures and the succeeding transition to turbulence occurs in the wake of a circular cylinder at Reynolds numbers 190≤Re≤330. This regime is investigated numerically by means of a spectral element method. Earlier numerical works aimed mainly at reproducing characteristic wake patterns observed in experiments. Small sizes of computational domains and short integration times were chosen to save computational resources. Consequently, the quantitative results show a considerable scatter. Within this work, a step by step approach to highly accurate direct numerical simulations is described. Thorough studies of the effect of resolution and blockage are performed in the laminar, two-dimensional regime, resulting in Reynolds number relationships that exactly reproduce experimental data. Based on these results, a stability analysis is performed to obtain wavelengths that are unstable against spanwise perturbations and the critical Reynolds number for the onset of three-dimensionality. The most unstable wavelengths of the “mode A” and “mode B” instabilities and its multiples are used as periodicity length for direct numerical simulations. Effects of integration time, resolution in streamwise as well as spanwise directions, and periodicity length on the flow quantities are studied. Numerically obtained Reynolds number relationships of Strouhal number and base-pressure coefficients that fit accurately within measured results are given for the first time. Curves for drag and lift coefficients are provided and compared with previous numerical studies. Furthermore, physical interpretations of the wake transition are discussed. Since the separation of physical features and effects of experimental arrangements are frequently an open question, our numerical results are able to supply a contribution to the understanding of the physics of cylinder flow.