Lock-in regions of laminar flows over a streamwise oscillating circular cylinder

In this paper, flow over a streamwise oscillating circular cylinder is numerically simulated to examine the effects of the driving amplitude and frequency on the distribution of the lock-in regions in laminar flows. At $Re=100$ , lock-in is categorized according to the spectral features of the lift coefficient as two different lock-in phenomena: harmonic and subharmonic lock-in. These lock-in phenomena are represented as maps on the driving amplitude–frequency plane, which have subharmonic lock-in regions and two harmonic lock-in regions. The frequency range of the subharmonic region is shifted to lower frequencies with increasing amplitude, and the lower boundary of this subharmonic region is successfully predicted. A symmetric harmonic region with a symmetric vortex pattern is observed in a certain velocity range for a moving cylinder. Aerodynamic features induced by different flow patterns in each region are presented on the driving amplitude–frequency plane. The lock-in region and aerodynamic features at $Re=200$ and $40$ are compared with the results for $Re=100$ . A subharmonic region and two harmonic regions are observed at $Re=200$ , and these show the same features as for $Re=100$ at a low driving amplitude. Lock-in at $Re=40$ also shows one subharmonic region and two harmonic regions. However, compared with the $Re=100$ case, the symmetric harmonic lock-in is dominant. The features of aerodynamic force at $Re=200$ and $40$ are represented on a force map, which shows similar characteristics in corresponding regions for the $Re=100$ case.