Xu S., Wang M., Zhou Y., Tu J.

It is of both fundamental and practical significance to investigate how the wake of an oscillating cylinder behaves. Investigations involving a streamwise oscillating cylinder in a cross-flow have been rather limited. Five typical flow structures, referred to as S-I, S-II, A-I, A-III and A-IV mode behind a longitudinally oscillating cylinder, have been reported in previous experimental and numerical simulations. This work proposes a theoretical model, based on the boundary vorticity theory, for the prediction of the flow structure behind a longitudinally oscillating cylinder. The 2-D incompressible N-S equations around the cylinder in a moving cylindrical coordinate were reduced to the boundary vorticity equation with the no-slip condition applied. The solution to the reduced vorticity equation unveils that vorticity generated by the cylinder surface comprises of two components: 1 unsteady and anti-symmetrical component, dependent of the cylinder oscillation; 2 steady alternating component associated with the natural vortex shedding. The competition between the two components results in the aforementioned five flow modes. The prediction of the occurrence of the flow modes was conducted based on the solution. In the first-stage work, the prediction of the occurrence of the S-II mode is in good agreement with previously reported experimental and numerical data. Further analysis is under way to predict the occurrence of all other flow modes.