Wake dynamics behind a rotary oscillating cylinder analyzed with proper orthogonal decomposition

Abstract

Two-dimensional high-order spectral/hp computations are carried out for a cylinder undergoing a sinusoidal rotary oscillation about its own axis. Results are examined for Re=200 and a fixed oscillation amplitude of θ0=π. The study concentrates on a domain of forcing frequencies ranging from 0 to 5f0, with f0 being the natural shedding frequency of the fixed cylinder. The drag of the cylinder is measured to reduce by up to 22% at the optimal frequency. This drag reduction is expected to result from the appearance of negative pressure in the windward regions of cylinder surface. Proper orthogonal decomposition (POD) is then utilized to extract the energetic modes that govern the dynamics of the flow. A novel force decomposition technique proposed by Miyanawala and Jaiman (2019) is reformulated, to allow quantification of the time-dependent contribution from each mode to the pressure drag. Such contribution is found to be affected, in a manner, by the forcing frequency. POD is further used to characterize the spatially evolving nature of the forced wake as it undergoes a transition from the near-wake two-layer shedding pattern to the far-wake Kármán-like shedding pattern. It is also found that a few modes suffice to reconstruct the near-wake accurately, while more modes must be retained to ensure an accurate approximation of the far-wake.