Coexistence of passive vortex-induced vibrations and active pitch oscillation triggered by a square cylinder attached with a deformable splitter plate

To understand passive vortex-induced vibrations (VIV) coexisting with active structure motions, this paper numerically investigates the use of pure pitch oscillation to control a square cylinder mounted with a deformable splitter plate at the Reynolds number of 333. The oscillation is enforced with an amplitude of 3° and different frequencies from 0 to 6 Hz. Direct numerical simulations using a partitioned method with a semi-implicit coupling algorithm are performed. According to the trajectories of the splitter-plate tip displacement with respect to the lift or drag force coefficient, a specific lock-in regime determined by the frequency of the enforced pitch oscillation is identified. Further spectral analyses of the tip displacement and lift force show that the lock-in frequencies are equal to the enforced frequencies. Next to the lock-in regime, semi-lock-in regimes with narrow bandwidths are distinguished, exhibiting both lock-in and non-lock-in features. In the non-lock-in regimes, the frequencies of the most predominant peaks in the spectra are found near the natural frequency of the splitter plate of 3.236 Hz, and the frequencies of the two secondary peaks are distributed along the characteristic lines following the ratios of these frequencies to the enforced frequency, which are ±1. Thus, the interaction is dependent on the combined effects of the passive VIV and the actively enforced pitch oscillations. Moreover, the intersection points of the characteristic lines are located close to the upper and lower frequency limits of the lock-in regime, inferring the conditions for the lock-in onset.