Pulsating Flow Past a Square Cylinder: Analysis of Force Coefficient Spectra and Vortex Structure Development

Abstract

This study examines the changes in force coefficients and wake flow structures of a square cylinder subject to pulsating in-flow at different frequencies. The Reynolds number is 200, according to previous literature. Over a range of forcing frequencies, a regime is observed where the shedding frequency scales with the forcing frequency rather than the natural shedding frequency, known as the lock-in phenomenon in literature. The change in spectral character across three frequency regimes—pre-lock-in, lock-in, and post-lock-in—are examined and characterized. During pre-lock-in, the shedding frequency remains equal to the natural shedding frequency. However, the corresponding peak in lift coefficient (CL) power spectral density (PSD) is a single decade larger than that of neighboring minima. This contrasts greatly with subsequent regimes where the amplitudes of the peaks are observed to be substantially larger than the amplitudes of neighboring minima. The onset of lock-in is sharp, and the corresponding excitation frequency is identified. The shedding frequency becomes a function of the forcing frequency within this regime, and the corresponding CL PSD peak is four decades larger than that of neighboring minima. The transition beyond the lock-in regime is gradual with peaks of the spectra broadening until separating into multiple discrete peaks. To comprehend the changes in the force coefficients, the vortex structure in the wake is characterized at different frequencies. The connection between the vortex development sequence and force profile is investigated, and z-vorticity probes are utilized to correlate these qualitative observations with prior quantitative analysis. Three-dimensional flow effects are also examined.