Effect of thickness-to-chord ratio on the wake of two-dimensional rectangular cylinders

Abstract

The dynamics of the nearly periodic highly modulated turbulent wakes of two-dimensional rectangular cylinders normal to a uniform flow are investigated experimentally for thickness-to-chord ratios between 0.05 and 1.92 at Reynolds numbers around $6600$. Measurements were conducted using planar, time-resolved stereoscopic particle image velocimetry. A generalized phase average analysis, which invokes elements of mean-field theory to relate the temporal modal coefficients of the fundamental harmonic and slow-varying base-flow drift, provided a statistically significant representation of the coherent cycle-to-cycle variation of the shedding process. It is shown that the characteristics of the wake velocity fluctuations change as a function of the thickness-to-chord ratio and can be related to structural differences in the wake topology. Moreover, the trajectory of shed vortices plays an important role in distinguishing the dynamics observed for different fluctuation-amplitude cycles. Based on differences in amplitude modulation characteristics and the vortex formation region topology, three flow regimes can be defined: a thin-plate regime, for which the feedback between forming vortices and base pressure is important; a cylinder-like thick-plate regime for which the obstacle afterbody suppresses the feedback; and a long-plate regime for which wake periodicity is not associated with the classical Kármán shedding process. The present analysis highlights the importance of the feedback mechanism for the thin-plate regime and helps reconcile differences in the reported critical thickness values between regimes.