Three-dimensional wake transition of a square cylinder. (6th March 2018)

• Record Type: Journal Article
• Authors: Jiang, Hongyi; Cheng, Liang; An, Hongwei
• Is Part Of: Journal of fluid mechanics. Volume 842(2018)
• Page Start: 102
• Page End: 127
• Publication Date: 2018-03-06
• Subjects: vortex instability, -- vortex streets, -- wakes; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.104
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : Three-dimensional (3-D) wake transition for flow past a square cylinder aligned with sides perpendicular and parallel to the approaching flow is investigated using direct numerical simulation. The secondary wake instability, namely a Mode A instability, occurs at a Reynolds number ( $Re$ ) of 165.7. A gradual wake transition from Mode A* (i.e. Mode A with vortex dislocations) to Mode B is observed over a range of $Re$ from 185 to 210, within which the probability of occurrence of vortex dislocations decreases monotonically with increasing $Re$ . The characteristics of the Strouhal–Reynolds number relationship are analysed. At the onset of Mode A*, a sudden drop of the 3-D Strouhal number from its two-dimensional counterpart is observed, which is due to the subcritical nature of the Mode A* instability. A continuous 3-D Strouhal–Reynolds number curve is observed over the mode swapping regime, since Mode A* and Mode B have extremely close vortex shedding frequencies and therefore only a single merged peak is observed in the frequency spectrum. The existence of hysteresis for the Mode A and Mode B wake instabilities is examined. The unconfined Mode A and Mode B wake instabilities are hysteretic and non-hysteretic, respectively. However, a spanwise confined Mode A could be non-hysteretic. It is proposed that the existence of hysteresis at a wake instability can be identified by examining the sudden/gradual variation of the 3-D flow properties at the onset of the wake instability, with sudden and gradual variations corresponding to hysteretic (subcritical) and non-hysteretic (supercritical) flows, respectively.