Turbulence and Heat Transfer of a Hairpin Vortex Formed Behind a Cube in a Laminar Boundary Layer

Formation mechanism of hairpin vortices in the wake of a truncated square cylinder in a duct

“…This corresponds to the base vortices identified by Etzold & Fiedler (1976) and Sau et al (2003). The foci were also detected in numerical simulations by Hwang & Yang (2004) and Yanaoka et al (2007), but were not linked to the formation of base vortices. At Re = 100, these vortices are very weak so that they only induce a weak pressure minimum that is difficult to capture with the iso-surfaces of λ 2 .…”

“…At Re = 200, unsteadiness appears through a periodic laminar symmetric shedding of hairpin vortices aligned on a single row along the wake centreline. This vortex shedding has been observed in experiments by Sakamoto & Arie (1983) and Sakamoto et al (1987) and numerical simulations by Hwang & Yang (2004) and Yanaoka et al (2007). The formation and release of hairpin vortices depicted by iso-surfaces of vorticity field and of λ 2 = −0.5 (0.5% of its absolute minimum) are .…”

“…The streamlines enter this three-vortex structure at the periphery of the symmetric vortices, spiral towards the axis and exit at the periphery of the centre vortex onto the wake centreline. Note that the head vortex is not generated by streamlines curling from the cylinder free end as in Hunt et al (1978), Slaouti & Gerrard (1981) and Wang & Zhou (2009), but from streamlines circulating upwards from the cylinder bottom half as in Sau et al (2003) and Yanaoka et al (2007).…”

“…At Re = 150, secondary recirculation regions appear on both lateral and top faces of the cylinder. The lateral recirculations are made of stretched and twisted blue streamlines and the top one results from flow separation at the cylinder top face as in Yanaoka et al (2007). The top recirculation deflects the outer stream further up, which, combined with the increased strength of the head vortex, results in the latter shifting into a position higher than the cylinder tip in the late stages of the steady flow regime.…”

“…The latter authors also included the tip and base vortices within the arch-vortices released in the wake. Yanaoka et al (2007) simulated the flow past a truncated square cylinder featuring γ = 1 at Re = 500 and claimed that hairpin vortices were originally vortices that detached from the free shear layer stretching from the cylinder free end and then grew into hairpin vortices. Until now though, the generation mechanism of hairpin vortices in the wake of a truncated cylinder has never been the object of any dedicated study so it remains rather unclear.…”