Two-dimensional wake dynamics behind cylinders with triangular cross-section under incidence angle variation

Abstract

The wakes behind cylinders having an equilateral triangular cross-section are studied numerically for various cylinder inclinations and Reynolds numbers. For steady flows, the development of the recirculation region near the onset of flow separation is described, and the separation Reynolds numbers mapped for different cylinder inclinations. Cylinder inclinations that are not reflection symmetric about the horizontal centreline produce asymmetric recirculation regions which persist until the flow becomes unstable. Flow separation is observed to initiate on the rear-face of the cylinder and develops in size with increasing Reynolds numbers until the separation points become defined at the triangular cross-section's vertices where they remain even at higher Reynolds numbers. Using the Stuart–Landau equation, the critical Reynolds numbers of the different flow cases are quantified. The inclination of the cylinder is seen to strongly affect the location of the separation points, the dimensions of the recirculation region, and ultimately the critical Reynolds numbers. Increasing the Reynolds number past the instability threshold, a Bénard–von Kármánvortex street is initially observed before the downstream region of the wake re-aligns to a bi-layered vortex structure. Beyond this regime, the vortex street is observed to develop variously. At most cylinder inclinations (α<30° and α≳42°), the bi-layered wake re-assembles into a secondary vortex street further downstream. For a small range of cylinder inclinations (30°≤α≲38°), the shedding vortices interact to form a vortex street similar to that produced by the 2P shedding mode for oscillating circular cylinders, while inclinations 38°≲α<54° describe the development of a P+S-like vortex street. The formation of these unsteady wakes are attributed to vortex interactions in the wake. The drag and lift force coefficients for various cylinder inclinations and Reynolds numbers are also summarised. Phase trajectories of the force coefficients reveal that the transition from the bi-layered wake to the 2P-like wake alters its profile significantly, while the transitions to the other vortex streets observed did not incur such changes.