Influence of cylinder breadth and shape on the onset of flow unsteadiness and the aeolian tone level

Abstract

The Reynolds number for the onset of flow unsteadiness is determined for several canonical geometries (triangles, rectangles, ellipses and lozenges) at different sectional breadth (L) to height (d) ratios (aspect ratio AR=L∕d), for more than 70 shapes. The flow is modeled using a direct Navier–Stokes incompressible two-dimensional solver and the shape is defined by an Immersed Boundary Method. The employed procedure takes the fluctuation of the velocity in the wake as the criterion to define the unsteadiness and a binary search to find the transition. This procedure yields critical Reynolds number Rec values in agreement with available data in the literature. When AR approaches zero, the five shapes lead to almost the same value of 31, which corresponds to Rec for a flat plate normal to the flow. It is then found that Rec grows exponentially with the aspect ratio, the influence of the cross section shape being accounted for by a single regression parameter. For all aspect ratios, the ellipse exhibits the highest Rec, and the front-pointing triangle the lowest, the three other geometries laying in between those two. The physics of the influence of cross-section shape on Rec is analyzed, considering its link with recirculation length in particular. An exploitation of the results is outlined for the analysis of recent aeroacoustic shape optimizations at fixed Re=150, through correlation between the lift fluctuation at this regime with the distance to the onset of unsteadiness it corresponds to.