Onset of vortex shedding from a bluff body modified from square cylinder to normal flat plate

Abstract

This study numerically investigates the time-resolved laminar flow over rectangular cylinders with cross-sectional aspect ratio Ar varying from square cylinder (Ar = 1) to normal flat plate (Ar = 0.1) for Reynolds number Re = 40–100. The focus is given on how Ar influences the wake structure, fluid force, St, and critical Reynolds number Rec associated with the onset of vortex shedding. The Stuart-Landau equation is employed to determine Rec. With increasing Re, time-mean drag coefficient C‾D increases and decreases for Ar < 0.5 and Ar > 0.5, respectively. The Re effect on C‾D is strongest for Ar = 0.1 and weakest for Ar = 0.5. On the other hand, St monotonically increases with Re for all Ar values examined. Both C‾D and St at a given Re diminish with increasing Ar. A decrease in Ar from 1.0 to 0.1 destabilizes the flow, reducing the Rec from 47.8 to 29.8. The dependence of Rec on the flow attack angle α = (0° - 45°) for the square cylinder shows Rec declining from Rec = 47.8 at α = 0° to Rec = 40.2 at α = 45°. A comparison of Ar effects on Rec is made between rectangular (present study) and elliptical cylinders, both changing toward the normal flat plate. The rectangular cylinders have a smaller Rec than the elliptical cylinders for Ar < 1 while the opposite is the case for Ar = 1.