Aerodynamic performances and wake topology past a square cylinder in the interface of two different-velocity streams

Abstract

We analyze the incompressible flow past a square cylinder immersed in the wake of an upstream splitter plate, which separates two streams of different velocities, UT (top) and UB (bottom). The Reynolds number associated with the flow below the plate is kept constant at ReB=DUB/ν=56, based on the square cylinder side D as characteristic length. The top-to-bottom flow dissymmetry is measured by the ratio R≡ReT/ReB∈[1,5.3] between the Reynolds numbers above and below the plate. The equivalent bulk Reynolds taken as the mean between top and bottom changes with R in the range Re≡(ReT+ReB)/2∈[56,178]. A Hopf bifurcation occurs at R=2.1±0.1 (Re=86.8±2.8), which results in an asymmetric Kármán vortex street with vortices only showing on the high-velocity side of the wake. A spanwise modulational instability is responsible for the three-dimensionalization of the flow at R≃3.1 (Re≃115) with the associated wavelength of λz≃2.4. For velocity ratios R≥4, the flow becomes spatiotemporally chaotic. The migration of the mean stagnation and base pressure points on the front and rear surfaces of the cylinder as R is increased determine the boundary layer properties on the top and bottom surfaces and, with them, the shear layers that roll up into the formation of Kármán vortices, which in turn help to clarify the evolution of the lift and drag coefficients. The symmetries of the different solutions across the flow transition regime are imprinted on the top and bottom boundary layers and can, therefore, be analyzed from the time evolution and spanwise distribution of trailing edge boundary layer displacement thickness at the top and bottom rear corners.