On the transition to 3D modes for channel flow past a square cylinder

Abstract

We consider the case of transient three-dimensional, incompressible and isothermal channel flow of a newtonian fluid past a symmetrically confined obstacle of square cross section at zero incidence. The blockage ratio (ratio of cylinder diameter to channel width) is fixed at 1/4. Results from both Laser Doppler (LDV) experiments and direct simulations upto Reynolds numbers (Re ≤ 250) have been reported.Starting from the onset of instability (Re cr ≈ 58), close examination of the apparent region of influence that envelopes the cylinder reveals a clear vortex shedding signature which extends up to about three diameters upstream. While the fundamental vortex shedding frequency displays a fairly steady monotonic increase with Reynolds number, the Strouhal number (St) shows an inflexion point around Re ≈ 115. No signs of hysteresis were detected around this region. Furthermore, incommensurate harmonics observed for Reynolds numbers in the range 127 ≤ Re ≤ 175 suggest a quasi-periodic transition to three-dimensionality. This is shown to be followed by an intermediate periodic window starting around Re ≈ 180. Results from direct simulations performed using OpenFOAM (the Open Source CFD Toolbox) are used not only to enhance confidence in the accuracy of the reported LDV measurements, but also to help explain the observed phenomena through frequency power spectra and spanwise velocity correlations. Finally, it is concluded that only a parametric variation of transverse and spanwise blockage ratios can bring closure to the subject of bluff-body wake transitions.

A review of experiments on stationary bluff body wakes

“…44, an increase in Reynolds number above 277 makes the instability longitudinal with a spanwise length scale of D. This longitudinal instability was shown to be similar to mode B recognized in the unconfined cylinder at Re = 230-260. The effects of confinement on the transition to three-dimensionality behind a square cylinder was also studied by Madhavan et al 227 for Re ≤ 250 and a blockage ratio of 0.25. Mean flow patterns, dynamic vortex shedding and pairing, critical blockage ratio and Reynolds shear stress of three bluff bodies, namely circular cylinder, square cylinder and flat plate, were analysed and compared by Wang et al 228 for blockage ratios from 0.25 to 0.5 at Reynolds numbers of 3200, 4600 and 5400.…”