Onset of vortex shedding and hysteresis in flow over tandem sharp-edged cylinders of diverse cross sections

Abstract

Numerical simulations are conducted to analyze flow characteristics around two tandem sharp-edged cylinders with cross sections of square (b1*=1) for the upstream cylinder and rectangle (b2*) for the downstream cylinder (b*=b/a, where a and b are the sides of the cylinder). This study investigates the effects of Reynolds numbers (Re = 30–150), cross-sectional aspect ratios of the downstream cylinder (b2*=1–4), and scaled gap-spacing between cylinders (S* = 1–6) on the flow structure, onset of vortex shedding, hysteresis, and aerodynamic parameters (such as drag coefficient, Strouhal number, root mean square lift and drag coefficients, and so on). The results reveal that increasing b2* suppresses the vortex shedding of the upstream cylinder, depending on S*. The suppression is attributed to the interference effect and the adhesion of the shear layers on the downstream cylinder. Three distinct time-mean flow patterns are identified based on the separation and reattachment of shear layers. Flow pattern Ι exhibits parallel flow along the side faces of the upstream cylinder, while the separation bubbles associated with reattachment points are formed in flow pattern II on these faces. For pattern III, no reattachment point is observed, and the separation bubbles cover the upstream cylinder' side faces. Additionally, two instantaneous flow patterns of extended-body and co-shedding are apperceived within the ranges of examined Re and S*. The behaviors of time-mean and varying forces as well as the vortex shedding frequency are correlated with the flow structures. The onset of vortex shedding and hysteresis dependence is discussed comprehensively. The results show that the critical Reynolds numbers for the onset of vortex shedding decrease from 127.5 ± 2.5 to 49.5 ± 2.5 with S* increasing from 1 to 6 (b1* = 1 and b2* = 4). The hysteresis limit is found within the range of 3.5≤S*≤4.5 for flow over two tandem cylinders (b1* = 1 and b2* = 4) at Re = 150.