Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification

Abstract

Flow structures, Strouhal numbers and their downstream evolutions in the wake of two-staggered circular cylinders are investigated at Re =7000 using hot-wire, flow-visualization and particle-image velocimetry techniques. The cylinder centre-to-centre pitch, P, ranges from 1.2 d to 4.0 d (d is the cylinder diameter) and the angle (α) between the incident flow and the line through the cylinder centres is 0° ∼ 90°. Four distinct flow structures are identified at x/d ≥ 10 (x is the downstream distance from the mid-point between the cylinders), i.e. two single-street modes (S-I and S-II) and two twin-street modes (T-I and T-II), based on Strouhal numbers, flow topology and their downstream evolution. Mode S-I is further divided into two different types, i.e. S-Ia and S-Ib, in view of their distinct vortex strengths. Mode S-Ia occurs at P/d ≤ 1.2. The pair of cylinders behaves like one single body, and shear layers separated from the free-stream sides of the cylinders roll up, forming one street of alternately arranged vortices. The street is comparable to that behind an isolated cylinder in terms of the topology and strength of vortices. Mode S-Ib occurs at α ≤ 10° and P/d > 1.5. Shear layers separated from the upstream cylinder reattach on or roll up to form vortices before reaching the downstream cylinder, resulting in postponed flow separation from the downstream cylinder. A single vortex street thus formed is characterized by significantly weakened vortices, compared with Mode S-Ia. Mode S-II is identified at P/d =1.2∼2.5 and α ≥ 20° or 1.5≤ P/d ≤4.0 and 10° < α≤20°, where both cylinders generate vortices, with vortex shedding from the upstream cylinder at a much higher frequency than from the downstream, producing two streets of different widths and vortex strengths at x/d ≤5.0. The two streets interact vigorously, resulting in a single street of the lower-frequency vortices at x/d ≥10. The vortices generated by the downstream cylinder are significantly stronger than those, originating from the upstream cylinder, in the other row. Mode T-I occurs at P/d ≥2.5 and α = 20°∼88° the two cylinders produce two streets of different vortex strengths and frequencies, both persisting beyond x/d = 10. At P/d ≥2.5 and α≥88°, the two cylinders generate two coupled streets, mostly anti-phased, of the same vortex strength and frequency (St ≈0.21), which is referred to as Mode T-II. The connection of the four modes with their distinct initial conditions, i.e. interactions between shear layers around the two cylinders, is discussed.