Two circular cylinders in cross-flow: A review

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex–structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

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On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism

The dominant vortex frequencies
f
s in the wake of two tandem circular cylinders of identical diameter d have been measured simultaneously using two hot wires placed behind each cylinder. Measurements were conducted over the Reynolds number
Re (≡U
∞
d/ν, where U
∞ and
ν are the free-stream velocity and the kinematic viscosity of fluid, respectively) =800–4.2×104 and the cylinder centre-to-centre spacing L/d=1–15. The Strouhal number
St (≡f
s
d/U
∞) exhibits a strong dependence on L/d and Re. For L/d (L/d)c, co-shedding occurs, that is, vortices are shed from the upstream as well as the downstream cylinder, and their frequencies are found to be identical.
St climbs with increasing
L/d, approaching a constant between 0.18 and 0.22 for L/d>10. The
St–Re relationship is classified into four categories, based on their behaviours, which are associated with distinct flow physics—category 1: for 1≤L/d 5 is characterized by co-shedding only. The present measurements reconfirm the previous observation of a bi-stable flow at the transition from the reattachment to co-shedding regime. It is found for the first time that another bi-stable flow occurs at the transition from category 1 to 2, that is, the stable reattachment co-exists with the stable rollup (behind the downstream cylinder) of shear layers separating from the upstream cylinder, resulting in two distinct vortex-shedding frequencies even at the same Re and L/d. The St behaviour is further discussed along with flow visualization using the laser-induced fluorescence technique.

Strouhal numbers in the wake of two inline cylinders

This paper presents the results of a numerical study on the flow characteristics and heat transfer over two equal square cylinders in a tandem arrangement. Spacing between the cylinders is five widths of the cylinder and the Reynolds number ranges from 1 to 200, Pr=0.71. Both steady and unsteady incompressible laminar flow in the 2D regime are performed with a finite volume code based on the SIMPLEC algorithm and non-staggered grid. A study of the effects of spatial resolution and blockage on the results is provided. In this study, the instantaneous and mean streamlines, vorticity and isotherm patterns for different Reynolds numbers are presented and discussed. In addition, the global quantities such as pressure and viscous drag coefficients, RMS lift and drag coefficients, recirculation length, Strouhal number and Nusselt number are determined and discussed for various Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd.

Chia-Hung Liu

Papers

Observations of hysteresis in flow around two square cylinders in a tandem arrangement