Flow-induced vibration of two cylinders in tandem and staggered arrangements

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. A numerical study of the flow-induced vibration of two elastically mounted cylinders in tandem and staggered arrangements at Reynolds number Re = 200 is presented. The cylinder centres are set at a streamwise distance of 1.5 cylinder diameters, placing the rear cylinder in the near-wake region of the front cylinder for the tandem arrangement. The cross-stream or lateral offset is varied between 0 and 5 cylinder diameters. The two cylinders are identical, with the same elastic mounting, and constrained to oscillate only in the cross-flow direction. The variation of flow behaviours is examined for static cylinders and for elastic mountings of a range of spring stiffnesses, or reduced velocity. At least seven major modes of flow response are identified, delineated by whether the oscillation is effectively symmetric, and the strength of the influence of the flow through the gap between the two cylinders. Submodes of these are also identified based on whether or not the flow remains periodic. More subtle temporal behaviours, such as period doubling, quasi-periodicity and chaos, are also identified and mapped. Across all of these regimes, the amplitudes of vibration and the magnitude of the fluid forces are quantified. The modes identified span the parameter space between two important limiting cases: two static bodies at varying lateral offset; and two elastically mounted bodies in a tandem configuration at varying spring stiffnesses. Some similarity in the response of extremely stiff or static bodies and extremely slack bodies is shown. This is explained by the fact that the slack bodies are free to move to an equilibrium position and stop, effectively becoming a static system. However, the most complex behaviour appears between these limits, when the bodies are in reasonably close proximity, and the natural structural frequency is close to the vortex shedding frequency of a single cylinder. This appears to be driven by the interplay between a series of time scales, including the vortex formation time, the advection time across the gap between the cylinders and the oscillation period of both bodies. This points out an important difference between this multi-body system and the classic single-cylinder vortex-induced vibration: two bodies in close proximity will not oscillate in a synchronised, periodic manner when their natural structural frequencies are close to the nominal vortex shedding frequency of a single cylinder.

Flow states and transitions in flows past arrays of tandem cylinders

“…Validation of the code for multiple body flows and further details of the actual implementation used here can be found in Griffith & Leontini (2017) and Griffith et al. (2017).…”

“…This process, and the critical value of pitch at which vortex shedding in the gap occurs, has been shown to be only weakly affected by the Reynolds number over the range (Zdravkovich 1987; Sumner, Price & Paidoussis 2000; Hu & Zhou 2008; Sumner 2010; Zhou & Alam 2016; Griffith et al. 2017).…”

Effect of Gap Flow on the Characteristics of Flow-Around and Flow-Induced Vibration for Two Circular Cylinders with Roughness Strips

“…With the slight increase of staggered spacing and reduced velocity, the two cylinders were still in the mode of periodic vibration. The difference is that the mode of periodic vibration was perioddoubling referred by Griffith [30], as shown in Figure 9b. When the staggered spacing increased to T/D = 0.8, the downstream cylinder was still in periodic vibration mode, while the upstream cylinder was in multi-periodic vibration mode.…”

“…It was found that the vortex shedding modes were different under different arrangement modes, and only the vibration of staggered arrangement was periodic and stable. Griffith et al [30] numerically simulated the FIV response of two staggered cylinders and classified the relationship between gap distance, reduced velocity and vibration response, which were divided into a low reduced velocity zone, a critical state zone, a wake dominant zone, a gap flow dominant zone, and so on. Borazjani et al [31] studied the VIV of two tandem cylinders in the wake-dominant region.…”

Relations of POD modes and Lyapunov exponents to the nonlinear dynamic states in flow over oscillating tandem cylinders

“…Flow passing through two identical stationary tandem cylinders is a simper version of this system that is only influenced by the Reynolds number and the center-to-center distance between the two cylinders. Experiments [5][6][7] and numerical simulations [8][9][10][11][12][13][14][15] have long been conducted. It was found that there are three wake-vortex/cylinder interaction regimes: vortex suppression, critical separation, and vortex formation, by changing the center to center distance between the two cylinders in both low Reynolds-number 1,8 and high Reynolds-number 16 flows.…”