Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity–wake interference region

Abstract

We investigate numerically vortex-induced vibrations (VIV) of two identical two-dimensional elastically mounted cylinders in tandem in the proximity-wake interference regime at Reynolds number Re = 200 for systems having both one (transverse vibrations) and two (transverse and inline) degrees of freedom (1-DOF and 2-DOF, respectively). For the 1-DOF system the computed results are in good qualitative agreement with available experiments at higher Reynolds numbers. Similar to these experiments our simulations reveal: (1) larger amplitudes of motion and a wider lock-in region for the tandem arrangement when compared with an isolated cylinder; (2) that at low reduced velocities the vibration amplitude of the front cylinder exceeds that of the rear cylinder; and (3) that above a threshold reduced velocity, large-amplitude VIV are excited for the rear cylinder with amplitudes significantly larger than those of the front cylinder. By analysing the simulated flow patterns we identify the VIV excitation mechanisms that lead to such complex responses and elucidate the near-wake vorticity dynamics and vortex-shedding modes excited in each case. We show that at low reduced velocities vortex shedding provides the initial excitation mechanism, which gives rise to a vertical separation between the two cylinders. When this vertical separation exceeds one cylinder diameter, however, a significant portion of the incoming flow is able to pass through the gap between the two cylinders and the gap-flow mechanism starts to dominate the VIV dynamics. The gap flow is able to periodically force either the top or the bottom shear layer of the front cylinder into the gap region, setting off a series of very complex vortex-to-vortex and vortex-to-cylinder interactions, which induces pressure gradients that result in a large oscillatory force in phase with the vortex shedding and lead to the experimentally observed larger vibration amplitudes. When the vortex shedding is the dominant mechanism the front cylinder vibration amplitude is larger than that of the rear cylinder. The reversing of this trend above a threshold reduced velocity is associated with the onset of the gap flow. The important role of the gap flow is further illustrated via a series of simulations for the 2-DOF system. We show that when the gap-flow mechanism is triggered, the 2-DOF system can develop and sustain large VIV amplitudes comparable to those observed in the corresponding (same reduced velocity) 1-DOF system. For sufficiently high reduced velocities, however, the two cylinders in the 2-DOF system approach each other, thus significantly reducing the size of the gap region. In such cases the gap flow is entirely eliminated, and the two cylinders vibrate together as a single body with vibration amplitudes up to 50% lower than the amplitudes of the corresponding 1-DOF in which the gap flow is active. Three-dimensional simulations are also carried out to examine the adequacy of two-dimensional simulations for describing the dynamic response of the tandem syst...

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

“…The tandem elastically mounted cylinder arrangement investigated by Borazjani & Sotiropoulos (2009) consisted of an inline offset of L/D = 1.5, with no cross-stream offset, T/D = 0.0. The cylinders were found to oscillate at greater amplitudes than a single isolated cylinder and also to experience greater lift force.…”

“…The cylinders were found to oscillate at greater amplitudes than a single isolated cylinder and also to experience greater lift force. Borazjani & Sotiropoulos (2009) categorised the flows into two states, with state 1 being the state where the front cylinder oscillated at a greater amplitude than the rear, and state 2 where the rear oscillated more. They found that the transition with reduced velocity (U * = U/f N D, where U is the free-stream velocity, f N = √ k/m/(2π) is the natural structural frequency, k is the spring stiffness coefficient and m is the sprung mass) from state 1 to state 2 occurred near U * = 5, identifying the maximum distance reached between the two cylinders, δy/D, as a defining characteristic, with state 1 exhibiting δy/D < 1.0 and state 2, δy/D > 1.0.…”

Calculation of fluid–structure interaction: methods, refinements, applications

“…Several different variants of the IMB method have evolved since the 1970s, which can be grossly divided into direct or feedback forcing methods (Fadlun et al, 2000;Kempe and Fröhlich, 2012;Kim et al, 2001;Lai and Peskin, 2000;Shin et al, 2008;Tseng and Ferziger, 2003;Uhlmann, 2005a;Yang and Balaras, 2006;Yang et al, 2009;Yu and Shao, 2007), sharp-interface cut-cell methods (Seo and Mittal, 2011;Udaykumar et al, 2001) and hybrid versions of the two (Gilmanov and Sotiropoulos, 2005). Regarding circular cylinder flows, the studies of Borazjani and Sotiropoulos (2009), Gazzola et al (2011), Kim and Choi (2006), Kolomenskiy and Scheider (2009) and Yang et al (2008) constitute a selection of studies in which flow past various arrangements of single or tandem cylinders that were either stationary, freely vibrating or a combination of the two, have been investigated using the IBM. The IBM continues to grow in popularity as a result of the considerable advantages it offers over body-fitted approaches, and can be considered as a stateof-the-art numerical method for the computation of complex FSI problems.…”

Fluid-structure interaction modeling with chimera grids in NSMB

“…An overall good agreement is observed for all our simulations. A discussion about the results of this vortex induced vibrations system can be found in [3]. 3.…”