Applied Ocean Research 69 (2017) 173–190 Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Vibration of two elastically mounted cylinders of different diameters in oscillatory flow Toni Pearcey, Ming Zhao ∗ , Yang Xiang, Mingming Liu School of Computing Engineering and Mathematics, Western Sydney University, Penrith, NSW 2751, Australia a r t i c l e i n f o Article history: Received 30 April 2017 Received in revised form 1 November 2017 Accepted 1 November 2017 Keywords: Flow induced vibration Numerical method Oscillatory flow Circular cylinder a b s t r a c t Vibration of two elastically mounted cylinders in an oscillatory flow at a Keulegan-Carpenter number of 10 is simulated numerically. The two cylinders are rigidly connected with each other and are allowed to vibrate in the cross-flow direction only. The aim of this paper is to identify the effects of the orientation of the cylinders and the gap between the cylinders on the vibration. The two-dimensional Reynolds- Averaged Navier-Stokes equations are solved to predict the flow and the cylinder vibration is predicted using the equation of motion. When the two cylinders are in a tandem arrangement, a combined single pair flow regime and attached pair flow regime are observed as reduced velocity exceeds 10 and this combined regime and the single pair regime occurs intermittently. Periodic vibration is found when the two cylinders are in a staggered arrangement with a 45 ◦ flow attack angle. When the two cylinders are in a side-by-side arrangement, a new single vortex regime is observed. This single vortex remains attached to the cylinder surface and rotates around the cylinder. The intermittent switch between this single vortex regime and the single pair regime are observed. © 2017 Published by Elsevier Ltd. 1. Introduction With increasing demand for energy resources from ocean including offshore oil and gas, renewable energy from wind, tidal currents and waves, more and more offshore structures are con- structed. Offshore structures for extracting energy from ocean have to survive severe storms without damaging their functionality. Many cylindrical structures are used in offshore engineering such as subsea pipelines, risers, mooring cables, etc. Oscillatory flow is often used to model the water motion due to waves when the impact of the waves on small scale cylindrical structures is studied. Many studies have been performed to understand the hydrody- namics and flow patterns around circular cylinders in oscillatory flows. It has been found that the hydrodynamic forces on cylindri- cal structures are mainly affected by the Keulegan-Carpenter (KC) number and the Reynolds number. The KC number is defined as KC = (U m T)/D, where U m and T are the velocity amplitude and period of the oscillatory flow, respectively, and D is the diameter of the cylinder. The Reynolds number is defined as Re = U m D/, where  is the kinematic viscosity of the fluid. The ratio of the KC number to the Reynolds number is called the viscous parameter, ˇ [15]. ∗ Corresponding author. E-mail address: m.zhao@westernsydney.edu.au (M. Zhao). [21] conducted an experimental study of oscillatory flow past a cir- cular cylinder for KC numbers ranging from 1 to 40 and classified the vortex flow into different flow regimes: Paring of attached vor- tices (non-vortex shedding regime) when KC < 7, single pair regime when 7 < KC < 15, double pair regime when 15 < KC < 24, three-pair regime when 24 < KC < 32 and four–pair regime when 32 < KC < 40. Obasaju et al. [13] conducted a detailed study of the relationship between the vortex shedding regime and the hydrodynamic forces on a circular cylinder in an oscillatory flow. It was found that the spanwise correlation of the flow is good when KC is at the center of a regime and poor when KC is at the boundary between two regimes. Numerical studies have been successfully conducted to inves- tigate oscillatory flow past a circular cylinder. Some studies are mainly focused on the inception of the three-dimensionality of flow at low Reynolds numbers and low KC numbers [3,1,17,4]. Recently, research has been performed to study flow induced vibration (FIV) of circular cylinders in oscillatory flows. In addition to the Reynolds number and the KC number, FIV of a cylinder in oscillatory flow is also dependent on the mass ratio and the reduced velocity. The mass ratio is defined as m* = m/m d , where m is the cylinder mass and m d is the displaced fluid mass, and the reduced velocity is defined as V r = U m /(f n D), where f n is the structural natural frequency mea- sured in vacuum in this study and many numerical studies. In many experimental studies of FIV in water, the natural frequency mea- sured in still water (defined as f nw in this study) is used to define https://doi.org/10.1016/j.apor.2017.11.003 0141-1187/© 2017 Published by Elsevier Ltd.