In this study, three-dimensional numerical simulations are performed to study the VIV of two side-by-side cylinders of different diameters in a steady flow. The two cylinders are rigidly connected together and elastically mounted as a single body. The main aim of the study is to identify the difference between the response of the two cylinder system and that of a single cylinder. It was found that the lock-in range of the reduced velocity of the two cylinder system is similar to that of a single cylinder. However, if the sum of the two cylinder diameter is used as the representative dimension of the system to calculate the reduced velocity, the lock-in regime is narrower that of a single cylinder.
Vortex-induced vibration of a circular cylinder has been studied extensively due to its engineering significance. It is well known that the vortex shedding frequency and the vibration frequency of the cylinder synchronize in a range of reduced velocity, and this range of reduced velocity is commonly called the lock-in range. The reduced velocity is defined as Vr=U/(fnD), where U is the fluid velocity, fn is the natural frequency of the cylinder and D is the cylinder diameter. Comprehensive reviews of VIV of a cylinder can be found in Sumer and Fredsøe (1997) Sarpkaya (2004), Bearman (1984) and Williamson and Govardhan (2004, 2008).
Recently, many numerical studies have been conducted to study VIV of cylinders. Due to the intrinsic three-dimensionality of the wake flow behind a vibrating cylinder, it is preferable to perform threedimensional simulations to study VIV. Recently, numerical studies of VIV of a circular cylinder have been extended from two-dimensional (2D) to three-dimensional (3D) simulations. Kondo (2012), Lucar et al. (2005), Navrose and Mittal (2013) and Zhao et al. (2014) studied VIV of a circular cylinder by solving the 3D Navier-Stokes equations and found some mechanisms of VIV that could not be found using 2D numerical models. For example, Lucor et al (2005) found that the correlation of the lift force along the span of the cylinder was poor at the reduced velocities in the hysteretic range between the upper and lower branches, and Zhao et al. (2014) found that the flow in the wake of a vibrating cylinder at Re=1000 is dominated by the streamwise vortices in the lock-in regime. Due to the limitation of the computer power, three-dimensional numerical studies of VIV are still performed at relatively low Reynolds numbers in the turbulent wake flow regime. For example, all the above examples of 3D numerical studies have been performed at Reynolds numbers less or equal to 1000.