Journal of Fluids and Structures 23 (2007) 715–731 The flow between a stationary cylinder and a downstream elastic cylinder in cruciform arrangement J. Deng, A.-L. Ren à , X.-M. Shao Department of Mechanics, Institute of Fluid Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China Received 1 May 2005; accepted 24 November 2006 Available online 30 January 2007 Abstract The flow past a stationary circular cylinder and a downstream elastic circular cylinder in cruciform arrangement is investigated at a constant Reynolds number of 150. The virtual boundary method is employed in this study. After the validation of the numerical method, two cases are simulated. In Case 1, both cylinders are stationary. A critical spacing is found to be about three diameters ðL=D ¼ 3Þ. Beyond this critical spacing, the modification of the wake of the upstream cylinder due to the presence of the downstream cylinder is limited to the mixed region, whereas below this critical spacing, the influenced region is significantly enlarged. In Case 2, we let the downstream cylinder vibrate in response to the fluid forces acting on it, and the vibration is modeled by a spring-damper-mass system. The results show that the peak amplitude of vibrations for the cruciform arrangement is lower than that for an isolated cylinder, and the resonance region is wider than that of an isolated cylinder. r 2007 Elsevier Ltd. All rights reserved. Keywords: Two cylinders in cruciform arrangement; Vortex-induced vibration; Virtual boundary method 1. Introduction Numerous experimental and numerical investigations on the flow-induced oscillation of a single cylinder have been carried out, as reviewed by Bearman (1984) and Williamson and Govardhan (2004). The interest in this class of problems emanates primarily from its practical applications in a variety of engineering flows, such as transmission lines, suspension bridges and heat exchangers. It is necessary to understand the complex phenomena exhibited by such systems. Some experimental works can be referred to: by Griffin (1971), Williamson and Roshko (1988), Ongoren and Rockwell (1988a, b) and Blevins (1990), and computational works by Mittal et al. (1991), Mittal and Tezduyar (1992), Mittal and Kumar (1999) and Zhou et al. (1999). Hydrodynamic interactions between a cylinder and another downstream one are significant. For example, experimental results showed that the mean velocity of the wake flow is reduced due to the presence of the downstream cylinder, and the fluctuating components of the force acting on the downstream one is altered by the wake (Ohya et al., 1989; Zdravkovich, 1977). It was also observed that aerodynamic quantities such as the drag and lift forces, the pressure distribution, the Strouhal number and the vortex-shedding patterns depend strongly on the member spacing. Zdravkovich (1977) also discovered the discontinuity of those quantities at a critical spacing ratio L=D ranging between ARTICLE IN PRESS www.elsevier.com/locate/jfs 0889-9746/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfluidstructs.2006.11.005 à Corresponding author. Tel.: +86 571 87952200. E-mail address: renanlu@zju.edu.cn (A.-L. Ren).