Numerical simulations are performed for the dynamic responses of two identical square cylinders in tandem arrangement oscillating separately in steady current. The results are presented based on a spacing ratio (L/B) ranging from 1.5 to 4 and a reduced velocity (Vr) ranging from 1 to 30 at a low Reynolds number (Re) of 180. The present numerical results show that the responses of both square cylinders are highly dependent on the spacing ratio and reduced velocity. When the spacing ratio is less than 2.5, a critical reduced velocity exists. The responses are dominated by vortex-induced vibration (VIV) when the reduced velocity is smaller than the critical reduced velocity and by galloping when the reduced velocity is larger than the critical reduced velocity. When the spacing ratio is 3.5, only VIV occurs for Vr is less than 20 while a response with combination of VIV and galloping appears for Vr over 20. Additionally, when the spacing ratio reaches 4, only VIV occurs. The results also show that the two square cylinders do not necessarily share the same synchronized mode. Moreover, besides the odd-number synchronized modes, an even-number synchronized mode is also identified.


VIVs of bluff bodies are of significance for both academic and practical applications, which have been widely investigated in recent several decades. In order to study the issue, the previous studies paid much attention to the fluid past an elastically-mounted circular cylinder. A typical phenomenon observed in the VIV of a circular cylinder is lock-in, characterized by the synchronization of vortex shedding frequency which synchronizes with the frequency of body oscillation (Williamson and Govardhan, 2004). Comprehensive investigations have been carried out in various aspects involving the VIV of circular cylindrical structures (e.g. Bearman, 1984; Sarpkaya, 2004; Gabbai and Benaroya, 2005; Williamson and Govardhan, 2008). In addition to circular cylinders, square-cross-section cylindrical structures have also been used in offshore engineering, for instance, the piers of bridges. However, less attention was focused on the dynamic responses of square cylinders in previous studies. Compared to the responses of circular cylinders, besides VIV, the dynamic response of a square cylinder presents another feature, i.e., transverse galloping, where the response amplitude increases with the reduced velocity. The transverse galloping is caused by the fluid force in phase with the body motion due to the change in the angle of attack (Zhao et al., 2014).

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