Proximity-interference wake-induced vibration at subcritical Re: Mechanism analysis using a linear dynamic model

Wake-induced vibration (WIV) contains rich and complex phenomena due to the flow interference between cylinders. The aim of the present study is to gain physical insight into the intrinsic dynamics of WIV via linear stability analysis (LSA) of the fluid-structure interaction (FSI) system. A reduced-order-model-based linear dynamic model, combined with the direct computational fluid dynamics/computational structural dynamics simulation method, is adopted to investigate WIV in two identical tandem cylinders at low Re. The spacing ratio L/D, with L as the center-to-center distance and D as the diameter of cylinders, is selected as 2.0 to consider the effect of proximity flow interference. Results show that extensive WIV along with the vortex shedding could occur at subcritical Re conditions due to the instability of one coupled mode (i.e., coupled mode I, CM-I) of the FSI system. The eigenfrequency of CM-I transfers smoothly from close to the reduced natural frequency of structure to the eigenfrequency of uncoupled wake mode as the reduced velocity U∗ increases. Thus, CM-I characterizes as the structure mode (SM) at low U, while it characterizes as the wake mode (WM) at large U. Mode conversion of CM-I is the primary cause of the "frequency transition" phenomenon observed in WIV responses. Furthermore, LSA indicates that there exists a critical mass ratio mcr, below which no upper instability boundary of CM-I exists (Uupper→∞). The unbounded instability of CM-I ultimately leads to the "infinite WIV" phenomenon. The neutral stability boundaries for WIV in the (Re, U) plane are determined through LSA. It is shown that the lowest Re possible for WIV regarding the present configuration is Relowest≈34. LSA accurately captures the dynamics of WIV at subcritical Re and reveals that it is essentially a fluid-elastic instability problem. This work lays a good foundation for the investigation of WIV at supercritical high Re and gives enlightenment to the understanding of more complex WIV phenomena therein.