Force element analysis of flow-induced vibration of tandem rigidly coupled square-circular cylinders under different configurations

This work numerically investigates the two-degree-of-freedom flow-induced vibration (FIV) of rigidly coupled square-circular cylinders at Reynolds number Re = 150, mass ratio m* = 2, and reduced velocity Ur = 2–16 under different configurations. The aim of this work is to understand the complex dynamic interactions between fluid and the structure. Force Element Theory (FET) is employed to analyze the underlying mechanisms of FIV, focusing on the influence of geometric parameters and configurations on the vibration characteristics of the coupled system. By systematically varying the spacing ratios and arrangements of square-circular cylinders, the force element contributions under various FIV conditions are quantified to identify optimal configurations. The results indicate that different configurations can alter the phase relationship between force elements and total hydrodynamic forces, thereby changing contributions of force elements. Instead of being placed upstream, the square cylinder placed downstream results in more chaotic vortex shedding patterns. Among the configurations, 4D-US and 6D-DS (where 4D and 6D is the center-to-center distance between the two cylinders, D is the cylinder diameter, US and DS are the different arrangements that square cylinder placed upstream and downstream, respectively) exhibit the highest drag and lift coefficients, respectively. The diagnostic analysis using FET helps to explain the mechanism of how the spacing and arrangement affect the vortex structure of whole flow field and phase of forces, thus determining the fact that the total drag and lift has been revealed. In general, the forces under different configurations can be inferred from the flow field morphology.