Examination of forces acting on two circular cylinders in tandem arrangement

Flow-induced vibrations of a two-dimensional circular cylinder in the wake of another stationary equal-sized cylinder under a Reynolds number of 150 are numerically simulated by a well-developed in-house code. The center-to-center distance between two cylinders is 4 diameters, and the downstream cylinder with a mass ratio of 50 is free to oscillate in the transverse direction only. The instantaneous frequencies of lift forces acting on both cylinders are obtained by the combined singular spectrum analysis and Hilbert transform method. The time-varying frequencies are consistent with those obtained by the wavelet transform of the original lift forces and also show very good agreement with the vortex shedding frequencies from both cylinders. The time-varying frequency and envelope of lift forces acting on the downstream cylinder are the result of nonlinear fluid-structure interactions, which is ascribed to the presence of multi-frequency components in the frequency spectrum obtained by harmonic analysis. Vibration of the downstream cylinder is the result of vortex shedding from both cylinders. The vortex shedding frequency from the downstream cylinder is greatly influenced by the wake from the upstream cylinder. On the other hand, the movement of the downstream cylinder slightly affects the vortex shedding frequency from the upstream cylinder. Consequently, the cylinder movement is locked upon the natural frequency when the vortex shedding frequency is close to the value of 0.155 in stationary situation, which results in a small synchronized region of the reduced velocity ranging from 6.2 to 6.4.