2-DOF vortex-induced vibration of two tandem square cylinders with varying natural frequency ratios

Abstract

In this paper, the two-degree-of-freedom (2-DOF) flow-induced vibrations of two square cylinders in tandem are studied numerically. Both cylinders have a mass ratio of 2 and are placed at a distance of 5D in the inline direction. A characteristics-based split (CBS) finite element algorithm is employed to solve the incompressible flow equations. The Reynolds number (Re) is kept constant at 100, whereas reduced velocity (Ur ) ranges from 3-13. Computations are made for three natural frequency ratios i.e. fr = fnx/fny = 1, 1.5 and 2. Results of the upstream cylinder are similar to that of an isolated square cylinder by other researches; however, the downstream cylinder shows different characteristics due to the effect of wake from the upstream cylinder. All the results for frequency ratios 1 and 1.5 overlapped to each other, indicating that the effect of frequency ratio is inconsiderable, however as fr increases to 2, the effect is observed in both the cylinders. It is to be noted that the effect is sensitive only in the lock-in region. For all fr, fully developed wake patterns at Ur corresponding to the peak vibration amplitudes are of C(2S) type while that for the other higher Ur , are of 2S type. Cylinder motion trajectories are also discussed; except Ur = 7 of fr= 2 at which phase between lift and the lateral displacement is 90°, all the trajectories are appeared to be figure “8” type.