Spacing effect on the two-degree-of-freedom VIV of two tandem square cylinders

Different spacing cases (L/B = 2-6) are numerically examined to identify the spacing effect on the two-degree-of freedom vortex-induced vibration (VIV) of two tandem square cylinders at Re = 150. According to the various vibration responses, force characteristics and flow patterns, spacing cases can be divided into three different situations. At a small spacing (L/B = 2, 2.5), the upstream cylinder (UC) has no traditional lock-in region (the frequency ratio f(y)/f(n) approximate to 0.95-1.05, and the reduced velocity V-r approximate to 6), and the downstream cylinder (DC) has a narrow lock-in region. However, there is a wide soft-lock-in region (the synchronization region of f(y)/f(n) approximate to 0.85) at high reduced velocities (V-r approximate to 9.5-12) for both cylinders. In this region, both cylinders experience large amplitude transverse vibrations, with the UC exhibiting a higher amplitude. At a moderate spacing (L/B = 3, 4), the UC does not exhibit lock-in or soft-lock-in regions, similar to a single cylinder at the same mass ratio, and the DC exhibits a relatively wide lock-in region (V-r approximate to 5.5-8) instead of a soft-lock-in region. Notably, two amplitude peaks appear within the lock-in region for the DC depending on V-r. At a large spacing (L/B = 5, 6), the amplitude of the DC is typically higher than that of a single cylinder, even within the narrow lock-in region.

Automated summary

Different spacing cases were numerically examined for the two-degree-of-freedom vortex-induced vibration of two tandem square cylinders at Re = 150, revealing three different situations based on vibration responses, force characteristics, and flow patterns. The impact of spacing on vibration and lock-in regions varied, with distinctive behavior observed at small, moderate, and large spacing scenarios between the cylinders.