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

Abstract 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 fy/fn ≈ 0.95–1.05, and the reduced velocity Vr ≈ 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 fy/fn ≈ 0.85) at high reduced velocities (Vr ≈ 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 (Vr ≈ 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 Vr. 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.