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 ≈ 0.95–1.05, and the reduced velocity V_r ≈ 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 ≈ 0.85) at high reduced velocities (V_r ≈ 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 ≈ 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.

对不同间距情况 ( L / B  = 2–6) 进行数值检验，以确定Re  = 150 时两个串联方圆柱体的二自由度涡激振动 (VIV) 的间距效应。振动响应、力特性和流动模式、间隔情况可以分为三种不同的情况。在小间距 ( L / B  = 2, 2.5) 处，上游圆柱体 (UC) 没有传统的锁定区域（频率比f _y / f _n  ≈ 0.95–1.05，降低的速度V _r ≈ 6)，并且下游圆柱体 (DC) 具有狭窄的锁定区域。然而， 在高减速速度 ( V _r  ≈ 9.5–12) 下，两个气缸都有一个很宽的软锁定区域（f _y / f _n ≈ 0.85的同步区域）。在这个区域，两个圆柱体都经历了大振幅的横向振动，UC 表现出更高的振幅。在中等间距 ( L / B  = 3, 4) 下，UC 不表现出锁定或软锁定区域，类似于相同质量比的单个圆柱体，而 DC 表现出相对较宽的锁定区域在区域 ( V _r ≈ 5.5–8) 而不是软锁定区域。值得注意的是，两个振幅峰值出现在 DC 的锁定区域内，这取决于V _r。在大间距 ( L / B  = 5, 6) 下，即使在狭窄的锁定区域内，DC 的幅度通常也高于单个圆柱体的幅度。