The Den Hartog stability criterion tests for galloping of an oscillator. A square cylinder satisfies this and is susceptible to galloping. This criterion being necessary for occurrence of galloping appears insufficient as certain parameters, i.e., angle of incidence, α; mass ratio, m*; damping ratio, ζ; reduced speed, U*; and Reynolds number, Re; also assume key roles in determining if the oscillator motion is vortex-induced vibrations (VIV) or galloping. At Re ≈ 150 and U* ≈ 10 or smaller, a square cylinder does not gallop despite satisfying the Den Hartog criterion. By coupling U* and Re, K. Sourav and S. Sen [“Transition of VIV-only motion of a square cylinder to combined VIV and galloping at low Reynolds numbers,” Ocean Eng. 187, 106208-1–106208-19 (2019)] two-degrees-of-freedom motion over Re ≤ 250, the minimum m* or mtr* as 3.4 below which galloping cannot develop. For transverse-only motion, X. Li et al. [“Mode competition in galloping of a square cylinder at low Reynolds number,” J. Fluid Mech. 867, 516–555 (2019)] considered U* = 40 only and determined mtr*≈4 at the least permissible Re of 150. For α = 0° and ζ = 0, we determine the mtr* numerically at Re = 150. By analyzing the transverse response and oscillation frequency over an extended U* range of 10–60, a novel “VIV-galloping transition map” is generated in the m*–U* plane. From this map, the value of mtr* converges to 3.4. The mtr* decays as U*−2.36. The conditions leading to “VIV forever” of a square cylinder are also identified.

中文翻译：

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确定最小允许雷诺数为 150 时方形圆柱开始飞驰的过渡质量比

Den Hartog 稳定性准则测试振荡器的飞驰。方形圆柱体满足了这一点，并且容易驰骋。由于某些参数，即入射角α；对于发生飞驰所必需的该标准似乎是不够的。质量比，m*；阻尼比，ζ；降低速度，U*；和雷诺数，Re；还在确定振荡器运动是涡激振动 (VIV) 还是疾驰方面发挥关键作用。在 Re ≈ 150 和 U* ≈ 10 或更小的情况下，尽管满足 Den Hartog 准则，方形圆柱体也不会疾驰。通过耦合 U* 和 Re，K. Sourav 和 S. Sen [“方圆柱体的仅 VIV 运动过渡到组合 VIV 和低雷诺数下的疾驰”，Ocean Eng。187, 106208-1–106208-19 (2019)] Re ≤ 250 上的两个自由度运动，最小 m* 或 mtr* 为 3。4以下不能发展疾驰。对于仅横向运动，X. Li 等人。[“低雷诺数下方形圆柱体的模式竞争”，J. Fluid Mech。867, 516–555 (2019)] 仅考虑 U* = 40 并在最小允许 Re 为 150 时确定 mtr*≈4。对于 α = 0° 和 ζ = 0，我们在 Re = 150 处以数值方式确定 mtr*。通过分析 10-60 的扩展 U* 范围内的横向响应和振荡频率，在 m*-U* 平面中生成了新的“VIV-galloping 过渡图”。从这张图中，mtr* 的值收敛到 3.4。mtr* 衰减为 U*−2.36。还确定了导致方形圆柱体“永远 VIV”的条件。516–555 (2019)] 仅考虑 U* = 40 并在最小允许 Re 为 150 时确定 mtr*≈4。对于 α = 0° 和 ζ = 0，我们在 Re = 150 处以数值方式确定 mtr*。通过分析横向响应和振荡频率在 10-60 的扩展 U* 范围内，在 m*-U* 平面中生成了一个新的“VIV 飞驰过渡图”。从这张图中，mtr* 的值收敛到 3.4。mtr* 衰减为 U*−2.36。还确定了导致方形圆柱体“永远 VIV”的条件。516–555 (2019)] 仅考虑 U* = 40 并在最小允许 Re 为 150 时确定 mtr*≈4。对于 α = 0° 和 ζ = 0，我们在 Re = 150 处以数值方式确定 mtr*。通过分析横向响应和振荡频率在 10–60 的扩展 U* 范围内，在 m*–U* 平面中生成了一种新的“VIV 飞驰过渡图”。从这张图中，mtr* 的值收敛到 3.4。mtr* 衰减为 U*−2.36。还确定了导致方形圆柱体“永远 VIV”的条件。mtr* 的值收敛到 3.4。mtr* 衰减为 U*−2.36。还确定了导致方形圆柱体“永远 VIV”的条件。mtr* 的值收敛到 3.4。mtr* 衰减为 U*−2.36。还确定了导致方形圆柱体“永远 VIV”的条件。