Determination of the transition mass ratio for onset of galloping of a square cylinder at the least permissible Reynolds number of 150

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, alpha; mass ratio, m(*); damping ratio, zeta; 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 approximate to 150 and U-* approximate to 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*approximate to 4 at the least permissible Re of 150. For alpha = 0 degrees and zeta = 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.