Galloping is one of typical wind-induced transverse vibrations. Slender structures could be damaged by galloping-induced large-amplitude oscillations. The majority of previous studies were devoted to study the galloping behavior of structures with their principle axes perpendicular to the oncoming flow. However, some slender structures in reality, such as the pylons of the Alamillo Bridge in Spain, the Kumdang Bridge in Korea and the Hong Shan Bridge in China, are inclined. It is speculated that the inclination results in non-negligible impacts on the galloping oscillation of an inclined structure.

This research investigated the effect of the inclination on galloping of a square cylinder and revealed the underlying mechanism in depth. Both experiments in the wind tunnel and num...[ Read more ]

Galloping is one of typical wind-induced transverse vibrations. Slender structures could be damaged by galloping-induced large-amplitude oscillations. The majority of previous studies were devoted to study the galloping behavior of structures with their principle axes perpendicular to the oncoming flow. However, some slender structures in reality, such as the pylons of the Alamillo Bridge in Spain, the Kumdang Bridge in Korea and the Hong Shan Bridge in China, are inclined. It is speculated that the inclination results in non-negligible impacts on the galloping oscillation of an inclined structure.

This research investigated the effect of the inclination on galloping of a square cylinder and revealed the underlying mechanism in depth. Both experiments in the wind tunnel and numerical simulations (i.e. large eddy simulation) were performed. First, effects of both forward and backward inclinations on galloping behaviors of a square cylinder were clarified by using aeroelastic tests in the wind tunnel. Then, aerodynamic characteristics of the forward and backward inclined cylinders were evaluated via pressure measurements in the wind tunnel. Meanwhile, the applicability of the quasi-steady theory on inclined cylinders was assessed based on the pressure data. Next, effects of the inclinations on the flow filed around the cylinder were investigated via large eddy simulations. Finally, mechanisms associated with the effects of the inclinations on the galloping behaviors of a square cylinder were revealed based on data from pressure measurements and numerical simulations.

According to the aeroelastic tests, the galloping amplitude reduces appreciably with increasing the forward inclination angle. By contrast, not all the cylinders inclined backward oscillate at amplitudes smaller than the vertical cylinder. For the quasi-steady theory, it is capable of predicting the variation trend in the galloping behavior induced by both the forward and backward inclinations, although it is unable to give accurate prediction on the galloping amplitudes of all the inclined cylinders. Thus, it is logical to use the parameters related to the quasi-steady theory to explore the reason for the variation in the galloping behavior induced by the inclinations. The reason was explained based on variations of local transverse force coefficients over the cylinder span with the inclinations.

Based on large eddy simulation results, the forward inclination is found to enhance the downwash, which is initially observed behind the free end of the vertical cylinder, and amplify it to a downward axial flow. Conversely, the backward inclination promotes upwash, which originates behind the base of the vertical cylinder, to be an upward axial flow. On the other hand, the vertical cylinder produces two pairs of counter-rotating streamwise vortices (quadrupole wake) in its wake, but only one pair of vortices (dipole wake) is observed to form behind both the forward and backward inclined cylinders. Moreover, only a free-end vortex pair is exhibited behind the forward inclined cylinder whereas a base vortex pair exists behind the backward inclined cylinder. They are considered to generate the downward and upward axial flow respectively.

In order to reveal the underlying mechanism of the effect of inclinations on galloping, the variations of local transverse force coefficients were explained based on results of large eddy simulations and pressure measurements. Results of large eddy simulation show that forward inclinations significantly increase the curvature of the shear layer near the free end of the cylinder whereas decrease it near the base. Conversely, backward inclinations reduce the curvature near the free end while increase it near the base. The variation in the curvature has remarkably influenced the pressure distributions on the side faces and hence the transverse force coefficient, which governs the galloping behavior of the cylinder. The particular curvature of the shear layer in the forward inclination case is a consequence of an inverted V-shaped spanwise vorticity distribution, which is induced by an “extended tip vortex pair” with an inverted V-shaped streamwise vorticity distribution. However, in the backward inclination case, the shear layer curvature is attributable to a V-shaped spanwise vorticity distribution caused by an “extended base vortex pair” with a V-shaped streamwise vorticity distribution.