Numerical Study On The Vortex-induced Vibration Of Rectangular 5:1 Cylinder

In recent years,the problem of vortex-induced vibration(VIV)on long-span Bridges has appeared frequently,but its mechanism still cannot be clearly explained.VIV of Bridges is a very complex phenomenon of fluid-structure interaction.In the field of civil engineering,it is considered to be a kind of restricted vibration with forced and self-excited properties,which occurs when the vortex frequency is close to the natural frequency.However,this explanation cannot clarify some properties of the vortex vibration,such as the obvious lock-in interval and the maximum VIV amplitude is not obtained under the wind speed where the vortex frequency is closest to the natural frequency.The traditional method of describing the influence of eddy impact on the structure also fails to give a reasonable answer.De Langre came to an innovative conclusion based on the linear stability analysis method on the VIV of the cylinder under low Reynolds number.He believes that the VIV is actually the coupled-mode flutter of the structure mode and the flow mode.This conclusion provides a whole new idea for the study of the VIV mechanism.On the basis of the unsteady linear reduced-order models(ROMs),Zhang and his colleagues studied the VIV of the cylinder near the critical Reynolds number and believed that the VIV should be divided into two types: resonance type and flutter type.In view of the abovementioned deficiencies in the previous research and the enlightenment of the latest literature,this paper takes the benchmark section 5:1 rectangular cylinder in the bridge wind engineering(BARC)as the research object mainly develops the following work and obtains the corresponding conclusion:1)The two-dimensional unsteady Reynolds-averaged Navier–Stokes(2D URANS),twodimensional Detached Eddy Simulation(3D DES)of flow around the rectangular 5:1 cylinder,and VIV simulation were calculated,and the results of the existing literature are compared to verify the reliability of the simulation results.In addition,in view of the inconsistency of the vortex identification method and threshold value in the current rectangular section vortex structure identification,the third-generation vortex identification method is used to identify the vortex structure and compared with the first and second-generation methods.The results show:The third-generation Ω method is more advantageous in terms of its relative insensitivity to the threshold and the capture of weak vortices,and is more suitable for vortex identification of rectangular sections.At the same time,the value of Ω can be adjusted from the recommended0.52 to 0.62.2)The unsteady aeroelastic reduced-order models(ROMs)of the cylinder near the critical Reynolds number is verified by a numerical example,but the method failed on the aeroelastic response of the 5:1 rectangular cylinder.And then,we processed the data extracted from the previous VIV simulation: From the displacement time history and frequency transformation under different wind speeds we can find that there exist two different VIV types.Combined with the energy extracted from the fluid by the structure,it can be preliminarily judged that VIV of the rectangular cylinder is similar to the cylinder that under the critical Reynolds number,which also can be divided to two types,namely resonance type and competition-induced type.3)The proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD)methods are used to mode decomposition of the flow field in the static state and the vibration state or the different stages of vibration under different wind speeds.The results show that the POD method does not perform well in capturing the dynamic characteristics of the flow field;while the DMD method can successfully identify the main frequency spatial modes in the outflow field.The DMD processing results also show that: from the perspective of changes in the fluid system,the VIV of the rectangular cylinder can also be divided into resonance type and competition-induced type.For resonant vortex vibration,the fluid system appears to be dominated by the vortex frequency and its harmonic mode at the initial stage of vibration,and reflected as a rapid decay from the time coefficient,and then rapidly develops into a state dominated by the structural modes and their harmonic modes;Under competitive-induced vortex vibration,the first few modes in the flow field include both the structural natural frequency mode and the vortex detachment frequency mode.They are in a state of energy competition,and the growth rate of the structural natural mode is significantly greater than the vortex detachment mode,so finally the flow mode is induced by the structural mode to vibrate at the same frequency.The analysis results of DMD further confirm these two different mechanisms of VIV in rectangular cylinder.4)A low mass ratio(M = 10)and a low damping ratio VIV simulation with the same Sc number was carried out,and it was found that the effect of the damping ratio on the VIV is manifested in the effect of the competitive induced vibration,and the vibration of second lockin region under low damping also belongs to the competitive induced type,which is caused by the another vortex demodulation state instability induced by structural mode due to the greatly reduced damping of the structure;but the decrease in mass mainly causes the development of the resonance VIV type.The reduction of the damping ratio did not change the frequency properties of the unsteady aeroelastic system,while the reduction of the mass ratio obviously changed the frequency characteristics of VIV.This may be due to the fact that the mass ratio is very small(M <10)in the entire aeroelastic system,has significant changed the weight of the fluid system in the system.Therefore,the influence of mass and damping parameters on VIV is essentially different.In addition,VIV simulations under different initial displacements were performed,and the results showed that the initial displacement hardly had affectd on the resonance VIV,it has a significant effect on the stability amplitude of competitive vortex vibration,which further verified the difference between resonant VIV and competitively induced VIV,and the energy competition relationship of the flow mode produced by competition induced type.