Study On The Mechanism Of Several Complex Phenomena In Flow-Induced Vibration Of Bluff Bodies

Flow-induced vibration(FIV)of bluff bodies exists widely in aeronautical,wind,nuclear and ocean engineering,and has significant theoretical and application value.Although a lot of researches have been carried out on this issue,the physical mechanisms underlying many complex fluid-structure interaction(FSI)phenomena have not yet been reasonably explained.By using direct CFD/CSD simulation and linear stability analysis(LSA),a unified analytical framework for various FIV problems is established.The mechanisms of vortex-induced vibration(VIV),transverse galloping and wake-induced vibration(WIV)are studied in detail.Based on the reduced-order model(ROM),feedback control of the unstable wake flow is also conducted.The main contents of this paper are listed as follows:(1)A reduced-order modeling approach for the unsteady aerodynamics of separated flows is proposed.The method is based on the steady-solution of unstable flow,and the flow is excited by the small-amplitude vibration of the structure.Then,system identification technologies(ARX,ERA)are employed to establish the aerodynamic input-output model.The results show that the model can precisely capture the stability characteristics of the flow past bluff bodies.Moreover,linear dynamic model for the FSI system is also constructed by coupling the ROM with the structural motion equation.The ROM-based FSI model can accurately predict the stability characteristics of the coupled system,which lays a good foundation for the subsequent mechanism analysis of the complex FIV phenomena.(2)The induced mechanism of frequency lock-in phenomenon in VIV is revealed.It is found that at low Re,frequency lock-in can be divided into two patterns: ‘resonance-induced lock-in' and ‘flutter-induced lock-in'.Flutter,manifested by the simultaneous instability of the structure mode(SM)and the wake mode(WM),is one of the root causes of lock-in.The lock-in regimes are strongly dependent on the Re,mass ratio,structural damping and shape of bluff body.For a circular cylinder at subcritical Re,only the SM is unstable,VIV is inherently a kind of single-degree-of-freedom flutter.However,at supercritical Re,the two lock-in patterns coexist.Whereas for VIV of a square cylinder,the lock-in is founded to be dominated by resonance,without any flutter regime.Therefore,the lock-in range and vibration amplitude of the square cylinder are much smaller than those of the circular cylinder.The lock-in boundaries predicted by the linear model are consistent with numerical simulation results,which proves that frequency lock-in has its origin in linear dynamics.(3)The mode competition mechanism in galloping is found,and the relationship between galloping and flutter is established.The results show that due to the FSI effect,the SM becomes unstable at relatively high reduced velocities,which is the primary cause of galloping phenomenon.However,the critical onset of galloping depends highly on the mode competition between the SM the leading fluid mode WM-I.In the pre-galloping region,the eigenfrequencies of SM and WM-I are very close,which results in strong competition between the two modes in the nonlinear stage.Ultimately,WM-I locks the SM and thereby postpones the occurrence of galloping.When the reduced velocity is further increased,no mode lock-in could happen due to the far apart of eigenfrequencies.Consequently,the response of the coupled system is determined by the joint action of SM and WM-I.Thus,galloping is essentially a kind of single-degree-of-freedom flutter,superimposed by a forced vibration induced by the natural vortex shedding.Finally,the dynamic mode decomposition(DMD)method is successfully applied to extract the corresponding coherent flow structures,which we refer to as the galloping mode and the von Karman mode,respectively.(4)The mechanism of WIV of two tandem cylinders at subcritical Re is revealed.Through LSA,we found that WIV occurring at subcritical Re is due to the instability of one coupled mode(CM-I)of the FSI system.This coupled mode characterizes as the SM at low reduced velocities while characterizes as the WM at large reduced velocities.Mode conversion of CM-I is the fundamental reason of the ‘frequency transition' observed in WIV responses.In addition,when the mass ratio is lower than a critical value,no upper instability boundary of CM-I exists,which ultimately leads to the ‘infinite WIV' phenomenon.LSA accurately predicts the instability boundaries of WIV,and the vibration frequency of the cylinder coincides with the eigenfrequency of CM-I,indicating that WIV at subcritical Re is essentially caused by the linear instability of the coupled system.(5)Based on the ROM of unsteady flow,active feedback control of the cylinder wake flow is conducted.The rotation of the cylinder is used as the controller,and the transverse velocity of the point on the wake axis is employed as the feedback signal.Proportional control and LQR control method are adopted in the study.The results show that both methods can completely suppress the unstable vortex shedding flow in the cylinder wake.However,the proportional control method is very sensitive to the position and time delay(phase angle)of the feedback signal.The ROM-based model can accurately predict the stability characteristics of the closed-loop system,and therefore can provide strong guidance for the selection of signal points.In addition,the effect of active control can be greatly improved by adjusting the delay time to change the angle between the control input and the feedback signal.Next,on the basis of ROM,a suboptimal control law based on output feedback is designed by the LQR method,and the effectiveness and robustness of the control law are verified by CFD simulations.The mechanism of sub-optimal control is to achieve the optimal phase angle by linear superposition of multiple feedback signals.