Unsteady Aerodynamic Force Model And Behavior Of Wake Galloping For A Downstream Circular Cylinder In Tandem

Wake galloping poses a serious threat to the security of transmission line system due to its large vibration amplitude and long duration.Thereofore,predicting and controlling wake galloping amplitude of transmission line system is necessary.If wake galloping mechanical model which could accurately predicts wake galloping responses can be established through wind tunnel experiment or numerical simulation results,anti-vibration measures will have twice the result with half the effort based on prediction results.Nowdays,research on wake galloping mechanical model is less because of its complex fluid-structure coupling characteristics.The wake galloping quasi-steady theory which is established under quasi-steady framework is commonly used.The quasi-steady theory ignores interaction feedback between fluid and structure.When fluid velocity is high,the unsteady flow around is weak because flow field changes very fast,wake galloping can be regard as steady approximately.However when fluid velocity is low,the unsteady effect is so strong that the unsteady vibration of vortex-induced vibration coupled with wake galloping is easy to occur,the quasi-steady assumption may be invalid.As construction of more flexible transmission line system which has lower quality and damping,the corresponding excitation wind velocity of wake galloping is lower,so applicability and accuracy prediction of the quasi-steady wake galloping mechanical model need to be verified.If low prediction accuracy is lower or prediction result is wrong,it is necessary to put forward a new unsteady wake galloping mechanical model for predicting.Based on these,the specific research works and conclusions of this paper are as follows:1)Based on the two-dimensional wind tunnel test model parameter by Sockel,numerical simulations by Fluent were performed on higher Scruton number which the excitation wind velocity was higher and lower Scruton number which the excitation wind velocity wa lower and the unsteady vibration was easy to appear.Compared with the wind tunnel test results of Sockel,the accuracy of simulation was verified.Then the differential equations of quasi-steady mechanical model were sloved by the simulation results.The applicability and accuracy of the predicting results on two simulation condictions of the quasi-steady theory was verified.Results indicated that:The simulation results have an excellent agreement with the experimental datas,the adopted simulation method is feasible.Whether the wake galloping amplitudes or the excitation wind velocity,the quasi-steady theory has higher applicability on higher Scruton number,the predicting results are in good agreement with simulation results.But the quasi-steady theory has lower applicability on lower Scruton number,the predicting results are far different from simulation results.It is necessary to put forward a new unsteady wake galloping mechanical model for predicting wake galloping at lower Scruton number.2)The unsteady wake galloping phenomenon of several cylinders at lower Scruton number was observed by wind tunnel experiments.In combination with numerical simulation by Fluent,the spectrum regularity of aerodynamic force was analyzed.The mathematical parameter expression of unsteady wake galloping mechanical model was given.Results indicated that:The unsteady coupling vibration excites from the vortex-induced vibration velocity.Before U _r/U_VIV=3,the increase slope of galloping amplitude decreases with the increasing wind velocity;after U _r/U_VIV=3,the galloping amplitude increases nearly linearly with the increasing wind velocity as a typical wake galloping phenomenon.The unsteady wake galloping aerodynamic force can be divided into the self-excited force and the vortex-induced force.The self-excited force can be expressed as the function of velocity and displacement of cylinder.The vortex-induced force can be expressed as the fuction of vortex frequency of the upstream cylinder and the downstream cylinder.The specific aerodynamic parameter expression of unsteady wake galloping mechanical model is successfully constructed.3)The aerodynamic parameters of unsteady wake galloping mechanical model were identified.The unified,reasonable and applicable mathematical formulas were put forward through the aerodynamic laws by fitting,which could predict the wake galloping response.By analyzing the relative error between the predicting results and the simulation results,the rationality,accuracy,completeness and reliability of the unsteady mechanical model and the aerodynamic parameter identification method for the wake galloping were strictly proved.The wake galloping mechanism and the self-limiting amplitude characteristics are demonstrated in detail.Finally,the influence of Scruton number on the development state of wake gallopling is discussed.Results indicate that:The total work does by vortex-induced force in the whole vibration process is almost zero.The first-order aerodynamic damping is always characterized by negative damping effect,which is the key factor on the development of wake galloping by self-excited.The third order aerodynamic damping and the fifth order aerodynamic damping are always opposite,which is the key factor on the self-limiting amplitude characteristics of wake galloping.When U _r/U_VIV＜3,the dimensionless aerodynamic damping parameters change sharply with wind velocity,which is the manifestation of unsteady effects.When U _r/U_VIV＞3,the dimensionless aerodynamic damping parameter finally tends to a constant value with the increase of wind velocity,which indicates that the unsteady effect is weakened and finally enters the quasi-steady vibration.The aerodynamic laws of different working conditions are very clear and similar,which could use united and specific mathematical formulars to represent.The predicting amplitude by formulars of the different working conditions are accurate and meet the precision requirement in engineering.The applicability,reliability and accuracy of the unsteady wake galloping mechanical model are verified.The Scruton number can effectively suppress the wake galloping of the structure.If the wake galloping phenomen is not permitted to appear in a certain wind velocity region,the cirtical Scruton number Sc＞max{2α（U_r）U_r/∏}.