Study On Wing Nonlinear Flutter In Transonic Flow

In recent years,wing nonlinear flutter in transonic air flow is one of the most popular topics in aeroelasticity.Because of the existence of shock wave on wing surface in transonic air flow,nonlinear aerodynamics should be considered in wing transonic flutter analysis,and wing transonic flutter is essentially a kind of nonlinear flutter.On the other hand,the structural nonlinearities inevitably exist in the joints of aircraft structures and the control system.Thus,it is necessary to consider the structural nonlinearity in wing transonic flutter analysis.The nonlinear aeroelastic system can display simple limit cycle oscillation(LCO),complex LCO,chaos and corresponding dynamic bifurcation in transonic air flow.Researches on the dynamic bifurcation behavior of the transonic aeroelastic system help understand wing transonic flutter mechanisms and avoid harmful dynamic bifurcations of aeroelastic system in aircraft design.Furthermore,it is of great academic importance to explore the route to chaos for the nonlinear aeroelastic system as a kind of fluid-structureinteraction system.Computational fluid dynamics(CFD)technique is adopted to solve the unsteady fluid governing equations to obtain the transonic nonlinear aerodynamic force,and structural nonlinearity is also considered in the present study.Wing transonic nonlinear flutter characteristics are investigated numerically by using equivalent linearized aerodynamic model in frequency domain and aerodynamic reduce order model technique in time domain,respectively.The nonlinear aeroelastic problem are studied and discussed from the perspective of nonlinear dynamics.The main contents are summarized as follows:(1)Aerodynamic describing function method is proposed for transonic LCO analysis in frequency domain.Firstly,CFD technique is used to obtain the transonic nonlinear aerodynamic force on the wing.The describing function is used to build an equivalent linearized aerodynamic model.And then the transonic LCO solutions can be obtained by using the traditional frequency domain flutter analysis approach.Several typical aeroelastic airfoil systems considering aerodynamic nonlinearity as well as considering both aerodynamic and structural nonlinearities are adopted to verify the accuracy of the aerodynamic describing function method.The results obtained are in good agreement with those in the existing literatures.(2)The dynamic bifurcation characteristics of control surface buzz in transonic air flow,as a kind of special transonic nonlinear flutter,are studied.The transonic control surface buzz system with linear structure exhibits sub-critical or super-critical bifurcation at different Mach numbers.For nonlinear structural model with free-play nonlinearity in the control surface system,the free-play nonlinearity changes the stability of LCOs with small amplitudes and the unstable LCO turns into a stable one.The LCO behavior is dominated by the aerodynamic nonlinearity for the case with large control surface oscillation amplitude but by the structural nonlinearity for the case with small amplitude.Good agreements between LCO behaviors obtained by the present method and available experimental results show that the present study can explain the experimental observation in transonic buzz wind tunnel tests and help understand the physical mechanism of transonic control surface buzz.(3)The bifurcation characteristics of an aeroelastic airfoil system with free-play at different Mach numbers are studied.Results show that the LCOs behave variously in different Mach number ranges.A sub-critical bifurcation is firstly observed in low Mach number range.Then in a narrow transonic regime with higher Mach numbers,the unstable LCO with small amplitudes turns to be a stable one.When the Mach number is increased further,the stable branch turns back to be unstable.It can be seen that the LCOs are observed over a wide range of air flow speed at the specific narrow Mach number range,and the so-called “chimney” phenomenon is observed.To address the reason of the stability variation for different Mach numbers at small amplitude LCOs and the “chimney” phenomenon,it is find that the Mach number freeze phenomenon provides a physics-based explanation.The high Mach number of the “chimney” can be estimated by the freeze Mach number,and the low one can be predicted by the freestream Mach number at which the aerodynamic center of the airfoil moves to its elastic axis.(4)Nonlinear dynamic behaviors of an aeroelastic airfoil system with free-play in transonic air flow are studied.For aeroelastic responses with small amplitudes,the flutter type of aeroelastic airfoil system should be single degree of freedom flutter,and the snap-though phenomenon can be observed.For responses with moderate amplitudes,the bifurcation diagram shows that the route to chaos for the present model is via perioddoubling,which is essentially caused by the free-play nonlinearity.For responses with large amplitudes,the aeroelastic response is dominated by the aerodynamic nonlinearity,and the aeroelastic system displays simple harmonic motions.The results demonstrate that Mach number is one important parameter that can trigger the period-doubling bifurcation of the aeroelastic system.The results of the present study are helpful for better understanding of the wing transonic flutter mechanisms,which contributes to the development of theoretical analysis in modern aircraft nonlinear aeroelasticity.