Researches On Flutter And Response Modes Of Blades Based On Reduced-order Aerodynamic Model

As designers strive to achieve better performance through a compact design of high rotational speed and high pressure ratio,the turbomachine blades are required,than ever before,to be lighter and thinner and to possess a capability of supporting higher workload.As a result,the flutter problem is further underscored and has become a challenge in the design of high-performance engines.It is difficult to conduct systematic experimental research on cascade flutter problems due to the high cost of experiments.As the computational capacity has improved rapidly in recent decades,the numerical approach is proved to be an important method to conduct such studies for its low cost and short design cycle.The classical energy method and aerodynamic influence coefficient(AIC)method neglect the effect of fluid-structure interaction,and their computational accuracy are low at small blade mass ratio,and can not be used in muti-mode coupling flutter analysis and investigation of vibration mode.Though the direct computational fluid dynamic(CFD)methods(the direct energy method and fluid-structure coupling method)are high fidelity methods,they can not satisfy requirements of engineering-oriented flutter calculation because of their time-consuming problems.To take into account the accuracy and the computational efficiency,this paper constructs the reduced-order aerodynamic models based on the high fidelity numerical method,and the main research issues are used the reduced-order models(ROMs)to calculate the stability of uncoupled and coupled,tuned and mistuned,linear and nonlinear aeroelastic system of cascade.A reduced order aerodynamic model is constructed with the unsteady CFD technique and the system identification technique,and is used for the uncoupled and coupled flutter analysis of cascades.Take a classical transonic turbine stator cascade(STCF 4)and a typical transonic turbofan compressor cascade(NASA Rotor 67)as an example,the uncoupled flutter analysis is to combine the ROM with the AIC method,and calculate the aerodynamic damping coefficients of all inter blade phase angle(IBPA)at observed frequency range through an unsteady CFD "training computation".The results are agreed well with those of the direct energy method,but the efficiency of the ROM method is improved by more than 10 times.The ROM is also coupling with structural dynamic equation in state-space,briefily called as the ROM based coupling method.The aeroelastic stability and vibration modes of the STCF 4 and NASA Rotor 67 cascade are investigated by solving eigenvalues of the aeroelastic equations.The efficiency and accuracy of the ROM based coupling method is verified by comparing with the direct fluid-structure method.The results shows that the efficiency of the ROM based coupling method is improved by 1-2 order of magnitude,and the ROM based coupling method is suitable for multi-modes coupling,cascade mistuning and parameter calculation analysis in next parts.The ROM based coupling method is next used for multiple structural modes coupling flutter analysis,and its accuracy and applicability is verified by the direct fluid-structure method.This method provides a fast and convenient way to calculate the range of cascade unstable frequency ratio caused by the structural modes coupling effect,and is benefit for the preliminary design of turbomachine blades.The effect of structural modes coupling is significant when two structural mode frequencies closes to each other,and can change the stability of cascade from stable to unstable at certain computational cases.In addition,the blade mass ratio has a adverse effect on stability of cascade when the blade mass ratio decreases.The ROM based coupling method is also used for investigating stability of mistuned cascades.The calculated cascade mistuning is a typical intentional mistuning pattern—the frequency alternate mistuning.The results show that the frequency alternate mistuning is benefit for cascade stability when mistuning ratio increases;the coupling stiffness of blade-disc has little effect on cascade stability at small mistuning ratio,but the blade mass ratio has a significant effect and increases mistuning ratio of critical stability.The critical eigenvalues of frequency alternate mistuned cascade are divided into two significant scatter clusters,and two eigenvalue clusters are corresponding to two different vibration modes,respectively.This paper has deduced the computational method of forced vibration based on the ROM,and the results of the forced vibration of mistuned cascade show that the different vibration modes can be excited by the forced vibration when the exiciting frequency close to the frequency of each eigenvalue cluster.A reduced-order nonlinear aerodynamic model is constructed by the neural network identification technique.The ROM can be used for calculating the limit cycle oscillation,and the results of ROM are agree well with those of the direct fluid-structure coupling method,but the efficiency of the nonlinear ROM is 10 times more than that of the direct fluid-structure coupling method.