基于Theodorsen理论的跨声速颤振非定常气动力建模

doi:10.7527/S1000-6893.2025.31434

Abstract

Abstract:

A transonic unsteady aerodynamic modeling method is proposed for coupled pitching and plunging flutter of aircraft wing. This method extends the classical incompressible Theodorsen theory to transonic unsteady flows. By considering the changes of lift-curve slope by compression effect in transonic flows， as well as the shifts of aerodynamic center caused by unsteady shock wave movement， a transonic correction function for Theodorsen’s theory is constructed， and an unsteady aerodynamic model is established to capture the changes in the amplitude and phase of unsteady aerodynamic forces in transonic flow. Using the Isogai wing as a case study， this study investigates the construction of the transonic correction function， the characteristics of the correction function and unsteady aerodynamic forces， the influence of the elastic axis， and the nonlinear features of flutter. The results indicate that the correction function effectively captures the oscillatory behavior of shock waves on the wing surface in transonic flow， leading to a reduction in amplitude and phase lag of unsteady aerodynamic forces. The parameter values of correction function obtained from a specific elastic axis can be generalized to any elastic axis condition. The unsteady modeling method in this paper can accurately represent the nonlinear characteristics of transonic aerodynamic forces and achieve efficient and accurate prediction of transonic flutter characteristics.

Key words: unsteady aerodynamic, Theodorsen’s theory, transonic correction, flutter, coupled pitching and plunging

CLC Number:

V215.3⁺4

Yongping LIU, Peng ZHANG, Kaichun ZENG, Li YU, Xiping KOU. Unsteady aerodynamic modeling for transonic flutter based on Theodorsen’s theory[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(12): 231434.

Figures/Tables 28

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Table 1

Parameters of Isogai model［30］

参数	数值
质量比μ	60
弹性轴位置参数 $a ¯$	-2
质心位置参数 $X ¯$	1.8
回转半径 $r 2$	3.48
俯仰固有频率 $ω α$ /（rad·s^-1）	100
浮沉固有频率 $ω h$ /（rad·s^-1）	100

Table 1

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References 32

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Unsteady aerodynamic modeling for transonic flutter based on Theodorsen’s theory

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