基于当地流活塞理论的气动弹性稳定性分析方法研究

AEROELASTIC ANALYSIS METHODS BASED ON LOCAL PISTON THEORY

基于改进的当地流活塞理论,推导了用模态坐标表示的弹性振动翼面的非定常广义气动力表达式。通过与非定常Euler方程的比较,证明该气动力模型具有较高的数值精度,放宽了原始活塞理论对翼型厚度、迎角、马赫数的限制。再耦合两自由度结构运动方程,在时域和频域内实现了超音速、高超音速气动弹性的稳定性分析。应用算例计算了一系列二元机翼和三维舵面的气动弹性特性。通过与耦合非定常Euler方法或实验结果的比较,证明该方法在保证精度的同时大大提高了超音速气动弹性的计算效率,在颤振分析中有较高的工程实用价值。

Based on the improved local piston theory, this paper presents the matrix expression of generalized aerodynamic forces expressed by the generalized coordinates. The results presented by this model agree well with those of solving unsteady Euler equations. This model greatly reduces the limitations of the classical piston theory on flight Math number, airfoil thickness, and angle of attack. Though it is a linear model, the characteristic nonlinear behavior of the aeroelastic system under varying Mach number or angle of attack were also taken into consideration. Coupled with 2-DOF （two degrees of freedom） structural equations, supersonic or hypersonic aeroelasticity is analyzed in time domain and frequency domain. A series of 2D airfoil and 3D wing numerical examples were computed. Compared with the coupling unsteady Euler method or experimental data, this method ensures the high precision while improving the computational efficiency greatly.