飞行器失稳平面振荡运动的物理机制

基于全局亚迭代耦合求解非定常流体动力学方程和刚体动力学方程(CFD/RBD),研究动不稳定飞行器在自由俯仰与自由沉浮二自由度下自激发平面失稳运动的非定常特征。数值研究表明:超声速锥-柱-裙飞行器的平面失稳运动发展为极限环形式,并伴随着波系结构非定常变化;平面运动保持了自由俯仰基本运动特征,但同步自由沉浮使得极限环周期运动的振幅更小、频率更快;平面自由运动中飞行器绕靠近头部的"不动点"转动。基于第二拉格朗日方程和虚功原理,导出能够描述迟滞现象的参数化非线性动力学模型。多尺度近似分析(MTS)获得参数化运动特征:自激振动过程是拟简谐运动;平衡点阻尼是决定运动稳定特性的分叉参数;振幅特性与阻尼非线性相关,频率特性与刚度非线性相关;模型分析证实了平面自由运动的"不动点"现象并自洽地解释了沉浮自由度存在使得极限环振幅变小的动力学机制。非线性模型的理论分析、重构都与数值结果高度一致,从而有效地佐证了自激振荡建模研究的合理性。

Physics of Planar Self-excited Oscillation of Flight Vehicles

By means of the global sub-iterative solution of fluid dynamic equations and rigid-body dynamic equations (CFD/RBD), a coupling numerical method is proposed to investigate the self-excited unsteady planar motion of a flight vehicle with two degrees of freedom, i.e., free pitching and free vertical motion. The numerical result shows that the unstable free planar motion of a flared cone-cylinder configuration develops a limit-cycle motion in the supersonic flow accompanied by the unsteady evolutions of the flow structure. The free planar oscillation maintains the major characteristics of free pitching, but with smaller amplitudes and higher frequencies. In addition, the vehicle in the free planar motion seems to turn around a fixed point near the nose of the vehicle. The nonlinear dynamic equation characterizing the hysteresis is deduced based on the second Lagrange equation and the principle of virtual work, and the parameterized motion is analyzed approximately by the multiple time scales (MTS) method. The self-oscillation is a quasi simple harmonic motion. The damping at the balance point is the bifurcation parameter that determines its dynamic stability. The amplitude is associated with the nonlinear damping and the frequency is correlated with the nonlinear rigidity. Theoretical analysis vali-dates the “fixed point” of the vehicle in free planar motion and in a self-consistent way makes clear why the oscillation amplitude becomes smaller with the additive vertical motion. It provides validation for the modeling method, with whose CFD results the theoretical analysis and numerical reconstruction agree well.