飞船返回舱俯仰振荡的动态稳定性研究  

Research on the dynamic stability of an orbital reentry vehicle in pitching

作　　者：张涵信[1,2] 袁先旭[1,2] 叶友达[1,2] 谢昱飞[1,2] 

机构地区：[1]国家计算流体力学实验室,北京100083 [2]中国空气动力研究与发展中心,四川绵阳621000

出　　处：《空气动力学学报》2002年第3期247-259,共13页Acta Aerodynamica Sinica

基　　金：国家自然科学基金资助项目(批准号 :10 0 3 2 0 60 )

摘　　要：本文研究了以平衡攻角为中心作单自由度俯仰振荡的飞船返回舱 ,其动态稳定形态随来流M∞ 的变化。设θ(t)是由平衡攻角起算的俯仰振荡角 ,Cm 是作用在飞船返回舱上的气动俯仰力矩系数 ,Cμ(θ, θ)· θ是机械阻尼力矩 (自由飞行时为零 ,实验时要计入其影响 ) ,文中给出飞船返回舱在平衡攻角处的俯仰振荡动态稳定性判据 ,并证明λ =λ(M∞) = Cm θ0+Cμ(0 ,0 ) 1 - Cm ¨θ0 是决定动稳定形态的重要参数。如果随M∞ 的变化 ,λ(M∞)由λ<0经过λ =0变化到λ>0 ,则飞船返回舱将由稳定的点吸引子形态 (即稳定在平衡攻角状态 )演化为周期吸引子形态 (即作周期振荡 )。对应于λ(M∞) =0的马赫数就是飞船返回舱的俯仰运动出现Hopf分叉的临界马赫数Mcr 。本文首先分析了飞船返回舱所受动态气动俯仰力矩的依赖状态变量 ,然后应用非线性动力学理论对飞船返回舱的俯仰运动进行了定性理论分析 ;最后耦合求解俯仰振荡方程和非定常Navier Stokes方程 ,数值模拟了飞船返回舱俯仰振荡随来流马赫数变化的Hopf分叉过程 。In this paper, the single-DOF (degree of freedom) pitching angular motion of an orbital reentry vehicle around static trim angle of attack is investigated by a nalytic and numerical methods. Criteria of the dynamic stability of the pitching motion are given by nonlinear dynamic theory. Supposing θ(t) is the pitching angle from static trim angle of attack, C m is the aerodynamic pitching mo ment coefficient, C μ(θ,[AKθ· )· AKθ· is the frictional damping m oment. It can be proved analytically that λ=λ(M ∞)=[JB(][JB([][JB((][SX(] C m[][AKθ·][SX)][JB))] 0+C μ(0,0)[JB)]][JB)/ JB([]1-[JB((][SX(] C m[][AKθ¨][SX)][JB))] 0[JB)]  is an important parameter to determin e the angular motion behavior, If λ(M ∞) changes from negative to positiv e with decrease in Mach numbers, then the pitching motion will become a stable L imit Cycle oscillation from damping oscillation with a point attractor. The Mach number corresponding to λ(M ∞)=0 is the critical Mach number M cr , at which the Hopf bifurcation is occuring.The Hopf bifurcation process of a single-DOF pitching motion of an orbital reentry vehicle around static trim ang le of attack is simulated by solving the coupled pitching motion equation and Na vier-Stokes equations, the agreement between the analysis and numerical simulat ion is quite satisfactory.

关 键 词：飞船 返回舱 俯仰振荡 动态稳定性 数值模拟 

分 类 号：V411.4[航空宇航科学与技术—航空宇航推进理论与工程]