摘要
本文研究了以平衡攻角为中心作俯仰振荡的飞船,其动态稳定形态随来流马赫数M∞的变化。设θ(t)是由平衡攻角起算的俯仰振荡角,cm(θ,θ)是作用于飞船上的气动力矩系数,cμ(θ,θ)θ是阻尼力矩(天上飞行时为零),可以证明λ=(cmθ)θ=θ=0+cμ(0,0)=λ(M∞)是决定动稳定形态的重要参数。如果随M∞变化,λ由小于零经λ=0变化到λ>0,则飞船将由稳定的点吸引子状态(即稳定在平衡攻角状态)发展为时间周期吸引子状态(即作周期振荡),对应于λ(M∞)=0的那个马赫数Mcr是出现该Hopf分岔的临界马赫数。本文利用耦合求解俯仰振荡方程和NS方程的数值模拟方法,模拟了这种运动形态。
In this paper,the angular motion of an orbital reentry vehicle around static trim angle of attack is investigated using a single degree of freedom method.The angular motion behavior with decrease in Mach number is discussed.Supposing θ(t) is the pitching motion angle from static trim angle of attack, c m(θ,) is the damping in pitch derivatives and c μ(θ,) is the frictional damping moment coefficint which is negative in proportion to θ, we have proved analytically that θ=c m θ==0 +c μ(0,0)=λ(M ∞) is an important parameter to determine the angular motion behavior.If λ changes from negative to positive with decrease in Mach number,then the angular motion will become a limiting cycle oscillation from damping oscillation with a point attractor.The Mach number M ∞ corresponding to λ(M ∞)=0 is the critical one appearing the Hopf bifurcation.In addition,the solution coupling of an angular motion of a vehicle with numerical simulation of NS equations is presented.The agreement between the analysis and numerical simulation is very satisfactory.
出处
《空气动力学学报》
CSCD
北大核心
1999年第2期123-129,共7页
Acta Aerodynamica Sinica