可变形翼型超声速非定常气动力的研究

Study on the supersonic unsteady aerodynamic force for the morphing airfoil

由小扰动线化方程出发,利用基于格林公式的边界元方法求解二维超声速流动速度场,进而对变形翼型气动特性进行理论分析和数值计算。计算结果显示虚拟质量力导致的非定常附加升力对厚度变化远比弦长或弯度变化敏感;弦长或弯度变化诱导的非定常效应影响很小,此时非定常气动升力和准定常气动升力近似相等,和不可压缩或亚声速时相类似,变形翼型的非定常气动升力近似等于准定常计算结果叠加上非定常附加升力,与具体的变形历史过程无关。同时还分析了超声速时翼型往复变形时的气动特性,和亚声速情况完全不同,随着马赫数升高,完成往复变形所需要外界输入的功逐渐减小,趋近一个常值。另外翼型完成往复变形所需做的功将不依赖于来流攻角,且与翼型参数的变化加速度a存在简单的数学关系:A ∝a～(1/2)。

The two-dimensional small-perturbation equations governing the supersonic flow past the morphing airfoils are calculated using the boundary element method based upon the Green formula.The supersonic unsteady aerodynamic characteristics for morphing airfoil are studied analytically and numerically.The numerical calculations show that the additional unsteady aerodynamic lift caused by the virtual mass force is much more sensitive to the thickness variation than the chord length and chamber variations.When the airfoil performs the deformation only by changing its chord length or chamber,the unsteady aerodynamic lift can be very well approximated by the pseudo-steady aerodynamic lift.For the supersonic morphing airfoil,similar to the incompressible and subsonic cases,the lift of morphing airfoil is approximately equal to the lift of quasi-steady solution adding the corresponding virtual mass force,which is independent of the evolutionary history of deformation.The aerodynamic characteristics of the morphing airfoil during reciprocating deformation are investigated.In sharp contrast to the subsonic cases,it is shown that the energy input to implement the reciprocating deformation for supersonic flow will decrease with increasing the free-stream Mach number and eventually tends to a constant limit.The energy input Ainduced by the virtual mass force is independent of the angle of attack and has a simple mathematical relation with the acceleration rates aof the geometry parameter variations:A ∝a～(1/2).