可变形儒可夫斯基翼型亚音速非定常气动力的研究

对于翼面变形速度远小于来流速度情况下的儒可夫斯翼型亚音速绕流问题,通过仿射变换将可压缩流动转换成不可压缩流动,将解析解和离散涡方法相结合计算变形机翼的不可压缩流动速度场,再利用逆变换得到变形机翼的亚音速流动速度场,进而分析非定常气动力特性,建立变形机翼的准定常升力系数和非定常附加升力系数在可压缩和不可压缩两种状态下的简单近似对应关系。计算结果显示变形机翼的非定常气动升力近似等于准定常计算结果叠加上虚拟质量力导致的非定常附加升力,该非定常附加升力随翼型变形速率呈线性关系,由机翼当前时刻飞行姿态、翼型及其变形速率确定,与具体变形历史过程无关。低来流马赫数时虚拟质量力导致的非定常效应显著,高亚音速流动时准定常升力起主导作用。同时还分析了不同马赫数下机翼往复变形过程中升力的变化特性,指出尽管高亚音速变形机翼的气动升力近似等于准定常气动升力,但不能忽视非定常附加升力的影响,非定常附加升力将导致完成往复变形需要外界输入正比于Ma∞/(1-Ma2∞)]的功。

Study on the Subsonic Unsteady Aerodynamic Force for the Morphing Joukowski Airfoil

For the case of the normal deformation velocity on the wing surface that was much smaller than free stream velocity,the subsonic flow for the morphing Joukowski airfoil was transformed into incompressible flow by using an affine transformation.Then the subsonic flow was calculated with the inverse affine transformation from the corresponding incompressible flow problem,which was solved by combining the analytical solution and the discrete vortex method together.For the quasi-steady aerodynamic force and the additional unsteady aerodynamic lift caused by the virtual mass force,the simple relationships between the subsonic flow and the corresponding incompressible flow were proposed.The numerical calculations show that the lift of morphing airfoil was approximately equal to the lift of quasi-steady solution adding the corresponding virtual mass force.The additional unsteady lift,being determined by the flight attitude,the airfoil profile and its deformation rate,has little relation with the evolutionary history of deformation.It was also shown that the additional unsteady lift was linear with the variation rates of the airfoil geometry parameters.The virtual mass force has the obvious effects upon the unsteady flows for low free-stream Mach number Ma∞,however,it will be much lower than the quasi-steady aerodynamic force for high subsonic flow.The aerodynamic characteristics of the morphing airfoil during reciprocating deformation were investigated.It was shown that the virtual mass force will induce that the energy proportional to Ma∞/(1-Ma2∞)] must be inputted for implementing the reciprocating deformation,i.e.,its effects can not be ignored even if the aerodynamic lift is approximately equal to the quasi-steady lift for high subsonic flows.