基于欧拉方程的二维振荡机翼非定常气动设计反命题方法(Ⅱ)

An approach of inverse problem for unsteady aerodynamic design of 2-D oscillating airfoil based on Euler equations (Ⅱ)

建立了二维振荡机翼的非定常反问题的有限差分解法,并通过若干算例对求解方法进行了验证。首先根据基于欧拉方程的非定常气动反问题数学模型确定了具体求解方案,接着重点讨论了壁面非定常反问题边界条件和远场非定常无反射边界条件的处理方法,编写了相应的计算程序,并以绕1/4弦长点做小幅俯仰周期振动的NA-CA-65-0012翼型为初始机翼,在不同目标压强的条件下进行了气动反问题计算得到新翼型,它们的压强分布与预设目标相吻合,这表明本文的反问题求解方案与计算方法都是可行的。

An approach for the unsteady inverse-problems of two-dimensional oscillating airfoils is developed using finite difference method （FDM）.The solution strategies are determined firstly according to the mathematical model based on the unsteady Euler equations. Then the treatment of the inverse-problem boundary conditions, including the unsteady nonrefleeting far-field boundary condition and the permeable wall boundary condition, are discussed. NACA-65-0012 is employed as the initial airfoil, which is assumed pitching around its 1/4 chord position. Several new airfoils corresponding to the different target pressure distributions are carried out. The pressure distributions over the new airfoils coincide with the design targets well. This indicates the solution strategies and calculation method for the unsteady inverse-problem are reliable.