解跨音速升力翼型的有限元法

 在应用解全速位方程的最小压强积分有限元法求解绕升力翼型的跨音速流动时,将不可压流中求解绕升力翼型的耦合单位环量流动和无环量流动的解法推广到可压流中。为了确定环量,本文所用Kutta条件是:在后缘处,气流流向平行于后缘角二等分线。因有限元法对网格无正交性要求,因而可在椭圆变换前后进行剪切和延伸变换。这种网格生成法易于构成适用于复杂形状的有限元网格。通过计算并将其结果与文献中的数据比较,表明这种方法应用方便且有较快的计算速度和较高的计算精度。

A FINITE ELEMENT METHOD FOR SOLVING LIFTING AIRFOIL IN TRANSONIC FLOW

The FEM about minium pressure integral solving potential equation is applied to solving lifting airfoils in transonic flow Two solutions corresponding to zero and unit circulation respectively are combined at each iteration in such a way that the result and potential satifies the Kutta condition, which is extended from calculating lifting airfoils in incompressiple flow. The Kutta condition enforced at the trailing edge is that the streamline leaving the trailing edge is tangent to its bisector. Since FEM has no such requirement that the grid line are of orthogonality, a sequence of shearing and stretching transformation, both prior to and subsequent to the elliptic mapping is used.The grid generation method can easily generate finite element meshes about complex geometries. The artificial compressibility method stabilizes the algorithm in transonic flow and allows the capture of embeded shock waves. The results obtained are compared with existing experimental measurement and the other numerical solutions.