Abstract:

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.

Key words: transonic flow, airfoil, finite element method