COMPRESSIBLE FLOW AIRFOIL DESIGN USING NATURAL COORDINATES

An irrotational inviscid compressible inverse design method for two-dimensional airfoil profiles is described. The potential (phi) and streamfunction (psi) are used as the independent natural coordinates. The physical space on which the boundaries of the airfoil are sought, is mapped onto the (phi, psi) space via a body-fitted coordinate transformation. A novel procedure based on differential geometry arguments is employed to derive the governing equations for the inverse problem, by requiring the curvature of the flat 2-D Euclidean space to be zero. An auxiliary coordinate transformation permits the definition of C-type computational grids on the (phi, psi) plane resulting in a more accurate description of the leading edge region. Geometry is determined by integrating Frenet equations along the grid lines. A two-parameter iterative scheme has been incorporated in the design procedure in order to assure closure of the trailing edge. To validate the method, inverse calculation results are compared with direct, 'reproduction', calculation results. The design procedure of a new airfoil shape is also presented.