A finite element solution of compressible flow through cascades of turbomachines

A finite element solution technique is developed for calculating the compressible flow through both stationary and rotating cascades. The computations are performed on a stream sheath of revolution of any shape, providing the flow solution in radial, mixed, or axial machines. The stream function is selected as the field variable, while the meridional coordinates and the tangential coordinate are the independent variables. The Galerkin approach is used to obtain thy finite element equations, and the eight-mode isoparametric quadrilateral elements are used to construct the shapes of the blades. Successive calculations using closure conditions are performed to provide the correct outlet and angle. This technique is applied to the solution of several test cases, including deviation angle prediction in a transonic turbine cascade, the axial flow compressor, and the radial flow in flow turbine cascades. It is found that convergence is generally obtained in three or four iterations. It is concluded that this technique gives rapid and satisfactory results for the solution of compressible flow through arbitrary cascades.