Finite Element Methods for Transonic Blade-to-Blade Calculation in Turbomachines

The transonic cascade flow is calculated with an efficient and flexible Galerkin Finite Element method applied to the full potential equation in Artificial Compressibility form. Some of the typical advantages of finite element techniques are demonstrated such as the use of higher order discretization with biquadratic elements besides the classical bilinear second order accurate element, automatic treatment of the body fitted mesh due to the locally defined isoparametric mapping, easy and exact introduction of arbitrary Neumann boundary conditions along curvilinear boundaries. On the other hand, the conceptual simplicity and efficiency of the finite difference methods based on the same equation and developed for external flows are fully maintained by the use of line relaxation or approximate factorization for the iterative solution algorithm, eventually combined with a multigrid approach. The important problem of obtaining a well-constructed mesh is solved satisfactorily by automatic grid generation based on the solution of two elliptic partial differential equations. Calculations are presented and compared with experimental data for both compressor and turbine cascade flows containing shocks.