Abstract

A recently developed inverse method for single blade rows is extended to 2-D and quasi 3-D multi-stage application. In that method, the pressure distribution on the blade surfaces or alternatively, the blade loading and their thickness distribution are specified and the blade shape is sought using a virtual wall movement. The blade walls move with a virtual velocity distribution that is derived from the difference between the current and the target pressure distribution on the blade surfaces. The scheme is fully consistent with the viscous flow assumption and it is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes equations that are expressed in an arbitrary Lagrangian-Eulerian (ALE) form to account for mesh movement. A cell-vertex finite volume method of the Jameson type is used to discretize the equations in space; time accurate integration is obtained using dual time stepping. An algebraic Baldwin-Lomax turbulence model is used for turbulence closure. In order to extend the present method to multistage applications a mixing plane approach using flux averaged flow conditions is employed to couple the vane (stator) and blade (rotor) regions and non-reflecting boundary conditions are implemented at the interface between the two regions to account for short distances between blade leading and trailing edges and the corresponding inlet and exit boundaries. The method is validated on two different cases. Finally three different stages are redesigned: The E/TU-3 single stage turbine, the E/TU-4 2.5 stage turbine and the E/CO-5 2.5 stage compressor. For all cases presented in this thesis the blade pressure distributions and pressure loadings, respectively were selected as design variables, and, by modifying the original profile, it was possible to improve the aerodynamic performance.