A Finite Element Inverse Method for the Design of Turbomachinery Blades

Abstract

We present a quasi-3D inverse method for the design of turbomachinery blades corresponding to a velocity distribution given arbitrarily. The theoretical aspect of the problem is first investigated, then the equations governing the quasi three-dimensional potential model are reviewed. The inverse method consists of solving the potential equation with Dirichlet boundary conditions on the profile, then modifying the profile iteratively until there is no mass flux through its surface. The convergence of the process is guaranteed by the preliminary theoretical study. The method is implemented using a finite element discretization, which relies on a mixed variational formulation involving two fields of unknowns: the velocity potential and the normal displacement of the profile. Several results are shown on subsonic and transonic compressor profiles. The modified profiles are then validated with direct calculations such as quasi three-dimensional Navier-Stokes computations. These results illustrate the behavior of the method, in particular its robustness and its effectiveness. The method was adapted to calculations on turbine blade profiles. Preliminary results are shown that illustrate an industrial use of the method on a subsonic profile.