Aerodynamic Inverse Design for Viscous Flow in Turbomachinery Blading

Abstract

An inverse design method for turbomachinery blading based on a time-accurate solution of the compressible viscous flow equations on a time-varying geometry is presented. The blade pressure loading and thickness distributions are the prescribed design parameters. The blade profile is modified as it moves at a virtual velocity distribution that would make the momentum flux on the blade surfaces equal to the flux corresponding to the prescribed loading distribution. The unsteady flow due to the blade motion is simulated by solving the Reynolds-averaged Navier-Stokes equations that are discretized using a cell-vertex finite volume method in which an arbitrary Lagrangian-Eulerian formulation is used to account for the mesh movement and deformation during the design procedure. The method is first verified by inversely designing an existing blade using its loading distribution as the design target and starting from a profile that has a different camberline. The robustness, flexibility, and usefulness of this design method are demonstrated by redesigning a subsonic turbine and a transonic compressor blade for which, for the latter case, the conventional quasi-steady approach failed. The redesign cases demonstrate that the blade aerodynamic performance can be improved by carefully tailoring the target loading distribution.