Turbine cascade design via multigrid-aided finite-difference progressive optimization

Abstract

This paper proposes an efficient and robust procedure for the design optimization of turbomachinery cascades in inviscid and turbulent transonic flow conditions. It employs a progressive strategy, based on the simultaneous convergence of the design process and of all iterative solutions involved (flow analysis, gradient evaluation), also including the global refinement from a coarse to a sufficiently fine mesh. Cheap, flexible and easy-to-program Multigrid-Aided Finite Differences are employed for the computation of the sensitivity derivatives. The entire approach is combined with an upwind finite-volume method for the Euler and the Navier-Stokes equations on cell-vertex unstructured (triangular) grids, and validated versus the inverse design of a turbine cascade. The methodology turns out to be robust and highly efficient, the converged design optimization being obtained in a computational time equal to that required by 15 to 20 (depending on the application) multigrid flow analyses on the finest grid.