Shape optimization of two turbine stages using the deformed polyhedron method and a three-dimensional RANS solver

Abstract

A combination of the Nelder-Mead deformed polyhedron method with a three-dimensional RANS solver is used in the paper for the constrained optimization of the shape of two selected turbine stages. The objective function is the total stage loss, with the exit kinetic energy also considered a loss. There are constraints imposed on the mass flowrate, exit angle, average reaction and reaction at tip and root. The exit angle and reactions are not allowed to assume values beyond prescribed ranges, whereas a penalty function is imposed on the mass flowrate if it falls outside the required interval. Among the optimized parameters are stator and rotor stagger and twist angles and stator sweep and lean, both straight and compound. The computations of the flowfield are compressible, viscous and three-dimensional. Turbulence effects are taken into account using the modified Baldwin-Lomax model. The process of optimization gives new designs with improved calculated efficiency. Part of the improvementis due to optimization of the stagger angles and blade numbers, as in classical one-dimensional optimization, and part of it is due to the fact that the blades assume new three-dimensional stacking lines.