Direct Constrained Computational Fluid Dynamics Based Optimization of Three-Dimensional Blading for the Exit Stage of a Large Power Steam Turbine

The paper describes results of direct constrained optimization using Nelder-Mead's method of deformed polyhedron and a Reynolds-averaged Navier-Stokes (RANS) solver to optimize the shape of three-dimensional blading for the exit stage of a large power steam turbine. The computations of the flowfield in the stator and rotor are compressible, viscous, and three-dimensional. Turbulence effects are taken into account using the modified model of Baldwin-Lomax. The objective function is the stage efficiency, with the exit energy considered a loss, and with constraints imposed on the mass flow rate in the form of a penalty function if the mass flow rate falls beyond the required range. The blade sections (profiles) are assumed not to change during the optimization. Two optimization tasks are reported in this paper; first-optimizing the stator straight and compound circumferential lean, and also stator and rotor stagger angles to keep the flow rate unchanged, giving a total number of optimized parameters equal to 5; second-optimizing the stator straight and compound axial sweep, also with stator and rotor stagger angles, also giving five optimized parameters. The process of optimization is carried out for a nominal load; however, due to the fact that exit stages of steam turbines operate over a wide range of flow rates away from the nominal conditions, the original and final geometries are also checked for low and high loads. The process of optimization gives new designs with new three-dimensional stacking lines of stator blades, and with significantly increased efficiencies, compared to the original design, at least for a larger part of the assumed range of load.