On the Use of Blades Stagger and Stacking in Turbine Stage Optimization

Abstract

The flow in modern turbines is highly three dimensional and fairly complex. This paper presents a practical and effective optimization approach to minimize 3D-related flow losses by re-staggering and re-stacking the blades. This approach is applied to the redesign of a low speed high subsonic single stage turbine, that was designed and tested in Hannover, Germany. The optimization is performed at the design point and the objective function is given by a weighted sum of individual objectives, namely stage efficiency and streamwise vorticity downstream of the rotor and stator, and is penalized with one constraint, namely the design mass flow rate. A Genetic Algorithm (GA) is coupled with a Response Surface Approximation (RSA) of the Artificial Neural Network (ANN) type. A relatively small data set of high fidelity 3D flow simulations that is obtained using Fluent, is used to train and test the ANN model. The variation of stagger angle and stacking are parametrically represented using a quadratic rational Bezier curve (QRBC). The QRBC parameters are directly related to the design variables, namely the rotor and stator lean & sweep angles, and their stagger distribution. Moreover, it results in eliminating infeasible shapes and in reducing the number of design variables to a minimum while providing a wide design space for the blade shape. This optimization approach results in an improvement of 1.74% to 1.91% in stage efficiency. This optimization approach is found to be helpful in understanding the physical implications of the design variables and in interpreting their effect on the stage performance.