A Strategy for Multi-Point Shape Optimization of Turbine Stages in Three-Dimensional Flow

Abstract

This paper presents an effective and practical shape optimization strategy for turbine stages so as to minimize the adverse effects of three-dimensional flow features on the turbine performance. The optimization method combines a genetic algorithm (GA), with a Response Surface Approximation (RSA) of the Artificial Neural Network (ANN) type. During the optimization process, the individual objectives and constraints are approximated using ANN that is trained and tested using a few three-dimensional CFD flow simulations; the latter are obtained using the commercial package Fluent. The optimization objective is a weighted sum of individual objectives such as isentropic efficiency, streamwise vorticity and is penalized with a number of constraints. To minimize three-dimensional effects, the stator and rotor stacking curves are taken as the design variable. They are parametrically represented using a quadratic rational Bezier curve (QRBC) whose parameters are related to the blade lean, sweep and bow, which are used as the design variables. The described strategy was applied to single and multipoint optimization of the E/TU-3 turbine stage. This optimization strategy proved to be successful, flexible and practical, and resulted in an improvement of around 1% in stage efficiency over the turbine operating range with as low as 5 design variables. This improvement is attributed to the reduction in secondary flows, in stator hub choking, and in the transonic region and the associated flow separation.