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International Journal of Rotating Machinery
Volume 10 (2004), Issue 5, Pages 373-385

Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

1Institute of Thermal Turbomachinery and Machinery Laboratory, University of Stuttgart, Stuttgart, Germany
2Siemens AG, Corporate Technology, Munich, Germany
3Siemens AG Power Generation Group, Mülheim an der Ruhr, Germany
4Institute of Thermal Turbomachinery and Machinery Laboratory, University of Stuttgart, Pfaffenwaldring 6, Stuttgart 70569, Germany

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.

The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.

This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.