Three-Dimensional Optimization of Turbomachinery Bladings Using Sensitivity Analysis

Abstract

This paper presents an approach to optimize the geometry of turbomachinery blades utilizing an automated optimization loop. Optimization examples of turbomachinery blade geometries with selected objective functions and a set of design variables are introduced. The presented optimization examples are performed for a 1.5-stage turbine test case. The blade geometries are fully parameterized, enabling three-dimensional changes to the blade shape during the optimization. Therefore various non-physical and physical parameters such as stacking line or stagger angle can be selected as design variables. Three-dimensional steady-state numerical flow simulations and a sensitivity equation method are part of the optimization process. The design sensitivities used within the optimization are obtained by numerically solving the analytical sensitivity equations. This optimization scheme uses the same numerical method for the flow simulation and for the computation of the sensitivity equation. A Navier-Stokes flow solver, which has especially been designed for turbomachinery applications was used for the implementation of the sensitivity equation method. The focus of this paper is on the application of the described optimization strategy to turbomachinery flows. The presented optimization examples are used to demonstrate and to discuss the capabilities of this approach.