Surface Parametrization of a Francis Runner Turbine for Optimum Design

The aim of this paper is to apply a surface parameterization to a blade. This geometric representation should be used as a practical tool in the process of design optimization. Most parameterizations are based on blade section approaches. The parameters are typically angles, lengths that have a clear meaning to the hydraulic designer. Spanwise functions are sometimes used to ensure coherence between the sections and the smoothness of the constructed blade surfaces. Here, the section-to-section approach is replaced by a purely surface method. The blade is modelled using a camber surface and thickness distributions, and the design parameters are kept as close as possible to their original physical meaning. Smooth blade surfaces are ensured, and a reduced number of variables are sufficient to describe realistic designs. The present line of research aims to introduce a surface parameterization approach, which provides a representation of the blade. One of the benefits of this methodology is the reduction of design parameters involved as this approach is no longer section dependent. Other advantages reside in the easiness to obtain smooth geometries. Finally, it is also important to point out that data exchange between programs (i.e. CAD, Mesh Generator) may now use surface representation. This entails that subjective reconstruction of this surface is no longer necessary. As a conclusion, with our approach and the reduction of design parameters, the design optimization process becomes shorter in terms of time and effort. In this sense, preliminary tests of geometry optimization will be presented.