Parametric generators of geometric models and computational meshes of Francis turbines runners

Abstract

In this paper, we present a fully automatic approach to generate a geometric model of a Francis turbine runner wheel based on NURBS surfaces from given shape parameters and also a fully automatic approach to generate NURBS meshes of the inner parts of the runner wheel based on NURBS volumes. All the steps of the presented approaches are described in detail, including several challenges that need to be overcome, such as e.g. obtaining conformal parameterizations of streamsurfaces or automatic determination of suitable B-spline approximation curves for representing spatial blade profiles. NURBS meshes generated by the presented method are of good quality and can be used directly for numerical simulations of incompressible turbulent fluid flows based on isogeometric analysis, or, after simple conversion to hexahedral meshes, based on finite element method. The presented approaches can also be used in automatic shape optimization algorithms for Francis turbine runners based on gradient or gradient-free approaches.