Several methodologies have successfully described the runner blade shape as a set of discrete sections joining the hub and shroud, defined by 3D geometrical forms of considerable complexity. This task requires an appropriate parametric approach for its accurate reconstruction. Among them, piecewise Bernstein polynomials have been used to create parametrizations of twisted runner blades by extracting some cross-sectional hydrofoil profiles from reference CAD data to be approximated by such polynomials. Using the interpolating polynomial coefficients as parameters, more profiles are generated by Lagrangian techniques. The generated profiles are then stacked along the spanwise direction of the blade via transfinite interpolation to obtain a smooth and continuous representation of the reference blade. This versatile approach makes the description of a range of different blade shapes possible within the required accuracy and, furthermore, the design of new blade shapes. However, even though it is possible to redefine new blade shapes using the aforementioned parametrization, a remaining question is whether the parametrized blades are suitable as a replacement for the currently used ones. In order to assess the mechanical feasibility of the new shapes, several stages of analysis are required. In this paper, bearing in mind the standard hydraulic test conditions of the hydrofoil test case of the Norwegian Hydropower Center, we present a structural stress–strain analysis of the reparametrization of a Francis blade, thus showing its adequate computational performance in two model tests.

The design of straight labyrinth seals for a steam turbine has had little progress concerning their geometry. As an auxiliary system, its current shape causes a significant loss of efficiency in this machine. Therefore, this study evaluates the application of an automatic optimization process to define more suitable seal profiles that increase the pressure ratio at each turbine stage. Multidisciplinary software, controlled by a Multi-Island Genetic Algorithm (MIGA), has been coupled to optimize the seal shape of a steam turbine used for geothermal operation. By parameterizing the seal geometry, the leading edge was automatically manipulated with the numerical algorithm, obtaining a tendency of its shape towards 45° at the tip to the leading edge of the steam, which decreased the outlet pressure of the seal system by 5%. It is inferred that this practical methodology could easily update the seal design during the turbine re-powering operations.

Introduction. The design of straight labyrinth seals for a steam turbine has had little progress concerning their geometry. As an auxiliary system, its current shape causes a significant loss of efficiency in this machine. Objective. This study aims to evaluate the use of an automatic optimization process to define a more suitable seal profile that increases the pressure ratio at the first stage of a steam turbine installed in a geothermal field in México. Materials and Methods. Multidisciplinary software, controlled by a PowerShell script, were coupled to optimize the seal shape in response to the flow and pressure field given by a computationally cheap CFD model of the first step of the labyrinth seal. Results and Discussion. By parameterizing the seal geometry, the leading edge was automatically manipulated with the numerical algorithm, obtaining an angle tendency towards 45°. This new leading edge decreased the outlet pressure of the seal system by 1.2%, which, for a total of 5 stages in the turbine with the same seals, would result in a 6% pressure reduction. Conclusions. It is inferred that this practical methodology could easily update the seal design during the turbine re-powering operations.