Numerical characterization of the hydrodynamic damping in a circular hydrofoil cascade

The growing awareness of climate change and the related environmental impacts is driving a progressive transformation in the energy market, with an increasing relevance of the role of renewable energy sources. However, due to their intermittent and variable nature, challenges arise towards their integration in the current electrical grid system. In this scenario, hydropower can be used to stabilize the system but this calls for an increased flexibility demanded to the power plants and all their components, especially the turbine. Francis turbines are widely diffused in Norway, Italy and Europe in general, therefore there is significant interest in the understanding of how to operate these types of machines in today's and future energy scenario. Prior research, conducted at the Waterpower Laboratory (NTNU, Trondheim), mainly within the Hydrocen framework, explored various aspects of structural and fluid dynamic phenomena across different turbines geometries. This research provided a comprehensive overview of dynamic loads, stresses, deflections, and vibrational behavior of the explored turbines systems. The primary objective of this master thesis is the characterization of the hydrodynamic damping of a Circular Blade Cascade (abbr. CBC), consisting of eight hydrofoils in radial symmetrical configuration. This specific configuration has been devised to extend previous studies conducted on hydrofoils in non-cylindrical symmetry configurations. The study relies exclusively on numerical simulations and is a fundamental complement for the upcoming experimental campaign. Firstly modal acoustic analysis has been carried out to assess natural frequencies and eigenmodes of the structure. Fluid presence was found to lower natural frequencies compared to those in air, with minimal impact on modal shape. Subsequently, transient vibro-simulations were performed for various speeds, focusing on the first vibrational mode of the first two nodal diameters. Special attention was given to speeds close to lock-in, a situation where a match occurs between the natural frequency of the structure and the vortex shedding frequency, potentially leading to catastrophic resonance effects. Using the "Aerodynamic Damping" tool in CFX, the work done by the fluid on the blade was calculated and then following the "Modal Work Approach," the hydrodynamic damping value was derived. The results align with previous experimental and numerical studies conducted in the Waterpower laboratory, demonstrating the almost-independence of hydrodynamic damping from velocity pre-lock-in and a linear dependence post-lock-in. In this context, the obtained values and trends will serve as a valuable benchmark for comparing the future experimental results.