The research project aims to investigate the boundary layer on the vibrating surface thorough experimental and numerical methods. As investigated in the work from Bergan (2019) and Tengs (2019), the fluid-hydrofoil coupled system can be assumed as a one degree of freedom system (SDOF system). This means that the system is governed by Newton’s second law of motion and is therefore f(mass, damping, stiffness, force). Among these parameters the damping factor has not been much addressed in the literature despite being critical when runner vibration is around resonance frequency (Monette et al., 2014). The theory behind this phenomena has been studied in the paper from Monette et al. (2014). Hydrodynamic damping investigation in singular hydrofoil configuration with different shapes has been carried out by both Bergan (2019) and Coutu et al. (2012). Bergan (2019) have also investigated a linear blade cascade of 3 double-fixed hydrofoils in a cavitation free test rig. The single hydrofoil research has found a linear relationship between damping ratio and water velocity, and a different gradient of this relationship depending if water velocity is below or above the lock in region. When water velocity is below lock-in the linear relationship gradient is slightly positive and almost constant, while above lock in the gradient is largely positive. Moreover the almost linear relationship in the area of velocity below the lock-in is maintained also for the structural natural frequency while is somehow disrupted above lock-in region where no further trends could be founded. Regarding the linear blade cascade work Bergan (2019) has stated that three blade system behaves as a one bladed system while doubts have been raised on the behaviour of a circular cascade configuration. The interaction between fluid and the structure takes place at the interface/boundary layer, moreover a strong interaction between blades and the surrounding water, which led to change of damping characteristics (Trivedi & Cervantes, 2017) has been demonstrated. Further investigations were performed using different trailing edge profiles and their interaction with the vortex shedding (Sagmo, 2021). Flow characteristics were studied in detail including the turbulent properties for different Reynolds numbers. The research clearly indicated a radial arrangement of the hydrofoil is essential to mimic the the turbine blade effect (Pirocca, 2020). The radial cascade, aim of this PhD, will help to understand how blades react to forced excitation and the interaction between neighbouring blades, with a focus on the hydrodynamic damping effect for a circular configuration.

The experiments will be conducted in a blade cascade, an improved version of previous work in the Waterpower Laboratory. The original work (2016 - 2019) focused on a single hydrofoil test case, studying hydrodynamic damping with respect to the flow Reynolds number. Later, the research extended to three hydrofoils arranged in parallel to examine the impact of nearby structures on hydrodynamic damping. This study observed a moderate impact on the added mass. However, in the linear arrangement, the acoustic waves are normal to the blade surface. In hydraulic turbines, the blades are arranged in a radial pattern, which differs from the linear arrangement of the hydrofoil. This work further extends to a radial arrangement of the hydrofoils to study the impact of the radial pattern during resonance conditions.

Damping is divided into three categories: (1) fluid added (hydrodynamic) damping, (2) structural (friction) damping, and (3) material damping. Hydrodynamic damping depends on changes in mode shape due to fluid pressure, convection through vortex shedding, viscous effects within the boundary layer, flow velocity, surface roughness, proximity of nearby structures, and submergence level. When a structure is subjected to a specific mode shape, it deforms, affecting the flow field, particularly near the antinode boundary of the vibrating structure. This results in rapid changes in pressure and velocity. It is crucial to understand what happens in the boundary layer when a structure vibrates at resonant frequency and undergoes different mode shapes, such as changes in viscosity, inertia, and shear stress within the boundary layer. During resonance, amplitudes near the vibrating wall follow a sinusoidal pattern, with small amplitudes at the node point and high amplitudes at the antinode point. Consequently, the pressure gradient constantly shifts from favorable to adverse, along with changes in Reynolds stresses and viscous effects. In the boundary layer, a three-dimensional fluid element travels upstream and downstream as the flow accelerates and decelerates depending on the mode shape. Reverse flow occurs in regions of low kinetic energy (near the vibrating node point), and large eddies bring outer-region momentum towards the wall, supplying some downstream flow. Generally, three regions are created when backflow occurs.

Investigate the effect of wall vibration on the instability of boundary layer with the variation of, velocity, and static pressure of flow, and study the relation of instability in boundary layer and hydro dynamic damping to establish an empirical relationship between them.