In a hydraulic power plant, it is essential to provide a reliable, sustainable and flexible energy supply. In recent years, in order to cover the variations of the renewable electricity production, hydraulic power plants are demanded to operate with more extended operating range. Under these off-design conditions, a hydraulic turbine is subject to cavitating swirl flow at the runner outlet. It is well-known that the helically/symmetrically shaped cavitation develops at the runner outlet in part load/full load condition, and it gives severe damage to the hydraulic systems under certain conditions. Although there have been many studies about partial and full load conditions, contributions reporting the deep part load condition are limited, and the cavitation behaviour at this condition is not yet understood. This study aims to unveil the cavitation phenomena at deep part load condition by high speed visualizations focusing on the draft tube cone as well as the runner blade channel, and pressure fluctuations associated with the phenomena were also investigated.

Francis turbines operating at part load condition experience the development of a cavitating helical vortex rope in the draft tube cone at the runner outlet. The precession movement of this vortex rope induces local convective pressure fluctuations and a synchronous pressure pulsation acting as a forced excitation for the hydraulic system, propagating in the entire system. In the draft tube, synchronous pressure fluctuations with a frequency different to the precession frequency may also be observed in presence of cavitation. In the case of a matching between the precession frequency and the synchronous surge frequency, hydro-acoustic resonance occurs in the draft tube inducing high pressure fluctuations throughout the entire hydraulic system, causing torque and power pulsations. The risk of such resonances limits the possible extension of the Francis turbine operating range. A more precise knowledge of the phenomenon occurring at such resonance conditions and prediction capabilities of the induced pressure pulsations needs therefore to be developed. This paper proposes a detailed study of the occurrence of hydro-acoustic resonance for one particular part load operating point featuring a well-developed precessing vortex rope and corresponding to 64% of the BEP. It focuses particularly on the evolution of the local interaction between the pressure fluctuations at the precession frequency and the synchronous surge mode passing through the resonance condition. For this purpose, an experimental investigation is performed on a reduced scale model of a Francis turbine, including pressure fluctuation measurements in the draft tube and in the upstream piping system. Changing the pressure level in the draft tube, resonance occurrences are highlighted for different Froude numbers. The evolution of the hydro-acoustic response of the system suggests that a lock-in effect between the excitation frequency and the natural frequency may occur at low Froude number, inducing a hydro-acoustic resonance in a random range of cavitation numbers.

At off-design operating points, Francis turbines develop cavitation vortex rope in the draft tube which may interact with the hydraulic system. Risk resonance assessment by means of eigenmodes computation of the system is usually performed. However, the system response to the excitation source induced by the cavitation vortex rope is not predicted in terms of amplitudes and phase. Only eigenmodes shapes with related frequencies and dampings can be predicted. Besides this modal analysis, the risk resonance assessment can be completed by a forced response analysis. This method allows identifying the contribution of each eigenmode into the system response which depends on the system boundary conditions and the excitation source location. In this paper, a forced response analysis of a Francis turbine hydroelectric power plant including hydraulic system, rotating train, electrical system and control devices is performed. First, the general methodology of the forced response analysis is presented and validated with time domain simulations. Then, analysis of electrical, hydraulic and hydroelectric systems are performed and compared to analyse the influence of control structures on pressure fluctuations induced by cavitation vortex rope.

In this paper, we present a 3-D FVPM which features rectangular top-hat kernels. With this method, interaction vectors are computed exactly and efficiently. We introduce a new method to enforce the no-slip boundary condition. With this boundary enforcement, the interaction forces between fluid and wall are computed accurately. We employ the boundary force to predict the motion of rigid spherical silt particles inside the fluid. To validate the model, we simulate the 2-D sedimentation of a single particle in viscous fluid tank and compare results with benchmark data. The particle resolution is verified by convergence study. We also simulate the sedimentation of two particles exhibiting drafting, kissing and tumbling phenomena in 2-D and 3-D. We compare the results with other numerical solutions.

The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets.

The required operating range for hydraulic machines is continually extended in an effort to integrate renewable energy sources with unsteady power outputs into the existing electrical grid. The off-design operation however brings forth unfavorable flow patterns in the machine, causing dynamic problems involving cavitation, which may represent a limiting factor to the energy production. In Francis turbines it is observed that the self-excited oscillation of a vortex rope in the draft tube cone prevents the delivery of maximum power when required. This phenomenon is referred to as full load pressure surge and has been the object of extensive research during the past decades. Several contributions deepened its understanding through measurement and simulation of the local flow properties and the global stability parameters. The draft tube pressure level and the runner outlet swirl are identified as key variables in the modelling of the vortex rope dynamics. Recently, a cyclic appearance of blade cavitation has been observed at overload conditions in a multiphase numerical simulation coupling the runner and the draft tube. From the analysis of the simulation it becomes obvious that the cyclic appearance of blade cavitation has a direct effect on the runner outlet swirl, thus introducing an additional interaction mechanism that is not accounted for in formerly published models. For the presented work, the results of this numerical study are confirmed experimentally on a reduced scale model of a Francis turbine. Several wall pressure measurements in the draft tube cone are performed, together with high speed visualizations of the vortex rope and the blade cavitation. The flow swirl is calculated based on Laser Doppler Velocimetry measurements. A possible mechanism explaining the coupling between the self-excited pressure and vortex rope oscillation and the cyclic appearance of the blade cavitation is proposed. Furthermore, the streamwise propagation speed of the flow swirl in the draft tube is calculated. The results offer important insights in the physics of high load pressure surge and contribute to the further development of numerical draft tube flow and stability models.