The increasing variability of the energy market has created a less favourable context for hydropower plants. The operating conditions of the hydraulic turbines are impacted by the fast power regulation required to compensate for the implementation of renewable energy resources such as wind, wave, or solarpower. The turbines are frequently working in off-design conditions and therefore, their efficiency and life span are reduced. Under damaging operating regimes such as part load and speed-no-load operation, unsteady flow structures, asymmetric flow and high-pressure fluctuations develop.

Low-head power plants are usually equipped with Kaplan turbines, i.e., double-regulated axial hydraulic machines. The guide vanes and the runner blades can be adjusted separately allowing Kaplan turbines to operate at high efficiency over a wider range of flow rates compared to single-regulated turbines. However, recurrent transient and off-cam operation is accounted for the premature wear, fatigue, and failure of Kaplan turbines.

Experimental and numerical studies are carried out to understand, prevent and mitigate the negative effects of transient operation on hydraulic turbines. Numerical simulations serve as a practical and cost-efficient supplement to model testing and can provide detailed flow information that is difficult to obtain otherwise. The experimental and numerical investigations carried out on small-scale turbine models are convenient and accessible but limited. Studies concerning full-scale large turbines are, on the other hand, challenging considering the production losses, large scales, high Reynolds numbers, and significant computational demands.

This thesis presents a numerical analysis of the flow developed inside a Kaplan turbine model and prototype, working as a propeller turbine, under different operation conditions. The objective was to explore the means of creating numerical models that could be used in the industry to test, diagnose and optimize the exploitation of axial turbines. The test case was the Porjus U9 Kaplan model and prototype. All the numerical simulations were validated against experimental data. Different operating regimes of the turbine model and prototype were modelled.

The model turbine was investigated numerically at the best efficiency point and during the transient operation from the best efficiency point to part load. The influence of different turbulence models and inlet boundary conditions on the accuracy of the numerical simulations was assessed. Additionally, a time step sensitivity analysis showed that the main parameters of the turbine model were reasonably predicted with large time step values, 61° and 121° of the runner rotation, considerably reducing the simulation time and computational costs. The formation of the rotating vortex rope was captured during the guide vane closure. The frequency of the pressure fluctuations monitored on the runner blade was accurately predicted compared to the experimental values.

The operation of the Porjus U9 prototype at the best efficiency point, part load and speed-no-load was investigated numerically. The sensitivity of the numerical models to the runner blade clearance size, the epoxy layer added to the runner blade in the experimental campaign to fix the pressure sensors in their position and the runner blade angle was explored. Similar to the model simulations, the rotating vortex rope was visible at part load in the prototype simulations. The frequency of the pressure pulsations was accurately predicted while the amplitude was poorly estimated regardless of the operating point and scale of the turbine.

The role of hydropower has become increasingly essential following the introduction of intermittent renewable energies. Quickly regulating power is needed, and the transient operations of hydropower plants have consequently become more frequent. Large pressure fluctuations occur during transient operations, leading to the premature fatigue and wear of hydraulic turbines. Investigations of the transient flow phenomena developed in small-scale turbine models are useful and accessible but limited. On the other hand, experimental and numerical studies of full-scale large turbines are challenging due to production losses, large scales, high Reynolds numbers, and computational demands. In the present work, the operation of a 10 MW Kaplan prototype turbine was modelled for two operating points on a propeller curve corresponding to the best efficiency point and part-load conditions. First, an analysis of the possible means of reducing the model complexity is presented. The influence of the boundary conditions, runner blade clearance, blade geometry and mesh size on the numerical results is discussed. Secondly, the results of the numerical simulations are presented and compared to experimental measurements performed on the prototype in order to validate the numerical model. The mean torque and pressure values were reasonably predicted at both operating points with the simplified model. An analysis of the pressure fluctuations at part load demonstrated that the numerical simulation captured the rotating vortex rope developed in the draft tube. The frequencies of the rotating and plunging components of the rotating vortex were accurately captured, but the amplitudes were underestimated compared to the experimental data.

Hydropower plants often work in off-design conditions to regulate the power grid frequency. Frequent transient operation of hydraulic turbines leads to premature failure, fatigue and damage to the turbine components. The speed-no-load (SNL) operating condition is the last part of the start-up cycle and one of the most damaging operation conditions of hydraulic turbines. Hydraulic instabilities and high-stress pressure fluctuations occur due to the low flow rate and unsteady load on the runner blades. Numerical simulations can provide useful insight concerning the complex flow structures that develop inside hydraulic turbines during SNL operation. Together with experimental investigations, the numerical simulations can help diagnose failures and optimize the exploitation of hydraulic turbines. This paper introduces the numerical model of a full-scale 10 MW Kaplan turbine prototype operated at SNL. The geometry was obtained by scaling the geometry of the corresponding model turbine as the model and prototype are geometrically similar. The numerical model is simplified and designed to optimize the numerical precision and computational costs. The guide vane and runner domains are asymmetrical, the epoxy layer applied to two runner blades during the experimental measurements is not modelled and a constant runner blade clearance is employed. The unsteady simulation was performed using the SAS-SST turbulence model. The numerical results were validated with torque and pressure experimental data. The mean quantities obtained from the numerical simulation were in good agreement with the experiment. The mean pressure values were better captured on the pressure side of the runner blade compared to the suction side. However, the amplitude of the pressure fluctuations was more accurately predicted on the suction side of the runner blade. The amplitude of the torque fluctuations was considerably underestimated.

The aim of this study is to develop a reliable numerical model that provides additional information to experimental measurements and contributes to a better exploitation of hydraulic turbines during transient operation. The paper presents a numerical analysis of the flow inside a Kaplan turbine model operated at a fixed runner blade angle during load variation from the best efficiency point (BEP) to part load (PL) operation. A mesh displacement is defined in order to model the closure of the guide vanes. Two different types of inlet boundary conditions are tested for the transient numerical simulations: linear flow rate variation (InletFlow) and constant total pressure (InletTotalPressure). A time step analysis is performed and the influence of the time discretization over the fluctuating quantities is discussed. Velocity measurements at the corresponding operating points are available to validate the simulation. Spectrogram plots of the pressure signals show the times of appearance of the plunging and rotating modes of the rotating vortex rope (RVR) and the stagnation region developed around the centerline of the draft tube is captured.

Hydropower plants are currently being intensively employed for electrical grid regulation. As a consequence, the frequency of start/stops and load variations is considerably increasing, leading to the operation of hydraulic turbines under improper conditions. During the last years, studies have focused on Francis turbines. The present paper aims to investigate a Kaplan turbine model. The flow through the turbine is modelled during transient operation, from the best efficiency point to a part load operating point, using a moving mesh for the guide vane displacement. The simulations are validated against experimental velocity profiles. A time step sensitivity analysis is performed in order to determine the optimum discretization time. The possibility of using large time steps is explored. The numerically simulated unsteady pressure pulsations on the runner blades are analysed. The influence of the inlet boundary conditions on the accuracy of numerical simulations is studied. The results show that a linear flow rate variation defined during the guide vane closure leads to an overestimation of the turbine head compared to the experimental value due to an overestimation of losses. The second type of boundary conditions, a constant total pressure, results in an underestimation of the flow rate compared to the experimental value due again to an overestimation of the losses.

This paper investigates the accuracy of Reynolds-averaged Navier-Stokes (RANS) turbulence modelling applied to complex industrial applications. In the context of the increasing instability of the energy market, hydropower plants are frequently working at off-design parameters. Such operation conditions have a strong impact on the efficiency and life span of hydraulic turbines. Therefore, research is currently focused on improving the design and increasing the operating range of the turbines. Numerical simulations represent an accessible and cost efficient alternative to model testing. The presented test case is the Porjus U9 Kaplan turbine model operated at best efficiency point (BEP). Both steady and unsteady numerical simulations are carried out using different turbulence models: k-epsilon, RNG k-epsilon and k-omega Shear Stress Transport (SST). The curvature correction method applied to the SST turbulence model is also evaluated showing nearly no sensitivity to the different values of the production correction coefficient Cscale. The simulations are validated against measurements performed in the turbine runner and draft tube. The numerical results are in good agreement with the experimental time-dependent velocity profiles. The advantages and limitations of RANS modelling are discussed. The most accurate results were provided by the simulations using the k-epsilon and the SST-CC turbulence models but very small differences were obtained between the different tested models. The precision of the numerical simulations decreased towards the outlet of the computational domain. In a companion paper, the pressure profiles obtained numerically are investigated and compared to experimental data.

The aim of the paper is to investigate the limitations of unsteady Reynolds-averaged Navier-Stokes (RANS) simulations of the flow in an axial turbine. The study is focused on modelling the pressure pulsations monitored on the runner blades. The scanned blade geometry renders the meshing process more difficult. As the pressure monitor points are defined on the blade surface the simulation relies on the wall functions to capture the flow and the pressure oscillations. In addition to the classical turbulence models, a curvature correction model is evaluated aiming to better capture the rotating flow near curved, concave wall boundaries. Given the limitations of Reynolds-averaged Navier-Stokes models to predict pressure fluctuations, the Scale Adaptive Simulation-Shear Stress Transport (SAS-SST) turbulence model is employed as well. The considered test case is the Porjus U9, a Kaplan turbine model, for which pressure measurements are available in the rotating and stationary frames of reference. The simulations are validated against time-dependent experimental data. Despite the frequencies of the pressure fluctuations recorded on the runner blades being accurately captured, the amplitudes are considerably underestimated. All turbulence models estimate the correct mean wall pressure recovery coefficient in the upper part of the draft tube.

This paper presents a comparison between steady turbulent flow simulation results in the U9 Kaplan turbine draft tube and experimental velocity and pressure measurements. Two turbulence models were tested, k-epsilon and Shear StressTransport (SST). The results show that the k-epsilon model performs better than the SST model.The objective is to find a correlation between the pressure measured below the runner in the draft tube cone, and the optimal guide vane angle for a given bladeangle. Such correlation may allow the continuous online optimization of the cam characteristic. For this purpose, the influence of the tangential velocity on the pressure in the draft tube was specifically investigated.

The paper presents a new method for in site discharge estimation in pressured pipes. The method consists in using the water hammer equations solved with the method of characteristics with an unsteady friction factor model. The differential pressure head variation measured during a complete valve closure is used to derive the initial flow rate, similarly to the pressure-time (Gibson) method. The method is validated with a numerical experiment, and tested with experimental laboratory measurements. The results show that the proposed method can reduce the discharge estimation error by 0.6% compared to the standard pressure-time (Gibson) method for the flow rate investigation.