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Francis turbines operating at part load conditions develop a cavitation precessing vortex known as a vortex rope in the draft tube cone below the runner outlet. At part load conditions, this vortex precession acts as an excitation source inducing pressure pulsations in the whole hydraulic system at the vortex precession frequency. Simultaneously, the lower pressure levels in the vortex core can lead to cavitation development, increasing the local flow compliance and reducing drastically the pressure wave speed. As a result, the eigen-frequencies of the hydraulic circuit are lowered and may match the vortex rope excitation frequency, leading to undesired resonance conditions. This paper presents a procedure to predict this type of resonance phenomenon in turbine prototypes by performing reduced scale physical turbine model measurements and eigenvalue calculations with linearized system matrices. This new procedure requires the transposition of hydroacoustic parameters from the reduced scale physical model to the prototype scale based on the swirl number and the local cavitation coefficient similarity. The procedure is validated by measurements performed on a turbine prototype featuring a peak of power swings and pressure pulsations in the predicted operating conditions. (C) 2019 Elsevier Ltd. All rights reserved.

For seamless integration of growing electricity production from intermittent renewable energy sources, Francis turbines are under increasing demand to extend their operating range. This requires Francis turbines to operate under off-design conditions, where various types of cavitation are induced. At deep part load condition, an interblade cavitation vortex observed in a runner blade channel is a typical cavitation phenomenon causing pressure fluctuations and erosion, which prevent a reliable operation of Francis turbines at deep part load. The underlying mechanisms of its development are, however, yet to be understood. In an objective of revealing its developing mechanisms, the present study is aimed at investigating flow structures inside runner blade channels by comparison of three different operating conditions at deep part load using numerical simulation results. After demonstrating interblade vortex structures are successfully simulated by performed computations, it is shown that flow inside the runner at deep part load operation is characterized by a remarkable development of recirculating flow on the hub near the runner outlet. This recirculating flow is concluded to be closely associated with interblade vortex development. The skin-friction analyses applied to the hub identify the flow separation caused by a nonuniform distribution of flow, which describes the underlying physical mechanism of interblade vortex development. Investigations are further extended to include a quantitative evaluation of the specific energy loss induced by interblade vortex development. The integration of energy flux defined by rothalpy evidences the energy loss due to the presence of strong interblade vortex structures.

Hydropower plants play an important regulatory role in the large scale integration of volatile renewable energy sources into the existing power grid. This duty however requires a continuous extension of their operating range, provoking the emergence of complex flow patterns featuring cavitation inside the turbine runner and the draft tube. When the power output is maximized at full load, self-excited pressure oscillations in the hydraulic system may occur, which translate into significant electrical power swings and thus pose a serious threat to the grid stability as well as to the operational safety of the machine. Today's understanding of the underlying fluid–structure interaction mechanisms is incomplete, yet crucial to the development of reliable numerical flow models for stability analysis, and for the design of potential countermeasures. This study therefore reveals how the unsteady flow inside the machine forces periodic mechanical loads onto the runner shaft. For this purpose, the two-phase flow field at the runner exit is investigated by Laser Doppler Velocimetry and high-speed visualizations, which are then compared to the simultaneously measured wall pressure oscillations in the draft tube cone and the mechanical torque on the runner shaft. The results are presented in the form of a comprehensive, mean phase averaged evolution of the relevant hydro-mechanical data over one period of the instability. They show that the flow in the runner, and thus the resulting torque applied to the shaft, is critically altered by a cyclic growth, shedding and complete collapse of cavitation on the suction side of the runner blades. This is accompanied by a significant flow swirl variation in the draft tube cone, governing the characteristic breathing motion of the cavitation vortex rope.

Hydropower units may be required to operate in condenser mode to supply reactive power. In this operating mode, the water level in the turbine or pump-turbine is decreased below the runner by closing the guide vanes and injecting pressurized air. While operating in condenser mode the machine experiences power losses due to several air–water interaction phenomena which cause air losses. One of such phenomena is the sloshing motion of the water free surface below the runner in the draft tube cone of a Francis turbine. The objective of the present work is to experimentally investigate the sloshing motion of the water free surface in the draft tube cone of a reduced scale physical model of a Francis turbine operating in condenser mode. Images acquisition and simultaneous pressure fluctuation measurements are performed and an image processing method is developed to investigate amplitude and frequency of the sloshing motion of the free surface. It is found that this motion is excited at the natural frequency of the water volume and corresponds to the azimuthal wavenumber $$m = 1$$ of a rotating gravity wave. The amplitude of the motion is perturbed by wave breaking and it decreases by increasing the densimetric Froude number. The sloshing frequency slightly increases with respect to the natural frequency of the water volume by increasing the densimetric Froude number. Moreover, it results that this resonant phenomenon is not related to the torque perturbation.

The large-scale penetration of the electrical grid by intermittent renewable energy sources requires a continuous operating range extension of hydropower plants. This causes the formation of unfavourable flow patterns in the draft tube of turbines and pump-turbines. At partial load operation, a precessing cavitation vortex rope is formed at the Francis turbine runner outlet, acting as an excitation source for the hydraulic system. In case of resonance, the resulting high-amplitude pressure pulsations can put at risk the stability of the machine and of the electrical grid to which it is connected. It is therefore crucial to understand and accurately simulate the underlying physical mechanisms in such conditions. However, the exact impact of cavitation and hydro-acoustic resonance on the flow velocity fluctuations in the draft tube remains to be established. The flow discharge pulsations expected to occur in the draft tube in resonance conditions have for instance never been verified experimentally. In this study, two-component Laser Doppler Velocimetry is used to investigate the axial and tangential velocity fluctuations at the runner outlet of a reduced scale physical model of a Francis turbine. The investigation is performed for a discharge equal to 64 % of the nominal value and three different pressure levels in the draft tube, including resonance and cavitation-free conditions. Based on the convective pressure fluctuations induced by the vortex precession, the periodical velocity fluctuations over one typical precession period are recovered by phase averaging. The impact of cavitation and hydro-acoustic resonance on both axial and tangential velocity fluctuations in terms of amplitude and phase shift is highlighted for the first time. It is shown that the occurrence of resonance does not have significant effects on the draft tube velocity fields, suggesting that the synchronous axial velocity fluctuations are surprisingly negligible compared to the velocity fluctuations induced by the vortex precession.

The massive penetration of the electrical network by renewable energy sources, such as wind and solar, pushes the operators to extend hydropower plant units operating range to meet the transmission system operator requirements. However, in off-design operating conditions, flow instabilities are developing in Francis turbines, inducing cavitation, pressure pulsations and potentially resonance that can threaten the stability of the whole system. Reduced scale model testing is commonly performed to assess the hydraulic behaviour of the machine for industrial projects. However, it is not possible to directly transpose pressure pulsations and resonance conditions from model to prototype since the characteristics of the hydraulic circuits are different from model to prototype. In this paper, a methodology developed in the framework of the HYPERBOLE European research project for predicting the eigenfrequencies of hydropower plant units operating in off-design conditions is introduced. It is based on reduced scale model testing and proper one-dimensional modelling of the hydraulic circuits, including the draft tube cavitation flow, at both the model and prototype scales. The hydro-acoustic parameters in the draft tube are identified at the model scale for a wide number of operating conditions and, then, transposed to the full-scale machine, together with the precession frequency for part load conditions. This enables the prediction of the eigenfrequencies and resonance conditions of the full-scale generating unit.

For Francis turbines at part load operation a helical vortex rope is formed due to the swirling nature of the flow exiting the runner. This vortex creates pressure fluctuations which can lead to power swings, and the unsteady loading can lead to fatigue damage of the runner. In the case that the vortex rope cavitates there is the additional risk that hydro-acoustic resonance can occur. It is therefore important to be able to accurately simulate this phenomenon to address these issues. In this paper an unsteady, multi-phase CFD model was used to simulate two part-load operating points, for two different cavitation conditions. The simulation results were validated with test-rig data, and showed very good agreement. These results also served as an input for FEA calculations and fatigue analysis, which are presented in a separate study.

At off-design operating operations, cavitating flow is often observed in hydraulic machines. The presence of a cavitation vortex rope may induce draft tube surge and electrical power swings at part load and full load operations. The stability analysis of these operating conditions requires a numerical pipe model taking into account the complexity of the two-phase flow. Among the hydroacoustic parameters describing the cavitating draft tube flow in the numerical model, the mass flow gain factor, representing the mass excitation source expressed as the rate of change of the cavitation volume as a function of the discharge, remains difficult to model. This paper presents a quasi-static method to estimate the mass flow gain factor in the draft tube for a given cavitation vortex rope volume in the case of a reduced scale physical model of a ν = 0.27 Francis turbine. The methodology is based on an experimental identification of the natural frequency of the test rig hydraulic system for different Thoma numbers. With the identification of the natural frequency, it is possible to model the wave speed, the cavitation compliance and the volume of the cavitation vortex rope. By applying this new methodology for different discharge values, it becomes possible to identify the mass flow gain factor and improve the accuracy of the system stability analysis.

At part load conditions, Francis turbines experience the formation of a cavitation vortex rope at the runner outlet whose precession acts as a pressure excitation source for the hydraulic circuit. This can lead to hydro-acoustic resonances characterized by high pressure pulsations, as well as torque and output power fluctuations. This study highlights the influence of the discharge factor on both the vortex parameters and the pressure excitation source by performing Particle Image Velocimetry (PIV) and pressure measurements. Moreover, it is shown that the occurrence of hydro-acoustic resonances in cavitation conditions mainly depend on the swirl degree of the flow independently of the speed factor. Empirical laws linking both natural and precession frequencies with the operating parameters of the machine are, then, derived, enabling the prediction of resonance conditions on the complete part load operating range of the turbine.

Francis turbines operating in part load conditions experience a swirling flow at the runner outlet leading to the development of a precessing cavitation vortex rope in the draft tube. This cavitation vortex rope changes drastically the velocity of pressure waves traveling in the draft tube and may lead to resonance conditions in the hydraulic circuit. The wave speed being strongly related to the cavitation compliance, this research work presents a simple model to explain how it is affected by variations of operating conditions and proposes a method to transpose its values. Even though the focus of this paper is on transpositions within the same turbine scale, the methodology is also expected to be tested for the model to prototype transposition in the future. Comparisons between measurements and calculations are in good agreement.

Francis turbines are subject to various types of the cavitation flow depending on the operating condition s. In order to compensate for the stochastic nature of renewable energy sources, it is more and more required to extend the operating range of the generating units, from deep part load to full load conditions. In the deep part load condition, the formation of cavitation vortices in the turbine blade-to-blade channel s called inter -blade cavitation vortex is often observed. The understanding of the dynamic characteristics of these inter -blade vortices and their formation mechanisms is of key importance in an effort of developing reliable flow simulation tools. This paper reports the numerical and experimental investigations carried out in order to establish the vortex characteristics, especially the inception and the development of the vortex structure. The unsteady RANS simulation for the multiphase flow is performed with the SST - SA S turbulence model by using the commercial flow solver ANSYS CFX. The simulation results in terms of the vortex structure and the cavitation volume are evaluated by comparing them to the flow visualization s of the blade channel acquired through a specially instrumented guide vane as well as from the downstream of the runner across the draft tube cone. The inter-blade cavitation vortex is successfully captured by the simulation and both numerical and experimental results evidence that the inter -blade vortices are attached to the runner hub.

Acoustic resonances in Francis turbines often define undesirable limitations to their operating ranges at high load. The knowledge of the mechanisms governing the onset and the sustenance of these instabilities in the swirling flow leaving the runner is essential for the development of a reliable hydroacoustic model for the prediction of system stability. The present work seeks to study experimentally the unstable draft tube flow by conducting a series of measurements on a reduced Francis Turbine model. The key physical parameters and their interaction with the hydraulic and mechanical system are studied and quantified. In particular, the evolution of the axial and tangential velocity components in the draft tube cone is analysed by means of Laser Doppler Anemometry. Combined with the calculation of the instantaneous vortex rope volume based on flow visualization and the measurement of the pressure fluctuations, the nature of the auto-oscillation in the draft tube flow is investigated.

At a deep part load operation, Francis turbines are subject to the formation of inter-blade cavitation vortices inside blade channels, however its characteristics are not fully understood yet. The present study aims to investigate the development of the inter-blade vortex as well as the flow characteristics associated with the vortex formation inside the blade channel, by using the unsteady RANS simulation. The velocity survey reveals the appearance of the back flow region in the vicinity of the hub near the trailing edge, which seems closely linked with the inter-blade vortex development. Furthermore, the local influence of the inter-blade vortex is evaluated by the specific energy loss calculated from the rothalpy in the blade channel. The comparison of the different operating conditions evidences the impact of the inter-blade vortex presence on the energy dissipation through the blade channel.

Resonance in hydraulic systems is characterized by pressure fluctuations of high amplitude which can lead to undesirable and dangerous effects, such as noise, vibration and structural failure. For a Francis turbine operating at partial load, the cavitating vortex rope developing at the outlet of the runner induces pressure fluctuations which can excite the hydraulic system resonance, leading to undesirable large torque and power fluctuations. At resonant operating points, the prediction of amplitude pressure fluctuations by hydro-acoustic models breaks down and gives unreliable results. A more detailed knowledge of the eigenmodes and a better understanding of phenomenon occurring at resonance could allow improving the hydro-acoustic models prediction. This paper presents an experimental identification of a resonance observed in a close-looped hydraulic system with a Francis turbine reduced scale model operating at partial load. The resonance is excited matching one of the test rig eigenfrequencies with the vortex rope precession frequency. At this point, the hydro-acoustic response of the test rig is studied more precisely and used finally to reproduce the shape of the excited eigenmode.

Full load pressure surge limits the operating range of hydro-electric generating units by causing significant power output swings and by compromising the safety of the plant. It appears during the off-design operation of hydraulic machines, which is increasingly required to regulate the broad integration of volatile renewable energy sources into the existing power network. The underlying causes and governing physical mechanisms of this instability were investigated in the frame of a large European research project and this paper documents the main findings from two experimental campaigns on a reduced scale model of a Francis turbine. The multi-phase flow in the draft tube is characterized by Particle Image Velocimetry, Laser Doppler Velocimetry and high-speed visualizations, along with synchronized measurements of the relevant hydro-mechanical quantities. The final result is a comprehensive overview of how the unsteady draft tube flow and the mechanical torque on the runner shaft behave during one mean period of the pressure oscillation, thus defining the unstable fluid-structure interaction responsible for the power swings. A discussion of the root cause is initiated, based on the state of the art. Finally, the latest results will enable a validation of recent RANS flow simulations used for determining the key parameters of hydro-acoustic stability models.

The cavitation helical vortex rope arising at Francis turbine partial load induces pressure fluctuations at the rope precession frequency, which can be decomposed into two components; the convective one and the synchronous one. The latter acts as an excitation source for the hydraulic system and is amplified in case of resonance. The present paper aims to highlight the impact of both components on the mechanical behaviour of the runner by performing on-board measurements. It is shown that the use of on-board pressure sensors enables to naturally separate the components of the pressure fluctuations. In addition, the synchronous component has little impact on the mechanical behaviour of the runner, even for the case in which hydro-acoustic resonance occurs.

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.

Francis turbines operating at off-design conditions experience the development of unfavourable cavitation flows in the draft tube at the runner outlet, which induce pressure pulsations and hydro-acoustic resonances in the worst cases. The assessment of hydropower plant units at off-design conditions is possible by means of one-dimensional numerical simulation, which however requires a proper modelling of the draft tube cavitation flow. The corresponding hydro-acoustic parameters can be identified for a wide number of operating points on the reduced scale model of the machine by modal analysis of the hydraulic test rig. This identification approach is efficient but can however be time-consuming for an industrial project. The paper aims at proposing and validating a faster procedure to identify the eigenfrequencies and the corresponding eigenmodes of a hydraulic test rig featuring a reduced scale model of a Francis turbine operating in off-design conditions. The test rig is excited by injecting a periodical discharge with a rotating valve whose frequency linearly increases from 0 to 7 Hz. Based on the response of the test rig, measured by pressure sensors placed along the pipes, the eigenfrequencies and the corresponding eigenmodes are identified for several operating conditions. The hydro-acoustic parameters are then identified by using a one-dimensional numerical model of the test rig. The results are in very good agreement with those obtained with the standard procedure, i.e. with a stepwise increase of the excitation frequency. This new approach represents an important gain of time and might be applied to assess hydropower plant stability in an industrial context. (C) 2018 Elsevier Ltd. All rights reserved.

Hydraulic machines operating in a wider range are subjected to cavitation developments inducing undesirable pressure pulsations which could lead to potential instability of the power plant. The occurrence of pulsating cavitation volumes in the runner and the draft tube is considered as a mass source of the system and is depending on the cavitation compliance. This dynamic parameter represents the cavitation volume variation with the respect to a variation of pressure and defines implicitly the local wave speed in the draft tube. This parameter is also decisive for an accurate prediction of system eigen frequencies. Therefore, the local wave speed in the draft tube is intrinsically linked to the eigen frequencies of the hydraulic system. Thus, if the natural frequency of a hydraulic system can be determined experimentally, it also becomes possible to estimate a local wave speed in the draft tube with a numerical model. In the present study, the reduced scale model of a Francis turbine (v=0.29) was investigated at off-design conditions. In order to measure the first eigenmode of the hydraulic test rig, an additional discharge was injected at the inlet of the hydraulic turbine at a variable frequency and amplitude to excite the system. Thus, with different pressure sensors installed on the test rig, the first eigenmode was determined Then, a hydro-acoustic test rig model was developed with the In-house EPFL SIMSEN software and the local wave speed in the draft tube was adjusted to obtain the same first eigen frequency as that measured experimentally. Finally, this method was applied for different Thoma and Froude numbers at part load conditions.

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.

At part load operation, Francis turbines experience the development of a cavitation vortex rope in the draft tube, whose precession acts as a pressure excitation source. In case of resonance, the resulting pressure pulsations lead to unacceptable torque and power fluctuations on the prototype machine, putting at risk the system stability. However, the accurate prediction of resonance conditions at the prototype scale remains challenging since it requires a proper hydro-acoustic modelling of the draft tube cavitation flow. Furthermore, both the head and discharge values have an impact on the precession frequency of the vortex and the natural frequency of the system. The present paper demonstrates for the first time that the influence of both parameters on the frequencies of interest can be represented by a single parameter, the swirl number. Its analytical expression is derived as a function of the operating parameters of the machine. It is used to establish empirical laws enabling the determination of both frequencies and finally the operating parameters in resonance conditions on the complete part load operating range at the model scale. The methodology presented in this paper represents a decisive step towards the prediction of resonances on the complete part load operating range of the prototype.

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.

The prediction of pressure fluctuations amplitudes on Francis turbine prototype is a challenge for hydro-equipment industry since it is subjected to guarantees to ensure smooth and reliable operation of the hydro units. The European FP7 research project Hyperbole aims to setup a methodology to transpose the pressure fluctuations measured on the reduced scale model to the prototype generating units. This paper presents this methodology which relies on an advanced modelling of the draft tube cavitation flow, and focuses on the transposition to the prototype of the draft tube model parameters identified on the reduced scale model. Different modelling assumptions of the draft tube are considered and their influence on the eigenmodes and the forced response of the system are presented.

Francis turbines operating at part-load experience the development of a precessing cavitation vortex rope at the runner outlet, which acts as an excitation source for the hydraulic system. In case of resonance, the resulting pressure pulsations seriously compromise the stability of the machine and of the electrical grid to which it is connected. As such off-design conditions are increasingly required for the integration of unsteady renewable energy sources into the existing power system, an accurate assessment of the hydropower plant stability is crucial. However, the physical mechanisms driving this excitation source remain largely unclear. It is for instance essential to establish the link between the draft tube flow characteristics and the intensity of the excitation source. In this study, a two-component particle image velocimetry system is used to investigate the flow field at the runner outlet of a reduced-scale physical model of a Francis turbine. The discharge value is varied from 55 to 81 % of the value at the best efficiency point. A particular set-up is designed to guarantee a proper optical access across the complex geometry of the draft tube elbow. Based on phase-averaged velocity fields, the evolution of the vortex parameters with the discharge, such as the trajectory and the circulation, is determined for the first time. It is shown that the rise in the excitation source intensity is induced by an enlargement of the vortex trajectory and a simultaneous increase in the precession frequency, as well as the vortex circulation. Below a certain value of discharge, the structure of the vortex abruptly changes and loses its coherence, leading to a drastic reduction in the intensity of the induced excitation source.

Francis turbines operating at part load conditions typically experience a cavitation vortex rope immediately at the runner outlet. As the compliance of this cavitation flow is much higher than the one in cavitation-free conditions, a decrease in the value of the eigen frequencies of the hydraulic circuit is observed. One of the eigen frequencies can eventually match the frequency of the vortex precession, which acts as an excitation source for the hydraulic system, inducing strong pressure pulsations and output power swings. To predict such undesirable resonance conditions in hydropower plants, the cavitation compliance in the draft tube cone can be identified beforehand at the model scale. This paper presents the identification of the cavitation compliance on a reduced scale model of a Francis turbine over a wide range of part load operating conditions, for different Thoma and Froude numbers. The first eigen frequency of the test rig is firstly identified by modal analysis. The cavitation compliance is then defined by adjusting a 1-D numerical model of the test rig to match this first eigen frequency. These compliance results could then be transposed to the prototype scale, enabling the prediction of the first eigen frequency of the hydropower plant in any part load condition.

In the course of the massive penetration of alternative renewable energies, the stabilization of the electrical power network significantly relies on the off-design operation of turbines and pump-turbines in hydropower plants. The occurrence of cavitation is, however, a common phenomenon at such operating conditions, often leading to critical flow instabilities, which undercut the grid stabilizing capacity of the power plant. In order to predict and extend the stable operating range of hydraulic machines, a better understanding of the cavitating flows and mainly of the transition between stable and unstable flow regimes is required. In the case of Francis turbines operating at full load, an axisymmetric cavitating vortex rope develops at the outlet runner in the draft tube. The cavity may enter self-oscillation, with violent periodic pressure pulsations propagating throughout the entire hydraulic system. The flow fluctuations lead to dangerous electrical power swings and mechanical vibrations through a fluid-structure coupling across the runner, imposing an inconvenient and costly restriction of the operating range. The paper deals with a numerical and experimental investigation of the transition from a stable to an unstable operating point on a reduced scale model of a Francis turbine at full load. Unsteady homogeneous two-phase RANS simulations are carried out using the ANSYS CFX solver. Cavitation is modelled using the Zwart’s model that required solving an additional transport equation for the void fraction. Turbulence is solved using the SST k-ω model. Simulations are compared with the experimental measurements and some insights are provided for a first comprehensive analysis of the transition between the stable and unstable states.

At partial load and overload conditions, Francis turbines are subjected to hydraulic instabilities that can potentially result in high dynamic solicitations of the turbine components and significantly reduce their lifetime. This study presents both experimental data and numerical simulations that were used as complementary approaches to study these dynamic solicitations. Measurements performed on a reduced scale physical model, including a special runner instrumented with on-board strain gauges and pressure sensors, were used to investigate the dynamic phenomena experienced by the runner. They were also taken as reference to validate the numerical simulation results. After validation, advantage was taken from the numerical simulations to highlight the mechanical response of the structure to the unsteady hydraulic phenomena, as well as their impact on the fatigue damage of the runner.

While operating at part load, Francis turbines feature a precessing cavitation vortex rope in its draft tube. The precession of this vortex in the elbow of the draft tube acts as a pres-sure pulsation source which frequency can match the first hydroacoustic eigenfrequency of the hydraulic system in some cases. Resonance phenomenon can be predicted by using reduced scale physical model tests and numerical simulations, but it remains challenging. This paper proposes a procedure to estimate the risk of part load resonance at the early stage of a hydropower project. The proposed procedure uses the hydroacoustic properties of a given reduced scale physical model and applies them to a large number of turbine de-signs and power plant configurations to assess the risk of resonance for each one of them. Results show that resonance are likely to occur in hydropower plants in a certain range of turbine rated head and rated discharge values. These results can then indicate if more detailed investigations in some specific hydropower projects are necessary.

Hydropower plant units operating in off-design conditions are subject to cavitation flow instabilities, potentially inducing hydro-acoustic resonances under certain conditions. They can be predicted by using one-dimensional numerical models of hydropower plants that rely on a proper modelling of the draft tube cavitation flow in off-design conditions. The latter is based on hydro-acoustic parameters that can be identified experimentally on the reduced scale physical model of the prototype on its complete operating range, which however requires an important number of measurements during model testing to consider the influence of both the head and the discharge. This article proposes a new methodology enabling the prediction of resonance conditions excited by a draft tube cavitation vortex on the complete head range of a hydropower plant unit. The methodology relies on the experimental identification at the model scale of the hydro-acoustic parameters and their transposition from the model to the prototype scale. By expressing the precession frequency of the vortex and the hydro-acoustic parameters of the draft tube cavitation flow as a function of the runner outlet flow swirl number, their value can be predicted on the complete part load operating range of the prototype whatever the value of both the head and discharge. The computation of the first natural frequency with a 1D numerical modelling of the hydropower plant enables finally the prediction of resonance conditions, which are compared with those identified by measurements on the full-scale machine.

The operation of Francis turbines at off-design conditions may cause the development of a cavitation vortex rope in the draft tube cone, acting as a pressure excitation source. The interactions between this excitation source and the hydraulic system at the natural frequency may result in resonance phenomena, causing serious hydro-mechanical oscillations. One-dimensional draft tube models for the simulation and prediction of part load resonances require an accurate modelling of the wave speed and the bulk viscosity for the draft tube flow. This paper introduces a new methodology for determining these two hydroacoustic parameters in the draft tube of a reduced scale physical model of a Francis turbine, based on experimental identification of the hydraulic natural frequency of the test rig. Finally, dimensionless numbers are derived to define both the wave speed and bulk viscosity for different operating points of the turbine.