Hydroacoustic modelling and numerical simulation of unsteady operation of hydroelectric systems

Hydropower represented in 1999 19% of the world electricity production and the absolute production is expected to grow considerably during the next 30 years. Francis turbines play a major role in the hydroelectric production due to their extended range of application. Due to the deregulated energy market, hydroelectric power plants are increasingly subjecting to off design operation, start-up and shutdown and new control strategies. Consequently, the operation of Francis turbine power plants leads to transients phenomena, risk of resonance or instabilities. The understanding of these propagation phenomena is therefore paramount. This work is a contribution to the hydroacoustic modelling of Francis turbine power plants for the investigation of the aforementioned problematic. The first part of the document presents the modelling of the dynamic behavior and the transient analysis of hydroelectric power plants. Therefore, the one-dimensional model of an elementary pipe is derived from the governing equations, i.e. momentum and continuity equations. The use of appropriate numerical schemes leads to a discrete model of the pipe consisting of a T-shaped equivalent electrical circuit. The accuracy in the frequency domain of the discrete model of the pipe is determined by comparison with the analytical solution of the governing equations. The modelling approach is extended to hydraulic components such as valve, surge tanks, surge shaft, air vessels, cavitation development, etc. Then, the modelling of the Francis, Pelton and Kaplan turbines for transient analysis purposes is presented. This modelling is based on the use of the static characteristic of the turbines. The hydraulic components models are implemented in the EPFL software SIMSEN developed for the simulation of electrical installations. After validation of the hydraulic models, transient phenomena in hydroelectric power plants are investigated. It appears that standard separate studies of either the hydraulic or of the electrical part are valid only for design purposes, while full hydroelectric models are necessary for the optimization of turbine speed governors. The second part of the document deals with the modelling and analysis of possible resonance or operating instabilities in Francis turbine power plants. The review of the excitation sources inherent to Francis turbine operations indicates that the draft tube and the rotor-stator interaction pressure fluctuations are of the major concern. As the modelling of part load pressure fluctuations induced by the cavitating vortex rope that develops in the draft tube at low frequencies is well established, the focus is put on higher frequency phenomena such as higher part load pressure fluctuations and rotorstator interactions or full load instabilities. Three hydroacoustic investigations are performed. (i) Pressure fluctuations identified experimentally at higher part load on a reduced scale model Francis turbine are investigated by means of hydroacoustic simulations and high speed flow visualizations. The resonance of the test rig due to the vortex rope excitation is pointed out by the simulation while the special motion and shape of the cavitating vortex rope at the resonance frequency is highlighted by the visualization. A description of the possible excitation mechanisms is proposed. (ii) A pressure and power surge measured on a 4 × 400 MW pumped-storage plant operating at full load is investigated. The modelling of the entire system, including the hydraulic circuit, the rotating inertias and the electrical installation provides an explanation of the phenomenon and the related conditions of apparition. A non-linear model of the full load vortex rope is established and qualitatively validated. (iii) The rotor-stator interactions (RSI) are studied in the case of a reduced scale pump-turbine model. An original modelling approach of this phenomenon based on the flow distribution between the stationnary and the rotating part is presented. The model provides the RSI pressure fluctuation patterns in the vaneless gap and enables to predict standing waves in the spiral case and adduction pipe. The proposed one-dimensional modelling approach enables the simulation, analysis and optimization of the dynamic behavior of hydroelectric power plants. The approach has proven its capability of simulating properly both transient and periodic phenomena. Such investigations can be undertaken at early stages of a project to assess the possible dynamic problems and to select appropriate solutions ensuring the safest and optimal operation of the facility.

Forced and Self Oscillations of Hydraulic Systems Induced by Cavitation Vortex Rope of Francis Turbines

Sébastien Alligné

With economical energy market strategies based on instantaneous pricings of electricity as function of the demand or the predictions, operators harness more hydroelectric facilities to off-design operating points to cover the variations of the electricity production. Under these operating conditions, Francis turbines develop a cavitating swirling flow at the runner outlet which induces pressure fluctuations propagating in the whole hydraulic system. The core of this cavitating vortex is usually called vortex rope. At resonance conditions, the superimposition of the induced traveling waves gives rise to a standing wave leading to undesirable large pressure and output power fluctuations. The aim of this present work is to predict and to simulate this resonance phenomenon which may happen both in part load or full load operating conditions. The identification of the excitation sources induced by the cavitating vortex rope is performed with numerical simulations based on a three dimensional incompressible model, so called hydrodynamic (HD) model. The assumption of plane wave propagation in the water passages connected to the turbine is set since low surging frequencies are involved. Hence, propagation of these sources is simulated with a one dimensional compressible model, so called hydroacoustic (HA) model. The HA model covers the entire hydraulic system including the source region corresponding to the draft tube of the Francis turbine whereas the HD model covers only the source region. In this present work, a specific HA draft tube model has been developed. A momentum source modeling the forces induced by the flow acting on the draft tube wall is considered. Moreover, the fluctuating cavitation volume is considered as a mass source. Finally, a thermodynamic damping is introduced to model energy dissipation during a phase change between liquid and gas. Investigations at part load conditions aim to simulate the upper part load resonance phenomenon for which frequency of pressure fluctuations are experienced between 2 and 4 times the runner frequency. Measurements were carried out in the framework of the FLINDT project which is therefore the case study for validation. First of all, HA draft tube model parameters have been derived for the investigated operating point considering both single phase and two phase unsteady simulations with the HD model. An analysis of these parameters is performed and comparison between single phase and two phase simulation results is made. It is shown that the cavitation modeling in the HD model is necessary to find the vortex rope precession frequency which depends on the cavitation amount in the vortex core. However, the volume of vapor is underestimated and a correction factor on the Thoma number is necessary to get a good agreement between experiments and simulation results. Moreover it has been shown that the three dimensional flow in the elbow gives rise to HA sources able to excite the hydraulic system. Intensity of the sources are higher when two phase flow simulations are considered. Before simulating the upper part load resonance phenomenon, a preliminary validation of these HA parameters is performed by simulating a standard part load resonance where the vortex rope precession frequency, near 0.3 times the runner frequency, matches with the first eigenfrequency of the hydraulic system. In out of resonance conditions, maximum of pressure fluctuations amplitudes are experienced in the draft tube cone with an amplitude being 1% of the turbine head. However, when resonance occurs, maximum amplitude of pressure fluctuations reaches up to 7%. A good agreement is obtained with the order of magnitudes found in measurements available in the literature. After this preliminary validation, simulation of the upper part load resonance phenomenon has been tackled. It has been found that the mechanism inducing this phenomenon is related to an undesirable fluctuation of the cavitation volume which frequency can match with an eigenfrequency of the hydraulic system. However, this fluctuation is captured for a Thoma number much higher than the experimental one leading to a cavitation volume very small compared to the experiments. A prototype installation of four 478 MW Francis turbines located in the Canada's province British Columbia, has been chosen as the case study to analyze the full load instability phenomenon. Indeed, this instability occurred on prototype and reduced scale model as well. Hence, experimental measurements have been carried out on the reduced scale model aiming to use experimental data to validate the numerical simulations performed with the HA draft tube model. The mass source defined in this model, is described by a decisive parameter which is the mass flow gain factor. Extensively used in previous works for the analysis of this phenomenon, this parameter is defined to represent the effect of the HA fluctuations of the downstream flow rate to the cavitation volume on the mass source. In this present work, the same formulation is used and has been combined with the introduction of a new parameter: the thermodynamic damping. First of all, these HA parameters have been derived for the different investigated experimental operating points from single phase steady simulations. Then, using these computed parameters, a small perturbation stability analysis in the frequency domain has been carried out to identify the stability of the different operating points. The experimental unstable characteristic frequencies have been found out with this modal analysis. However, this analysis in the frequency domain does not give any information about the amplitude of the pressure fluctuations induced by the instability. Hence, time domain HA simulations have been performed. It has been shown that the using of constant HA draft tube model parameters leads to divergent time domain simulations, whereas nonlinear parameters depending on the pressure variable, lead to a limit cycle of finite amplitude fluctuations. Moreover, nonlinearity of the thermodynamic damping is decisive to reach this limit cycle. Finally, a methodology has been set up to predict the instability of the prototype from the investigations on the reduced scale model. A combination of measurements, numerical simulations and computation of the eigenmodes of the reduced scale model installed on test rig, allows the accurate calibration of the HA draft tube model parameters at the model scale. Finally, transposition of these parameters to the prototype according to similitude laws is applied for the stability analysis of the power plant.

EPFL2011

Dynamics of the cavitation precessing vortex rope for Francis turbines at part load operating conditions

Arthur Tristan Favrel

The massive penetration of the existing electrical grid by renewable energy sources requires a continuous extension of the operating range of hydroelectric powerplants, which can lead to cavitation flow instabilities inducing undesirable mechanical vibrations and large fluctuations of pressure and output power, putting at risk the structural integrity of the machine and ultimately the grid stability. A typical example is the development of a cavitation precessing vortex rope at the outlet of a Francis turbine runner operating at part load conditions. It acts as an excitation source for the hydraulic system, leading to the propagation of pressure fluctuations in the hydraulic circuit which are greatly amplified in case of resonance. Therefore, the assessment of the stability of hydropower plants operating at part load is crucial in order to ensure the safe extension of their operating range. The accurate prediction and transposition of pressure fluctuations from the model scale to the prototype scale by means of one-dimensional hydro-acoustic models represents a major challenge, as the physical mechanisms driving the excitation source and its interaction with the hydraulic system remain partially unclear. The main objective of this research work is to experimentally investigate the influence of the operating conditions on the dynamics of the cavitation precessing vortex rope and the excitation source it induces, as well as the interaction with the system. The test-case is a reduced scale physical model of a Francis turbine, accurately reproducing the behaviour of a real size machine. Experimental investigations include study of the flow field in the draft tube cone by means of Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV), high-speed visualizations of the cavitation vortex and pressure measurements performed at various part load operating conditions, including cavitation-free and cavitation conditions. PIV measurements of the tangential flow field in the draft tube cone in cavitation-free conditions highlight the influence of the flow discharge on the vortex characteristics in terms of trajectory, circulation and structure, as well as the link between the vortex dynamics and the intensity of the excitation source. The effect of cavitation on the vortex rope dynamics and its interaction with the surrounding system is also studied, with a particular focus on resonance conditions. Flow velocity measurements performed for different values of the Thoma number reveal that the axial and tangential velocity fields in the draft tube cone are not impacted by the propagation of large synchronous pressure fluctuations. Among the other observations is a phenomenon of frequency lock-in between the excitation source and the system's oscillations occurring for low values of the Froude number. This phenomenon is assumed to be a consequence of the non-linear coupling taking place in resonance conditions between the excitation source and the oscillation of the cavitation volume. Finally, it is shown that the convective component of the pressure fluctuations at the precession frequency represents the main source of mechanical excitation for the runner.

EPFL2016

Multiscale Computational Methodology Applied to Hydroacoustic Resonance in Cavitating Pipe Flow

Nicolas Ruchonnet

The present work is a contribution to the physical analysis and numerical simulation of the pressure surges in hydraulic machinery and connected conduit systems. Localized hydrodynamic instabilities including cavitation are prone to interact with the entire conduit through the propagation of acoustic plane waves. At resonance, the superimposition of the acoustic waves leads to the formation of large amplitudes standing waves along the entire conduit. The resulting fluctuation of velocity and pressure in the source region may have a significant role on the hydrodynamic instability. A computational methodology based on two fields is proposed to simulate this interaction in the time domain: a 1D hydroacoustic model (HA model) is selected to analyze the entire acoustic field including the source region, a 3D incompressible hydrodynamic model (HD model) is used to describe the flow in the source region. The acoustic perturbation due to the instability is precisely evaluated with the HD model and injected in the HA model through discrete sources. To describe the complete interaction between the fields, two methods are proposed: the acoustic feedback is either fully modeled (two way coupled simulation) or accounted for using interaction parameters (one way concurrent simulation). In the first method, the boundary conditions of the HD model are adjusted dynamically using the solution field of the HA model and all components of the sources are evaluated in the HD model. In the second method, the acoustics and hydrodynamics components of the sources are considered as independent. The components due to the hydrodynamic field are evaluated in the HD model with steady boundary conditions and injected in HA model through discrete sources. The components of the sources due to the acoustic fluctuations are accounted for with specific parameters of the HA model; those interaction parameters, i.e. cavity compliance and mass flow gain factor, are evaluated with the help of the HD model. A reference case study has been setup; video analysis and dynamic pressure measurement have been performed to validate the simulations. The case study consists in a straight pipe connecting two constant pressure tanks. A bluff body is placed at 3/4 of the pipe length, the resulting flow instability is characterized by the alternate shedding of vortices at a frequency proportional to the flow velocity. The hydroacoustic resonator is the pipe itself. Measurements have been performed for resonant and non-resonant conditions in cavitating and cavitation free flow regime. In cavitation free flow regime, the hydrodynamic source is identified as a pure momentum source associated with the drag force on the bluff body. The flow conditions leading to resonance can be evaluated with the two way coupled simulation. At resonance, the distribution, frequency and amplitude of pressure fluctuation predicted in the simulation is in good agreement with the measurement. For the selected case study, the acoustic feedback is very weak and has no significant effect on the momentum source. In cavitating flow regime, two hydrodynamic sources have been identified, the momentum source and the mass source. The momentum source is associated with the drag force on the bluff body, the mass source is associated with the volume fluctuation of the fl vapor phase in the wake of the bluff body. The strength of the mass source is orders of magnitude larger and the momentum source can therefore be neglected. One way concurrent simulations using dynamic update of the interaction parameters have been performed. Fair agreement is obtained between the simulations and the measurements. The amplification of the fluctuation observed experimentally below incipient cavitation is reproduced. At intermediate cavitation index, the pressure fluctuation amplitude and the spectral energy distribution is in fair agreement with the experiment. The modifications of the pipe eigenmodes and eigenfrequencies due to cavitation is satisfactorily reproduced with the cavity compliance.

EPFL2010