Cavitation Vortex Rope Research Articles

Stereoscopic TR PIV measurement and POD analysis of flow behind the turbine prototype of model size

When measuring turbine prototype flow, a number of modes with different flow rates and cavitating vortex rope settings have been measured. The turbulent flow in the draft tube of diameter 240 mm reaches the Reynolds number of 105. The vortex and highly swirling flow is developed in the draft tube. The usage of kHz-order frame rates was necessary to resolve the velocity field. The investigated area in the mixing vessel was examined by the stereoscopic time-resolved PIV technique. Further mode evaluation allows comparison of cross-sectional velocities in the vector map. The Proper orthogonal decomposition analysis was applied on 3D vector maps, those including u, v, w velocity compounds. In the selected regimes – operating points with volume flow rate 97 l/sec and 114 l/sec, the greatest risk of transition to cavitation mode was identified, so they were studied in detail.

New insight in Francis turbine cavitation vortex rope: role of the runner outlet flow swirl number

ABSTRACTAt 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.

URANS Models for the Simulation of Full Load Pressure Surge in Francis Turbines Validated by Particle Image Velocimetry

Due to the penetration of alternative renewable energies, the stabilization of the electrical power network relies on the off-design operation of turbines and pump-turbines in hydro-power 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 cavitation vortex rope develops at the runner outlet. The cavity may enter self-oscillation, with violent periodic pressure pulsations. The flow fluctuations lead to dangerous electrical power swings and mechanical vibrations, dictating an inconvenient and costly restriction of the operating range. The present paper reports an extensive numerical and experimental investigation on a reduced scale model of a Francis turbine at full load. For a given operating point, three pressure levels in the draft tube are considered, two of them featuring a stable flow configuration and one of them displaying a self-excited oscillation of the cavitation vortex rope. The velocity field is measured by two-dimensional (2D) particle image velocimetry (PIV) and systematically compared to the results of a simulation based on a homogeneous unsteady Reynolds-averaged Navier–Stokes (URANS) model. The validation of the numerical approach enables a first comprehensive analysis of the flow transition as well as an attempt to explain the onset mechanism.

Experimental investigation of the mass flow gain factor in a draft tube with cavitation vortex rope

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.

RANS computations for identification of 1-D cavitation model parameters: application to full load cavitation vortex rope

Due to the massive penetration of alternative renewable energies, hydropower is a key energy conversion technology for stabilizing the electrical power network by using hydraulic machines at off design operating conditions. At full load, the axisymmetric cavitation vortex rope developing in Francis turbines acts as an internal source of energy, leading to an instability commonly referred to as self-excited surge. 1-D models are developed to predict this phenomenon and to define the range of safe operating points for a hydropower plant. These models require a calibration of several parameters. The present work aims at identifying these parameters by using CFD results as objective functions for an optimization process. A 2-D Venturi and 3-D Francis turbine are considered.

Transposition of Francis turbine cavitation compliance at partial load to different operating conditions

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.

Prediction of Francis Turbine Prototype Part Load Pressure and Output Power Fluctuations with Hydroelectric Model

The prediction of pressure and output power 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 induced by the cavitation vortex rope from the reduced scale model to the prototype generating units. A Francis turbine unit of 444MW with a specific speed value of ν = 0.29, is considered as case study. A SIMSEN model of the power station including electrical system, controllers, rotating train and hydraulic system with transposed draft tube excitation sources is setup. Based on this model, a frequency analysis of the hydroelectric system is performed for all technologies to analyse potential interactions between hydraulic excitation sources and electrical components. Three technologies have been compared: the classical fixed speed configuration with Synchronous Machine (SM) and the two variable speed technologies which are Doubly Fed Induction Machine (DFIM) and Full Size Frequency Converter (FSFC).

Numerical Prediction of Cavitating Vortex Rope in a Draft Tube of a Francis Turbine with Standard and Calibrated Cavitation Model

Transient simulations of flow in a Francis turbine were performed with a goal to predict pressure pulsation frequencies and amplitudes caused by rotating vortex rope at part load operating regime. Simulations were done with the SAS SST turbulence model with curvature correction on basic and refined computational meshes. Without cavitation modelling too small values of frequency and amplitudes were obtained. With mesh refinement the calculated amplitudes were a bit closer to the measured values, while the accuracy of predicted frequency did not improve at all. Agreement between measured and numerical values was significantly improved when cavitation was included in simulations. In addition, the predicted value of the dominant frequency was slightly more accurate when, in the Zwart et al. cavitation model, the default condensation and evaporation model constants were replaced with previously calibrated ones.

Dynamics of the precessing vortex rope and its interaction with the system at Francis turbines part load operating conditions

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.

Fluid–structure interaction mechanisms leading to dangerous power swings in Francis turbines at full load

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.

Hydroelectric System Response to Part Load Vortex Rope Excitation

The prediction of pressure and output power 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 induced by the cavitation vortex rope on the reduced scale model to the prototype generating units. A Francis turbine unit of 444MW with a specific speed value of v = 0.29, is considered as case study. A SIMSEN model of the power station including electrical system, controllers, rotating train and hydraulic system with transposed draft tube excitation sources is setup. Based on this model, a frequency analysis of the hydroelectric system is performed to analyse potential interactions between hydraulic excitation sources and electrical components.

RANS computations for identification of 1-D cavitation model parameters: application to full load cavitation vortex rope

Due to the massive penetration of alternative renewable energies, hydropower is a key energy conversion technology for stabilizing the electrical power network by using hydraulic machines at off design operating conditions. At full load, the axisymmetric cavitation vortex rope developing in Francis turbines acts as an internal source of energy, leading to an instability commonly referred to as selfexcited surge. 1-D models are developed to predict this phenomenon and to define the range of safe operating points for a hydropower plant. These models involve several parameters that have to be calibrated using experimental and numerical data. The present work aims to identify these parameters with URANS computations with a particular focus on the fluid damping rising when the cavitation volume oscillates. Two test cases have been investigated: a cavitation flow in a Venturi geometry without inlet swirl and a reduced scale model of a Francis turbine operating at full load conditions. The cavitation volume oscillation is forced by imposing an unsteady outlet pressure conditions. By varying the frequency of the outlet pressure, the resonance frequency is determined. Then, the pressure amplitude and the resonance frequency are used as two objectives functions for the optimization process aiming to derive the 1-D model parameters.

Transient two-phase CFD simulation of overload operating conditions and load rejection in a prototype sized Francis turbine

An increasing shift in operating conditions of hydropower turbines towards peak load operations comes with the necessity for numerical methods to account for such operations. This requires modifications to state-of-the-art CFD simulations. In the first part of this paper a 1D hydroacoustic model to represent the pressure oscillations in the penstock was introduced and coupled with a commercial CFD solver. Based on previous studies, various changes in cavitation and turbulence modeling were done to influence the behavior of a cavitating vortex rope typically occurring at high load conditions of a Francis turbine. In the second part, mesh motion was added to this model to simulate a load rejection starting from full load conditions. It was shown that additional extensions to the 3D CFD model are compulsory to model specific operating conditions as well as transient operations. Thus, accordance with measurement data at overload operation was improved and only small deviations remained. For the load rejection the maximum overspeed was well captured and the comparison of guide vane torques with model test measurements showed a sufficient agreement. With the gained insights, occurring effects which influence the performance and the life-time can be detected and conclusions for the hydraulic design as well as the operating mode can be drawn. Upcoming studies will focus on evaluating the flow field in detail and on reducing the remaining deviations by further extending the mathematical model.

LDV survey of cavitation and resonance effect on the precessing vortex rope dynamics in the draft tube of Francis turbines

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.

Local wave speed and bulk flow viscosity in Francis turbines at part load operation

ABSTRACTThe 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.

Simulations of Steady Cavitating Flow in a Small Francis Turbine

The turbulent flow through a small horizontal Francis turbine is solved by means of Ansys-CFX at different operating points, with the determination of the hydrodynamic performance and the best efficiency point. The flow structures at different regimes reveal a large flow eddy in the runner and a swirl in the draft tube. The use of the mixture model for the cavity/liquid two-phase flow allowed studying the influence of cavitation on the hydrodynamic performance and revealed cavitation pockets near the trailing edge of the runner and a cavitation vortex rope in the draft tube. By maintaining a constant dimensionless head and a distributor vane opening while gradually increasing the cavitation number, the output power and efficiency reached a critical point and then had begun to stabilize. The cavitation number corresponding to the safety margin of cavitation is also predicted for this hydraulic turbine.

Study of the vortex-induced pressure excitation source in a Francis turbine draft tube by particle image velocimetry

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.

The numerical research of runner cavitation effects on spiral vortex rope in draft tube of Francis turbine

The spiral cavitating vortex rope developed in the draft tube of Francis turbine under part load condition maybe causes serious pressure fluctuations and power swings, which threatens the safety and stability of the power plant operations. Many works have been performed to explore the mechanisms of it. In this paper, the runner cavitation and spiral vortex rope under part load conditions were studied to investigate the relations of runner cavitation and the spiral vortex rope. The results proved the existence of obvious interaction between them. The swirl flow at the runner outlet plays an important role in the formation of vortex rope. And the periodic procession of vortex rope in turn intensifies the uneven pressure distribution near the runner outlet and causes the asymmetric cavitation on the runner blades, which then give rise to the modification of swirl flow at the runner blades and thereby affects the characteristics of vortex rope.

Identification of the wave speed and the second viscosity in cavitating flow with 2D RANS computations - Part II

The 1D modelling of cavitation vortex rope dynamics in Francis turbine draft tube is decisive for prediction of pressure fluctuations in the system. However, models are defined with parameters which values must be quantified either experimentally or numerically. In this paper a methodology based on CFD simulations is setup to identify these parameters by exciting the flow through outlet boundary condition. A simplified test case is considered to assess if 1D cavitation model parameters can be identified from CFD simulations. It is shown that a low wave speed and a second viscosity due to the cavitating flow can be identified.

Forced response analysis of hydroelectric systems

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.