Arthur Favrel

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

ABSTRACT 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.

Hydro-acoustic resonance behavior in presence of a precessing vortex rope: observation of a lock-in phenomenon at part load Francis turbine operation

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.

On the physical mechanisms governing self-excited pressure surge in Francis turbines

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.

Pressure measurements and high speed visualizations of the cavitation phenomena at deep part load condition in a Francis turbine

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.

Experimental investigation of the local wave speed in a draft tube with cavitation vortex rope

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.

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

ABSTRACT 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.

Interaction of a pulsating vortex rope with the local velocity field in a Francis turbine draft tube

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.

Francis turbine draft tube modelling for prediction of pressure fluctuations on prototype

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.

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.

Experimental Identification and Study of Hydraulic Resonance Test Rig with Francis Turbine operating at Partial Load

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.