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With the integration of renewable energies into the electricity grid, new requirements have been defined by power station operators. These changes bring new challenges for hydraulic turbine manufacturers, such as more flexibility during machines operation. In recent years, investigations have been focused on off-design conditions, since unsteady phenomena occur far from the classical Francis turbine operating range. This is especially the case at partial load, where dynamic stresses on the runner could impact the machine lifetime. The main objective of the study presented in this paper is to gain a better understanding of Francis turbine partial load flows. Thus, different runners are compared, based on test rig measurement campaigns already realized on model scale turbines. Pressure sensors and strain gauges signals are compared, using Fast Fourier Transform (FFT) analysis and Spatial Harmonic Decomposition (SHD). Finally, an attempt to classify these sets of frequencies is realized, according to their dynamical loading on the structure operating in off- design conditions and their impact on the turbine lifetime.

An accurate prediction of pressure fluctuations in Francis turbines has become more and more important over the last years, due to the continuously increasing requirements of wide operating range capability. Depending on the machine operator, Francis turbines are operated at full load, part load, deep part load and speed-no-load. Each of these operating conditions is associated with different flow phenomena and pressure fluctuation levels. The better understanding of the pressure fluctuation phenomena and the more accurate prediction of their amplitude along the hydraulic surfaces can significantly contribute to improve the hydraulic and mechanical design of Francis turbines, their hydraulic stability and their reliability.

With the objective to acquire a deeper knowledge about the pressure fluctuation characteristics in Francis turbines and to improve the accuracy of numerical simulation methods used for the prediction of the dynamic fluid flow through the turbine, pressure fluctuations were experimentally measured in a mid specific speed model machine. The turbine runner of a model machine with specific speed around n_q,_opt = 60 min^-1, was instrumented with dynamic pressure transducers at the runner blades. The model machine shaft was equipped with a telemetry system able to transmit the measured pressure values to the data acquisition system. The transient pressure signal was measured at multiple locations on the blade and at several operating conditions. The stored time signal was also evaluated in terms of characteristic amplitude and dominating frequency.

The dynamic fluid flow through the hydraulic turbine was numerically simulated with computational fluid dynamics (CFD) for selected operating points. Among others, operating points at full load, part load and deep part load were calculated. For the fluid flow numerical simulations more advanced turbulence models were used, such as the detached eddy simulation (DES) and scale adaptive simulation (SAS). At the different operating conditions, distinct flow phenomena were available for evaluating the accuracy of the simulation method, e.g. rotor- stator interaction, rotating vortex rope and runner channel vortex. The experimentally obtained pressure time signals at the runner, characteristic amplitude and frequency at several operating points offered the possibility to assess the precision in the prediction of the pressure fluctuations in the Francis turbine using the numerical simulation methods.

In this paper the characteristics of one type of channel vortex and the effect of different parameters on this channel vortex have been investigated experimentally with the aid of high speed photography. The results show that locations of the channel vortices move from near the hub down to near the band with the increase n₁₁ or the decrease Q₁₁ Meanwhile, with the decrease of Q₁₁ or σ channel vortices become thicker with increasing appearing frequency. When the channel vortices come out near the hub or in the middle of the blade at low or moderate n₁₁, the main frequency of pressure pulsation in the draft tube is the swirling frequency of vortex rope. However when the channel vortices come out near the band at high n₁₁, the pressure pulsation in the draft tube has a wide-band spectrum with the frequency within 0.7∼1f_n (rotating frequency). Then detailed numerical simulations were carried out to investigate the observed phenomenon. The results reveal this channel vortex is caused by the reversed flow in the draft tube. The mechanism is that channel vortices are induced when the reversed fluid flows up along the suction side of the blade and meets the upstream main flow.

Francis-99 is a set of workshop aiming to determine the state of the art of high head model Francis turbine simulations (flow and structure) under steady and transient operating conditions as well as to promote their development and knowledge dissemination openly. The first workshop (Trondheim, 2014) was concerned with steady state operation. The second workshop will focus on transient operations such as load variation and start-stop. In the present work, 2-D particle image velocimetry (PIV) with synchronized pressure measurements performed in the draft tube cone of the Francis-99 test case during load rejection is presented. Pressure sensors were mounted in the vaneless space and draft tube cone to estimate the instantaneous pressure fluctuations while operating the turbine from the best efficiency point (9.8°) to part load (6.7°) with the presence of a rotating vortex rope (RVR). The time-resolved velocity and pressure data are presented in this paper showing the transition in the turbine from one state to another.

Francis turbines are subject to various types of the cavitation flow depending on the operating conditions. 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 channels 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- SAS 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 visualizations 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.

Francis turbines operating at high load conditions produce a typical flow pattern in the draft tube cone characterized by the presence of an axisymmetric central vortex. This central cavity could become unstable, generating synchronic pressure pulsations, usually called self-excited oscillations, which propagate into the whole machine.

The on-set and size of the central vortex cavity depend on the geometry of the runner and draft tube and on the operating point as well. Numerical flow simulations and model tests allow for the characterization of the different flow patterns induced by each particular Francis turbine design and, when studied in combination with the hydraulic system, including the intake and penstock, could predict the prototype hydraulic behavior for the complete operation zone.

The present work focuses the CFD simulation on the development and dynamic behavior of the central axisymmetric vortex for a medium-head Francis turbine operating at high load conditions. The CFD simulations are based in two-phase transient calculations. Oscillation frequencies against its cavity volume development were obtained and good correlation was found with experimental results.

To validate the investigations of a high-resolution CFD simulation of a Francis turbine, measurements with 2D Laser-Doppler-Anemometry are carried out. The turbine is operated in part load, where a rotating vortex rope occurs. To validate both, mean velocities and velocity fluctuations, the measurements are classified relative to the vortex rope position. Several acrylic glass windows are installed in the turbine walls such as upstream of the spiral case inlet, in the vaneless space and in the draft tube. The current investigation is focused on a measurement plane below the runner. 2D velocity components are measured on this whole plane by measuring several narrow spaced radial lines. To avoid optical refraction of the laser beam a plan parallel window is inserted in the cone wall. The laser probe is positioned with a 2D traverse system consisting of a circumferential rail and a radial aligned linear traverse. The velocity data are synchronized with the rotational frequency of the rotating vortex rope. The results of one measurement line show the dependency of the axial and circumferential velocities on the vortex rope position.

Pressure and power fluctuations of hydro-electric power plants in part-load operation are an important measure for the quality of the power which is delivered to the electrical grid. It is well known that the unsteadiness is driven by the flow patterns in the draft tube where a vortex rope is present. However, until today the equivalent vortex rope parameters for common numerical 1D-models are a major source of uncertainty.

In this work, a new optimization-based grey box method for experimental vortex rope modelling and parameter identification is presented. The combination of analytical vortex rope and test rig modelling and the usage of dynamic measurements allow the identification of the unknown vortex rope parameters. Upscaling from model to prototype size is achieved via existing nondimensional parameters. In this work, a new experimental setup and system identification method is proposed which are suitable for the determination of the full set of part load vortex rope parameters in the lab. For the vortex rope, a symmetric model with cavity compliance, bulk viscosity and two pressure excitation sources is developed and implemented which shows the best correspondence with available measurement data. Due to the non-dimensional parameter definition, scaling is possible. This finally provides a complete method for the prediction of prototype part-load pressure and power oscillations.

Since the proposed method is based on a simple limited control domain, limited modelling effort and also small modelling uncertainties are some major advantages. Due to the generality of the approach, a future application to other operating conditions such as full load will be straightforward.

In hydraulic turbines operating at part loads, a cavitating vortex structure appears at runner outlet. This helical vortex, called vortex rope, can be cavitating in its core if the local pressure is lower that the vaporization pressure. An actual concern is the detection of the cavitation apparition and the characterization of its level. This paper presents a potentially innovative method for the detection of the cavitating vortex presence based on acoustic methods. The method is tested on a reduced scale facility using two acoustic transceivers positioned in "V" configuration. The received signals were continuously recorded and their frequency content was chosen to fit the flow and the cavitating vortex. Experimental results showed that due to the increasing flow rate, the signal - vortex interaction is observed as modifications on the received signal's high order statistics and bandwidth. Also, the signal processing results were correlated with the data measured with a pressure sensor mounted in the cavitating vortex section. Finally it is shown that this non-intrusive acoustic approach can indicate the apparition, development and the damping of the cavitating vortex. For real scale facilities, applying this method is a work in progress.

The paper investigates an unexpected feature of the unsteady pressure field resulting from the self-induced instability of the decelerated swirling flow in a straight diffuser. Firstly, the self-induced instability is experimentally investigated on the swirl generator test rig. As a result, the asynchronous (rotating) pressure pulsation associated with the rotating vortex rope of 15 Hz and it second harmonic are discriminated. Also, a low frequency synchronous (plunging) pulsation around of 2.5 Hz is identified based on unsteady pressure field measured at the wall and LDV measurement of the velocity components in the flow. The low frequency plunging pressure fluctuations is superimposed on the rotating pressure pulsations associated with the vortex rope. The numerical simulations are performed to explore the vortex rope dynamics. The numerical results are compared against experimental data to assess the accuracy of the models. Next, the pressure pulsation dynamics is correlated with the time evolution of the vortex rope. The main conclusion emerging from the analysis of the vortex rope evolution in time is that the cycle with low frequency is responsible for the plunging (synchronous) pressure fluctuations superimposed over the rotating (asynchronous) pressure field associated with the precession of the vortex rope.

Francis turbines operating at part load conditions experience the development of a high swirling flow at the runner outlet, giving rise to the development of a cavitation precessing vortex rope in the draft tube. The latter acts as an excitation source for the hydro-mechanical system and may jeopardize the system stability if resonance conditions are met. Although many aspects of the part load issue have been widely studied in the past, the accurate stability analysis of hydro-power plants remains challenging. A better understanding of the vortex rope dynamics in a wide range of operating conditions is an important step towards the prediction and the transposition of the pressure fluctuations from reduced to prototype scale. For this purpose, an investigation of the flow velocity fields at the outlet of a Francis turbine reduced scale physical model operating at part load conditions is performed by means of 2D-PIV in three different horizontal cross-sections of the draft tube cone. The measurements are performed in cavitation-free conditions for three values of discharge factor, comprised between 60% and 81% of the value at the Best Efficiency Point. The present article describes a detailed methodology to properly recover the evolution of the velocity fields during one precession cycle by means of phase averaging. The vortex circulation is computed and the vortex trajectory over one typical precession period is finally recovered for each operating point. It is notably shown that below a given value of the discharge factor, the vortex dynamics abruptly change and loose its periodicity and coherence.

Modern hydraulic turbines require optimized runners within a range of operating points with respect to minimum weighted average draft tube losses and/or flow instabilities. Tractable optimization methodologies must include realistic estimations of the swirling flow exiting the runner and further ingested by the draft tube, prior to runner design. The paper presents a new mathematical model and the associated numerical algorithm for computing the swirling flow at the trailing edge of Francis turbine runner, operated at arbitrary discharge. The general turbomachinery throughflow theory is particularized for an arbitrary hub-to-shroud line in the meridian half-plane and the resulting boundary value problem is solved with the finite element method. The results obtained with the present model are validated against full 3D runner flow computations within a range of discharge value. The mathematical model incorporates the full information for the relative flow direction, as well as the curvatures of the hub-to-shroud line and meridian streamlines, respectively. It is shown that the flow direction can be frozen within a range of operating points in the neighborhood of the best efficiency regime.

The decelerated swirling flow in the discharge cone of Francis turbines operated at partial discharge develops a self-induced instability with a precessing helical vortex (vortex rope). In an axisymmetric geometry, this phenomenon is expected to generate asynchronous pressure fluctuations as a result of the precessing motion. However, numerical and experimental data indicate that synchronous (plunging) fluctuations, with a frequency lower than the precessing frequency, also develops as a result of helical vortex filament dynamics. This paper presents a quantitative approach to describe the precessing vortex rope by properly fitting a three-dimensional logarithmic spiral model with the vortex filament computed from the velocity gradient tensor. We show that the slope coefficient of either curvature or torsion radii of the helix is a good indicator for the vortex rope dynamics, and it supports the stretching - breaking up - bouncing back mechanism that may explain the plunging oscillations.

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.

A swirling flow in a diffuser such as a draft tube of a hydro turbine may induce the flow instabilities accompanied by pressure fluctuations known as vortex rope behaviour and cavitation surge. Cavitation surge is the self-excited oscillation, which induces the large flow rate fluctuation that results from the change of the cavity volume. In this research, the investigation of the effect of the pipe length and the swirl intensity on the flow instabilities in a diffuser was performed by experiments and numerical analyses using the draft tube component experimental facility. The length of the pipe was modified by up to about 25 times as long as the diameter of the throat in order to validate the one-dimensional analyses. In addition, the swirl intensity was changed by replacing another swirl generator. The frequency of cavitation surge was changed with regard to the swirl intensity as the one-dimensional analyses in the previous study has predicted it. Unsteady numerical simulations of the swirling flow with cavitation in the diffuser was performed. The results of experiments and numerical analyses correspond qualitatively with the result of the one-dimensional analyses, which suggested that the coupling with the experiments, CFD analyses and the one-dimensional analyses is the more effective way in order to predict the flow instabilities in the diffuser.

The cavitating vortices causes the unsteady phenomena like the pressure fluctuation, the noise and the vibration in the draft tube at the overload condition which is the far operating point from the design point. Because the full load was normally near the design point, there were few troubles due to cavitating vortices at the full load. Today, however, the design point is sometimes set to lower load to achieve the high efficiency from the partial load to the full load in low specific speed Francis turbines, which have good performance to a change in a discharge. Then, the full load is relatively further from the design point. As the result, the potential for the cavitating vortices at the full load is increased. To control of the unsteady phenomena at the full load, the study focused on the cavitating vortices at the overload condition is important. This paper presents the unsteady behavior of the cavitating vortices at the overload condition with the scaled model of specific speed N_QE=0.083. On the experimental approach, the pressure pulsation in the upper draft tube was measured and the unsteady behavior of cavitating vortices was taken movies with a high speed camera. On the numerical approach, Computational Fluid Dynamics (CFD) adopting a two-phase unsteady analysis was carried out. The pressure fluctuation and the velocity distribution of two runners, an original and a newly designed, were compared.

In this paper, the influence of Thoma number and model testing head on pressure fluctuation of Francis turbines was studied through experimental method. Firstly, the influence of model testing head on pressure fluctuation in the draft tube was carried out by varying model testing head at 6 typical operating conditions including no load, deep part load, part load, optimum, rated and overload points. It is found that model testing head has little influence on amplitudes of the pressure fluctuation in the draft tube of Francis turbine within the test range, which represented the influence of similitude number such as Reynolds number, Froude number, Weber number and so on. Then, analysis of the influence of Thoma number on pressure fluctuation amplitudes in the draft tube as well as frequency was performed at the part load and rated load conditions. It shows that the Thoma number not only influences pressure fluctuation amplitude but also the distribution of the frequency components in the draft tube. Finally, comparison of pressure fluctuation with two different cavitation levels was carried out. It is reasonable that selection of guide vane centerline is as cavitation reference level in the pressure fluctuation tests for France turbines. Hence, when pressure fluctuation similarity is studied, apart from load condition, the influence of the difference of Thoma number and the selection of cavitation reference level should be considered.

The hydraulic turbines operated at partial discharge (especially hydraulic turbines with fixed blades, i.e. Francis turbine), developing a swirling flow in the conical diffuser of draft tube. As a result, the helical vortex breakdown, also known in the literature as "precessing vortex rope" is developed. A passive method to mitigate the pressure pulsations associated to the vortex rope in the draft tube cone of hydraulic turbines is presented in this paper. The method involves the development of a progressive and controlled throttling (shutter), of the flow cross section at the bottom of the conical diffuser. The adjustable cross section is made on the basis of the shutter-opening of circular diaphragms, while maintaining in all positions the circular cross-sectional shape, centred on the axis of the turbine. The stagnant region and the pressure pulsations associated to the vortex rope are mitigated when it is controlled with the turbine operating regime. Consequently, the severe flow deceleration and corresponding central stagnant are diminished with an efficient mitigation of the precessing helical vortex. Four cases (one without diaphragm and three with diaphragm), are numerically and experimentally investigated, respectively. The present paper focuses on a 3D turbulent swirling flow simulation in order to evaluate the control method. Numerical results are compared against measured pressure recovery coefficient and Fourier spectra. The results prove the vortex rope mitigation and its associated pressure pulsations when employing the diaphragm.

Today's energy market has a high demand of flexibility due to introduction of other intermittent renewables as wind and solar. To ensure a steady power supply, hydro turbines are often forced to operate more at part load conditions. Originally, turbines were built for steady operation around the best efficiency point. The demand of flexibility, combined with old designs has showed an increase in turbines having problems with hydrodynamic instabilities such as pressure pulsations. Different methods have been investigated to mitigate pressure pulsations. Air injection shows a significant reduction of pressure pulsation amplitudes. However, installation of air injection requires extra piping and a compressor. Investigation of other methods such as shaft extension shows promising results for some operational points, but may significantly reduce the efficiency of the turbine at other operational points. The installation of an extension of the runner cone has been investigated at NTNU by Vekve in 2004. This has resulted in a cylindrical extension at Litjfossen Power Plant in Norway, where the bolt suffered mechanical failure. This indicates high amplitude pressure pulsations in the draft tube centre. The high pressure pulsation amplitudes are believed to be related to high tangential velocity in the draft tube. The mentioned runner cone extension has further been developed to a freely rotating extension. The objective is to reduce the tangential velocity in the draft tube and thereby the pressure pulsation amplitudes.

One of the mechanisms of generation of powerful pressure pulsations in the circuit of the turbine is a precessing vortex core, formed behind the runner at the operation points with partial or forced loads, when the flow has significant residual swirl. To study periodic pressure pulsations behind the runner the authors of this paper use approaches of experimental modeling and methods of computational fluid dynamics. The influence of velocity distributions at the output of the hydro turbine runner on pressure pulsations was studied based on analysis of the existing and possible velocity distributions in hydraulic turbines and selection of the distribution in the extended range. Preliminary numerical calculations have showed that the velocity distribution can be modeled without reproduction of the entire geometry of the circuit, using a combination of two blade cascades of the rotor and stator. Experimental verification of numerical results was carried out in an air bench, using the method of 3D-printing for fabrication of the blade cascades and the geometry of the draft tube of hydraulic turbine. Measurements of the velocity field at the input to a draft tube cone and registration of pressure pulsations due to precessing vortex core have allowed building correlations between the velocity distribution character and the amplitude-frequency characteristics of the pulsations.

Computational flow analysis is an essential tool for hydraulic turbine designers. Grid generation is the first step in the flow analysis process. Grid quality and solution accuracy are strongly linked. Even though many studies have addressed the issue of mesh independence, there is still no definitive consensus on mesh best practices, and research on that topic is still needed. This paper presents a mesh convergence study for turbulence flow in hydraulic turbine draft- tubes which represents the most challenging turbine component for CFD predictions. The findings from this parametric study will be incorporated as mesh control rules in an in-house automatic mesh generator for turbine components.

When Francis-turbines and pump-turbines operate at off-design conditions, typically a vortex rope develops. The vortex rope causes pressure oscillations leading to fluctuations of the forces affecting the runner. The presence of dynamic runner forces over a long period of time might damage the bearings and possibly the runner. In this experimental investigation, the fluctuating part of the runner forces and the pressure oscillations on the draft tube wall were measured on a model pump-turbine with a simplified straight cone draft tube in different operating conditions. The investigation focuses on the correlation of the pressure fluctuations frequency measured at the draft tube wall with the frequency of the fluctuating forces on the runner. The comparison between pressure fluctuations and dynamic forces shows a significant correlation in all operating points. For the comparison of different components in the spatial directions of the forces, the pressure fluctuations were separated in a synchronous part and a rotating part for operating points with higher amplitudes. The rotating pressure fluctuations correlate with the radial forces especially in the operating points with a rotating vortex rope. At frequencies with higher amplitudes in the pressure fluctuations caused by the vortex rope movement, there are also higher amplitudes in the radial forces at the same frequencies.

To understand the effect of rotation in the dynamic response of pump-turbine runners, simplified models such as disk-like structures can be used. In previous researches the natural frequencies and mode shapes of rotating disk-like structures submerged and confined have been analysed from the rotating frame. Nevertheless to measure these parameters experimentally from the rotating point of view can be a difficult task, since sensors have to withstand with large forces and dynamic loads. In this paper the dynamic response of rotating disk-like structures is analysed from the stationary frame. For this purpose an experimental test rig has been used. It consists on a disk confined that rotates inside a tank. The disk is excited with a PZT attached on it and the response is measured from both rotating frame (with miniature accelerometers) and from the stationary frame (with a Laser Doppler Vibrometer). In this way the natural frequencies and mode shapes of the rotating structure can be determined from the stationary reference frame. The transmission from the rotating to the stationary frame is compared for the case that the rotating structure rotates in a low density medium (air) and in a high density medium (water).

The thrust bearing is an essential element of a hydropower machine. Not only does it carry the total axial load but it also introduces stiffness and damping properties in the system. The focus of this study is on the influence of the thrust bearing on the lateral vibrations of the shaft of a 72-MW propeller turbine. The thrust bearing has a non-conventional design with a large radius and two rows of thrust pads. A numerical model is developed to estimate natural frequencies. Numerical results are analyzed and related to experimental measurements of a runaway test.

The results show the need to include the thrust bearing in the model. In fact, the vibration modes are substantially increased towards higher frequencies with the added properties from the thrust bearing. The second mode of vibration has been identified in the experimental measurements. Its frequency and mode shape compare well with numerical results.

The swirling flow in the discharge cone of hydroturbine is characterized by various self-induced instabilities and associated low frequency phenomena when the turbine is operated far from the best efficiency point. In particular, the precessing vortex rope develops at part-load regimes in the draft tube. This rope can serve a reason of the periodical low- frequency pressure oscillations in the whole hydrodynamical system. During the experimental research of flow structure in the discharge cone in a regime of free runner new interesting phenomenon was discovered. Due to instability some coils of helical vortex close to each other and reconnection appears with generation of a vortex ring. The experiments were fulfilled at the cavitational conditions when a cavity arises in the vortex core. So the phenomenon was registered with help of visualization by the high speed video recording. The vortex ring after the reconnection moves apart from the main vortex rope toward the wall and downstream. When it reaches the area with high pressure the cavity collapses with generation of pressure impact. The mechanism of cavitational vortex rings generation and their further collapse can serve as a prototype of the aperiodical pressure impacts inside the turbine draft tube.