This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbo-pumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.

A review of cavitation in hydraulic machinery

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.

Hydroacoustic modelling and numerical simulation of unsteady operation of hydroelectric systems

Hydropower is a clean and renewable source of energy which is widely used to generate electric power and stabilize the power grid. It can respond quickly to any change in demand with the flexibility to operate over a wide range of time scales. At steady-state part-load operation, a flow structure known as precessing vortex rope develops in the draft tube of singly regulated reaction turbines, which causes large pressure pulsations. The vortex rope develops pressure pulsations in the draft tube cone, structural vibrations, power swings, pulsative pressure recovery, which are the main concerns in the hydropower sector. Studies were carried out to understand the inception as well as mitigation of these detrimental effects due to the rotating vortex rope (RVR) development. The primary focus of the present study is to comprehensively review the experimental investigations carried out to study the formation of RVR, its effects on turbine performance, and the methodologies developed to mitigate its impact.

Rotating vortex rope formation and mitigation in draft tube of hydro turbines – A review from experimental perspective

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.

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

Since the birth of the first prototype of the modern reaction turbine, cavitation as conjectured by Euler in 1754 always presents as a challenge. Following his theory, the evolution of modern reaction (Francis and Kaplan) turbines has been completed by adding the final piece of the element ‘draft-tube’ that enables turbines to explore water energy at efficiencies of almost 100%. However, during the last two and a half centuries, with increasing unit capacity and specific speed, the problem of cavitation has been manifested and complicated by the draft-tube surges rather than being solved. Particularly, during the last 20 years, the fierce competition in the international market for extremely large turbines with compact design has encouraged the development of giant Francis turbines of 700–1000 MW. The first group (24 units) of such giant turbines of 700 MW each was installed in the Three Gorges project. Immediately after commission, a strange erosion phenomenon appeared on the guide vane of the machines that has puzzled professionals. From a multi-disciplinary analysis, this Three Gorges puzzle could reflect an unknown type of cavitation inception presumably triggered by turbulence production from the boundary-layer streak transitional process. It thus presents a fresh challenge not only to this old turbine industry, but also to the fundamental sciences.

Tiny bubbles challenge giant turbines: Three Gorges puzzle.

Although the studies on pressure surge in elbow draft tubes of Francis turbines have been carried out by many researchers, pressure fluctuations associated with the unstable behavior of the cavitated vortex rope in the tube are still unclarified, and further understanding of their occurrence is required. In this paper, the author demonstrate the experimental results of the pressure fluctuations with irregular nature, which are induced by the vortex rope in an elbow draft tube having a longer inlet once. The spectrum method was used to analyze the fluctuating wall-pressures measured at both inlet cone and elbow sections of the draft tube. A high speed video system was also employed for observing the behavior of the cavitated vortex rope. From the experiment, three types of pressure fluctuations with different dominant frequencies were found out, and the mechanism of draft-tube-surging was explained reasonable based on the relationships among those pressure fluctuations.

Further investigation on the pressure fluctuations caused by cavitation vortex rope in an elbow draft tube

A quasi-three dimensional analytical model is proposed to simulate swirling flow with spiral vortex core in a pipe. The vortex core is expressed as a helical vortex filament, and the boundary condition of zero normal velocity at the pipe wall is specified by distributing image helical vortex filaments on a cylindrical surface which is located outside the pipe. Thus, the velocity in a pipe is given by the superposition of velocity induced by helical vortex filaments and that of an exisymmetric base flow. The proposed model is applied to the swirling flow in the draft tube of a hydraulic turbine for predicting the flow pattern at the inlet section and the rotating frequency of the vortex core. The calculated results are compared with experimental ones, and reasonable agreement is obtained.

Analysis of Swirling Flow with Spiral Vortex Core in a Pipe

To evaluate pressure surge caused by a spiral vortex core in an elbow draft tube, the technique for processing the ensemble-averaged pressure data measured at two points at an angle 0f 90 degrees in the cross section of an inlet cone is regarded as the minimum essential. However, this is not applicable to fluctuating pressure data having a random nature, which are sometimes observed in model testing of a Francis turbine. Thus, the present study aims to develop a new method based on spectrum analysis instead of Fourier analysis for the diagnosis of pressure fluctuations for those cases mentioned above. Experiments were conducted using an elbow draft tube having a long inlet cone under three kinds of swirl strength. The dominant frequencies derived from the cross spectrum of fluctuating pressure were classified and correlated with the behavior of the vortex core inside the tube, which was observed by using a high-speed video system.

Pressure Fluctuations Having Random Nature Caused by Cavitated Spiral Vortex Core in Elbow Draft Tube.

Previous investigations on the flow in diffusers suggest that study on the flow characteristics in the elbow draft tubes of Francis turbines, especially in the case of strong swirling flow involved, is still required. As one of the steps to investigate the surge phenomena in the elbow draft tubes, we carried out a series of time-averaged measurements in a conventional draft tube, which was installed in an air test rig, by using a five-hole probe. Flow pattern and pressure distributions in the draft tube were studied in the range of swirl rate mex from 0 to 1.8. The variations of area-mean pressure and mass-averaged pressure at each measuring section are discussed, and the effect of swirl rate mex on the pressure recovery coefficients of a typical draft tube is also shown.

Time-Averaged Flow Pattern of Swirl Flow and Pressure Recovery in an Elbow Draft Tube.

Abstract Porosity is one of the most critical quality issues in Additive Manufacturing (AM). As process parameters are closely related to porosity formation, it is vitally important to study their relationship for better process optimization. In this article, motivated by the emerging application of metal AM, a three-level hierarchical mixed-effects modeling approach is proposed to characterize the relationship between microstructural images and process parameters for porosity prediction and microstructure reconstruction. Specifically, a Two-Point Correlation Function (TPCF) is used to capture the morphology of the pores quantitatively. Then, the relationship between the TPCF profile and process parameters is established. A blocked Gibbs sampling approach is developed for parameter inference. Our modeling framework can reconstruct the microstructure based on the predicted TPCF through a simulated annealing optimization algorithm. The effectiveness and advantageous features of our method are demonstrated by both the simulation study and the case study with real-world data from metal AM applications.

https://vtechworks.lib.vt.edu/bitstream/10919/113676/2/J30-Hierarchical%20Modeling%20of%20Microstructural%20Images%20for%20Porosity%20Prediction%20in%20Metal%20Additive%20Manufacturing%20via%20Two%20point%20Correlation%20Function.pdf

Xinming Wang

Papers

Further investigation on the pressure fluctuations caused by cavitation vortex rope in an elbow draft tube

Analysis of Swirling Flow with Spiral Vortex Core in a Pipe

Pressure Fluctuations Having Random Nature Caused by Cavitated Spiral Vortex Core in Elbow Draft Tube.

Time-Averaged Flow Pattern of Swirl Flow and Pressure Recovery in an Elbow Draft Tube.

Hierarchical modeling of microstructural images for porosity prediction in metal additive manufacturing via two-point correlation function