Cavitation Vortex Rope Research Articles

Exploration of the mechanism of cavitation vortex rope and vortex development in the draft tube of tubular turbine units

Exploration of the mechanism of cavitation vortex rope and vortex development in the draft tube of tubular turbine units

Analysis of Cavitation-Induced Unsteady Flow Conditions in Francis Turbines under High-Load Conditions

Hydraulic vibrations in Francis turbines caused by cavitation profoundly impact the overall hydraulic performance and operational stability. Therefore, to investigate the influence of cavitation phenomena under high-load conditions, a three-dimensional unsteady numerical simulation is carried out for a Francis turbine with different head operating conditions, which is combined with the SST k-w turbulence model and two-phase flow cavitation model to capture the evolution of cavitation under high-load conditions. Additionally, utilizing entropy production theory, the hydraulic losses of the Francis turbine during cavitation development are assessed. Contrary to the pressure-drop method, the entropy production theory can quantitatively reflect the characteristics of the local hydraulic loss distribution, with a calculated error coefficient τ not exceeding 2%. The specific findings include: the primary sources of energy loss inside the turbine are the airfoil cavitation and cavitation vortex rope, constituting 26% and 71% of the total hydraulic losses, respectively. According to the comparison with model tests, the vapor volume fraction (VVF) inside the draft tube fluctuates periodically under high-load conditions, causing low-frequency pressure pulsation in the turbine’s power, flow rate, and other external characteristic parameters at 0.37 Hz, and the runner radial force fluctuates at a frequency of 1.85 Hz.

Investigation of cavitating vortex rope instabilities and its suppression inside a Francis turbine model with Thoma number variation

Cavitating vortex rope at part load (PL) condition at lower values of the Thoma number (σ) induces severe pressure fluctuation and efficiency reduction in a Francis turbine, which ultimately hinders continuous energy production. Installation of fins at draft tube (DT) can mitigate these instabilities and can safeguard the turbine operation with lower maintenance costs. The effect of fins on hydraulic performance and internal flow physics at PL condition with the variation of σ is examined in the present numerical investigation. For the two extreme opposite values of σ, the flow characteristics are predicted accurately for the turbine with and without fins by conducting transient simulations using ANSYS-CFX. The numerical findings on the structured and unstructured grid points are validated with the experimental results. The turbine's performance remains constant for higher values of Thoma numbers, and as the value decreases, the performance declines. The cavitation vortex rope formation inside the DT with fins is mitigated significantly at the minimum σ, while at the maximum value, the vortex rope with bubble generation is restricted. Compared to the without fin case, the swirl intensity is minimized remarkably (68%) with the presence of fins at the lowest σ. The maximum cavitation rate is manifested by the DT without fins, which is about 60% higher than the DT with fins. At minimum σ, extreme pressure pulsations are induced inside the DT without fins, which are reduced by 43% in the finned draft tube. Therefore, stable energy production is maximized with the installation of fins at both Thoma numbers.

Hydroacoustic interaction between draft tube and penstock eigenmodes under Francis turbine full load instability

At high load, Francis Turbines may experience self-sustained pressure surge leading to significant power swing and pressure fluctuations along the waterway. The physical mechanism initiating this instability phenomenon has been the subject of much research. The development of the axisymmetric cavitating vortex rope at the runner outlet modifies the hydroacoustic properties of the draft tube waterway. Very low wave speed due to high cavitation volume combined with a high swirling number initiates the unstable axial pulsations of the cavitating vortex rope which frequency corresponds to a penstock’s eigenfrequency. The 15 MW power plant of Monceaux-la-Virole in France, composed of two units fed by a single penstock, experiences such full-load surge. On-site tests have been carried out to analyze the envelope of pressure fluctuations along the penstock once instability occurs. Combined with a 1D SIMSEN model of the power plant, these measurements have allowed to enhance the understanding of this instability phenomenon. To achieve this, an advanced draft tube modelling taking into account distributed wave speed, convective terms and divergent geometry is used and frequency analysis is carried out. Unstable draft tube eigenmodes and stable penstock eigenmodes are predicted. The key draft tube model parameters such as wave speed and second viscosity are calibrated to set the draft tube eigenmode frequency to the unstable measured frequency for different operating points. This frequency analysis concludes that high load instability occurs when a matching between the draft tube and the penstock eigenfrequencies is experienced. Moreover, it is shown that the unstable draft tube eigenmode is able to interact with different order penstock eigenmodes as function of the operating point of the unit.

Laser Doppler Velocimetry Test of Flow Characteristics in Draft Tube of Model Pump Turbine

For Francis pump turbines, the pressure pulsation characteristics of the draft tube are some of the key concerns during the operation of the units. The pressure pulsation characteristics of the draft tube are directly related to the draft tube spiral cavitating vortex rope. In this paper, the velocity distribution in the draft tube of a Francis pump turbine is tested by means of laser Doppler velocimetry. The velocity pulsation was found to be directly related to the pressure pulsation, while the velocity pulsation was also influenced by the cavitation coefficient. The main frequency of the velocity pulsation was close to the main frequency of the pressure pulsation and became larger as the cavitation factor increased.

Experimental study of cavitating vortex rope and water column separation in a pump turbine

During the transient processes in load rejection in a pumped-storage system, water column separation (WCS) can occur in the draft tube when the local pressure is less than the vapor pressure. The reverse water hammer due to water column bridging affects the safety of the unit and the tailrace tunnel. However, what are the conditions that trigger WCS? What is the physical mechanism? These questions have not been elucidated experimentally. Therefore, it is necessary to investigate the conditions that lead to WCS and the impact of the reverse water hammer generated by WCS bridging on the stability of the unit. In this study, a semi-open test rig was modified by installing a variable-frequency pump to reduce the static pressure, resulting in a cavitation vortex in the draft tube. The static pressure and the water hammer pressure derived from load rejection cause the pressure at the draft tube wall to fall below the vapor pressure for some time, interrupting the flow in the draft tube. This is a typical case of WCS in a pump turbine. If the pressure in the draft tube does not remain at the minimum pressure for long enough, imperfect water column separation may occur with bubble groups. The amplitude of the pressure pulsations during the initial and development stages was (−0.2 m, 0.2 m). It was 4.96% of the initial static pressure. Thus, the pressure fluctuations have a negligible effect on WCS.

Spatio-temporal evolution mechanism of cavitation vortex ropes in a swirling flow

Cavitation vortex rope widely occurs in hydraulic machinery, leading to the decrease in performance characteristic and increase in pressure fluctuation. The objective of this study was to explore the generation and transformation of cavitation vortex ropes in a swirling flow. A visual swirling-flow generator platform was designed to investigate their spatiotemporal evolution mechanism. A flow pattern observation system with a high-speed camera was built to capture the vortex rope forms, and pressure fluctuation experiments were carried out to present fluctuating characteristics of corresponding cavitation vortex ropes. Cavitation vortex rope forms and pressure fluctuation characteristic under different operating conditions were exhibited. Four types of stable cavitation vortex ropes (broken, dual, single, and subulate) were observed. Regional distribution of vortex ropes under different Reynolds and cavitation numbers was characterized, which showed that broken and subulate vortex ropes account in large Reynolds and cavitation ranges. Pressure fluctuation analyses revealed dominant characteristic frequencies were 2.13, 1.98, 1.74, and 1.93 times the rotational frequency of the runner for the broken, dual, single, and subulate cavitation vortex ropes, respectively. In addition, two unstable transitions were identified during the conversion process. One is an unstable transitional triple-vortex rope during from a dual- to single-vortex rope process, and the other is an unstable subulate-vortex rope between the occurrence of the single- and stable subulate-vortex ropes. The present study could give a deep understanding of the generation of cavitation vortex ropes and provide some references to improve the hydraulic instabilities induced by cavitation vortex ropes in hydraulic machinery.

Multi-objective optimization of a hydro-wind-photovoltaic power complementary plant with a vibration avoidance strategy

Hydropower has the advantages of quickly responding to load variability, which overcomes the unpredictable and unstable variabilities of solar and wind power. Therefore, such power generation can be combined into a hydro-wind-photovoltaic complementary plant (HWPCP). However, hydropower units running at partial load are prone to suffer from hydraulic instabilities generated by a cavitating vortex rope, which may lead to power swings and high vibrations. Operation in these vibration zones may affect the operation and ultimately cause structural damage and affect the power plant. The problem of avoiding running hydropower units in the vibration zones is effectively addressed in this study. This is achieved by adopting a vibration avoidance strategy to determine a rational power distribution scheme for hydropower units. Multi-objective optimization is performed to maximize power generation, minimize output power fluctuations, and minimize the deviation between the power generation and the planned output. The power distribution strategies of hydropower units under 12 scenarios, composed of different inflow and weather conditions, are analyzed. The results indicate that the vibration avoidance strategy effectively avoids the operation of hydropower units in the vibration zones and ensures the operation of hydropower units in the non-vibration zone for more than 99.31% of the operation time. This study contributes to the identification of the relationship between conflicting objectives and provides operational strategies for the safe and stable operation of hydropower units.

Identification of 1-D cavitation model parameters by means of computational fluid dynamics

Hydropower is a key energy conversion technology for stabilizing electrical power. When running at full load, a 3-D cavitation vortex rope develops in Francis turbines that acts as an internal source of energy and instability. 1-D models allow this phenomenon to be predicted and the range of safe operating points to be defined. These models involve three parameters: the mass flow gain factor, the wave speed and the second viscosity that must be calibrated. For the first time, the present work aims at identifying these parameters using 3-D URANS cavitating simulations. Two cavitation test cases are considered: a 2-D Venturi and a reduced scale model of a Francis turbine at full load operating conditions. RANS simulations allow the mass flow gain factor to be determined, whereas URANS simulations coupled with an optimization process allow the determination of the wave speed and the second viscosity. The new methodology shows its ability to identify the three parameters.

Dynamic behaviour of a full-load cavitation vortex in a Francis turbine draft tube excited at its eigenfrequencies

The operating range of Francis turbines is limited at full-load conditions by the formation of a cavitation vortex rope that may enter self-oscillations under certain conditions. This induces severe pressure pulsations in the entire system, as well as output power swings putting at risk the integrity of the electro-mechanical components. The understanding of the underlying physical mechanisms and the prediction of the stability of hydropower units at full-load conditions are therefore crucial to ensure a safe extension of their operating range. In the present paper, the dynamic behaviour of a stable cavitation vortex rope at full load is investigated by high-speed visualizations while the test rig is excited at its first and second hydroacoustic eigenfrequencies. It is first demonstrated that the cavitation volume and the pressure in the draft tube are more likely to oscillate at the first eigenfrequency, in agreement with the observations of self-excited oscillations at the first eigenfrequency of the cavitation vortex rope during unstable full-load conditions. In addition, it is observed that the amplitude of both the cavitation volume and pressure fluctuations in the draft tube reach a limit value when the amplitude of the excitation is further increased. Further investigations will determine if this behaviour can be generalized to any full-load conditions and will focus on the determination of the hydro-acoustic parameters of the draft tube cavitation flow based on the behaviour of the vortex rope during forced oscillations.

Numerical simulation of the unsteady cavitating flow in a Francis turbine draft tube at Upper-Part-Load (UPL) conditions

At part-load conditions, Francis turbines experience the development of a precessing vortex rope in their draft tube (DT), rotating with a frequency between 0.2 and 0.5 times the runner frequency. It induces pressure pulsations at the precession frequency in the whole hydraulic system, undesirable vibrations and noise putting at risk the stability of the system and the lifetime of the machine components. In specific machines, a dramatic amplification of the noise and vibrations can be observed between 70% and 85% of the design conditions. In these cases, synchronous pressure pulsations with a high frequency, typically between 2 and 4 times the runner frequency, are observed, referred to as the so-called Upper-Part-Load (UPL) pulsations. These pulsations are induced by a self-excitation of the entire hydraulic system including the cavitation vortex rope at one of its high order eigenmodes. Besides, the cavitation vortex rope features an elliptical cross-section rotating around the vortex axis at a high frequency. In this manuscript, unsteady two-phase flow simulations using a Scaled-Adaptive-Simulation (SAS) turbulence model and ZGB cavitation model of a Francis turbine draft tube at 80% of the design condition are performed to clarify the mechanisms responsible for the formation of the elliptical shape of the vortex and the UPL pulsations. However, the numerical simulation with a constant inlet boundary condition cannot reproduce the UPL pulsation phenomenon since it is a self-excited oscillation at one eigenmode of the complete system, which is not considered. Therefore, the UPL pulsations component is extracted from the measured pressure fluctuations data by applying a band-pass filter and is then set as the inlet boundary condition in the numerical simulation. The flow field is therefore artificially excited which aims to confirm whether the same phenomenon can be observed and to compare with the flow field obtained with constant inlet boundary condition. The numerical simulations are validated by experimental results, and the wave propagation in the DT is clarified.

Increasing the operating range and energy production in Francis turbines by an early detection of the overload instability

With the increasing entrance of wind and solar power for the generation of electricity, more flexibility is demanded to hydropower plants. More flexibility means that hydro turbines have to increase the operating range between minimum and maximum power. In Francis turbines the maximum power is limited by the appearance of a strong hydraulic excitation called overload instability. When the turbine operates at loads higher than design, the cavitating vortex rope that is generated in the draft tube may become unstable, producing huge pressure fluctuations, vibrations and power swing. Turbines are not allowed to operate under these conditions in order to avoid the destruction of the unit. The overload instability emerges abruptly, even when the machine is operating in a smooth condition. No visible transition can be detected by the monitoring system, so turbine operators have no margin to react. To avoid this phenomenon, operators limit the maximum power much before reaching this condition. By doing that, the maximum power is limited as well as the regulation capacity of the unit. In this paper, the feasibility of detecting the onset of this phenomenon is analyzed. Data-driven methods and artificial intelligence techniques, including principal component analysis, self-organizing map and artificial neural networks, are applied to the data available from experimental tests in a Francis turbine. The signals of vibration, pressure fluctuations and other parameters are combined and studied. The possibilities of a premature detection of the instability before it occurs are discussed. The method could be implemented in the monitoring system of the unit so that the operating range could be safely increased.

Experimental research on pressure fluctuation characteristics of high-head Francis turbine under part load conditions

Pressure fluctuation at partial load operation is an obvious and harmful phenomena in Francis turbines. It could be induced by rotor stator interaction and cavitation vortex rope in draft tube and must be minimized during the design of Francis turbine. To reduce the pressure fluctuation at partial load operation, accurate assessment of the cause of this phenomena is crucial. In this paper, a reduced-scale physical model of a high head Francis turbine is used as the research object, and the test technique is applied to investigate the excitation source of the pressure fluctuation at two partial load operation conditions. Based on experimental data, it can be concluded that the amplitude of pressure fluctuation in the draft tube significant is increased with the decrease of the power of turbine, which is indicated that the stability of turbine deteriorated sharply with the power reduced. But the dominant frequency of the pressure fluctuation is almost the same. And the strong pressure fluctuation in the draft tube can be transmitted to the upstream components, which are affected the pressure fluctuation caused by rotor stator interaction.

Visualization of the elliptical form of a cavitation vortex rope and its collapse by two cameras

This article presents preliminary results of an experimental study of the upper-part load instability and the associated elliptical form of the cavitation vortex rope in a Francis turbine draft tube. The influence of the operating parameters on the onset and the development of the instability is first briefly studied by pressure measurements in the draft tube. Visualizations of the cavitation vortex rope and its associated elliptical form are performed by using two synchronized high-speed cameras spaced by an angle of 90°. This allows to reconstruct the instantaneous position of the vortex center along the draft tube. It is confirmed that using a single camera leads to biased estimations of the cavitation volume fluctuations. The breathing behaviour of the vortex rope, responsible for the pressure pulsations according to several authors, cannot be definitely demonstrated without a proper reconstruction of the vortex shape based on high-speed videos from several positions. Finally, unique intermittent collapses of cavitation in the vortex center, giving rise to two distinct cavities connecting on both sides the vortex rope, are highlighted.

On the High-partial-load Pulsation in Francis Turbines

Francis turbines with high specific speed may produce intense pulsations of system pressure when operating at approximately 70-85% of best-efficiency discharge. Frequencies between 1 and 4 times runner rotation are typical. The paper recalls and explains the particular set of properties. The pulsation is due to instability of the second-lowest eigenmode of the hydraulic system containing a cavitating draft tube vortex. A 1D model in frequency domain is used - with emphasis on the crucial role of the finite velocity of swirl propagation - to show how this mode can become unstable and give rise to a strong ‘breathing’ pulsation. A parameter study shows the well-known influence of draft tube pressure and why the behavior of prototype turbines is often different from the reduced-scale model. Some of the phase properties are explained by a 2D acoustic model. The phase reversal between upstream and downstream pressures is a consequence of the mode shape, with roughly two quarter waves of pressure along the cavitating vortex rope. The stability is quite sensitive to 2D effects; therefore the present 1D model, while useful for understanding the phenomena, is not likely to permit reliable predictions.

Investigation of the correlation mechanism between cavitation rope behavior and pressure fluctuations in a hydraulic turbine

Vortex ropes occurred in the draft tube when hydraulic turbines operating at off-design conditions, which can generate pressure fluctuations. Cavitation vortex rope is one of the most harmful factors to the safety of hydroturbines which may induce further pressure fluctuations. A study of the multiphase flow in a model turbine is presented in this paper using the software ANSYS CFX. The main emphasis is spending on understanding the mechanism of cavitation evolution and underlying its correlation mechanism with flow instabilities. The results indicate that two types of pressure variations can be captured with a cavitation rope: 1) The type due to the vortex rope rotating whose frequency is 1/5–1/4 times runner rotating frequency; 2) The type due to cavitation volume surge, whose frequency is less than that of vortex rope rotating. The frequency of pressure fluctuation due to cavitation keep contanst as the cavitation number decreases, while the amplitude much increases. While the frequency and amplitude of the pressure variation caused by votex rope rotating increase a little. Based on vorticity transport equation, the vortex and cavitation have a close relation. Cavitation increases the vortex production as well as the pressure fluctuation frequency caused by the rotation of vortex rope.

Vortical structures in the cavitating flow in the Francis-99 draft tube cone under off-design conditions with the new omega vortex identification method

The Francis turbine that operates at an off-design load exhibits a strong twist flow near the runner outlet, which causes a cavitating vortex rope on the draft tube cone. The purpose of this study is to apply the new omega vortex identification method (Ω method) and analyze and compare it with traditional methods in regard to its ability to capture the vortex rope in a Francis-99 draft tube cone under an off-design load. The advances of the Ω method for vortex identification on the cavitating flow are elaborated and analyzed. The significance of parameter ε in the Ω method is also highlighted. The determination of ε is further examined and adjusted in this study. Finally, this study demonstrates that the Ω method can be successfully applied to capture vortex structures in the cavitating flow of Francis turbines.

Numerical investigation of the cavitation dynamic parameters in a Francis turbine draft tube with columnar vortex rope

The cavitation developed in the Francis turbine draft tube is known to be a source of the hydraulic instability, especially under the conditions with columnar cavitation vortex rope occurring in the draft tube. The hydraulic system will suffer from the risk of the self-excitation and the high pressure pulsations because of the dynamic features of the complex cavitation vortex rope. The links between the cavitation dynamic characteristics and the hydraulic system stability are important for an accurate system instability prediction. For this purpose, the cavitating flows in a Francis turbine operating under the overload conditions are simulated by using the Zwart-Gerber-Belamri (ZGB) cavitation model. The cavitation dynamic parameters in different cavitation development stages and the evolutions under various overload conditions are analyzed and compared in this paper. It is shown that the cavitation dynamic parameters, including the cavitation compliance, the mass flow gain factor and the wave speed, can well represent the cavitation characteristics with the vortex rope evolution. The predicted cavitation dynamic parameters are in a reasonable agreement with other available results, with an obvious dependency on the loads. The results obtained in this study are relevant to the system stability analysis.

Very large eddy simulation of the vortex rope in the draft tube of Francis turbine

There is usually a strong swirling flow between runner and draft tube of Francis turbine at part load, which would lead to a vortex rope in draft tube. RANS and LES models are used by lots of authors to simulate this phenomenon, and the calculated results is almost similar with test observation. However, these turbulent models can’t predict the length of helical vortex rope exactly, especially the low pressure and high vorticity in the core of vortex. Very large eddy simulation, as a hybrid RANS-LES methodology, could combine the advantages of RANS and LES, which has been proved by many authors. This paper presents a VLES simulation of draft tube flow field compared with other three turbulence models. The results show that VLES model is able to effectively reduce the eddy viscosity and velocity dissipation in vortex rope field, leading to lower pressure and longer rope than other models Moreover, it is demonstrated that proper mesh is also significant for VLES to predict the cavitation vortex rope observed in model test.

Suppression of cavitation in the draft tube of Francis turbine model by J-Groove

Cavitation is recognized as a phenomenon that can cause serious damage to a hydro turbine and can reduce its performance when operating at off-design point. This is an undesired phenomenon, which needs to be improved. In order to suppress the cavitation in the Francis turbine draft tube, a technology with grooved draft tube named J-Groove is introduced in the Francis turbine. The Francis turbine performance and the internal flow characteristic are investigated both with and without J-Groove installation by the experimental method and numerical simulation. Visualization was used to capture the cavitation rope in the Francis turbine draft tube to compare with the computational fluid dynamics analysis result. The results show that the turbine performance both with and without J-Groove installation is quite similar. Regardless of impact on performance of Francis turbine by J-Groove, it suppresses the cavitation vortex rope and pressure fluctuation in the Francis turbine draft tube efficiently.