Numerical and experimental evidence of the inter-blade cavitation vortex development at deep part load operation of a Francis turbine

Francis turbines are subject to various types of the cavitation flow depending on the operating condition s. 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 channel s 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 - SA S 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 visualization s 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

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

Space and time reconstruction of the precessing vortex core in Francis turbine draft tube by 2D-PIV

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 hydropower 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

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 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

Gametogenesis in the Pacific Oyster Crassostrea gigas: A Microarrays-Based Analysis Identifies Sex and Stage Specific Genes

Background: The Pacific oyster Crassostrea gigas (Mollusca, Lophotrochozoa) is an alternative and irregular protandrous hermaphrodite: most individuals mature first as males and then change sex several times. Little is known about genetic and phenotypic basis of sex differentiation in oysters, and little more about the molecular pathways regulating reproduction. We have recently developed and validated a microarray containing 31,918 oligomers (Dheilly et al., 2011) representing the oyster transcriptome. The application of this microarray to the study of mollusk gametogenesis should provide a better understanding of the key factors involved in sex differentiation and the regulation of oyster reproduction. Methodology/Principal Findings: Gene expression was studied in gonads of oysters cultured over a yearly reproductive cycle. Principal component analysis and hierarchical clustering showed a significant divergence in gene expression patterns of males and females coinciding with the start of gonial mitosis. ANOVA analysis of the data revealed 2,482 genes differentially expressed during the course of males and/or females gametogenesis. The expression of 434 genes could be localized in either germ cells or somatic cells of the gonad by comparing the transcriptome of female gonads to the transcriptome of stripped oocytes and somatic tissues. Analysis of the annotated genes revealed conserved molecular mechanisms between mollusks and mammals: genes involved in chromatin condensation, DNA replication and repair, mitosis and meiosis regulation, transcription, translation and apoptosis were expressed in both male and female gonads. Most interestingly, early expressed male-specific genes included bindin and a dpy-30 homolog and female-specific genes included foxL2, nanos homolog 3, a pancreatic lipase related protein, cd63 and vitellogenin. Further functional analyses are now required in order to investigate their role in sex differentiation in oysters. Conclusions/Significance: This study allowed us to identify potential markers of early sex differentiation in the oyster C. gigas, an alternative hermaphrodite mollusk. We also provided new highly valuable information on genes specifically expressed by mature spermatozoids and mature oocytes

Towards a resolution of some outstanding issues in transitive research: an empirical test on middle childhood

Transitive Inference (deduce B > D from B > C and C > D) can help us to understand other areas of sociocognitive development. Across three experiments, learning, memory, and the validity of two transitive paradigms were investigated. In Experiment 1 (N = 121), 7-year-olds completed a three-term nontraining task or a five-term task requiring extensive-training. Performance was superior on the three-term task. Experiment 2 presented 5–10-year-olds with a new five-term task, increasing learning opportunities without lengthening training (N = 71). Inferences improved, suggesting children can learn five-term series rapidly. Regarding memory, the minor (CD) premise was the best predictor of BD-inferential performance in both task-types. However, tasks exhibited different profiles according to associations between the major (BC) premise and BD inference, correlations between the premises, and the role of age. Experiment 3 (N = 227) helped rule out the possible objection that the above findings simply stemmed from three-term tasks with real objects being easier to solve than computer-tasks. It also confirmed that, unlike for five-term task (Experiments 1 & 2), inferences on three-term tasks improve with age, whether the age range is wide (Experiment 3) or narrow (Experiment 2). I conclude that the tasks indexed different routes within a dual-process conception of transitive reasoning: The five-term tasks indexes Type 1 (associative) processing, and the three-term task indexes Type 2 (analytic) processing. As well as demonstrating that both tasks are perfectly valid, these findings open up opportunities to use transitive tasks for educability, to investigate the role of transitivity in other domains of reasoning, and potentially to benefit the lived experiences of persons with developmental issues

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

Hydropower plants play an important regulatory role in the large scale integration of volatile renewable energy sources into the existing power grid. This duty however requires a continuous extension of their operating range, provoking the emergence of complex flow patterns featuring cavitation inside the turbine runner and the draft tube. When the power output is maximized at full load, self-excited pressure oscillations in the hydraulic system may occur, which translate into significant electrical power swings and thus pose a serious threat to the grid stability as well as to the operational safety of the machine. Today's understanding of the underlying fluid structure interaction mechanisms is incomplete, yet crucial to the development of reliable numerical flow models for stability analysis, and for the design of potential countermeasures. This study therefore reveals how the unsteady flow inside the machine forces periodic mechanical loads onto the runner shaft. For this purpose, the two-phase flow field at the runner exit is investigated by Laser Doppler Velocimetry and high-speed visualizations, which are then compared to the simultaneously measured wall pressure oscillations in the draft tube cone and the mechanical torque on the runner shaft. The results are presented in the form of a comprehensive, mean phase averaged evolution of the relevant hydro-mechanical data over one period of the instability. They show that the flow in the runner, and thus the resulting torque applied to the shaft, is critically altered by a cyclic growth, shedding and complete collapse of cavitation on the suction side of the runner blades. This is accompanied by a significant flow swirl variation in the draft tube cone, governing the characteristic breathing motion of the cavitation vortex rope

U-RANS Simulations and PIV Measurements of a Self-excited Cavitation Vortex Rope in a Francis Turbine

In the course of the massive penetration of alternative renewable energies, the stabilization of the electrical power network significantly relies on the off-design operation of turbines and pump-turbines in hydropower plants. The occurrence of cavitation is, however, a common phenomenon at such operating conditions, often leading to critical flow instabilities, which undercut the grid stabilizing capacity of the power plant. In order to predict and extend the stable operating range of hydraulic machines, a better understanding of the cavitating flows and mainly of the transition between stable and unstable flow regimes is required. In the case of Francis turbines operating at full load, an axisymmetric cavitating vortex rope develops at the outlet runner in the draft tube. The cavity may enter self-oscillation, with violent periodic pressure pulsations propagating throughout the entire hydraulic system. The flow fluctuations lead to dangerous electrical power swings and mechanical vibrations through a fluid-structure coupling across the runner, imposing an inconvenient and costly restriction of the operating range. The paper deals with a numerical and experimental investigation of the transition from a stable to an unstable operating point on a reduced scale model of a Francis turbine at full load. Unsteady homogeneous two-phase RANS simulations are carried out using the ANSYS CFX solver. Cavitation is modelled using the Zwart’s model that required solving an additional transport equation for the void fraction. Turbulence is solved using the SST k-ω model. Simulations are compared with the experimental measurements and some insights are provided for a first comprehensive analysis of the transition between the stable and unstable states