Fractional-Order Modeling and Dynamical Analysis of a Francis Hydro-Turbine Governing System with Complex Penstocks

This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The parameter switching algorithm is used to numerically study the dynamic behaviors of the system.Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors.A self-excited attractor with the change of its parameters is also recognized.In addition,numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra,Lyapunov dimensions,bifurcation diagrams,phase space orbits,and basins of attraction.Consequently,the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable.These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems,and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.

Experimental Investigation of Inter-Blade Vortices in a Model Francis Turbine

The inter-blade vortex in a Francis turbine becomes one of the main hydraulic factors that are likely to cause blade erosion at deep part load operating con- ditions. However, the causes and the mechanism of inter- blade vortex are still under investigation according to present researches. Thus the causes of inter-blade vortex and the effect of different hydraulic parameters on the inter-blade vortex are investigated experimentally. The whole life cycle of the inter-blade vortex is observed by a high speed camera. The test results illustrate the whole life cycle of the inter-blade vortex from generation to separation and even to fading. It is observed that the inter- blade vortex becomes stronger with the decreasing of flow and head, which leads to pressure fluctuation. Meanwhile, the pressure fluctuations in the vane-less area and the draft tube section become stronger when inter-blade vortices exist in the blade channel. The turbine will be damaged if operating in the inter-blade vortex zone, so its operating range must be far away from that zone. This paper reveals the main cause of the inter-blade vortex which is the larger incidence angle between the inflow angle and theblade angle on the leading edge of the runner at deep part load operating conditions.

Numerical simulation of cavitation turbulence in Francis turbine runner with splitter blades

Cavitation will reduce the turbine performance and even damage the turbine components.To verify the effects of splitter blades on improving the cavitation performance,the cavitation flow inside a Francis turbine runner with splitter blades was numerically simulated by using the Singhal cavitation model and the standard k-ε turbulence model.The distributions of static pressure and gas volume fractions on the surface of the runner blades were predicated under different conditions,and the cavitation in the flow field of the runner was analyzed.The results show that the static pressure and gas volume fractions are more uniformly distributed on the short blades than those on the long blades in Francis turbines with splitter blades,and there is almost no cavitation on the short blades;their distributions are more uniform under small flow conditions than those under large flow conditions;and large gas volume fractions are concentrated at the outlet tip near the band on the suction side of the long blade.The installation of splitter blades can improve the cavitation performance of conventional Francis turbines.

On Hemingway's Iceberg Theory——From The Short Happy Life of Francis Macomber

Ernest Hemingway's world-wide influence and distinctive writing style-the Iceberg Style-caused a stylistic revolution in the field of literature all over the world.Hemingway always tries his best to avoid depicting things by piling gorgeously big words;on the contrary,he adopts direct description and short sentences which are precise,laconic,bright and vivid.For instance,the novel titled The Short and Happy Life of Francis Macomber is universally acknowledged as his masterpiece,in which "Iceberg Theory"is skillfully presented.With a full analysis of the story,the uniqueness of "Iceberg Theory"will be emphasized in this paper.

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.

Numerical Study on the Blade Channel Vorticity in a Francis Turbine

A relevant way to promote the sustainable development of energy is to use hydropower.Related systems heavily rely on the use of turbines,which require careful analysis and optimization.In the present study a mixed experimental-numerical approach is implemented to investigate the related mixed water flow.In particular,particle image velocimetry(PIV)is initially used to verify the effectiveness of the numerical model.Then numerical results are produced for various conditions.It is shown that an increase in the guide vane opening can reduce the extension of the region where the fluid velocity is 0 at the inlet of the runner blade,i.e.,it can counteract the generation of the channel vortex;an increase in the guide vane opening also contributes to mitigate the pressure acting on the runner blade;no matter what the working conditions are,the surface pressure is usually higher than that on the suction surface,and there is a cliff-like drop of pressure at the tail of the blade,which indicates that the runner blade tail is more prone to develop backflow.

A Fatigue Analysis of a Hydraulic Francis Turbine Runner

In this work, the estimation of crack initiation life of a hydraulic Francis turbine runner is presented. The life prediction is based on the local strain approach to predict the initiation life. First, the analysis is carried out in air and in water condition and the runner’s natural frequencies were calculated using the finite element (FE) method. The analysis in air is compared with experimental analysis in order to have a representative model of real runner and subsequently the numerical analysis was perform in water. In the case of the runner immersed in water, the added mass effect due to the fluid structure interaction (FSI) is considered. Second, the static and dynamic stresses were calculated according to life estimation. For the calculation of static stresses, the pressure distribution of water and the centrifugal forces were applied to the runner. The dynamic stresses were estimated for interactions between the guide vane and the runner. Lastly, the estimation of the crack initiation life of the runner was obtained.

On the Unequal Relationship in “The Short Happy Life of Francis Macomber” from the Perspective of Discourse Framework

"The Short Happy Life of Francis Macomber",is a representative short story of Hemingway since it clearly embodies hisprinciple of creation.To illustrate the unequal relationship between the hero Macomber and the heroine Margot,this paper employsBurton’s(1980)Discourse Framework theory to analyze the distribution,classification and pattern of these two characters’chal-lenging moves.On the basis of the dialogue analysis,the author attempts to analyze the patterns of their challenging moves,whichcan reflect Macomber is in a more inferior position in marriage than his wife.And the reasons for this are Margot not only holdsmany challenging moves but also seizes the speaking rights in communication.

FRANCIS QL ALGORITHM FOR FINDING THE EIGENVALUES OF ANTI-SYMMETRIC MATRICES

In this paper,we demonstrate that the double-shift QL algorithm for an irreducible anti-symmetric iridiagonal matrix with the shifts being two eigenvalues of the 2×2 matrix in the left upper corner of this matrix is convergent and the convergence rale of Ms kind of algorithm is generally cubic.

Prediction of Hydraulic Stability of Francis Turbines of Three Gorges Hydropower Station

The Francis turbine of Three Gorges hydropower station is one of the large turbines with great head variation in the world. The operational stability of the turbine has been the top subject for departments of design, research, manufacture and operation to be concerned about. During the course of preparing bid invitation documents and executing the contract for the Three Gorges left power plants turbogenerator units, the hydraulic stability of the turbine was regarded as the most important problem and specific stability indexes of the model turbine and the prototype turbine were respectively specified in the contract. In the model tests for turbine model acceptance, pressure fluctuation phenomena in the case of partial load were found to be different from the usual ones as people had known. Within the range of operating water head, there existed a peak value zone of pressure fluctuations with higher frequencies, and large amplitude pressure fluctuations simultaneously occurred in several localities from the spiral case entrance to the draft tube. On the basis of test results from the model, the influence of cavitation coefficient and aeration on pressure fluctuations is analyzed, and some measures to improve the hydraulic stability of turbines of Three Gorges hydropower station are expounded.

Stability analysis of hydro-turbine governing system based on machine learning

Hydro-turbine governing system is a time-varying complex system with strong non-linearity,and its dynamic characteristics are jointly affected by hydraulic,mechanical,electrical,and other factors.Aiming at the stability of the hydroturbine governing system,this paper first builds a dynamic model of the hydro-turbine governing system through mechanism modeling,and introduces the transfer coefficient characteristics under different load conditions to obtain the stability category of the system.BP neural network is used to perform the machine study and the predictive analysis of the stability of the system under different working conditions is carried out by using the additional momentum method to optimize the algorithm.The test set results show that the method can accurately distinguish the stability category of the hydro-turbine governing system(HTGS),and the research results can provide a theoretical reference for the operation and management of smart hydropower stations in the future.

Francis Turbine and Governor Improved Models Considering Step Closing Law of Guide Vanes for Power System Stability Analysis

The Francis turbine governing system models in PSD-BPA can’t precisely reflect the actual characteristics. Endeavor was done in this paper to solve the problem. An improved model of actuating mechanism was developed, which could reflect the step closing characteristic of hydro guide vanes. The effect of the inflection point value of actuating mechanism on load rejection was analyzed based on simulation. The non-linear Francis turbine model with power versus gate position module was researched in this paper. Based on field test, comparisons of simulation results with measured data were presented. The analysis demonstrates that the improved models of Francis turbine and governor proposed in this paper are more realistic than the models of BPA, and can be applied in power system simulation analysis better.

The Pact of the Catacombs: An Early Harbinger of Pope Francis’ Vision of the Church

Fifty-four years ago, the Pact of the Catacombs was signed by a small group of churchmen, determined to make a difference. It was the time of the Second Vatican Council. It was the closing phase of that momentous experience in the Church’s life―a transforming event about which many still talk about, half a century later. A handful of bishops―40 out of an impressive 2,000-plus contingent meeting in St Peter’s Basilica―decided to assemble at the dead of night in the Catacombs of Domitilla, outside Rome. During that eventful night of 16 November 1965, they dreamt of a poor servant church. In that holy place, beneath the earth’s surface, where many generations of early Christians met to pray and to bury their loved ones, those 40 modern-day bishops met in heartfelt prayer to celebrate the Eucharist. They also signed the Pact of the Catacombs as they committed themselves to the ideals of Vatican II. The group of like-minded courageous shepherds was led by Archbishop Helder Camara of Recife, Brazil, the revered champion of the downtrodden poor and marginalized. Those gathered made a common pledge to live according to the daily manner of ordinary people, with regard to housing, food, means of transport, and such routine needs. In the Pact, they renounced the appearance and trappings of wealth, especially the use of gaudy vestments, resembling those of earthly monarchs, and symbols of precious metals, insisting that such signs should rather be according to the spirit of the Gospel. They promised to divest themselves of earthly riches and properties, and if they had to possess anything they placed it in the name of the diocese or some charitable foundation. In the humble consoling light of flickering candles, the group renounced all those aspects which appeared to be associated with privilege, prominence, and the wealthy echelons of society. In line with this, they expressed their desire not to be addressed verbally or in writing with titles expressing power, but rather with the more scriptural and homely title of “Father”. Their evangelical intention was focused on avoiding any sort of vanity. The signatories that night at the Domitilla Catacombs affirmed that “we will give whatever is needed in terms of our time, our reflection, our heart, our means, etc., to the apostolic and pastoral service of workers and labour groups and to those who are economically weak and disadvantaged, without allowing that to detract from the welfare of other persons or groups of the diocese. We will support lay people, religious, deacons and priests whom the Lord calls to evangelize the poor and the workers, by sharing their lives and their labours”. This paper shows how the Pact of the Catacombs was to be an early harbinger of Pope Francis’ vision of the church.

The San Francisco Peace Treaty and the Problems Regarding Japan’s Exemption from Blame for the Colonization of Korea

The 1951 San Francisco Peace Treaty was the one and only international opportunity that would have allowed demanding for Japan’s responsibility of the colonization of Korea.However,the United States did not demand of such to be done.Soon,Korea and Japan resumed their diplomatic relationship and had their first summit in 1952.After numerous negotiations,finally in 1965,the“Korea-Japan Treaty”was agreed upon.Even in this treaty,the interpretation of the colonization was different for both countries and ultimately resulted as an unresolved issue.This is because of the Japanese dependence to the San Francisco Peace Treaty.On the other hand,the League of Nations,founded in 1920,believed that the systematization of international law was vital to keeping international peace.Therefore,they put much effort in and successfully carried out the codification of international law.The“Report on the law of Treaties”which was completed in 1935,noted that the“1905 Protectorate Treaty”,which was the ultimate treaty that led to Korea being annexed by the Japanese,was one of the three treaties that had no effective standing.This decision was carried out to the International Law Commission of the United Nations in 1963 and became a Resolution after being submitted to the General Assembly in the end of the same year.Using the decisions of the League of Nations and the United Nations as evidence,this paper critically reviews the San Francisco Peace Treaty’s lack of reviewing the Japanese responsibility of the colonization of Korea.

Francis Tchiegue

Francis Tchiegue,a Cameroonian,is something of a legend in China.He came to the country in 2003 for doctoral studies,but is now known to Chinese television audiences as Jie Gai,a crosstalk performer. The art of crosstalk[A stand-up comedy routine],or xiangsheng,is difficult even for native Chinese speakers to do,let alone foreigners. Tchiegue’s success has kept him performing across China.He recently spoke with ChinAfrica about his story.