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The purpose of this paper is to study the pressure fluctuation characteristics in the sidewall gaps of a centrifugal dredging pump in detail and discover the excitation sources.

An unsteady numerical simulation with shear–stress transport–scale-adaptive simulation (SAS-SST) model was conducted for a centrifugal pump considering the sidewall gaps. The numerical codes were validated by a model test carried out in China Water Resources Beifang Investigation, Design and Research Co., Ltd. Fast Fourier transform was used to obtain the frequency components of the pressure fluctuation.

Pressure fluctuation characteristics inside the pump were analyzed for a condition near the design point. In the sidewall gaps, the circumferential, radial and axial distribution of the pressure fluctuation amplitude follow different laws. The non-axisymmetrical distribution of pressure fluctuation in the sidewall gaps shows that the unsteady flow in the volute casing which has a non-axisymmetrical geometry imposes an evident effect on the flow field in the sidewall gaps and the interaction between the main flow and the clearance flow cannot be neglected. There are several frequency components appearing as the dominant frequencies at different locations in the sidewall gaps, but the relatively stronger pressure fluctuations are all dominated by the rotating frequency. It indicates that the rotating impeller, which originally makes the shrouds rotate, is the primarily excitation source of the pressure fluctuations in the sidewall gaps.

The pressure fluctuation characteristics in the sidewall gaps of centrifugal pumps were first comprehensively analyzed. Unsteady flows in the sidewall gaps should be considered during the design and operation of centrifugal pumps.

The purpose of this paper is to analyze lubrication characteristics of a tilting pad thrust bearing considering the effect of the thermal elastic deformation of the pad and collar.

This study used the fluid–solid interaction (FSI) technique to investigate the lubrication characteristics of a tilting pad thrust bearing for several typical operating conditions. The influences of the rotational speed, the thrust load and the oil supply temperature on the lubrication characteristics were analyzed.

The three-dimensional (3D) film model clearly shows that there is no pressure gradient but large temperature gradients across the film thickness. The wall heat transfer coefficients on the pad surfaces distribute in a very complex way and change within a large range. The rotational speed, the thrust load and the oil supply temperature have great but different influences on the lubrication characteristics.

This paper has preliminarily revealed the lubrication mechanism of the tilting-pad thrust bearings. The 3D FSI method is suggested to evaluate the thermal-elastic-hydrodynamic deformations of thrust bearings instead of the conventional method which iteratively solves the Reynolds equation, the energy equation, the heat conduction equation and the elastic equilibrium equation. Using FSI method, the heat transfer coefficients on the pad surfaces can be evaluated better.

Numerically analyzed the flow characteristic and explored the hydrodynamic mechanism of the pump mode hump district formation of a Francis pump-turbine.

Numerical simulations were conducted of the entire pump-turbine flow passage under different discharge conditions by adopting the SST-CC turbulence model. The internal flow at hump district has been explained in detail combined with the model test in this paper. The unsteady flow and pressure fluctuation characteristics are analysed under five different discharge conditions in the hump and nearby region. The reason of the hump district formation is explored combined with the flow components hydraulic loss.

The large hydraulic loss, high relative peak-to-peak amplitudes and low dominant frequencies are on account of the disorganized internal flow condition. The formation of the hump district is concerned with the large hydraulic loss inside the draft tube, runner and guide vanes as there occurs secondary flow, backflow even vortex in the hump district. In addition, the low dominant frequencies at recording points inside the flow passage are always accompanied with the change of flow patterns and the spreading of the pressure fluctuations.

The analysis method of each flow components hydraulic loss combined with internal flow structure is adopted to explore the mechanism of pump mode hump characteristic. The flow characteristic and pressure pulse characteristics all correspond to the flow components hydraulic loss.

Numerically analyzed the flow characteristic and explored the hydrodynamic mechanism of the S-shaped region formation of a Francis pump-turbine.

Three-dimensional steady and unsteady simulations were performed for a number of operating conditions at the optimal guide vanes opening. The steady Reynolds averaged Navier-Stokes equations with the SST turbulence model were solved to model the internal flow within the entire flow passage. The predicted discharge-speed curve agrees well with the model test at generating mode. This paper compared the hydrodynamic characteristics of for off-design cases in S-shaped region with the optimal operating case, and more analysis focuses particularly on very low positive and negative discharge cases with the same unit speed.

At runaway case towards smaller discharge, the relative circumferential velocity becomes stronger in the vaneless, which generates the “water ring” and blocks the flow between guide vane and runner. The runner inlet attack angle becomes larger, and the runner blade passages nearly filled with flow separation and vortexes. The deterioration of runner blade flow leads to the dramatic decrease of runner torque, which tends to reduce the runner rotation speed. In this situation, the internal flow can’t maintain the larger rotating speed at very low positive discharge cases, so the unit discharge-speed curves bend to S-shaped near runaway case.

The analysis method of four off-design cases on S-shaped region with the comparison of optimal operation case and the calculated attack angles are adopted to explore the mechanism of S characteristic. The flow characteristic and quantitative analysis all explain the bending of the unit discharge-speed curves.

The purpose of this paper is to investigate, experimentally and numerically, the pressure pulse characteristics and unsteady flow behavior in a Francis turbine runner for moderate flow heads. The pressure pulses in the runner blade passage were predicted numerically for both moderate and high heads. The calculations were used to partition the turbine operating regions and to clarify the various for the unsteady flow behavior, especially the blade channel vortex in the runner.

Experimental and numerical analyses of pressure pulse characteristics at moderate flow heads in a Francis turbine runner were then extended to high heads through numerical modeling with 3D unsteady numerical simulations performed for a number of operating conditions. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω‐based shear stress transport turbulence model were used to model the unsteady flow within the entire flow passage of a Francis turbine.

The dominate frequency of the predicted pressure pulses at runner inlet agree with the experimental results in the head cover at moderate flow heads. The influence of the blade passing frequency causes the simulated peak‐to‐peak amplitudes in the runner inlet to be larger than in the head cover. The measured and predicted pressure pulses at different positions along the runner are comparable. At the most unstable operating condition of 0.5a₀ guide vane opening, the pressure pulses in the runner blade passage are due to the blade channel vortex and the rotor‐stator interference. The predictions show that the frequency of the blade channel vortex is relatively low and it changes with the operating conditions.

The paper describes a study which experimentally and numerically investigated the pressure pulses characteristics in a Francis turbine runner at moderate flow heads. The pulse characteristics and unsteady flow behavior due to the blade channel vortex in the runner at high heads were investigated numerically, with the turbine operating regions then partitioned to identify safe operating regions.

The purpose of this paper is to describe how the hydraulic performance and pressure fluctuations in the entire flow passage of a Francis turbine were predicted numerically for the highest head. The calculations are used to partition the turbine operating regions and to clarify the unsteady flow behavior in the entire flow passage including the blade channel vortex in the runner and vortex rope in the draft tube.

Three‐dimensional unsteady numerical simulations were performed for a number of operating conditions at the highest head. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω based SST turbulence model were solved to model the unsteady flow within the entire flow passage of a Francis turbine.

The predicted pressure fluctuations in the draft tube agree well with the experimental results at low heads. However the peak‐to‐peak amplitudes in the spiral case are not as well predicted so the calculation domain and the inlet boundary conditions need to be improved. The unsteady simulation results are better than the steady‐state results. At the most unstable operating condition of case a0.5h1.26, the pulse in the flow passage is due to the rotor‐stator interference between the runner and the guide vanes, the blade channel vortex in the runner blade passage and the vortex rope in the draft tube.

This study investigates the characteristics of the dominant unsteady flow frequencies in different parts of the turbine for various guide vane openings at the highest head. The unsteady flow patterns in the turbine, including the blade channel vortex in the runner and the helical vortex rope in the draft tube, are classified numerically, and the turbine operating regions are partitioned to identify safe operating regions.

The purpose of this paper is to experimentally and numerically investigate the interference characteristics between two ski-jump jets on the flip bucket in a large dam spillway when two floodgates are running.

The volume of fluid (VOF) method together with the Realizable k-ε turbulence model were used to predict the flow in two ski-jump jets and the free surface motion in a large dam spillway. The movements of the two gates were simulated using a dynamic mesh controlled by a User Defined Function (UDF). The simulations were run using the prototype dam as the field test to minimize errors due to scale effects. The simulation results are compared with field test observations.

The transient flow calculations, accurately predict the two gate discharges compared to field data with the predicted ski-jump jet interference flow pattern similar to the observed shapes. The transient simulations indicate that the main reason for the deflected nappe is the larger opening difference between the two gates as the buttress side gate closes. When both gates are running, the two ski-jump jets interfere in the flip bucket and raise the jet nappe to near the buttress to form a secondary flow on this jet nappe surface. As the gate continues to close, the nappe surface continues to rise and the surface secondary flow become stronger, which deflects the nappe over the side buttress.

A dynamic mesh is used to simulate the transient flow behavior of two prototype running gates. The transient flow simulation clarifies the hydraulics mechanism for how the two ski-jump jets interfere and deflect the nappe.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.