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The velocity head is usually neglected in the energy equation for a pipeline junction when one-dimensional (1D) hydraulic transient flow is solved by method of characteristics. The purpose of this paper is to investigate the effect of velocity head on filling transients in a branched pipeline by an energy equation considering velocity head.

An interface tracking method is used to locate the air–water interface during pipeline filling. The pressured pipe flow is solved by a method of characteristics. A discrete gas cavity model is included to permit the occurrence of column separation. A universal energy equation is built by considering the velocity head. The numerical method is provisionally verified in a series pipeline and the numerical results and experimental data accord well with each other.

The numerical results show that some differences in filling velocity and piezometric head occur in the branched pipeline. These differences arise because the velocity head in the energy equation can become an important contributor to the hydraulic response of the system. It is also confirmed that a local high point in the profile is apt to experience column separation during rapid filling. Significantly, the magnitude of overpressure and cavity volume induced by filling transients at the local high point is predicted to increase with the velocity in the pipes.

The velocity head in the energy equation for a pipeline junction could play an important role in the prediction of filling velocity, piezometric head and column separation phenomenon, which should be given more attention in 1D hydraulic transient analysis.

The gaps between runner and nearby structures play an important role in the dynamic response of runner, especially for pump-turbines. This paper aims to evaluate the gap influence on the added mass and dynamic stress of pump-turbine runner and provide an improved method to predict the resonance of runner.

Acoustic-structural coupling method was used to evaluate the added mass factors of a reduced scale pump-turbine with different axial and radial gap size between runner and nearby rigid walls. Improved one-way fluid-structural interaction (FSI) simulation was used to calculate the dynamic stress of the runner, which takes into account fluid added mass effect. The time-dependent hydraulic forces on the runner surfaces that were obtained from unsteady CFD simulation were transferred to the runner structure as a boundary condition, by using mesh-matching algorithm at the FSI surfaces.

The results show that the added mass factors increase as the gap size decreases. The axial gaps have greater influence on the added mass factors for the in-phase (IP) modes than the counter-phase (CP) and crown-dominant (CD) modes, while the CP and CD modes are very sensitive to the radial gaps. The largest added mass factor is observed in (2 + 4)ND-CP mode (resonance mode). The results reveal that the transient structural dynamic stress analysis, with the consideration of gaps and fluid added mass, can accurately predict the resonance phenomenon. Resonance curve of the pump-turbine has been obtained which agrees well with the test result. The gap fluid has great influence on the resonance condition, while for non-resonance operating points, the effect of gaps on the dynamic stress amplitude is quite small.

This paper provides an accurate method to analyze the dynamic response during runner design stage for safety assessment. The resonance curve prediction has more significance than previous methods which predict the resonance of runner by modal or harmonic analysis.

For Francis turbine, the vortex flow in the draft tube plays an important role in the safe and efficient operating of hydraulic turbine. The swirling flow produced at the blade trailing edge at off-design conditions has been proved to be the fundamental reason of the vortex flow. Exploring the swirling flow variations in the non-cavitation flow and cavitation flow field is an effective way to explain the mechanism of the complex unsteady flow in the draft tube.

The swirling flow in different cavitation evolution stages of varying flow rates was studied. The swirl number, which denotes the strength of the swirling flow, was chosen to systematically analyze the swirling flow changes with the cavitation evolutions. The Zwart–Gerber–Blemari cavitation model and SST turbulence model were used to simulate the two-phase cavitating flow. The finite volume method was used to discrete the equations in the unsteady flow field simulation. The Frozen Rotor Stator scheme was used to transfer the data between the rotor-stator interfaces. The inlet total pressure was set to inlet boundary condition and static pressure was set to outlet boundary condition.

The results prove that the mutual influences exist between the swirling flow and cavitation. The swirling flow was not only affected by the load but also significantly changed with the cavitation development, because the circumferential velocity decrease and axial velocity increase presented with the cavitation evolution. At the high load conditions, the system stability may improve with the decreasing swirling flow strength.

Further experimental and simulation studies still need to verify and estimate the reasonability of the swirling flow seen as the cavitation inception signal.

One interesting finding is that the swirl number began to change as the inception cavitation appeared. This is meaningful for the cavitation controlling in the Francis turbine.

This study analyzes the blade channel vortices inside Francis runner with a particular focus on the identification of different types of vortices and their causes.

A single-flow passage of the Francis runner with refined mesh and periodic boundary conditions was used for the numerical simulation to reduce the computational resource. The steady-state Reynolds-averaged Navier–Stokes equations closed with the k-ω shear–stress transport (SST) turbulence model were solved by ANSYS CFX to determine the flow field. The vortices were identified by the second largest eigenvalue of velocity.

Four types of vortices were identified inside the runner. Three types were related to the inlet flow. The last one (Type 4) was caused by the reversed flow near the runner crown and had the lowest pressure inside the core near the runner outlet. Thus, in the blade channel vortex inception line, Type 4 vortex would appear earlier than the other three ones. Besides, the Type 4 vortex emerged from the crown and shed toward the blade-trailing edge. And its location moved from near the crown down to near the band when the unit speed increased or unit discharge decreased.

Although the refined mesh was used and the main vortices in the Francis runner were well predicted, the current mesh is not enough to accurately predict the lowest pressure in the channel vortex core.

This knowledge is instructive in the runner blade design and troubleshooting related to the channel vortex.

This study gives an overview of the main observed blade channel vortices and their causes, and points out the important role the reversed flow plays in the formation of blade channel vortices. This knowledge is instructive in the runner blade design and troubleshooting related to blade channel vortices.

The purpose of this paper is to reveal the transient thermo-elasto-hydrodynamic lubrication mechanism of a bidirectional thrust bearing in a pumped-storage unit, and to propose the transient simulation method of two-way fluid-solid-thermal interaction of thrust bearing.

The transient fluid-solid-thermal interaction method is used to simulate the three-dimensional lubrication of the thrust bearing, during the start-up and shutdown process of a pumped storage unit. A pad including an oil hole is modelled to analyze the temporal variation of lubrication characteristics, such as the film pressure, thickness and temperature, during the transient operation process.

The injection of the high-pressure oil sufficiently affects the lubrication characteristics on film, in which the hysteresis phenomena were found between the start-up and shutdown possess.

This paper reveals the transient lubrication mechanism of tilting pad in a thrust bearing, by means of transient fluid-solid-thermal interaction method. Lubrication characteristics are simulated without assuming the temperature relationship between the oil film inlet and the outlet and the heat transfer on the pad free surface. This paper provides a theoretical basis for the safe design and stable operation of thrust bearings.

The purpose of this paper is to analyze lubrication characteristics of a bidirectional thrust bearing in a pumped storage, 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 bidirectional thrust bearing for several typical operating conditions. The influences of the operating conditions and the thrust load on the lubrication characteristics were analyzed. Then, various pivot eccentricities were investigated to analyze the effects of the pivot position.

It is found that the effect of the radial tilt angle of the collar runner on the oil film is compensated for by the radial tilt of the pad. The central pivot support system is the main factor limiting the loads of bidirectional thrust bearings.

This paper has preliminarily revealed the lubrication mechanism of bidirectional tilting-pad thrust bearings. A three-dimensional 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.

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.

Hydraulic instabilities are one of the most important reasons causing vibrations and fatigues in hydraulic turbines. The present paper aims to find the relationship between pressure pulsations and fatigues of key parts of a Kaplan turbine.

3D unsteady numerical simulations were preformed for a number of operating conditions at high heads for a prototype Kaplan turbine, with the numerical results verified by online monitoring data. The contact method and the weak fluid‐structure interaction method were used to calculate the stresses in the multi‐body mechanism of the Kaplan turbine runner body based on the unsteady flow simulation result.

The results show that vortices in the vaneless space between the guide vanes and blades cause large pressure pulsations and vibrations for high heads with small guide vane openings. The dynamic stresses in the runner body parts are small for high heads with large guide vane openings, but are large for high heads with small guide vane openings.

A comprehensive numerical method including computational fluid dynamics analyses, finite element analyses and the contact method for multi‐body dynamics has been used to identity the sources of unit vibrations and key part failures.

The pump of the Taipuhe Pump Station, larger flow discharge, lower head, is one of the largest 15° slanted axial‐flow pumps in the world. However, few studies have been done for the larger slanted axial‐flow pump on safe operation. The purpose of this paper is to analyze the impeller elevation, unsteady flow, hydraulic thrust and the zero‐head flow characteristics of the pump.

The flow field in and through the pump was analyzed numerically during the initial stages of the pump design process, then the entire flow passage through the pump was analyzed to calculate the hydraulic thrust to prevent damage to the bearings and improve the operating stability. The zero‐head pump flow characteristics were analyzed to ensure that the pump will work reliably at much lower heads.

The calculated results are in good agreement with experimental data for the pump elevation effects, the performance curve, pressure oscillations, hydraulic thrust and zero‐head performance.

Since it is assumed that there is no gap between blades and shroud, gap cavitations are beyond the scope of the paper.

The paper indicates the slanted axial‐flow pump characteristics including the characteristic curves, pressure fluctuations, hydraulic thrust and radial force for normal operating conditions and zero‐head conditions. It shows how to guarantee the pump safety operating by computational fluid dynamics.