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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 vortex ropes in draft tube of Francis turbine always cause fluctuation and vibration, which consequently threaten the safety and stability of hydro turbines. The purpose of this paper is to use a cavitation flow computational method to simulate spiral vortex ropes under part load conditions and columnar vortex ropes under high-load conditions in draft tube. The unsteady cavitating flow characteristics in draft tube and its interaction with runner cavitation were analyzed.

The calculation method was verified by cavitation simulation around a 3D hydrofoil. The results show that the Large Eddy Simulation (LES) turbulence model with the Zwart-Gerber-Blemari cavitation model have comparative advantage in cavitation simulations whether from capture of cavity shape or prediction of pressure changes. So it was chosen to simulate the two-phase cavitation flow in Francis turbine. The boundary conditions for inlet and outlet were set to inlet total pressure and outlet static pressure. The finite volume method with the central difference was adopted to discretize the equations.

The calculated Thoma number agreed well with the experimental data. The vortex rope diameter and length increased with the cavitation development for both of the two types of vortex ropes conditions. The maximum peak-to-peak values of pressure pulsations located in the draft tube elbow part under all of the Thoma numbers conditions. Under spiral vortex rope conditions, the pressure pulsation in the same section of draft tube cone show obviously phase shift. The vortex rope affects the development of runner cavitation, which induces the symmetric and axisymmetric cavitation region in the suction side of blades for spiral and columnar vortex rope condition, respectively.

The mesh independence had been checked only in non-cavitation flow; in addition, the mesh density did not well satisfy the requirements of LES due to the limitations of computing power. The higher mesh density on a simplified model with one blade flow path and the entire draft tube may be helpful for obtaining more precise results.

The spiral and columnar vortex ropes in a Francis turbine were compared and analyzed. The annular hydraulic jump appeared in the columnar vortex rope conditions has little effects on the pressure pulsations. The uneven flow field caused by spiral vortex led to the asymmetric cavitation development.

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 special structure of the vortex pump contributes to its complex internal flow pattern. A type of horizontal 150WX-200-20 vortex pump is taken as a research subject to deeply study the progression and distribution of flow pattern in its channel. To explain the mechanism of flow in this pump, numerical analysis of the whole flow and experiment have been conducted.

The authors studied and analyzed the distribution and evolution of flow pattern under different flow, such as circulating-flow, through-flow and other forms. Finally, a model of flow pattern in the vortex pump has been built, which has more perfectly fit the reality.

They are through-flow affected by circulating-flow, main and subsidiary circulating-flow, vortices between vanes and other vortices (or liquid impingement) in volute. Entering the pump, part of the flow stays in vanes and turn into vortices while the other goes into the front chamber. The flow that runs into the front chamber will be divided into two parts. One part will be collected by viscosity into a vortex rope when it passing through the interface between the impeller and the vaneless chamber, which closely relates to the circulating-flow, and the rest directly goes out of the field through the diffuser. Besides, a fraction of circulating-flow joins the through-flow when it goes through the section V and leaves the pump.

The research results build a theoretical foundation for working out the flow mechanism of the vortex pump, improving its efficiency and optimizing its hydraulic design.

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 predict pressure pulsation in Kaplan hydraulic turbines.

State of the art numerical simulation techniques are employed to simulate three‐dimensional flows in the whole flow passage of a Kaplan turbine so that pressure pulsations can be computed in both time domain and frequency domain. Numerical results are verified by experiments carried out on the most advanced experimental platform in China.

It is found that the proposed numerical model is a viable tool for prediction of pressure pulsations. The simulation shows that the model turbine and prototype turbine have the same pressure pulsation frequencies and rotating frequencies and the same transmission patterns under similar operation conditions. However, there is no similarity for the amplitude of the pressure pulsation between the model turbine and the prototype turbine. Therefore pressure pulsations in a prototype turbine cannot be obtained by scaling the experimental results of the model turbine using a similarity relationship.

The findings will be very valuable for the design of hydraulic turbines and large‐scale hydraulic power stations.

The proposed numerical method provides a viable tool for hydraulic turbine and power station designers to predict the pressure pulsations in prototype turbines. It is a useful tool to help improve the performance of hydraulic turbines. The findings made in the numerical simulation have been verified by experiments, which is also a valuable reference for hydraulic turbine designers.

Some comparison of unsteady flow calculation and the measured stress showed that the dynamic stresses in blades are closely related to hydraulic instability. However, few studies have been conducted for the hydraulic machinery to calculate dynamic stresses caused by the unsteady hydraulic load. The present paper aims to analyse the stresses in blades of a Kaplan turbine.

By employing a partially coupled solution of 3D unsteady flow through its flow passage, the dynamic interaction problem of the blades was analyzed. The unsteady Reynolds‐averaged Navier‐Stokes equations with the SST κ‐ω turbulence model were solved to model the flow within the entire flow path of the Kaplan turbine. The time‐dependent hydraulic forces on the blades were used as the boundary condition for the dynamics problem for blades.

The results showed that the dynamic stress in the blade is low under approximately optimum operating conditions and is high under low‐output conditions with a small guide vane opening, a small blade angle and a high head.

It is assumed that there is no feedback of blade motion on the flow. Self‐excited oscillations are beyond the scope of the present paper.

The authors developed a code to transfer the pressure on blades as a boundary condition for structure analysis without any interpolation. The study indicates that the prediction of dynamic stress during the design stage is possible. To ensure the safety of the blades it is recommended to check the safety coefficient during the design stage for at least two conditions: the 100 percent output with lower head and the 50 percent output with the highest head.

This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows.

The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure.

A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy.

This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

This paper aims to gain a clear understanding of the ventilated cavity evolution around an NACA0015 hydrofoil by using both experimental and numerical investigation.

The bubble evolution around an NACA0015 hydrofoil with or without air injection was observed in a water tunnel, and the simulation was conducted using a modified turbulence model and homogeneous cavitation model.

The present simulation method can successfully predict the bubble evolutions around the NACA0015 hydrofoil with or without air injection. Air injection can alleviate the nature cavitation oscillation, and the suppression effect on nature cavitation depends on the air-entrant coefficient. It is confirmed that the air and vapor cavity have the same shedding frequency. It is seen that the air sheet closely attaches to the hydrofoil surface and is surrounded by the vapor sheet. Thus, the injected air promotes vapor growth and results in an increase in the cavity shedding frequency. Further, with a large air-entrant coefficient, the pressure fluctuation is suppressed completely.

The new simulation method is adopted to explore the mechanism of ventilated cavitation. The bubble evolutions with and without air injection have been comprehensively studied by experimental and numerical investigation. The effects of air injection on natural cavity oscillations and pressure fluctuations have been revealed in the present study.