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.

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.

Improving the Energy Performance of a High-Pressure Hydraulic Turbine by Researching the Flow in the Flow Part

In this study, the goal is to increase the efficiency of a high-pressure hydraulic turbine. The goal is achieved by numerical flow simulation using CFX-TASCflow. This approach reduces costs and time compared to the experimental approach and allows for improving the turbine productivity and its design. The analysis of energy losses in the flow part of the turbine Fr500, as well as the analysis of the influence of the opening of the guide vanes on changes in energy losses. The results showed that the greatest losses occur in the guide vane 3.02% based on the two-dimensional model and 2.5% based on the 3D model, which significantly affects the efficiency. The analysis was carried out using programs for calculating fluid flow in two-dimensional and three-dimensional formulations. With the help of the study, the main energy problem is solved—increasing efficiency.

Dynamic Stresses in a Francis Turbine Runner Based on Fluid-Structure Interaction Analysis

Fatigue and cracks have occurred in many large hydraulic turbines after they were put into production. The cracks are thought to be due to dynamic stresses in the runner caused by hydraulic forces. Computational fluid dynamics （CFD） simulations that included the spiral case, stay vane, guide vane, runner vane, and draft tube were run at various operating points to analyze the pressure distribution on the runner surface and the stress characteristics in the runner due to the fluid-structure interactions （FSI）. The dynamic stresses in the Francis turbine runner at the most dangerous operating point were then analyzed. The results show that the dynamic stresses caused by the hydraulic forces during off-design operating points are one of the main reasons for the fatigue and cracks in the runner blade. The results can be used to optimize the runner and to analyze other critical components in the hydraulic turbine.

Numerical analyses of pressure fluctuations induced by interblade vortices in a model Francis turbine

Interblade vortices can greatly influence the stable operations of Francis turbines. As visible interblade vortices are essentially cavitating flows, i.e., the ones to cause interblade vortex cavitations, an unsteady simulation with a method using the RNG k- ？ turbulence model and the Zwart-Gerber-Belamri（ZGB） cavitation model is carried out to predict the pressure fluctuations induced. Modifications of the turbulence viscosity are made to improve the resolutions. The interblade vortices of two different appearances are observed from the numerical results, namely, the columnar and streamwise vortices, as is consistent with the experimental results. The pressure fluctuations of different frequencies are found to be induced by the interblade vortices on incipient and developed interblade vortex lines, respectively, on the Hill diagram of the model runner＇s parameters. From the centrifugal Rayleigh instability criterion, it follows that the columnar interblade vortices are stable and the streamwise interblade vortices are unstable in the model Francis turbine.

Simulation of the load rejection transient process of a francis turbine by using a 1-D-3-D coupling approach

This paper presents the simulation and the analysis of the transient process of a Francis turbine during the load rejection by employing a one-dimensional and three-dimensional （1-D-3-D） coupling approach. The coupling is realized by partly overlapping the I-D and 3-D parts, the water hammer wave is modeled by defining the pressure dependent density, and the guide vane closure is treated by a dynamic mesh method. To verify the results of the coupling approach, the transient parameters for both typical models and a real power station are compared with the data obtained by the 1-D approach, and good agreements are found. To investigate the differences between the transient and steady states at the corresponding operating parameters, the flow characteristics inside a turbine of the real power station are simulated by both transient and steady methods, and the results are analyzed in details. Our analysis suggests that there are just a little differences in the turbine outer characteristics, thus the traditional 1-D method is in general acceptable. However, the flow patterns in the spiral casing, the draft tube, and the runner passages are quite different： the transient situation has obvious water hammer waves, the water inertia, and some other effects. These may be crucial for the draft tube pul- sation and need further studies.

NUMERICAL SIMULATION AND ANALYSIS OF PRESSURE PULSATION IN FRANCIS HYDRAULIC TURBINE WITH AIR ADMISSION

In this article, the three-dimensional unsteady multiphase flow is simulated in the whole passage of Francis hydraulic turbine. The pressure pulsation is predicted and compared with experimental data at positions in the draft tube, in front of runner, guide vanes and at the inlet of the spiral case. The relationship between pressure pulsation in the whole passage and air admission is analyzed. The computational results show： air admission from spindle hole decreases the pressure difference in the horizontal section of draft tube, which in turn decreases the amplitude of low-frequency pressure pulsation in the draft tube; the rotor-stator interaction between the air inlet and the runner increases the blade-frequency pressure pulsation in front of the runner.

ANALYSIS AND ESTIMATION OF HYDRAULIC STABILITY OF FRANCIS HYDRO TURBINE

With the development of large-capacity hydro turbines, the hydraulicinstability of hydro turbines has become one of the most important problems that affect the stableoperation of the hydro-electric units. The hydraulic vibration and unstable operation of Francishydro turbines are primarily caused by the unsteady pressure pulsations inside draft tubes. Theforced rotating vortex core at the runner exit and the channel vortices inside Francis turbinerunners are origins of the unsteady pressure pulsations when operating at partial load. This paperbriefly analyzes the hydraulic instability of operation caused by the vortex core and channelvortices at partial load, then, presents a way to estimate the hydraulic stability by calculation ofthe flow behavior at the runner exit. The validity of estimation is examined by comparison withexperimental data. This will be helpful to evaluate the alternative design and predict the hydraulicstability for both the prototype and model hydro turbines.

LARGE-EDDY SIMULATION OF TURBULENT FLOW CONSIDERING INFLOW WAKES IN A FRANCIS TURBINE BLADE PASSAGE

Turbulent flow in a 3-D blade passage of a Francis hydro turbine was simulated with the Large Eddy Simulation （LES） to investigate the spatial and temporal distributions of the turbulence when strongly distorted wakes in the inflow sweep over the passage, In a suitable consideration of the energy exchanging mechanism between the large and small scales in the complicated passage with a strong 3-D curvature, one-coefficient dynamic Sub-Grid-Scale （SGS） stress model was used in this article. The simulations show that the strong wakes in the inflow lead to a flow separation at the leading zone of the passage, and to form a primary vortex in the span-wise direction. The primary span-wise vortex evolves and splits into smaller vortex pairs due to the constraint of no-slip wall condition, which triggers losing stability of the flow in the passage. The computed pressures on the pressure and suction sides agree with the measured data for a working test turbine model.

Prediction of the precessing vortex core in the Francis-99 draft tube under off-design conditions by using Liutex/Rortex method

The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube of a Francis turbine with splitter blades is not well understood, especially the vortex rope property. This letter presents a prediction of the behavior of the vortex rope in the draft tube of the Francis-99 turbine obtained by the computational fluid dynamics (CFD), where the Liutex/Rortex method, as the most recent vortex definition, is applied to analyze the periodical precession of the vortex rope in the draft tube cone. The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent the vortex rope structurewith the vortex-core lines. Furthermore, since it seems to be very hard to define a sharp boundary surface for the whole vortex structure, it is advantageousfocusing only on the vortex core line,by which different vortex structures can be clearly differentiated. The evolution of the vortex core and the process of the vortex breakdown in the draft tube are revealed, which might help to comprehend the development of the turbulent flow in the draft tube.

Experimental investigations of transient pressure variations in a high head model Francis turbine during start-up and shutdown

Penetration of the power generated using wind and solar energy to electrical grid network causing several incidents of the grid tripping, power outage, and frequency drooping. This has increased restart （star-stop） cycles of the hydroelectric turbines significantly since grid connected hydroelectric turbines are widely used to manage critical conditions of the grid. Each cycle induces significant stresses due to unsteady pressure loading on the runner blades. The presented work investigates the pressure loading to a high head （ He = 377 m, De = 1.78 m） Francis turbine during start-stop. The measurements were carried out on a scaled model turbine （HM = 12.5 m, DM = 0.349 m）. Total four operating points were considered. At each operating point, three schemes of guide vanes opening and three schemes of guide vanes closing were investigated. The results show that total head variation is up to 9% during start-stop of the turbine. On the runner blade, the maximum pressure amplitudes are about 14 kPa and 16 kPa from the instantaneous mean value of 121 kPa during rapid start-up and shutdown, respectively, which are about 1.5 times larger than that of the slow start-up and shutdown. Moreover, the maximum pressure fluctuations are given at the blade trailing edge.

Three-Dimensional Simulation of Unsteady Flow in a Model Francis Hydraulic Turbine

For Francis hydraulic turbines, unsteady flow caused by vortex ropes in the draft tube leads to a problem of stability in operation. The unsteady flow field of a model Francis hydraulic turbine was simulated under part-load operation. A sliding mesh model was used to calculate a time-accurate solution for the strong rotor-stator interactions between the runner and guide vanes, and the draft tube. Based on three-dimensional incompressible Reynolds averaged Navier-Stokes equations and on a renormalization group k-?turbulence model, spatial discretization was obtained by using the finite volume method with unstructured grid elements, and a second order fully implicit scheme was applied for time. Pressure fluctuations in the draft tube were recorded and analyzed via a fast Fourier transform calculation. The results were compared with the experimental data, and show that the vortex rope in the draft tube and the induced pressure fluctuations are well simulated.

Numerical investigation of alleviation of undesirable effect of inter-blade vortex with air admission for a low-head Francis turbine

In order to compensate for the stochastic nature of the power grid due to the tremendous development and the integration of renewable energy resources and meet its other requirements,the hydraulic turbines are forced to operate more frequently under partial load conditions with singular and misaligned flows inevitably excited by the inter-blade vortex.This paper presents numerical investigations of the unsteady characteristics of the inter-blade vortex for a low-head model Francis turbine.The SST k-ωturbulent model is used to close the unsteady Reynolds-averaged Navier-Stokes(RANS)equation.The flow structure of the inter blade vortex predicted by the numerical simulation is confirmed by experimental visualizations.It is shown that the total vortex volume in the runner sees a quasi-periodical oscillation,with significant flow separations created on the suction side of the runner blade.A counter measure by using the air admission into the water from the head cover is implemented to alleviate the undesirable effect of the inter-blade vortex.The analyses show that the development of the inter-blade vortex is significantly mitigated by the injecting air that controls and changes the spatial distribution of streamlines.Furthermore,the flow aeration with a suitable air flow rate can reduce the energy dissipation caused by the inter-blade vortex and plays a critical role in preventing the excessive amplitudes of the pressure fluctuation on the suction side of the runner blade.This investigation provides an insight into the flow mechanism underlying the inter-blade vortex and offers a reference to alleviate and mitigate the adverse consequences of the inter-blade vortex for the Francis turbine.

Numerical predictions and stability analysis of cavitating draft tube vortices at high head in a model Francis turbine

Draft tube vortex is one of the main causes of hydraulic instability in hydraulic reaction turbines,in particular Francis turbines.A method of cavitation calculations was proposed to predict the pressure fluctuations induced by draft tube vortices in a model Francis turbine,by solving RANS equations with RNG k-turbulence model and ZGB cavitation model,with modified turbulence viscosity.Three cases with different flow rates at high head were studied.In the study case of part load,two modes of revolutions with the same rotating direction,revolution around the axis of the draft tube cone,and revolution around the core of the vortex rope,can be recognized.The elliptical shaped vortex rope causes anisotropic characteristics of pressure fluctuations around the centerline of the draft tube cone.By analyzing the phase angles of the pressure fluctuations,the role of the vortex rope as an exciter in the oscillating case can be recognized.An analysis of Batchelor instability,i.e.instability in q-vortex like flow structure,has been carried out on the draft tube vortices in these three cases.It can be concluded that the trajectory for study case with part load lies in the region of absolute instability(AI),and it lies in the region of convective instability(CI)for study case with design flow rate.Trajectory for study case with over load lies in the AI region at the inlet of the draft tube,and enters CI region near the end of the elbow.

Suppression of vortex rope oscillation and pressure vibrations in Francis turbine draft tube using various strategies

The vortex rope usually occurs in the draft tube of the Francis turbine operated under part-load conditions,to induce strong low-frequency pressure vibrations,and therefore,is very harmful to the safety of the hydropower unit.In the present work,three kinds of strategies are extensively investigated,i.e.,the installations of the ventilation and the fin,as well as the hybrid strategy of the air admission through a fin,so as to effectively suppress the vortex rope oscillation and the pressure vibration in the draft tube of a Francis turbine,whose specific speed is 125 m-kW.For the unsteady flow simulation,the Reynolds averaged Navier-Stokes(RANS)method is applied coupled with the k-ω SST turbulence model and a homogeneous cavitation model.The flow analysis confirms that the low-frequency pressure vibrations are originated from the periodical oscillation of the vortex rope,and the cavitation usually enhances the vortex rope oscillation in the draft tube.Under the part-load condition,the dominant component of the pressure vibration in the draft tube has a frequency,for example,f_(1),lower than the runner rotating frequency f_(n).It is shown that all three strategies can be adopted to alleviate the vortex rope oscillation and the pressure vibrations in the draft tube,but their suppression mechanisms are quite different.The ventilation of an adequate amount from the turbine runner cone can change the vortex rope geometry from the spiral type to the cylindrical type,suppress the vortex rope oscillation,and consequently create the homogeneous distributions of the pressure and the pressure gradient in the draft tube.On the other hand,a fin installed at the draft tube wall can induce a small extra rope,and the interaction between the main vortex rope and the extra rope changes the flow field and alleviates the pressure vibration in the draft tube.It should be noted that a fin is much more effective to suppress the pressure vibration in the draft tube under the cavitation condition than under the non-cavitation condition.A better effect of suppressing the vortex rope oscillation can be achieved by the air admission through a fin,which is studied numerically in this paper.The result indicates that the air admission can further improve the effect of a fin for suppressing the pressure vibration in the inlet cone of the draft tube.This improvement is due to the stronger interaction between the main vortex rope and the extra air rope.However,the air admission through a fin should be carefully treated because the strong interaction may induce a larger pressure vibration in the elbow of the draft tube.Finally,it is clear that any strategy for suppressing the pressure vibration hardly changes the dominant component frequency f_(1),which is in the range of 0.22 f_(n)-0.23 f_(n) due to the main vortex rope oscillation in this study.The current results may be used in various engineering applications,where the active control of the vortex oscillation and the pressure vibrations with or without the cavitation is necessary.

Design and development of guide vane cascade for a low speed number Francis turbine

Guide vane cascade of a low speed number Francis turbine is developed for the experimental investigations. The test setup is able to produce similar velocity distributions at the runner inlet as that of a reference prototype turbine. Standard analytical methods are used to design the reference turbine. Periodic walls of flow channel between guide vanes are identified as the starting profile for the boundary of the cascade. Two alternative designs with three guide vanes and two guide vanes, without runner, are studied. A new approach, for the hydraulic design and optimization of the cascade test setup layout, is proposed and investigated in details. CFD based optimization methods are used to define the final layout of the test setup. The optimum design is developed as a test setup and experimental validation is done with PIV methods. The optimized design of cascade with one guide vane between two flow channels is found to produce similar flow conditions to that in the runner inlet of a low speed number Francis turbine.

Influence of upstream disturbance on the draft-tube flow of Francis turbine under part-load conditions

Owing to the part-load operations for the enhancement of grid flexibility, the Francis turbine often suffers from severe low-frequency and large-amplitude hydraulic instability, which is mostly pertinent to the highly unsteady swirling vortex rope in the draft tube. The influence of disturbances in the upstream（e.g., large-scale vortex structures in the spiral casing） on the draft-tube vortex flow is not well understood yet. In the present paper, the influence of the upstream disturbances on the vortical flow in the draft tube is studied based on the vortex identification method and the analysis of several important parameters（e.g., the swirl number and the velocity profile）. For a small guide vane opening（representing the part-load condition）, the vortices triggered in the spiral casing propagate downstream and significantly affect the swirling vortex-rope precession in the draft tube, leading to the changes of the intensity and the processional frequency of the swirling vortex rope. When the guide vane opening approaches the optimum one（representing the full-load condition）, the upstream disturbance becomes weaker and thus its influences on the downstream flow are very limited.

Runner cone optimization to reduce vortex rope-induced pressure fluctuations in a Francis turbine

Pressure fluctuations induced by a vortex rope are the major causes of hydraulic turbine vibration in partial load operating conditions. Hence, an effective control strategy should be adopted to improve rotating characteristics of the vortex rope and reduce the corresponding pressure fluctuation. In this study, two new types of runner cones(i.e., abnormally shaped and long straight cones) were proposed to optimize the pressure distribution in the draft tube, and unsteady numerical simulations were performed to determine their mechanism of action. Numerical results were validated using flow observation and pressure fluctuation experiments. Detailed analyses were conducted to understand the effects of the helical vortex rope operating conditions. The results indicated that pressure fluctuations in the draft tube at partial load operation result primarily from low frequency fluctuations induced by the rotation of the helical vortex rope, whose amplitudes are related to the rotating radius of the helical vortex rope. Both runner cone types could effectively reduce the pressure-fluctuation amplitude. The long straight type could reduce the amplitude of low-frequency fluctuation induced by vortex rope to a maximum of 74.08% and the abnormalshape type to 38.31%. Thus, the effective optimization of the runner cone can potentially reduce pressure-fluctuation amplitudes.Our research findings were applied to a real hydraulic plant in China.

Master equation and runaway speed of the Francis turbine

The master equation of the Francis turbine is derived based on the combination of the angular momentum（Euler） and the energy laws. It relates the geometrical design of the impeller and the regulation settings（guide vane angle and rotational speed） to the discharge and the power output. The master equation, thus, enables the complete characteristics of a given Francis turbine to be easily computed. While applying the energy law, both the shock loss at the impeller inlet and the swirling loss at the impeller exit are taken into account. These are main losses which occur at both the partial load and the overloads and, thus, dominantly influence the characteristics of the Francis turbine. They also totally govern the discharge of the water through the impeller when the impeller is found in the standstill. The computations have been performed for the discharge, the hydraulic torque and the hydraulic efficiency. They were also compared with the available measurements on a model turbine. Excellent agreement has been achieved. The computations also enable the runaway speed of the Francis turbine and the related discharge to be determined as a function of the setting angle of the guide vanes.