Francis Turbine Runner Research Articles

Optimization of a Francis Turbine Runner by Means of Inverse Design and CFD Calculation

A Francis turbine runner was optimized by a combination of means of the 3D Inverse Design Method and Computational Fluid Dynamics (CFD). An experiment of the directly optimized conventional turbine confirms the validation of CFD calculation. A new meridional shape was designed by Design of Experiments with CFD and the database of meridional shape factors. Angular momentum at the runner inlet was corrected to cover the effects of the boundary layer from runner upstream domains such as stay vanes and guide vanes. Using the meridional shape and the corrected angular momentum and considering the secondary flow mechanism, blade loading distribution and stacking condition were optimized. It led to the decrease of secondary flow energy near the runner inlet and of the runner loss. The full-domain CFD calculation confirms that the total loss of the new turbine at the design point is 4[%] lower than that of the conventional one. This result shows the 3D Inverse Design Method is practical to control the secondary flow in the Francis turbine runners and optimize the shape.

Optimization of Variable Discharge Characteristics for Design of Francis Turbine Runner

In the design of Francis turbine runner, improvement of variable flow characteristics is one of the problems. Conventionally, performances at not only the design point but also non-design points were optimized using various optimization methods such as multi-objective genetic algorithm. However, since general Pareto ranking technique treats all objective function with the same priority, the solutions with high efficiency at non-design point but low efficiency at design point might be obtained. The highest efficiency point of such solutions would deviate from the design point, therefore, a technique to match those points is needed. In this study, we developed the Bayesian optimization system for Francis turbine runner design using computational fluid dynamics (CFD), Gaussian process regression (Kriging) model, and multi-objective genetic algorithm. To match the highest efficiency point and design point, non-swirling discharge of each solution was evaluated from CFD results, and a constraint was considered using the discharge predicted by Kriging model. Finally, it was confirmed that the solutions obtained by Bayesian optimization with the constraint of non-swirling discharge is superior to the one without the constraint.

Influence of structural parameters on the modal characteristics of a Francis runner

The modal characteristics are important issues of a Francis turbine runner. It is prone to cause excessive vibration even resonance of turbine if the natural frequency is close to the excitation frequency. Thus, in the runner design and optimization processes, not only hydraulic characteristics but also dynamic characteristics should be considered to ensure the safe and stable operation of the unit. The modal analysis of hydrofoil NACA0009 is calculated by means of coupled acoustic fluid–structure model to verify the feasibility of the method and the results show good agreement with the experimental results. Then the effect of gap and structure parameters are discussed. Results show that the effect of fluid in the crown gap and seal on natural frequency and added mass is small, but the effect of fluid in the band gap and seal is considerable. The mode shapes are similar under different structural parameters, but the natural frequency and added mass factor are different. The effect of root rounding radius is more obvious than that of blade thickness and band thickness. Besides, the effect mechanism of band thickness on modal characteristics is quite complex, the lower-order frequency decreases while the higher-order frequency increases with the increase of the band thickness. The results in this paper are helpful to avoid the typical resonance frequency such as rotor–stator interaction frequency in the design and optimization processes.

Numerical investigation of the added mass effect of submerged blade disk structures: From simplified models to Francis turbine runners

In daily operations, there are lots of blade disk structures operating in water, e.g., hydraulic turbines and pumps, whose dynamic behavior may be severely affected by the added mass effect. Their mode shape change problem from vacuum to water due to the added mass effect has been studied in this paper. The added mass effect of simplified blade disk structures submerged in still water has been studied numerically first in this paper. Acoustic fluid–structure interaction technology has been used to simulate the fluid and structure coupling effect. Through comparing the strain energy percentage of the disk part in water with those in air under different disk material densities, it showed that different parts of the submerged blade disk structures can suffer from different average added mass factors, which makes the modal shapes of some modes with strong blade disk interactions change a lot from vacuum to water, thus produces a large influence on the optimal design of submerged blade disk structures. Based on the conclusions of the simplified model, the situation of a Francis turbine runner model was investigated, and the results fit the conclusions on the simplified model very well.

A proposal for the dynamic strain interpolation on hydroelectric turbine runner

The large operation range of hydroelectric turbine, caused by the increasing changes in the electrical network usage, leads to higher dynamic stress fluctuation on runner. However, the experimental data cannot cover all the possible operating conditions. The missing data in some turbine operation zones generates a challenge for the recovery of the highest dynamic strain. This paper proposes a methodology for the interpolation of such strains between operating conditions by using the kriging method. The case study focuses on the interpolation of the part load rope which is an important component in the dynamic strain of a Francis turbine runner. Two interpolation approaches, inspired by spatio-temporal kriging and cokriging, are applied and compared. Finally, some suggestions are proposed to improve the recovery of operating conditions using interpolation process.

Multi-objective shape optimization of Francis runner using metamodel assisted genetic algorithm

Nowadays evolutionary optimization techniques become an integral part of the design process of hydraulic turbine runners. For optimization the shape of the runner is parameterized by a set of geometrical parameters. The objective functions of each runner geometry, being the efficiency and cavitation performance, are evaluated through CFD analysis of 3D flow-field. As usual, some kind of genetic algorithm is used for searching the Pareto front, due to its inherent possibility of parallel evaluation of different runner variants within one generation. This approach requires extensive CFD computations of hundreds and thousands of runner variants. In order to speed up the optimization process a metamodel (approximate, surrogate model) can be utilized. The metamodel provides an approximation of true dependency of the objective functions on the design parameters. The metamodel is built based on the known objective functions for some initial set of points randomly taken form the design space. Once built, it can be used to replace time consuming CFD computations during the optimization process. In the present paper a metamodel, based on Gaussian processes, is implemented and integrated into a multi-objective genetic algorithm. The obtained algorithm is applied for shape optimization of the Francis turbine runner. The number of the design parameters varied from 4 to 24. The objective functions are multi-point efficiency and cavitation characteristics. True values of the objective functions are evaluated using Reynolds averaged Navier-Stokes computations of the flow field in a reduced turbine domain, including wicket gate, runner and draft tube. These values are used to train the initial metamodel. In order to enhance predictive capabilities of the metamodel, it is retrained periodically during the optimization loop. The results of metamodel-assisted optimization runs are compared to that obtained without metamodel. It is shown that application of metamodel significantly reduces the number of actual CFD computations even for high number of design parameters and thus speeds up the overall optimization process.

Optimization procedure to design a Francis turbine runner using 2D Through-flow analysis

Due to increasing usage of Feed-in Tariff (FIT), which is a subsidy system to encourage expansion of renewable energy and to reduce costs associated with introduction of renewable energy, demand for hydraulic turbine designers has increased solely for the purpose of improving turbine performance. With these requirements, CFD simulation is a powerful tool for designers to improve the internal flow and pressure distribution in turbines. Traditionally, most designers use a trial-and-error process based on previous experience to design new turbines. Usually, achieving the goal is a lengthy and painstaking process. This paper proposes a novel method which combines both CFD and optimization methods to automatically optimize a Francis turbine. This procedure includes four components: a design program, a CFD solver, a scheduler, and an optimization algorithm. This paper describes an attempt to automatically optimize a Francis turbine runner by using ANSYS Vista TF as the 2D CFD solver based on through-flow theory, and ANSYS CFX 19.1 as the 3D CFD solver based on Finite Volume Method (FVM). The runner geometry is parameterized by Bezier curves in the design program. CFD analysis is performed to assess the efficiency of the runner, and also the output power is calculated by runner torque. These two parameters are used as the objective function of the optimization algorithm. This method is used to optimize the runner geometry, which consists of two parts: the meridional plane and profile camber lines. We confirmed that the new turbine, which was optimized by the above-mentioned method, has better efficiency than the existing one.

Limitations of Modern Diagnostic and Prognostic Systems for a Hydraulic Unit’s Health

Modern diagnostic systems for the hydraulic unit’s health play an important role in ensuring the reliability and safety of the hydroelectric power plant (HPP). However, they cannot provide timely detection of such dangerous operational defects as fatigue cracks. This article reflects two main reasons for this problem. The first one is a high level of the individuality of hydraulic units, which does not allow the effective use of statistical methods of information processing, including BIG DATA and MACHINE LEARNING technologies. The second is the fundamental impossibility to identify cracks in some key components of hydraulic units only on the basis of data analysis from a standard diagnostic system usually used at the HPP. Developed computational studies on the example of Francis turbines confirmed this. It is proposed to supplement the functionality of standard diagnostic systems with a prognostic block for an individual analytical forecast of the unit’s residual lifetime based on the calculated assessment of fatigue strength. This article presents the developed conceptual diagram and the demonstration version of the proposed analytical predictive system. The comparison of the standard vibration diagnostic system and the proposed solution as a tool for the early detection of cracks in a Francis turbine runner shows some advantages of the proposed approach.

Coherent Structures Decomposition of Flow Field in Francis Turbine Runner Under Different Working Conditions

Coherent Structures Decomposition of Flow Field in Francis Turbine Runner Under Different Working Conditions

Experimental and numerical study of a prototype Francis turbine startup

Nowadays, the dynamical energy market in Europe requires fast response times and advanced grid control. As a result, Francis turbine runners are subject to complex hydrodynamic forces based on low-load flow phenomena. However, transient events and in particular the turbine startup is considered as the most damaging operating condition. Therefore, experimental and numerical methods are combined to investigate the behavior of a prototype Francis turbine runner during startup. In the experimental part of the study dynamical stress is obtained by strain gauges and used to predict the runner lifetime. Additional to the conventional startup, a second scheme aiming for a higher life expectancy by reducing the opening limit is tested. The experimental part reveal high stress amplitudes during the fast opening process of the guide vanes. The reason therefore is a counter rotating draft tube vortex formation which is discovers by the use of numerical simulation. These 3 up to 4 small vortices are inducing unsteady pressure pulsations at approximately 36 Hz. With the application of the second startup schema, a reduction of the stress amplitudes of around 17% is archived. It is verified that the change of the startup schema can significantly impact the runner lifetime.

Solving the runner blade crack problem for a Francis hydro-turbine operating under condition-complexity

Runner blade crack is a problem that affects the operation security of hydro-turbines. In this study, penetrating cracks were found by inspection on the runner blade of a Francis turbine near hub and shroud on trailing-edge. To solve this problem, prototype test was conducted to find the conditions under strong hydraulic instabilities. The turbine vibration region was classified based on the test and found mainly at small guide vane opening angles or low-head high-load conditions. In these regions, vibration was strong and the numerical-predicted flow regime was disordered. Analyzed by fluid-solid interaction method, stress concentrations were found on the blade-hub and blade-shroud connections on trailing-edge. By excluding the influence of resonance, the runner blade crack problem was found as the combination of concentrating static stress, hydraulic excited pulsating stress and residual stress. Triangle-blocks, which were helpful for eliminating the concentrating static stress, were welded on the blades after cutting-off the old crack sites. Polishing and buffing were conducted for reducing potential residual stress. After a long-time re-operation, the improved runner was found without runner blade cracks. Prototype re-testing showed no impacts on the efficiency. This study provided a good solution for the Francis turbine runner blade crack problem under condition-complexity.

Design Calculation of 40 MW Francis Turbine Runner

Design Calculation of 40 MW Francis Turbine Runner

Added Mass Effects on a Francis Turbine Runner with Attached Blade Cavitation

To have a safe structural design, an analysis of the dynamic behavior of a Francis turbine runner with consideration of the added mass effects of surrounding water is necessary during design phase. Both in design and at off-design operations, large-scale forms of attached cavitation may appear on runner blades and can change the added mass effects of the surrounding fluid in relation to a single water domain. Consequently, a numerical investigation of the modal response of a Francis runner has been carried out by reproducing the presence of various sizes of leading edge cavitation (LEC) and trailing edge cavitation (TEC). The fluid–structure interaction problem has been solved by means of an acoustic-structural coupling method. The calculated added mass effects with cavitation have been compared with those corresponding to the pure water condition without cavitation. Firstly, a single blade has been investigated to evaluate the level of significance for the proposed cavity shapes and dimensions. Afterwards, based on the results obtained, the complete runner structure has been considered, factoring in similar cavity shapes and locations. The results prove that significant added mass effects are induced on the entire runner by the attached cavitation that increase the natural frequencies of the first modes. Moreover, the added mass effects increase with cavity size and amplitude of blade deformation below the cavity.

Parametric optimization to reduce erosion in a Francis turbine runner

More than a half of the overall power capacity in Ecuador uniquely depends on hydroelectric power, thanks to its geographical position and large water resources. Most of them use Francis turbines, which present detriment in their lifetime due to the presence of high hardness sediments in the water reservoirs located close to the Andean mountains. In order to mitigate such effect, a structured methodology, which identifies design space variables and defines parameters that governs the phenomenon is developed. The optimization is carried out through genetic algorithms formulated to determine optimal geometrical features and hydraulic parameters based on Euler meanline turbomachinery equation. The objective function for the optimization study at this preliminary stage was erosion factor, whilst the decision variables used were: outlet diameter, acceleration flow, degree of reaction and percentage of curvature deviation from a linear of the blade angle distribution. The results obtained showed that the erosion factor can be reduced by 49 % and that the relative flow velocity at the exit was a key optimization parameter to decrease the runner erosion. This great improvement at preliminary design has been compared with other similar studies, showing a good enough prediction of erosion and the capturing of the phenomena. Furthermore, the important contribution of the present methodology is the development of a simple and versatile tool to define the design space for erosion phenomena and in this way improve the lifetime of the blade turbine runner and hence decreasing maintenance costs.

Comprehensive Hydraulic Improvement and Parametric Analysis of a Francis Turbine Runner

Hydraulic turbines are usually required to operate in a wide range. The operation at off-design conditions not only reduces the unit efficiency, but also significantly deteriorates the dynamic stability of the turbines. In order to develop a turbine runner with good performances under multi operation conditions, a comprehensive hydraulic improvement has been done of a Francis turbine runner with a multipoint and multi-objective optimization design system. Compared with the initial runner, the runner generated from this method has a satisfactory improvement. In detail, unit efficiencies of the preferred runner are increased by 0.91%, 0.47% and 0.37%, respectively, under the rated head, a high head and the maximum head. The lowest pressure at blade surface is improved by 376.2 kPa under the rated head. CFD calculations are conducted to analyze the flow conditions inside of the preferred runner. In addition, runners with different main design inputs, namely blade lean, blade loading and blade meridional shape are furtherly investigated to reveal their relationship with runner’s internal flow and outer performances. In summary, this optimization system supplies satisfactory results and convincing recommendations to determine the design inputs for low-head Francis turbine runners.

Numerical and experimental investigation of the effect of baffles on flow instabilities in a Francis turbine draft tube under partial load conditions

An improved method for preventing vortex rope formation and alleviating the associated pressure fluctuations in turbine draft tubes is investigated using baffles in the draft tube to hinder the swirling flow emerging from a Francis turbine runner. A strong swirl produces flow instabilities and pressure fluctuations. Partial load operating conditions at the rated water head and three flow rates are taken into consideration. It is demonstrated using a computational fluid dynamics simulation that this method effectively eliminates the vortex rope, particularly when using four baffles. The amplitude of the pressure pulsation in the draft tube modified with four baffles was 0.42 times that in a traditional draft tube. The baffles were found to reduce the tangential velocity of the flow in the draft tube and consequently hinder the development of the fierce swirling flow. This type of decrease is more significant compared to the gradual decay due to viscous effects of the solid wall in a traditional draft tube. The conclusion was verified by the results of experiments conducted using a novel device. The measured increase in turbine efficiency exceeded 3% at the evaluated partial loading point, indicating improved economic performance of the turbine.

Investigation for Improvement of Francis Turbine Runner Performance Using Multi-Objective Genetic Algorithm

Investigation for Improvement of Francis Turbine Runner Performance Using Multi-Objective Genetic Algorithm

Experimental investigation on the effect off near walls on the eigen frequency of a low specific speed francis runner

The importance to correctly predict the natural frequency of a turbine runner have been demonstrated several times. It is now common practice to include the added mass effect of the surrounding water when calculating the natural frequencies. In this paper the added mass effect of water on a simplified low specific speed francis turbine runner is experimentally investigated. Three cases are investigated. 1: The runner hanging in air. 2: The runner hanging in a tank of water. 3: The runner installed into the turbine housing. The measurements reveal a frequency reduction of about 40% when the runner is hanging in water. Installing the runner into the turbine housing does not significantly change the natural frequency of the main blade modes. Modes which vibrate heavily on the outside of the runner are visible in the water tank but becomes dampened when installed into the turbine housing.

Numerical Study on the Dynamic Behavior of a Francis Turbine Runner Model with a Crack

Crack appearance in the blade is the most common type of fatigue damage in Francis turbines. However, it is sometimes difficult to detect cracks in time using the current monitoring system, even when they are very large. To better monitor cracks, it is imperative to research the effect of a crack on the dynamic behavior of a Francis turbine. In this paper, the dynamic behavior of a Francis turbine runner model with a crack has been researched numerically. The intact numerical model was first validated by the experimental data available. Then, a crack was created at the intersection line between one blade and the crown. The change in dynamic behavior with increasing crack length has been investigated. Crack-induced vibration localization theory has been used to explain the dynamic behavior changes due to the crack. Modal analysis showed that the adopted theory could basically explain the modal behavior change due to the crack. The FFT results of the modal shapes and the localization factors (LF) has been used to explain the forced response changes due to the crack. Based on the above analysis, the challenge of crack monitoring has been analyzed. This research provides some references for more advanced monitoring technologies.

Simplified hydrodynamic analysis on the general shape of the hill charts of Francis turbines using shroud-streamline modeling

The paper presents a simplified one-dimensional calculation of the efficiency hill-chart for Francis turbines, based on the velocity triangles at the inlet and outlet of the runner’s blade. Calculation is done for one streamline, namely the shroud streamline in the meridional section, where an efficiency model is established and iteratively approximated in order to satisfy the Euler equation for turbomachines at a wide operating range around the best efficiency point (BEP). Using the presented method, hill charts are calculated for one splitter-bladed Francis turbine runner and one Reversible Pump-Turbine (RPT) runner operated in the turbine mode. Both turbines have similar and relatively low specific speeds of nsQ = 23.3 and nsQ = 27, equal inlet and outlet diameters and are designed to fit in the same turbine rig for laboratory measurements (i.e. spiral casing and draft tube are the same). Calculated hill charts are compared against performance data obtained experimentally from model tests according to IEC standards for both turbines. Good agreement between theoretical and experimental results is observed when comparing the shapes of the efficiency contours in the hill-charts. The simplified analysis identifies the design parameters that defines the general shape and inclination of the turbine’s hill charts and, with some additional improvements in the loss models used, it can be used for quick assessment of the performance at off-design conditions during the design process of hydraulic turbines.