Francis Hydro Turbine Research Articles

Real-Time Hybrid Modeling of Francis Hydroturbine Dynamics via a Neural Controlled Differential Equation Approach

Real-Time Hybrid Modeling of Francis Hydroturbine Dynamics via a Neural Controlled Differential Equation Approach

Dynamic Simulation of Starting and Emergency Conditions of a Hydraulic Unit Based on a Francis Turbine

The Francis hydro-turbine is a typical nonlinear system with coupled hydraulic, mechanical, and electrical subsystems. It is difficult to understand the reasons for its operational failures, since the main cause of failures is due to the complex interaction of the three subsystems. This paper presents an improved dynamic model of the Francis hydro-turbine. This study involves the development of a nonlinear dynamic model of a hydraulic unit, given start-up and emergency processes, and the consideration of the effect of water hammer during transients. To accomplish the objectives set, existing models used to model hydroelectric units are analyzed and a mathematical model is proposed, which takes into account the dynamics during abrupt changes in the conditions. Based on these mathematical models, a computer model was developed, and numerical simulation was carried out with an assessment of the results obtained. The mathematical model built was verified on an experimental model. As a result, a model of a hydraulic unit was produced, which factors in the main hydraulic processes in the hydro-turbine.

Suppression of flow instability in the Francis hydro turbine draft tube by J-groove shape optimization at a partial flow rate

Suppression of flow instability in the Francis hydro turbine draft tube by J-groove shape optimization at a partial flow rate

A numerical study on the performance characteristics of low head Francis turbine with different turbulence models

A Francis hydro turbine can be used in large as well as small hydro power plant. Due to complex flow phenomenon in turbine, deriving a hydrodynamic behaviour of flow through experimentation is a tedious job. These phenomena such as flow separation around turbine blade, pressure drop in runner and draft tube, etc. can be captured through a numerical study. A numerical approach needs turbulence modelling to capture fluctuating component of flow variables. In view of that, a comprehensive study has been carried out to find the sensitiveness of various turbulence modelling on the stability of numerical solution. In present study, three different turbulence models such as Standard k-ε, Standard k-ω and SST model have been considered. To carried out this study, three different loading conditions have been chosen i.e. part-load, BEP and over-load condition. This study has been carried out by using ANSYS CFX (18.1) CFD solver.It has been observed that at part-load condition, Standard k-ε model performed better as compared to other model but at other loading conditions SST model delivered accurate results. Also, turbulent nature of flow at the outlet of runner is well captured by SST model.

Nonlinear modal interaction analysis and vibration characteristics of a francis hydro-turbine generator unit

The Francis hydro-turbine generator unit (FHTGU) is a typical nonlinear system with the coupling hydraulic, mechanical and electric subsystems. It is a challenge to understand the reasons for its operational failures because the major reason for failures involves complex interactions of the three subsystems. Subsystems’ model interaction with the method of normal forms has been well developed and investigated, overcoming the linear methods used in the FHTGU’s stability analysis. However, these methods have not to quantify higher-order terms in a mathematically accurate type to capture dynamic modal interactions between subsystems. Due to the accelerating expansion of hydropower stations, stability of FHTGU shows singular nonlinear oscillations and new methods have to be upgraded to cope with this new situation. In this study, the nonlinear modal method is introduced to analyze the dynamic modal interactions between subsystems, and results given by the different methods are compared to verify the method’s feasibility. The effect of the second order modes is quantified to investigate its effect on the dynamic characteristics of FHTGU, and the vibration characteristics affected by the wind generation system are also investigated. The result shows that the intensity of modes can be effectively reduced to satisfy the stable requirements. All of these results provide a theoretical guidance for the stable operation of FHTGUs.

Suppression of flow instabilities in the stay vane passage of the Francis hydro turbine model by design optimization

The oscillating flow is a problem occurring in the stay vane passage of hydro turbines. The improper shape of the stay vane causes wake formation and sheds large eddies in the trailing edge of the stay vane. The wake at the trailing edge of the stay vane produces pressure fluctuation in the stay vane passage, which leads to noise and vibration during the turbine operation. Therefore, the improper shape of the stay vane may cause flow oscillation in the stay vane passage. Thus, a proper shape design of the stay vane considering the oscillating flow is necessary to mitigate the flow instability. Consequently, experiment and CFD analyses showed that the initial stay vane (ISV) shape causes recirculation and pressure fluctuation. An optimum design methodology is adopted to improve the flow behavior around the stay vane. Optimization of the stay vane is also conducted by using two objective functions (turbine efficiency and flow uniformity) and 12 design variables. The optimal stay vane (OSV) shape is attained by a multi-objective genetic algorithm. Finally, the flow behavior in the stay vane passage with ISV and OSV is compared by experiment and CFD analyses. Thus, the flow instabilities are mitigated with OSV. The installation of OSV improved the flow angle distribution, secondary flow, and pressure fluctuation in the Francis hydro turbine.

Air Injection as a Solution to the Problem for Reducing High-Frequency Acoustic Noise in Some Operating Modes of Francis Hydro Turbines

During operation of Francis hydro turbines at the regimes of 70–95 % of Nrated, high-frequency acoustic phenomena (noise) were recorded. In order to study and identify the causes of these phenomena, special field tests were conducted. The main objectives of the tests were: determination of the main frequencies of acoustic phenomena, comparison with natural frequencies of the turbine water passages elements and the search for solutions to reduce acoustic phenomena. During the tests, the natural frequencies of the elements of turbine water path were investigated. Several methods of air injection to the turbine water path were also tested. The most effective way (including by the amount of air) to reduce acoustic phenomena was the air injection from industrial air piping into the spiral case and into the area of guide vanes.

Takagi–Sugeno fuzzy sampled‐data model‐based less conservative stability criterion for a Francis hydropower unit's governing system

In this study, the stability analysis and controller design of a hydropower unit's governing system (HUGS) were studied based on a Takagi–Sugeno (T–S) fuzzy model and constant sampled-data control. First, according to the T–S fuzzy theory, the non-linear Francis hydro-turbine governing system under rigid water hammer is linearised and then the approximate linear system was obtained. Second, a fuzzy sampled-data controller was designed in the case of periodic sampling, and the closed-loop sampling system was discretised. After constructing the Lyapunov function and using the forward difference method, the stabilisation condition was given with less conservatism in a symmetrical linear matrix inequality form. Finally, the numerical simulation results showed that under four different sampling periods, the HUGS can quickly achieve stability and that it has different stability performance. In addition, the superiority of the controller was verified in comparison with traditional proportional–integral–derivative control and fuzzy control techniques.

Feature Selection for Monitoring Erosive Cavitation on a Hydroturbine

This paper presents a method for comparing and evaluating cavitation detection features - the first step towards estimating remaining useful life (RUL) of hydroturbine runners that areimpacted by erosive cavitation. The method can be used to quickly compare features created from cavitation survey data collected on any type of hydroturbine, sensor type, sensor location, and cavitation sensitivity parameter (CSP). Although manual evaluation and knowledge of hydroturbine cavitation is still required for our feature selection method, the use of principal component analysis greatly reduces the number of plots that require evaluation. We present a case study based on a cavitation survey data collected on a Francis hydroturbine located at a hydroelectric plant and demonstrate the selection of the most advantageous sensor type, sensor location, and CSP to use on this hydroturbine for long-term monitoring of erosive cavitation. Our method provides hydroturbine operators and researchers with a clear and effective means to determine preferred sensors, sensor placements, and CSPs while also laying the groundwork for determining RUL in the future.

A CFD-Based Shape Design Optimization Process of Fixed Flow Passages in a Francis Hydro Turbine

In recent times, optimization began to be popular in the turbomachinery field. The development of computational fluid dynamics (CFD) analysis and optimization technology provides the opportunity to maximize the performance of hydro turbines. The optimization techniques are focused mainly on the rotating components (runner and guide vane) of the hydro turbines. Meanwhile, fixed flow passages (stay vane, casing, and draft tube) are essential parts for the proper flow uniformity in the hydro turbines. The suppression of flow instabilities in the fixed flow passages is an inevitable process to ensure the power plant safety by the reduction of vortex-induced vibration and pressure pulsation in the hydro turbines. In this study, a CFD-based shape design optimization process is proposed with response surface methodology (RSM) to improve the flow uniformity in the fixed flow passages of a Francis hydro turbine model. The internal flow behaviors were compared between the initial and optimal shapes of the stay vane, casing, and the draft tube with J-Groove. The optimal shape design process for the fixed flow passages proved its remarkable effects on the improvement of flow uniformity in the Francis hydro turbine.

Improvement of flow behavior in the spiral casing of Francis hydro turbine model by shape optimization

A spiral casing is an important component of Francis hydro turbine for the even distribution of kinetic energy along the stay and guide vanes. The fluid flow around the runner is dependent on the flow condition of a spiral casing. The shape of the casing plays an important role in proper flow distribution. In this study, the optimization of the shape of a spiral casing is based on a steady-state flow analysis. Numerical optimization is performed using response surface methodology (RSM) and multiobjective genetic algorithm (MOGA). The flow uniformity and head loss in the spiral casing are selected as objectives for the optimal design of the spiral casing. The optimal design is selected from the solution acquired by RSM and MOGA. Moreover, the flow characteristics in the initial and optimal designs of the spiral casing are compared. The flow conditions in the optimal design improve significantly with the optimal design of the spiral casing. Thus, the inlet conditions for the stay vane are improved with the optimal design of the spiral casing.

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.

Transient phenomena in the draft tube model of a Francis hydro-turbine

This article is devoted to the study of pressure pulsations behind the runner of a hydro turbine model caused by the precessing vortex core (PVC). Pressure pulsations are investigated under conditions of stationary load and transient modes of the hydro-turbine operation. Studies were performed in model conditions on the aerodynamic setup. The map of pressure pulsations was built for stationary modes using acoustic sensors and served to find rotational speeds of the swirler and flow rates at which the PVC occurs. On the basis of the data presented by parametric dependences, the initial and final parameters of the transition process were chosen. In the article, a sudden (fast) transition from part-load regime to the best efficiency point and back was considered. The characteristic times for the formation of PVC and the establishment of the flow regime when changing the controlling parameters of the installation have been determined using a continuous wavelet transform.

Design of a Robust Controller by LQG/LTR Formalism for Francis hydro Turbine Driving a Synchronous Generator

This paper presents the design and application of a robust controller by Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery (LQG \LTR) at the same time to carefully attain performance and robustness objectives. To improve Stability, the robust controller has been shown to provide good performance in normal operations conditions. Objectives cannot be suitable unless the controller can perpetuate such quality in the presence of plant uncertainties or any working conditions in the hydroelectric power plants. The approach is based to synthesizing a robust controller minimizing a quadratic criterion (controller LQG) while using the Loop Transfer Recovery (LTR), to restore robustness properties of the Estimator. In this study, we applied this robust control law on the model of a Francis hydro turbine. Computer simulations are carried out to establish a n d compare the performance and robustness of using the Infinite horizon control ( H ), internal model control (IMC), Proportional Integral Derived (PID) and LQG/LTR controllers.

Stabilization of Arbitrary Switched Nonlinear Fractional Order Dynamical Systems: Application to Francis Hydro-Turbine Governing System

This paper is a theoretical and practical study on the stabilization of fractional order Lipschitz nonlinear systems under arbitrary switching. The investigated system is a generalization of both switched and fractional order dynamical systems. Firstly, a switched frequency distributed model is introduced as an equivalent for the system. Subsequently, a sufficient condition is obtained for the stabilizability of the system based on the Lyapunov approach. Finally, the results are extended to synthesis mode-dependent state feedback controller for the system. All the results are expressed in terms of coupled linear matrix inequalities, which are solvable by optimization tools and directly reducible to the conditions of the integer order nonlinear switching systems as well as the conventional non-switched nonlinear fractional order systems. The proposed method has various practical implications. As an example, it is utilized to control Francis hydro-turbine governing system. This system is represented as a switching structure and supposed to supply a load suffering abrupt changes driven by an arbitrary switching mechanism. The simulation results support the usefulness of the method.

Viscous stress tensor and stability of laminar contravortical flows

Introduction: coaxial layers in contravortical flows rotate in the opposite directions. This determines their complicated spatial structure. The relevance of the subject is in the uniquely effective mixing of the moving medium. This property has a great potential of application from microbiology and missile building for obtaining highly dispersed mixtures to heat engineering for increasing the intensity of heat transfer. However, contravortical flows have a high degree of hydrodynamic instability. This hinders effective development of these technologies. Contravortical flows are observed behind Francis hydroturbines, whose derated operation causes modes with a significant increase of hydraulic unit vibrations up to destruction of the units. The purpose of the study is to identify physical laws of the contravortical flow hydrodynamics, common for both laminar and turbulent fluid flow modes.
 Materials and methods: theoretical analysis of the viscous stress tensor and local stability zones of contravortical laminar flows.
 Results: the article provides a mathematical description of the tensor of viscous tangential (τij) and normal (σii) stresses as well as local stability zones of the flow according to Rayleigh (Ra) and Richardson (Ri) criteria. The graphs of the radial-axial distributions of the viscous stress components are given, local stability zones are shown and the point of “vortex breakdown” is indicated. The solutions are obtained in the form of Fourier – Bessel series. The hydrodynamic structure of the flow is analysed.
 Conclusions: it is established that the most significant viscous stresses are observed at the beginning of the interaction zone of contrarotating layers. It is established that the areas with the most unstable flow are localized in the flow vortex core. Three zones can be distinguished in the vortex core: a zone of weak instability with local Richardson numbers to Ri = –1, passing into a zone of flow destabilization with high negative values of Richardson numbers Ri = –10 to –100, in turn, transforming into a zone with rapidly increasing instability up to Ri = –1000. This is a zone of loss of flow stability, culminating in the “ortex breakdown”.

Correlation of the Sediment Properties and Erosion in Francis Hydro Turbine Runner

Sediment erosion is the main problem for the hydropower situated in South Asia and South America. Due to sediment erosion, hydropower in those areas cannot operate in their full potential. Sediment erosion is a significant problem in turbomachinery and associated with degradation of turbine performance. The sediment erosion removes the turbine material from its surface. It can cause fracture of the turbine, which leads to an economic loss. In this paper, the sediment properties and its influence on erosion have discussed. Sediment properties like shape, size, and concentration have a direct influence on erosion. The numerical analysis was conducted to visualize the erosion in Francis hydro turbine. The most vulnerable area for the sediment erosion in Francis hydro turbine has predicted. The precise prediction of the sediment erosion in the turbine is the difficult task due to the synergetic effect of sediment parameters (shape, size, concentration, hardness, velocity). The accurate and precise indication of the sediment erosion required both experimental and computational analysis. In this study, solid-fluid computational analysis has done to identify the susceptible area on runner blade and influence of sediment parameters on erosion.

프란시스 수차 모델의 블레이드 내 와류 특성에 대한 수치해석적 분석

In this study, a numerical analysis of the inter-blade vortex characteristics of a Francis hydro turbine model was performed with various flow rate conditions in the operating range. The model turbine demonstrated notably different internal flow characteristics for different operating conditions. Particularly, an inter-blade vortex between the runner blade passages was observed at lower flow rate conditions. An inter-blade vortex can cause reduction in performance, and vibration and instability in the operation of a turbine system. Therefore, understanding inter-blade vortex characteristics is important for the safe and stable operation of turbines. To investigate internal flow and unsteady pressure characteristics, three-dimensional steady and unsteady Reynolds-averaged Navier-Stokes calculations using a shear stress transport turbulence model were performed with two-phase flow analysis. Inter-blade vortices were captured at the leading and trailing edges of the near runner hub between blade passages. This vortex region exhibited flow separation and lower velocity and contributed to decreased hydraulic performance and higher unsteady pressure characteristics.

Numerical studies on sediment erosion due to sediment characteristics in Francis hydro turbine

Sediment erosion is the wear phenomenon from the hard abrasive particle found in the rivers. Sediment erosion is an inevitable process in the hydropower. It deteriorates the turbine shape and structure and increasing the maintenance expenses. There are various methods to improve the runner to operate against the sediment erosion. Firstly, the turbine material can be modified to the harder material but it will be costly and difficult for the manufacturing. Secondly, regular maintenance of the turbine needs to be done but it is the tedious task and hinder the power generation from the hydropower. Thirdly, the critical area of the runner blade surface which is vulnerable to sediment erosion need to identify and modification of the turbine shape according to it by altering the design parameter of the blade. The modification such as a change in thickness, blade angle and coating is possible for minimizing the effect of sediment erosion. The determination of the vulnerable area in the runner for the sediment erosion is a difficult task considering the many parameters included in sediment erosion phenomenon. The parameter such as sediment size, sediment shape, sediment concentration, sediment velocity, sediment hardness, impact angle and operating condition of hydropower. The precise prediction of the sediment erosion in the turbine is the difficult task due to the synergetic effect of parameters. The accurate and precise indication of the sediment erosion required both experimental and computational analysis. After identification of the susceptible area of sediment erosion, modification and optimization will be performed to reduce the effect of the sediment erosion without falling in the performance of the turbine.

Influence of guide vane clearance on internal flow of medium-specific speed Francis turbine

In Francis hydro turbines, a small clearance between the guide vane blade and the facing plate is crucial in pivoting the guide vane blade and controlling the flow rate of the turbine. This clearance-to-blade height ratio is inversely proportional to the scale of the hydro turbine. Smaller hydro turbines have higher clearance-to-blade height ratio than larger ones. Most of the time, this clearance is not included in the simulation model for it can cause inconsistencies between the computation and model turbine. This paper is focused on the various guide vane clearance and its influences on the flow. Firstly, steady numerical calculation of the turbine model (casing, stay vanes, guide vanes and draft) with and without guide vane reference clearance was carried out using the commercial code ANSYS CFX. Experiments were conducted on model turbine of specific speed 180 [m-kW] with guide vane reference clearance. The inter-blade pressure near the leading edge (LE), mid-chord and the trailing edge (TE) of the guide vane were obtained using the pressure sensor located along the circumference of the turbine casing. The result shows a good agreement between numerical computation and experiment. Furthermore, guide vane models with different clearance heights were simulated and the impact on runner inlet energy loss was investigated. In conclusion, it can be clarified that the roll-up flow from the guide vane clearance interacted with the main flow upstream of the runner which then caused loss to the turbine performance.