Francis Runner Research Articles

Hydro-dynamic damping theory in flowing water

Fluid-structure interaction (FSI) has a major impact on the dynamic response of the structural components of hydroelectric turbines. On mid-head to high-head Francis runners, the rotor-stator interaction (RSI) phenomenon always has to be considered carefully during the design phase to avoid operational issues later on. The RSI dynamic response amplitudes are driven by three main factors: (1) pressure forcing amplitudes, (2) excitation frequencies in relation to natural frequencies and (3) damping. The prediction of the two first factors has been largely documented in the literature. However, the prediction of fluid damping has received less attention in spite of being critical when the runner is close to resonance. Experimental damping measurements in flowing water on hydrofoils were presented previously. Those results showed that the hydro-dynamic damping increased linearly with the flow. This paper presents development and validation of a mathematical model, based on momentum exchange, to predict damping due to fluid structure interaction in flowing water. The model is implemented as an analytical procedure for simple structures, such as cantilever beams, but is also implemented in more general ways using three different approaches for more complex structures such as runner blades: a finite element procedure, a CFD modal work based approach and a CFD 1DOF approach. The mathematical model and all three implementation approaches are shown to agree well with experimental results.

Dynamic load on a Francis turbine runner from simulations based on measurements

The frequency of the Nordic power grid has become more volatile during recent years. This gives rise to two effects in synchronous machines. Firstly, as grid frequency changes the rotational speed of synchronous machines must change likewise. Secondly, the Nordic grid uses speed droop operation extensively as the primary governing; hence the power produced is a function of the grid frequency. These two coupled effects will lead to the runner and axle on synchronous machines having to cope with a varying level of torque. Even if the unit is supposedly operating at steady state via a fixed set point for the production, the influence of the varying grid frequency is that the torque in not steady at all. Recent years' new high head Francis runners in Norway have shown a tendency towards experiencing fatigue to a greater extent than what seem to be the case for new runners decades ago. Leading to this paper, measurements have been made of the rotational speed; generator power; main servo motor position and grid frequency at a Francis turbine unit. Based on these measurements simulations that include the hydraulic domain have then been performed. From these simulation results a property is constructed which is intended as a qualitative measure of the material stresses induced in the rotating masses of the unit, and is representative of the dynamical loads on the material of the rotating masses. The work is a part of a longer term goal, namely identifying the stress oscillations in a Francis turbine runner operating at speed of rotation oscillating because of grid frequency variations.

Multi-objective shape optimization of runner blade for Kaplan turbine

Automatic runner shape optimization based on extensive CFD analysis proved to be a useful design tool in hydraulic turbomachinery. Previously the authors developed an efficient method for Francis runner optimization. It was successfully applied to the design of several runners with different specific speeds. In present work this method is extended to the task of a Kaplan runner optimization. Despite of relatively simpler blade shape, Kaplan turbines have several features, complicating the optimization problem. First, Kaplan turbines normally operate in a wide range of discharges, thus CFD analysis of each variant of the runner should be carried out for several operation points. Next, due to a high specific speed, draft tube losses have a great impact on the overall turbine efficiency, and thus should be accurately evaluated. Then, the flow in blade tip and hub clearances significantly affects the velocity profile behind the runner and draft tube behavior. All these features are accounted in the present optimization technique. Parameterization of runner blade surface using 24 geometrical parameters is described in details. For each variant of runner geometry steady state three-dimensional turbulent flow computations are carried out in the domain, including wicket gate, runner, draft tube, blade tip and hub clearances. The objectives are maximization of efficiency in best efficiency and high discharge operation points, with simultaneous minimization of cavitation area on the suction side of the blade. Multiobjective genetic algorithm is used for the solution of optimization problem, requiring the analysis of several thousands of runner variants. The method is applied to optimization of runner shape for several Kaplan turbines with different heads.

Major historical developments in the design of water wheels and Francis hydroturbines

The first record of water wheels dates back to ancient Greece. Over the next several centuries the technology spread all over the world. The process of arriving at the design of the modern Francis runner lasted from 1848 to approximately 1920. Though the modern Francis runner has little resemblance to the original turbines designed by James B. Francis in 1848, it became know as the Francis turbine around 1920, in honor of his many contributions to hydraulic engineering analysis and design. The modern Francis turbine is the most widely used turbine design today, particularly for medium head and large flow rate situations, and can achieve over 95% efficiency.

Development of rotating disc apparatus for test of sediment-induced erosion in Francis runner blades

Sediment erosion in hydraulic turbines has been a major challenge in development of hydropower projects in Nepal. The hard abrasive material present in the river water of this region cause rapid erosion of turbine components and affect the performance of turbines, which in turn decreases the efficiency, reliability and operating life of such projects. There is a need of a new design methodology to develop turbines to resist erosion in high sediment conditions. The first step towards such development would be to investigate different design options in laboratory, which needs a standard methodology to carry out sediment erosion test in controlled environment. This study is focused on design and development of a laboratory test setup suitable for carrying out sediment erosion test in Francis runner blades. A test rig called rotating disc apparatus has been developed and installed in Turbine Testing Laboratory, Kathmandu University, Nepal, which uses Francis runner blades as test specimens. The test carried out in this setup has shown that the Francis turbines designed with traditional design methodology is highly prone to loss of material due to sediment erosion.

On the Fatigue Reliability of Hydroelectric Francis Runners

The reliability assessment of large rotating structures like hydroelectric Francis runners is often limited by our capacity to define a proper limit state combined with a relevant degradation model. In this paper, we propose that the proper limit state for fatigue reliability of such structures is the onset of high cycle fatigue (HCF). Based on this premise, a prior interval for our limit state based on available literature is presented. The prior assumptions are believed to be the first step toward validation of the applicability and suitability of the proposed model. The paper includes an overview of the theoretical background for reliability assessment of Francis turbine runners, the methodology used, and the results obtained from the information gathered from the available literature.

Evaluation of RSI-induced stresses in Francis runners

Modern design of hydraulic turbines aims to achieve very high levels of efficiency and structural integrity in the environment of highly variable loading conditions. To combine those requirements, a profound knowledge of static and dynamic loads acting on hydraulic components is necessary. Dynamic loadings of Francis runners strongly depend on head range and required operating conditions. For higher head (low specific speed) Francis runners, the main dynamic loading is caused by Rotor-Stator Interaction (RSI). The knowledge of dynamic loads and stresses in Francis runners is often derived from strain gauge measurements and/or simulation of flow interacting with structural components. Reliable simulations of Fluid-Structure Interaction (FSI) are necessary to predict the dynamic behavior, especially in terms of hydrodynamic mass and damping properties. This contribution describes the equipment and procedure of strain gauge measurements in Francis prototype runners, including the challenges to overcome during such tests. It provides an overview of strain gauge test results for Francis runners in different head ranges and describes the characteristic differences depending on specific speed. Measurement data is compared with state of the art simulations of Francis runner dynamics to predict dynamic stresses caused by RSI. The contribution underlines the fact that a calibrated analysis procedure is the key to optimize the design of Francis runners.

Optimizing runner blade profile of Francis turbine to minimize sediment erosion

Hard sediment particles as quartz are present in high amount in the rivers across Asian and Andes mountain ranges. This cause the run-off-river hydropower plants in these regions to suffer from erosion wear. The hydro turbine components erode severely during the monsoon periods. Due to high relative velocity the turbine runners are more vulnerable. Loss of turbine efficiency and high cost of repair and maintenance are the major consequences of the erosion. Several attempts including surface coatings to control the sediment erosion in Francis runners have not shown satisfactory results. One of the emerging solutions is to reduce the relative velocity inside the runner by improving the hydraulic design. This includes optimization of the runner blade profile to reduce sediment erosion, while avoiding cavitation and still maintaining the highest possible efficiency. This study has been conducted to identify the alternative blade profiles of high head Francis runners and estimate the effects of sediment erosion on each new profile. A new design program named as "Khoj" has been developed to facilitate this study. The program can generate the profiles of Francis runner based on the traditional equations. It is also capable to export the designs for CFD and FEM analysis. Erosion factor has been defined as a means to compare the relative change in sediment erosion due to the variation of the runner design. A reference turbine has been established and alternative blade profiles have been designed. CFD analysis has been conducted to evaluate the performance of the alternative designs relative to the erosive conditions of the reference turbine. It has been observed that the shape of runner blade has a significant effect on velocity distribution and hence on the sediment erosion of the runner. Results of CFD analysis validates prediction from the design program that the blade profile with higher blade loading at outlet can reduce the sediment erosion in runner up to 33%. It was also observed that this condition improves the runner efficiency without any change in the runner main dimensions. Results of this study can be useful to design Francis turbines operating in sediment conditions.

Influence of the rotor-stator interaction on the dynamic stresses of Francis runners

Thanks to advances in computing capabilities and Computational Fluid Dynamics (CFD) techniques, it is now possible to calculate realistic unsteady pressure fields in Francis turbines. This paper will explain methods to calculate the structural loads and the dynamic behaviour in order to optimize the turbine design and maximize its reliability and lifetime. Depending on the operating conditions of a Francis turbine, different hydraulic phenomena may impact the mechanical behaviour of the structure. According to their nature, these highly variable phenomena should be treated differently and specifically in order to estimate the potential risks arising on submerged structures, in particular the runner. The operating condition studied thereafter is the point at maximum power with the maximum head. Under this condition, the runner is excited by only one dynamic phenomenon named the Rotor-Stator Interaction (RSI). The origin of the phenomenon is located on the radial gap of the turbine and is the source of pressure fluctuations. A fluid-structure analysis is performed to observe the influence of that dynamic pressure field on the runner behaviour. The first part of the paper deals with the unsteady fluid computation. The RSI phenomenon is totally unsteady so the fluid simulation must take into account the entire machine and its rotation movement, in order to obtain a dynamic pressure field. In the second part of the paper, a method suitable for the RSI study is developed. It is known that the fluctuating pressure in this gap can be described as a sum of spatial components. By evaluating these components in the CFD results and on the scale model, it is possible to assess the relevance of the numerical results on the whole runner. After this step, the numerical pressure field can be used as the dynamic load of the structure. The final part of the paper presentsthe mechanical finite element calculations. A modal analysis of the runner in water and a harmonic analysis of its dynamic behaviour using the CFD results are carried out. These calculations will show that the RSI on the medium head Francis runner does not create damage on the runner even if the natural frequencies are closed to the wicket gates passing frequency. The numerical results are reinforced by experimental observations done on runner prototypes showing that the wicket gates passing frequency does not have significant influence on low and medium head Francis runner behaviour.

Hydraulic design of a low-specific speed Francis runner for a hydraulic cooling tower

The air blower in a cooling tower is normally driven by an electromotor, and the electric energy consumed by the electromotor is tremendous. The remaining energy at the outlet of the cooling cycle is considerable. This energy can be utilized to drive a hydraulic turbine and consequently to rotate the air blower. The purpose of this project is to recycle energy, lower energy consumption and reduce pollutant discharge. Firstly, a two-order polynomial is proposed to describe the blade setting angle distribution law along the meridional streamline in the streamline equation. The runner is designed by the point-to-point integration method with a specific blade setting angle distribution. Three different ultra-low-specificspeed Francis runners with different wrap angles are obtained in this method. Secondly, based on CFD numerical simulations, the effects of blade setting angle distribution on pressure coefficient distribution and relative efficiency have been analyzed. Finally, blade angles of inlet and outlet and control coefficients of blade setting angle distribution law are optimal variables, efficiency and minimum pressure are objective functions, adopting NSGA-II algorithm, a multi-objective optimization for ultra-low-specific speed Francis runner is carried out. The obtained results show that the optimal runner has higher efficiency and better cavitation performance.

Investigation of free discharge through the hydro units of high head Francis turbine

Free discharge through the units is applied in the course of construction of hydro power plant or in case of excessive water inflow during floods or emergency situation. Free discharges throw the hydro units at 80 m head and more are unknown. Possibility of high velocity swirling flow discharged through the whole hydro unit consisting of penstock, turbine (with Francis runner and distributor or without them) and draft tube is being analyzed in the present paper. Investigation method is based on mathematical simulation of unsteady flow through the hydro unit under the following conditions: with the free running or locked runner and with removed runner. Physical researches of the swirling flow behavior in the model bent penstocks and model turbine water passages have been performed. Based on the results of calculations and model tests the following extensive data have been obtained: pressure fluctuation in the whole hydro unit, fluctuation of hydrodynamic forces acting on guide vanes, torque fluctuation on the runner and discharge fluctuation. Thus, based on this data preferable designs of free discharge are proposed.

Efficient runner safety assessment during early design phase and root cause analysis

Fatigue related problems in Francis turbines, especially high head Francis turbines, have been published several times in the last years. During operation the runner is exposed to various steady and unsteady hydraulic loads. Therefore the analysis of forced response of the runner structure requires a combined approach of fluid dynamics and structural dynamics. Due to the high complexity of the phenomena and due to the limitation of computer power, the numerical prediction was in the past too expensive and not feasible for the use as standard design tool. However, due to continuous improvement of the knowledge and the simulation tools such complex analysis has become part of the design procedure in ANDRITZ HYDRO. This article describes the application of most advanced analysis techniques in runner safety check (RSC), including steady state CFD analysis, transient CFD analysis considering rotor stator interaction (RSI), static FE analysis and modal analysis in water considering the added mass effect, in the early design phase. This procedure allows a very efficient interaction between the hydraulic designer and the mechanical designer during the design phase, such that a risk of failure can be detected and avoided in an early design stage.The RSC procedure can also be applied to a root cause analysis (RCA) both to find out the cause of failure and to quickly define a technical solution to meet the safety criteria. An efficient application to a RCA of cracks in a Francis runner is quoted in this article as an example. The results of the RCA are presented together with an efficient and inexpensive solution whose effectiveness could be proven again by applying the described RSC technics. It is shown that, with the RSC procedure developed and applied as standard procedure in ANDRITZ HYDRO such a failure is excluded in an early design phase. Moreover, the RSC procedure is compatible with different commercial and open source codes and can be easily adapted to apply for other types of turbines, such as pump turbines and Pelton runners.

A discussion on turbine design for safe operation

The paper gives a brief description of the hydraulic design of Francis and Pelton runners. The dynamic behaviour at part load has been a major problem for low head and medium head Francis turbines. The main reason for this has been inter blade separation and unstable swirl flow in the draft tube. A description is given on the hydraulic design of X-BLADE runners to obtain stable operation on the whole range of operation by reducing the cross flow.A classical theoretical analysis is also given on the dynamic hydraulic load on Pelton buckets. Several CFD analyses of this non stationary flow have been presented during the last decade, but the velocity distribution in the jets have not been correct. Experimental research work is presented on the complexity of this problem.

Hydrodynamics automatic optimization of runner blades for reaction hydraulic turbines

The aim of this paper is to optimize the hydrodynamics of the runner blades of hydraulic turbines. The runner presented is an axial Kaplan one, but the methodology is common also to Francis runners. The whole methodology is implemented in the in-house software QTurbo3D. The effect of the runner blades geometry modification upon its hydrodynamics is shown both from energetic and cavitation points of view.

The role of high cycle fatigue (HCF) onset in Francis runner reliability

High Cycle Fatigue (HCF) plays an important role in Francis runner reliability. This paper presents a model in which reliability is defined as the probability of not exceeding a threshold above which HCF contributes to crack propagation. In the context of combined Low Cycle Fatigue (LCF) and HCF loading, the Kitagawa diagram is used as the limit state threshold for reliability. The reliability problem is solved using First-Order Reliability Methods (FORM). A study case is proposed using in situ measured strains and operational data. All the parameters of the reliability problem are based either on observed data or on typical design specifications. From the results obtained, we observed that the uncertainty around the defect size and the HCF stress range play an important role in reliability. At the same time, we observed that expected values for the LCF stress range and the number of LCF cycles have a significant influence on life assessment, but the uncertainty around these values could be neglected in the reliability assessment.

Current research in hydraulic turbines for handling sediments

Kathmandu University (KU) is one of the leading educational institutes in Nepal with a decade long experience with R&D of micro-hydro turbines. With a technical collaboration with Norwegian University of Science and Technology (NTNU), KU has also conducted several studies related to sediment erosion in hydro turbine.In the presented study a new program has been developed to create and optimize the design of Francis runners. The program is also featured to compare erosion in runner blades for different design cases. The final design can be exported to Computational Fluid Dynamics (CFD) and Fluid Structure Interaction (FSI) for further analysis. Parametric survey was carried out with this program to evaluate the relative effect of each design parameter on sediment erosion. Several optimized designs were developed and analyzed with CFD tools to fulfill the desired condition of minimum erosion and maximum efficiency.This paper summaries the problem of sediment erosion of hydro turbines in South Asia region. Some of the important achievements in R&D of hydro turbine and sediment erosion at KU are also presented. The findings of design optimization of Francis turbine for effective reduction in sediment erosion is discussed in details.

Empirical modelling of sediment erosion in Francis turbines

Sediment particles passing through the turbine components erode the surface in contact. Gradual removal of base material changes the runner profile and also weakens its structure. One of the major consequences of this is gradual loss of turbine efficiency. Attempts have been made from past researches to develop empirical relations to estimate the effects of sediment erosion in hydraulic turbines.Present study is conducted to identify an appropriate erosion model for Francis turbine. Two standard erosion models have been selected to estimate erosion rates and consecutive reduction in efficiency of the runner. Improved empirical relation to estimate the sediment erosion in Francis runner has been proposed. Comparison of results from the improved empirical relation has been done with the results of experimental measurements at the site.It has been found that sediment data from the site can be analysed to predict the damage in Francis runner due to erosion. The results from the improved erosion model are found to be consistent with the earlier studies and experimental measurements. A simple erosion model as the proposed one can help to formulate appropriate design, operation and maintenance strategy for Francis runner at a specific site conditions.

Research on the Length Ratio of Splitter Blades for Ultra-high Head Francis Runners

The flow field of ultra-high head Francis runner with different length radio splitter blades was simulated. The calculating process was based on continuity equation and Navies-Stokes equation and S-A turbulence model was used to make the equation group closed. The control equation was discretized by finite-volume method and SIMPLIC method was applied to solve the equation. Through calculation, the efficiency and the flow field of the runners with different length radio splitter blades at different points was obtained. It was found that the efficiency are higher when length radio is between 60% to 75% and when the radio is more than 75%, the cavitation performance became worse at design point and large discharge point.

Impact of startup scheme on Francis runner life expectancy

Francis runners are subject to complex dynamic forces which might lead to eventual blade cracking and the need for corrective measure. Damage due to cracks in runner blades are usually not a safety issues but might generate unexpected down time and high repair cost. Avoiding the main damaging operating conditions is often the only option left to plant operators to maximize the life expectancy of their runner. The startup scheme is one of the available parameter which is controlled by the end user and could be used to minimize the damage induced to the runner. In this study, two startup schemes have been used to investigate life expectancy of Francis runner using in situ measurements. The results obtained show that the induced damage during the startup event could be significantly reduced with change to the startup scheme. In our opinion, an optimization of the startup scheme with regard to fatigue damage could extend significantly the life expectancy and the reliability of Francis runner.

Optimization of hydraulic machinery by exploiting previous successful designs

A design-optimization method for hydraulic machinery is proposed. Optimal designs are obtained using the appropriate CFD evaluation software driven by an evolutionary algorithm which is also assisted by artificial neural networks used as surrogate evaluation models or metamodels. As shown in a previous IAHR paper by the same authors, such an optimization method substantially reduces the CPU cost, since the metamodels can discard numerous non-promising candidate solutions generated during the evolution, at almost negligible CPU cost, without evaluating them by means of the costly CFD tool. The present paper extends the optimization method of the previous paper by making it capable to accommodate and exploit pieces of useful information archived during previous relevant successful designs. So, instead of parameterizing the geometry of the hydraulic machine components, which inevitably leads to many design variables, enough to slow down the design procedure, in the proposed method all new designs are expressed as weighted combinations of the archived ones. The archived designs act as the design space bases. The role of the optimization algorithms is to find the set (or sets, for more than one objectives, where the Pareto front of non-dominated solutions is sought) of weight values, corresponding to the hydraulic machine configuration(s) with optimal performance. Since the number of weights is much less that the number of design variables of the conventional shape parameterization, the design space dimension reduces and the CPU cost of the metamodel-assisted evolutionary algorithm is much lower. The design of a Francis runner is used to demonstrate the capabilities of the proposed method.