Table of contents

Sub- and super-synchronous self-excited vibrations due to axial clearance flows were observed in a columnar rotor with an upstream seal in experiments. A smaller clearance on the downstream seal had a larger effect of stabilizing the rotor. In computations, it was found that the rotordynamic fluid force tangential to the whirling orbit, which is caused as a response to the vibrations (whirling motions), destabilizes the rotor in the case of the upstream seal and stabilizes the rotor in the case of the downstream seal. It was clarified in the 1-D flow model that the tangential rotordynamic fluid force is mainly caused by an inertia of the clearance flow.

The objective of this paper is to investigate the flow induced vibration of a flexible hydrofoil in cavitating flows via combined experimental and numerical studies. The experiments are presented for the modified NACA66 hydrofoil made of POM Polyacetate in the closed-loop cavitation tunnel at Beijing Institute of Technology. The high-speed camera and the single point Laser Doppler Vibrometer are applied to analyze the transient flow structures and the corresponding structural vibration characteristics. The hybrid coupled fluid structure interaction model is conducted to couple the incompressible and unsteady Reynolds Averaged Navier-Stokes solver with a simplified two-degree-of-freedom structural model. The k-ω SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the present simulations. The results showed that with the decreasing of the cavitation number, the cavitating flows display incipient cavitation, sheet cavitation, cloud cavitation and supercavitation. The vibration magnitude increases dramatically for the cloud cavitation and decline for the supercavitation. The cloud cavitation development strongly affects the vibration response, which is corresponding to the periodically developing and shedding of the large-scale cloud cavity. The main frequency of the vibration amplitude is accordance with the cavity shedding frequency and other two frequencies of the vibration amplitude are corresponding to the natural frequencies of the bending and twisting modes.

To estimate structural fatigue, vibrational response to realistic spectrum of excitations and associated equivalent damping are of paramount importance. In this paper, an approach to quantify flow-induced damping of a relatively heavy fluid on a vibrating hydraulic turbine blade using numerical simulations is presented. First, mode shapes and frequencies of the immersed structure are obtained by modal analysis using the finite element method. Then, forced oscillatory modal motion is prescribed on the structural boundary of unsteady Reynolds-averaged Navier-Stokes flow simulations. Damping is finally computed as the normalized work done by the resulting fluid load on the structure. Validation is achieved by comparing the numerical results with available experimental data for a steel hydrofoil oscillating in flowing water. For this case, the linear increase in the damping ratio with the flow velocity is reproduced within 10% of the experimental values. Application of the method to an actual hydroelectric propeller turbine blade yields a fluid damping value of around 15% of critical damping for its first vibration mode.

Natural frequencies estimation of Francis turbines is of paramount importance in the stage of design in order to avoid vibration and resonance problems especially during transient events. Francis turbine runners are submerged in water and confined with small axial and radial gaps which considerably decrease their natural frequencies in comparison to the same structure in the air. Acoustic-structural FSI simulations have been used to evaluate the influence of these gaps. This model considers an entire prototype of a Francis turbine, including generator, shaft, runner and surrounding water. The radial gap between the runner and the static parts has been changed from the real configuration (about 0.04% the runner diameter) to 1% of the runner diameter to evaluate its influence on the machine natural frequencies. Mode-shapes and natural frequencies of the whole machine are discussed for all the boundary conditions tested.

The increasing energy consumption and highly stressed power grids influence the operating conditions of turbines and pump turbines in the present situation. To provide or use energy as quick as possible, hydraulic turbines are operated more frequent and over longer periods of time in lower part load at off-design conditions. This leads to a more turbulent behavior and to higher requirements of the strength of stressed components (e.g. runner, guide or stay vanes). The modern advantages of computational capabilities regarding numerical investigations allow a precise prediction of appearing flow conditions and thereby induced strains in hydraulic machines. This paper focuses on the calculation of the unsteady pressure field of a high head Francis turbine with a specific speed of n_q ≈ 24 min^-1 and its impact on the structure at different operating conditions. In the first step, unsteady numerical flow simulations are performed with the open-source CFD software OpenFOAM. To obtain the appearing dynamic flow phenomena, the entire machine, consisting of the spiral casing, the stay vanes, the wicket gate, the runner and the draft tube, is taken into account. Additionally, a reduced model without the spiral casing and with a simplified inlet boundary is used. To evaluate the accuracy of the CFD simulations, operating parameters such as head and torque are compared with the results of site measurements carried out on the corresponding prototype machine. In the second part, the obtained pressure fields are used for a fluid-structure analysis with the open-source Finite Element software Code_Aster, to predict the static loads on the runner.

Fluid-structure interaction (FSI) has a major impact on the dynamic response of the structural components of hydroelectric turbines. On mid- to high-head Francis runners, the rotor-stator interaction (RSI) phenomenon has to be considered carefully during the design phase to avoid operational issues on the prototype machine. The RSI dynamic response amplitudes of the runner are driven by three main factors: (1) pressure forcing amplitudes, (2) excitation frequencies in relation to natural frequencies and (3) damping. All three of the above factors are significantly influenced by both mechanical and hydraulic parameters. The prediction of the first two factors has been largely documented in the literature. However, the prediction of hydro-dynamic damping has only recently and only partially been treated. Two mode-based approaches (modal work and coupled single degree of freedom) for the prediction of flow-added dynamic parameters using separate finite element analyses (FEA) in still water and unsteady computational fluid dynamic (CFD) analyses are presented. The modal motion is connected to the time resolved CFD calculation by means of dynamic mesh deformation. This approach has partially been presented in a previous paper applied to a simplified hydrofoil. The present work extends the approach to Francis runners under RSI loading. In particular the travelling wave mode shapes of turbine runners are considered. Reasonable agreement with experimental results is obtained in parts of the operating range.

Reliable assessments of dynamic phenomena in hydraulic machinery require the consideration of fluid-structure interaction (FSI) if natural frequencies or damping properties of submerged structural parts clearly change due to the surrounding water or if the interaction may cause instabilities. Exemplarily, three different applications of strongly coupled FSI are presented which all have a high impact on operational safety or dynamic stresses and fatigue life. At first, flow induced damping effects at a Francis runner exhibit a strong dependency on operating condition and mode shape. Secondly, if a rotating disc is submerged, a splitting of natural frequencies is observed for mode shapes with different spinning direction. Finally, a hydroelastic instabilitiy is identified in a bypass valve at small opening.

In this study, multiphysic simulations are carried out in order to model fluid loading and structural stresses on propeller blades during startup and runaway. It is found that air admission plays an important role during these transient events and that biphasic simulations are therefore required. At the speed no load regime, a large air pocket with vertical free surface forms in the centre of the runner displacing the water flow near the shroud. This significantly affects the torque developed on the blades and thus structural loading. The resulting pressures are applied to a quasi-static structural model and good agreement is obtained with experimental strain gauge data.

The article covers a choice of main vibration parameter at an assessment of a vibration state of vertical Francis hydroturbines. At present time vibration velocity and vibration displacement are adopted as main parameters of non-rotating parts vibration in the international standard ISO 10816-5:2000 «Mechanical vibration — Evaluation of machine vibration by measurements on non-rotating parts — Part 5: Machine sets in hydraulic power generating and pumping plants» (further ISO 10816-5:2000).

The hydraulic turbines refer to the slow-speed machines with rotation speed from 60 to 600 rpm (∼ 1 - 10 Hz).

So maximum vibration displacements and dynamic stresses in hydraulic turbines supporting parts are in low-frequency region of vibration spectrum.

In this report comparative data of hydro units supporting parts vibration velocity and vibration displacement measurements are presented. Using these data assessment of hydro units vibration state has been done.

It is shown that the assessment of a hydro unit vibration state using parameter "vibration displacement" corresponds to the fundamental principles of operational reliability and fatigue strength of hydro units supporting parts.

It is noted that when hydro units operate at small and partial loads with high low-frequency unsteady flow (f < frot) we have the smallest vibration velocity and the greatest vibration displacement of hydro units supporting parts.

Specialists of LMZ (Saint-Petersburg) have developed Russian standard RD 24.023.117-88 «Vibration measurement and evaluation vibration state of vertical hydraulic turbines» which was published in 1989. In this document vibration displacement was considered as a main parameter. Evaluation of turbine vibration was performed according to the effecrive value of turbine supporting parts vibration displacement.

Design of heavy duty process pumps usually based on the end user requirements. Operating conditions of pumps in the system dictate technical solution to reach high performance pump design. Pumps for special application like nuclear power plants, petroleum, petrochemical and natural gas industry should reach very high design criteria and have to fulfil requirements of different international standards for pumps. Usually energetic and cavitation characteristics are necessary issues of the development procedure. In this paper structural analysis that include thermo-mechanical loading and fatigue phenomena are also considered, because they are very important for estimation of long service life. Repeated thermomechanical loading and unloading which leads to fatigue of pumps are obtained using unsteady Computational Fluid Dynamics (CFD) with taking into account also thermodynamics equations. Complete numerical analysis is done for an example of centrifugal pump with the specific speed around n_q=24. The results show energetic characteristics, thermal stresses and deformations and maximal number of operation cycles for safe and reliable operation.

The refurbishment of the Lipno I TG2 Francis turbine, situated on River Vltava, with maximum net head of 165 m and required operational range from 0 to 67MW of turbine power was performed in 2014. The new hydraulic design of the spiral case, distributor and runner was developed for this project. After about 1000 hours of operation the site inspection was performed and the cracks were found on 8 runner blades of 17 blades altogether. The all cracks were found near runner hub beginning from the trailing edge. The dimensions of the cracks were different with maximum length of 123 mm and minimum length of 3 mm. The runner was repaired and the intensive investigation was started to define the main cause of the cracks creation and to determine the measures for their elimination. This paper presents the program of this investigation which consists of static and dynamic blade strain measurement, CFD and FEM analysis, discusses the crack causes and overview the solution how to return the turbine successfully to operation.

In the present paper considered is the problem of the numerical simulation of Francis turbine runner fatigue failure caused by fluid-structure interaction. The unsteady 3D flow is modeled simultaneously in the spiral chamber, each wicket gate and runner channels and in the draft tube using the Euler equations. Based on the unsteady runner loadings at each time step stresses in the whole runner are calculated using the elastic equilibrium equations solved with boundary element method. Set of static stress-strain states provides quasi-dynamics of runner cyclic loading. It is assumed that equivalent stresses in the runner are below the critical value after which irreversible plastic processes happen in the runner material. Therefore runner is subjected to the fatigue damage caused by high-cycle fatigue, in which the loads are generally low compared with the limit stress of the material. As a consequence, the stress state around the crack front can be fully characterized by linear elastic fracture mechanics. The place of runner cracking is determined as a point with maximal amplitude of stress oscillations. Stress pulsations amplitude is used to estimate the number of cycles until the moment of fatigue failure, number of loading cycles and oscillation frequency are used to calculate runner service time. Example of the real Francis runner which has encountered premature fatigue failure as a result of incorrect durability estimation is used to verify the developed numerical model.

High temperature level recorded on the thrust bearing of a 45 MW hydro generating unit was resulting in frequent production stoppage. In spite of improvements brought to the oil cooling system since the rehabilitation in 2008, the operator had to activate the bearing oil lift system to keep the temperature below acceptable limits. Primary root cause analysis first pointed to the design of the shoe that was centrally pivoted, not allowing the formation of a thick hydrodynamic film. The removal of a strip of the soft metal layer near the trailing edge of the shoe resulted in a significant surface temperature reduction (about 15 deg. C), as predicted by a CFD model of the oil film. The goal of this machining was to increase the pivoting angle by moving the centre of hydrodynamic pressure. Proximity sensors were installed at each corner of the redesigned shoe to measure the film thickness and the bearing attitude. Signal analysis revealed a step of a magnitude close to the oil film thickness between the two halves of the rotating thrust block. This was the cause of another failure few hours since restarting the unit.

The lessons learnt through these measurements and analyses were carefully applied to the ultimate build. The unit now runs with a robust thrust bearing and even survived a significant cooling flow reduction event. This paper presents the CFD analysis results and the measurements acquired during these events.

Turbine start-up transients are induced by the wicket gates opening sequence and generate high amplitude stress cycles. These stress cycles have a detrimental effect leading to faster crack growth in the runner blades. Using a series of direct measurements taken on a prototype runner in order to find the optimal start-up parameters exposes both the runner and the instrumentation to a series of successive damaging transient events during the optimization process. To solve this, finding sensors strongly correlated to strain gauges and whose signals can be easily obtained to identify a model to predict the strain, instead of directly measuring it, would reduce the risk, cost and downtime associated with a measurement campaign. This paper shows that turbine shaft torsion measurements is highly correlated to the strain at a runner blade hotspot, and we demonstrate that the ARMAX model can be used to represent the dynamic system in order to minimize the strain on blades.

Extending the operating zone of Francis turbines toward low load is a major stake to allow the optimization of the electrical grid. The dynamic phenomena encountered at low load are potential sources of pressure fluctuations, power instability and runner fatigue. Traditionally, the peak to peak value of pressure fluctuations is used to assess these risks. However, this estimator is not sufficient to analyse separately the various dynamic phenomena and their impact on the stability of the turbine. In this paper the recent Spatial Harmonic Decomposition (SHD) method is used to analyse the pressure fluctuations through more relevant indicators. The evolution of these indicators along a load variation is compared with the associated runner strain measured with on-board gauges. It is shown that the use of the Spatial Harmonic Decomposition is a powerful tool to evaluate the risks for the industrial turbine and thus improve its behaviour and its reliability.

In the operation of hydraulic turbines, no-load and very low load conditions are among the most damaging. Even though there is no power generation, there is still a significant amount of energy which has to be entirely dissipated, mainly in the runner, where the flow is quite complex, with large scale unsteady and chaotic vortices resulting from partial pumping. This paper presents different approaches to perform stress analyses at low load conditions on a Francis turbine, taking into account the pressure fluctuations on the runner blades due to the large stochastic flow structures inherent in no-load operating regimes. With appropriate mesh density and time step, unsteady computational fluid dynamics (CFD) simulations using the SAS-SST turbulence model can be used on a Francis runner to predict the pressure fluctuations with reasonable accuracy when compared to measurements. These calculated pressure loads can then be used to predict the dynamic stresses with finite-element analyses (FEA). Different approaches are discussed ranging from quasi-static single-blade models to full runner time- dependent one-way fluid-structure interaction (FSI). Pros and cons of the different modelling strategies will be discussed in a detailed analysis of the structural results with comparisons to experimental data. Once the time signal of the stochastic stress at no-load conditions is obtained, the runner fatigue damage related to this operating condition can be estimated using different tools such as time signal extrapolation and rainflow counting.

Despite the fact that vortex-induced vibration (VIV) in hydraulic turbines components (especially in stay vanes) is a well-known phenomenon, it still remains challenging for operation and maintenance teams in several power plants around the world. Since the first publication of a similar problem in 1967, literature shows that at least 27 other turbines witnessed strong stay vane vibrations associated with vortex shedding. Recurrent stay vane cracks in a 250 MW Francis turbine in Brazil motivated an engineering study involving prototype measurements, structural and Computational Fluid Dynamics (CFD) analysis in order to determine a proper geometry modification that could eliminate the periodic vortex wake generated at the stay vanes trailing edge. First cracks appeared in 1978 just after the machine was put into operation. A study published in 1982 associated these cracks with dynamic excitations caused by the water flow at high flow conditions. New stay vane profiles were proposed and executed as well as improved welding recommendations. Cracks however, continued to appear requiring welding repairs roughly every two years. Although Voith Hydro was not the original equipment manufacturer for these units, the necessary information was available to study the issue and propose and execute new stay vane profiles. This paper details the approach taken for the study. First, indirect vibration measurements were used to determine vibration frequencies to help to characterize the affected mode shapes. These results were compared to finite element (FE) calculations. Strain gage measurements performed afterwards confirmed the conclusions of this analysis. Next, transient CFD calculations were run to reproduce the measured phenomenon and to serve as a basis for a new stay vane geometry. This modification was then implemented in the actual turbine stay vanes. A new set of indirect vibration measurements indicated the effectiveness of the proposed solution. Final confirmation will come from new strain gage measurements.

Traditionally, hydro power plants have been operated close to best efficiency point, the more stable operating condition for which they have been designed. However, because of changes in the electricity market, many hydro power plants operators wish to operate their machines differently to fulfil those new market needs. New operating conditions can include whole range operation, many start/stops, extensive low load operation, synchronous condenser mode and power/frequency regulation. Many of these new operating conditions may impose more severe fatigue damage than the traditional base load operation close to best efficiency point. Under these conditions, the fatigue life of the runner may be significantly reduced and reparation or replacement cost might occur sooner than expected.

In order to design reliable Francis runners for those new challenging operating scenarios, Andritz Hydro has developed various proprietary tools and design rules. These are used within Andritz Hydro to design mechanically robust Francis runners for the operating scenarios fulfilling customer's specifications. To estimate residual life under different operating scenarios of an existing runner designed years ago for best efficiency base load operation, Andritz Hydro's design rules and tools would necessarily lead to conservative results.

While the geometry of a new runner can be modified to fulfil all conservative mechanical design rules, the predicted fatigue life of an existing runner under off-design operating conditions may appear rather short because of the conservative safety factor included in the calculations. The most precise and reliable way to calculate residual life of an existing runner under different operating scenarios is to perform a strain gauge measurement campaign on the runner. This paper presents the runner strain gage measurement campaign of a mid-head Francis turbine over all the operating conditions available during the test, the analysis of the measurement signals and the runner residual life assessment under different operating scenarios. With these results, the maintenance cost of the change in operating mode can then be calculated and foreseen by the power plant owner.