Eduard Egusquiza

Frequencies in the Vibration Induced by the Rotor Stator Interaction in a Centrifugal Pump Turbine

The highest vibration levels in large pump turbines are, in general, originated in the rotor stator interaction (RSI). This vibration has specific characteristics that can be clearly observed in the frequency domain: harmonics of the moving blade passing frequency and a particular relationship among their amplitudes. It is valuable for the design and condition monitoring to count on these characteristics. A CFD model is an appropriate tool to determine the force and its characteristics. However, it is time consuming and needs highly qualified human resources while usually these results are needed immediately and in situ. Then, it is useful to determine these characteristics in a simple, quick, and accurate method. At present, the most suitable method indicates a large amount of possible harmonics to appear, without indicating the relative importance of them. This paper carries out a theoretical analysis to predict and explain in a qualitative way these frequencies and amplitudes. The theoretical analysis incorporates the number of blades, the number of guide vanes, the RSI nonuniform fluid force, and the sequence of interaction. This analysis is compared with the method currently in use, and both methods are applied to a practical case. The theoretical analysis gives a resulting force over the pump turbine, which corresponds well to the measured behavior of a pump turbine in terms of its frequencies and the relationship between their amplitudes. A corrective action is proposed as a result of the analysis and after it is carried out in one of the units, the vibration levels are reduced. The vibration induced by the RSI is predicted considering the sequence of interaction and different amplitudes in the interactions between the same moving blade and different stationary blades, giving a different and original interpretation about the source of the vibration characteristics. A successful corrective action is proposed as a consequence of this new interpretation.

Cavitation Influence on von Kármán Vortex Shedding and Induced Hydrofoil Vibrations

The present study deals with the shedding process of the von Karman vortices at the trailing edge of a 2D hydrofoil at high Reynolds number. This research focuses mainly on the effects of cavitation and fluid-structure interaction on the mechanism of the vortex generation. The vortex shedding frequency, derived from the flow-induced vibration measurement, is found to follow the Strouhal law provided that no hydrofoil resonance frequencies are excited, i.e., lock-off. For such a regime, the von Karman vortices exhibit strong spanwise 3D instabilities and the cavitation inception index is linearly dependent on the square root of the Reynolds number. In the case of resonance, the vortex shedding frequency is locked onto the hydrofoil eigenfrequency and the spatial coherence is enhanced with a quasi-2D shape. The measurements of the hydrofoil wall velocity amplitude and phase reveal the first torsion eigenmotion. In this case, the cavitation inception index is found to be significantly increased compared to lock-off conditions. It makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index, a new correlation relationship that encompasses the entire range of Reynolds numbers, including both the lock-off and the lock-in cases, is proposed and validated. In contrast to the earlier models, the new correlation takes into account the trailing edge displacement velocity. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. This effect is important in the context of the fluid-structure interaction, since it implies that the velocity of the hydrofoil trailing edge increases the fluctuating forces on the body. It is also demonstrated that cavitation developing in the vortex street cannot be considered as a passive agent for the turbulent wake flow. In fact, for fully developed cavitation, the vortex shedding frequency increases up to 15%, which is accompanied by the increase of the vortex advection velocity and reduction of the streamwise vortex spacing. In addition, a significant increase of the vortex-induced vibration level is found at cavitation onset. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation.

Dynamic analysis of Francis Runners-Experiment and numerical simulation

The present paper shows the results of numerical and experimental modal analyses of Francis runners, which were executed in air and in still water. In its first part this paper is focused on the numerical prediction of the model parameters by means of FEM and the validation of the FEM method. Influences of different geometries on modal parameters and frequency reduction ratio (FRR), which is the ratio of the natural frequencies in water and the corresponding natural frequencies in air, are investigated for two different runners, one prototype and one model runner. The results of the analyses indicate very good agreement between experiment and simulation. Particularly the frequency reduction ratios derived from simulation are found to agree very well with the values derived from experiment. In order to identify sensitivity of the structural properties several parameters such as material properties, different model scale and different hub geometries are numerically investigated. In its second part, a harmonic response analysis is shown for a Francis runner by applying the time dependent pressure distribution resulting from an unsteady CFD simulation to the mechanical structure. Thus, the data gained by modern CFD simulation are being fully utilized for the structural design based on life time analysis. With this new approach a more precise prediction of turbine loading and its effect on turbine life cycle is possible allowing better turbine designs to be developed.

Feasibility of Using PZT Actuators to Study the Dynamic Behavior of a Rotating Disk due to Rotor-Stator Interaction

In this paper, PZT actuators are used to study the dynamic behavior of a rotating disk structure due to rotor-stator interaction excitation. The disk is studied with two different surrounding fluids—air and water. The study has been performed analytically and validated experimentally. For the theoretical analysis, the natural frequencies and the associated mode shapes of the rotating disk in air and water are obtained with the Kirchhoff-Love thin plate theory coupled with the interaction with the surrounding fluid. A model for the Rotor Stator Interaction that occurs in many rotating disk-like parts of turbomachinery such as compressors, hydraulic runners or alternators is presented. The dynamic behavior of the rotating disk due to this excitation is deduced. For the experimental analysis a test rig has been developed. It consists of a stainless steel disk (r = 198 mm and h = 8 mm) connected to a variable speed motor. Excitation and response are measured from the rotating system. For the rotating excitation four piezoelectric patches have been used. Calibrating the piezoelectric patches in amplitude and phase, different rotating excitation patterns are applied on the rotating disk in air and in water. Results show the feasibility of using PZT to control the response of the disk due to a rotor-stator interaction.

Monitoring of Rotor-Stator Interaction in Pump-Turbine Using Vibrations Measured with On-Board Sensors Rotating with Shaft

Current trends in design of pump-turbines have led into higher rotor-stator interaction (RSI) loads over impeller-runner. These dynamic loads are of special interest having produced catastrophic failures in pump-turbines. Determining RSI characteristics facilitates the proposal of actions that will prevent these failures. Pressure measurements all around the perimeter of the impeller-runner are appropriate to monitor and detect RSI characteristics. Unfortunately most installed pump-turbines are not manufactured with in-built pressure sensors in appropriate positions to monitor RSI. For this reason, vibration measurements are the preferred method to monitor RSI in industry. Usually vibrations are measured in two perpendicular radial directions in bearings where valuable information could be lost due to bearing response. In this work, in order to avoid the effect of bearing response on measurement, two vibration sensors are installed rotating with the shaft. The RSI characteristics obtained with pressure measurements were compared to those determined using vibration measurements. The RSI characteristics obtained with pressure measurements were also determined using vibrations measured rotating with shaft. These RSI characteristics were not possible to be determined using the vibrations measured in guide bearing. Finally, it is recommended to measure vibrations rotating with shaft to detect RSI characteristics in installed pump-turbines as a more practical and reliable method to monitor RSI characteristics.

Dynamics and Intensity of Erosive Partial Cavitation

An experimental work has been carried out to investigate the dynamic behavior and the intensity of erosive partial cavitation on a 2-D hydrofoil. Both sheet (stable) and cloud (unstable) cavitation have been tested in a cavitation tunnel for various free stream velocities. Special attention has been given to validate the use of acceleration transducers for studying the physical process. In particular, the modulation in amplitude of the cavitation induced vibrations in a high frequency band has allowed us to determine the shedding frequency and the relative intensity of the collapse process for each testing condition. Regarding the cavity dynamics, a typical Strouhal value based on its length of about 0.28 has been found for cloud cavitation; meanwhile, for sheet cavitation, it presents a value of about 0.16. Furthermore, the level of the vibration modulation in the band from 45 kHz to 50 kHz for cloud cavitation shows a power law dependency on the free stream velocity as well as a good correlation with the pitting rate measured on stainless steel samples mounted on the hydrofoil.

Dynamic behaviour of pump-turbine runner: From disk to prototype runner

In recent decades, in order to increase output power of hydroelectric turbomachinery, the design head and the flow rate of the hydraulic turbines have been increased greatly. This has led to serious vibratory problems. The pump-turbines have to work at various operation conditions to satisfy the requirements of the power grid. However, larger hydraulic forces will result in high vibration levels on the turbines, especially, when the machines operate at off-design conditions. Due to the economic considerations, the pump-turbines are built as light as possible, which will change the dynamic response of the structures. According to industrial cases, the fatigue damage of the pump-turbine runner induced by hydraulic dynamic forces usually happens on the outer edge of the crown, which is near the leading edges of blades. To better understand the reasons for this kind of fatigue, it is extremely important to investigate the dynamic response behaviour of the hydraulic turbine, especially the runner, by experimental measurement and numerical simulation. The pump-turbine runner has a similar dynamic response behaviour of the circular disk. Therefore, in this paper the dynamic response analyses for circular disks with different dimensions and disk-blades-disk structures were carried out to better understand the fundamental dynamic behaviour for the complex turbomachinery. The influences of the pattern and number of blades were discussed in detail.

Analysis of the dynamic response of pump-turbine runners-Part I: Experiment

When in operation, pump-turbine runners have to withstand large pressure pulsations generated by the rotor-stator interaction. The analysis of the dynamic behavior of these structures is necessary to avoid damage. For this analysis a realistic model of the runner is necessary. When the runner is submerged in water and inside the casing, its dynamic response is greatly affected. The added mass effects of the surrounding fluid and the proximity of the head-cover and bottom-cover may reduce the natural frequencies. The frequency reduction produced by the added mass effects and the influence of the boundary conditions has to be known for a safe design of the runner. In this paper an experimental investigation on the dynamic response of a model runner is presented. A reduced scale model of a pump-turbine was tested outside and inside the casing with different boundary conditions. For the excitation of the runner at different frequencies piezoelectric patches were used. The response was measured with miniature accelerometers located in several positions inside the runner. From the measurements the natural frequencies and mode-shapes of the runner were calculated using EMA. The influence of the added mass and of the boundary conditions is presented and discussed.

Modal behavior of a reduced scale pump-turbine impeller. Part 1: Experiments

An experimental investigation has been carried out to quantify the effects of surrounding fluid on the modal behavior of a reduced scale pump-turbine impeller. The modal properties of the fluid-structure system have been obtained by Experimental Modal Analysis (EMA) with the impeller suspended in air and inside a water reservoir. The impeller has been excited with an instrumented hammer and the response has been measured by means of miniature accelerometers. The Frequency Response Functions (FRFs) have been obtained from a large number of impacting positions in order to ensure the identification of the main mode shapes. As a result, the main modes of vibration have been well characterized both in air and in water in terms of natural frequency, damping ratio and mode shape. The first mode is the 2 Nodal Diameter (ND), the second one is the 0ND and the following ones are the 3ND coupled with the 1ND. The visual observation of the animated mode shapes and the level of the Modal Assurance Criterion (MAC) have permitted to correlate the homologous modes of vibration of the fluid-structure system in air and in water. From this comparison the added mass effect on the natural frequencies and the fluid effect on the damping ratios have been quantified for the most significant modes. With the surrounding water, the natural frequencies decrease in average by 10%. On the other hand, the damping ratios increase in average by 0.5%. In any case, the damping ratio appears to decrease with the frequency value of the mode.

Modal behavior of a reduced scale pump-turbine impeller. Part II. Numerical Simulation

A numerical simulation has been carried out to analyze the modal behavior of a reduced scale pump-turbine impeller. The simulation has been done using FEM method, in air and in water. The same boundary conditions than in the experiment were considered: free body in air and free body submerged in a reservoir of water. A sensitivity analysis to determine the influence of the number of elements was done. The influence of the input parameters was also taken into account. Finally, a mesh with 165000 elements for the impeller in air and of 508676 for the impeller in water was used. The results obtained with the simulation have been compared with the experimental ones (paper 1). Both the natural frequency values and the mode-shapes were compared. The numerical results showed small deviation from experiment in the first modes in modes with low modal density. In some coupled modes been found. With the updated model the mode-shapes have been analyzed. Some modes with high modal density have been found. As indicated in the experiment, the effect of the added mass reduces the natural frequencies and also changes the characteristics of the coupled modes.