Analysis of large scale hydrodynamic phenomena in turbine draft tubes

Hydraulic power is a renewable energy with a very advantageous price, and its flexibility of use coupled with its storage possibilities easily enables to meet the peak demand. Refurbishment of old hydraulic power plants is an important topical issue and the upgrading of the power stations of the years 1940 to 1960 can considerably increase both efficiency and power with minimal costs. The current challenge for the turbine manufacturers is the accurate flow prediction in the whole turbine and across a broad operating range, taking into account the unsteady features of the flow. For further developing flow computation tools, the major hydraulic turbine manufacturers : ALSTOM Power Hydro, GE Hydro, VATECH Escher Wyss, VOITH-SIEMENS Hydro have joined Electricité de France and EPFL, in the European initiative framework EUREKA n° 1625. This project has been financially supported by CTI – Swiss Commission for Technology and Innovation. The aim of the project was to analyze the flow within the draft tube of a turbine theoretically, experimentally and numerically, and the present work is a part of the project. In this general framework, the objective of the thesis was to set up PIV measurements for analyzing the flow behavior in the draft tube of a Francis turbine. Several enhancements of the PIV technique have been carried out for acceding to the 3D velocity field, both in single and two-phase flows, in the cone and at the outlet of the draft tube. Due to the complex geometry of the draft tube, particular attention has been given to calibration, allowing obtaining 3% uncertainty on the measured velocity field. In two-phase flow, corresponding to partial load operation in cavitation conditions, two measurement methods have been set up, allowing simultaneous measurement of the velocity field and volume of the vapors-core vortex. The first one relies on the 2D PIV method: two cameras focused on the same measurement zone provide separately the shape of the vapors core and the velocity of fluorescent seeding particles in the flow. The second method, 3D PIV, is based on the separation on the same image of the fluorescent seeding particles from the shape of the vapors core, taking advantage of background lighting in a specific wavelength. Using two cameras in stereoscopic arrangement allows, in this case, obtaining the third component of the velocity. Adaptive image processing algorithms have been developed in both cases for detecting the vapors core boundary and calculating its geometrical characteristics in the measurement section. These experimental developments have allowed studying several phenomena and characterizing several flow types in the draft tube. For this draft tube, the efficiency characteristic shows a severe drop close to the best efficiency point, and this part has been particularly addressed. The 3D velocity field has been measured at the runner outlet and diffuser outlet for a flow rate range of ± 20 % of the best efficiency point flow rate, and these results allowed explaining the source of the hydraulic losses that lead to the drop of the efficiency characteristic. A second issue concerns the spatial distribution of the non-uniformity of the velocity field at the runner outlet, synchronous with the runner blades passage. The velocity field development in the cone of the draft tube from the runner outlet to the cone outlet has been determined and the mixing length of the sheared flow has been studied. In low charge operating conditions (70% of the best efficiency point flow rate), relevant results of unsteady velocity field and related vapors volume are obtained for different pressure levels in the draft tube, which correspond to different cavitation conditions from single-phase flow to vortex-circuit interaction in two-phase flow. The shape of the vortex core has been determined and a parametrical model is proposed. Its influence on the flow, as well as its stability, has been evaluated depending on the pressure level. Particular attention has been paid to the characterization of the interaction of the synchronous part of the vortex-induced pulsations and the circuit. These results have been used to calibrate and validate flow computation codes and they form a database available to the project partners. An example is given of the validation of the vortex flow simulation at partial load in single-phase flow conditions. Unlike the usual data comparison based on wall pressure signals, the velocity field and vortex filament are also assessed.

Physical Mechanisms governing Self-Excited Pressure Oscillations in Francis Turbines

Andres Müller

The importance of renewable energy sources for the electrical power supply has grown rapidly in the past decades. Their often unpredictable nature however poses a threat to the stability of the existing electric grid. Hydroelectric powerplants play an important role in regulating the integration of renewable energy sources into the network by supplying on-demand load balancing as well as primary and secondary power network control. Therefore, the operating ranges of hydraulic machines has to be continuously extended, which potentially produces undesirable flow phenomena involving cavitation. An example is the formation of a gaseous volume in the swirling flow leaving a Francis turbine runner at off-design operating conditions. At high load, this so called vortex rope is shaped axisymmetrically and may enter a self-excited oscillation, measurable through significant fluctuations of the pressure throughout the system and the mechanical torque transferred to the generator. The main objective of the present work is the identification of the physical mechanisms governing this self-sustained, unstable behavior by measurement. Furthermore, the key parameters of numerical approaches using one-dimensional hydroacoustic flowmodels or CFD require experimental validation. For this purpose, the measurements provide a comprehensive data base of various flow and system parameters at varying operating conditions. Two test cases are studied, a small scale hydraulic circuit with a micro-turbine as well as a reduced scale physical model of an existing Francis turbine. On the first test case, the study of the flow rate fluctuations up- and downstream of the oscillating vortex rope in the draft tube, together with the volume of the cavity, revealed the destabilizing effect of the flow swirl in the draft tube inlet. The second test case accurately simulates the behavior of an actual hydraulic power plant. Investigations range from a local study of the flow field in the draft tube cone bymeans of LDV, PIV, high speed visualization and wall pressure measurements to a global analysis, considering the response of the hydraulic and mechanical system to the excitation by the vortex rope oscillation. Among the main observations is a periodical variation of the flow swirl in the draft tube, synchronized with the pressure oscillations. This is likely to be caused by a cyclically appearing volume of cavitation on the runner blades, modifying the relative flow angle at the outlet. The interaction of the blade cavitation and the vortex rope oscillation via the flow swirl is found to play a crucial role in the occurrence of self-excited pressure oscillations in Francis turbines.

EPFL2014

Forced and Self Oscillations of Hydraulic Systems Induced by Cavitation Vortex Rope of Francis Turbines

Sébastien Alligné

With economical energy market strategies based on instantaneous pricings of electricity as function of the demand or the predictions, operators harness more hydroelectric facilities to off-design operating points to cover the variations of the electricity production. Under these operating conditions, Francis turbines develop a cavitating swirling flow at the runner outlet which induces pressure fluctuations propagating in the whole hydraulic system. The core of this cavitating vortex is usually called vortex rope. At resonance conditions, the superimposition of the induced traveling waves gives rise to a standing wave leading to undesirable large pressure and output power fluctuations. The aim of this present work is to predict and to simulate this resonance phenomenon which may happen both in part load or full load operating conditions. The identification of the excitation sources induced by the cavitating vortex rope is performed with numerical simulations based on a three dimensional incompressible model, so called hydrodynamic (HD) model. The assumption of plane wave propagation in the water passages connected to the turbine is set since low surging frequencies are involved. Hence, propagation of these sources is simulated with a one dimensional compressible model, so called hydroacoustic (HA) model. The HA model covers the entire hydraulic system including the source region corresponding to the draft tube of the Francis turbine whereas the HD model covers only the source region. In this present work, a specific HA draft tube model has been developed. A momentum source modeling the forces induced by the flow acting on the draft tube wall is considered. Moreover, the fluctuating cavitation volume is considered as a mass source. Finally, a thermodynamic damping is introduced to model energy dissipation during a phase change between liquid and gas. Investigations at part load conditions aim to simulate the upper part load resonance phenomenon for which frequency of pressure fluctuations are experienced between 2 and 4 times the runner frequency. Measurements were carried out in the framework of the FLINDT project which is therefore the case study for validation. First of all, HA draft tube model parameters have been derived for the investigated operating point considering both single phase and two phase unsteady simulations with the HD model. An analysis of these parameters is performed and comparison between single phase and two phase simulation results is made. It is shown that the cavitation modeling in the HD model is necessary to find the vortex rope precession frequency which depends on the cavitation amount in the vortex core. However, the volume of vapor is underestimated and a correction factor on the Thoma number is necessary to get a good agreement between experiments and simulation results. Moreover it has been shown that the three dimensional flow in the elbow gives rise to HA sources able to excite the hydraulic system. Intensity of the sources are higher when two phase flow simulations are considered. Before simulating the upper part load resonance phenomenon, a preliminary validation of these HA parameters is performed by simulating a standard part load resonance where the vortex rope precession frequency, near 0.3 times the runner frequency, matches with the first eigenfrequency of the hydraulic system. In out of resonance conditions, maximum of pressure fluctuations amplitudes are experienced in the draft tube cone with an amplitude being 1% of the turbine head. However, when resonance occurs, maximum amplitude of pressure fluctuations reaches up to 7%. A good agreement is obtained with the order of magnitudes found in measurements available in the literature. After this preliminary validation, simulation of the upper part load resonance phenomenon has been tackled. It has been found that the mechanism inducing this phenomenon is related to an undesirable fluctuation of the cavitation volume which frequency can match with an eigenfrequency of the hydraulic system. However, this fluctuation is captured for a Thoma number much higher than the experimental one leading to a cavitation volume very small compared to the experiments. A prototype installation of four 478 MW Francis turbines located in the Canada's province British Columbia, has been chosen as the case study to analyze the full load instability phenomenon. Indeed, this instability occurred on prototype and reduced scale model as well. Hence, experimental measurements have been carried out on the reduced scale model aiming to use experimental data to validate the numerical simulations performed with the HA draft tube model. The mass source defined in this model, is described by a decisive parameter which is the mass flow gain factor. Extensively used in previous works for the analysis of this phenomenon, this parameter is defined to represent the effect of the HA fluctuations of the downstream flow rate to the cavitation volume on the mass source. In this present work, the same formulation is used and has been combined with the introduction of a new parameter: the thermodynamic damping. First of all, these HA parameters have been derived for the different investigated experimental operating points from single phase steady simulations. Then, using these computed parameters, a small perturbation stability analysis in the frequency domain has been carried out to identify the stability of the different operating points. The experimental unstable characteristic frequencies have been found out with this modal analysis. However, this analysis in the frequency domain does not give any information about the amplitude of the pressure fluctuations induced by the instability. Hence, time domain HA simulations have been performed. It has been shown that the using of constant HA draft tube model parameters leads to divergent time domain simulations, whereas nonlinear parameters depending on the pressure variable, lead to a limit cycle of finite amplitude fluctuations. Moreover, nonlinearity of the thermodynamic damping is decisive to reach this limit cycle. Finally, a methodology has been set up to predict the instability of the prototype from the investigations on the reduced scale model. A combination of measurements, numerical simulations and computation of the eigenmodes of the reduced scale model installed on test rig, allows the accurate calibration of the HA draft tube model parameters at the model scale. Finally, transposition of these parameters to the prototype according to similitude laws is applied for the stability analysis of the power plant.

EPFL2011

The effect of pressure gradient on the collapse of cavitation bubbles in normal and reduced gravity

Marc Tinguely

When water flows through hydraulic turbomachines, the local pressure can become low enough to vaporize the water and create vapor cavities. This phenomenon is called cavitation. When the cavities collapse, shock waves and liquid jets traveling through the inclusions can erode nearby solid surfaces. The collapse of cavitation bubbles has been extensively investigated in the case of a single bubble in a liquid at rest. However, in the case of hydraulic machines, the bubbles collapse in a flowing liquid subject to strong pressure gradients. The objective of this thesis is thus to investigate the effect of the pressure gradient on the collapse of a spherical cavitation bubble. We have performed a preliminary investigation of bubble dynamics in a flowing liquid with a pressure gradient. To this end, we have placed a Naca0009 hydrofoil in the test section of EPFL High Speed Cavitation Tunnel and used a high energy pulsed laser focusing technique to generate a single vapor bubble close to the hydrofoil’s leading edge. We have observed a significant influence of the pressure gradient on the bubble dynamics. Particularly, if the collapse phase occurs near the minimum pressure point, the microjet is no more directed towards the solid surface but towards the lower pressure zone in the stream wise direction. We have also observed a peculiar feature of a cluster of bubble dynamics, which behaves almost similar to a single bubble, exhibiting a microjet during its collapse. These unprecedented re- sults are of major importance for a better understanding of the cavitation erosion mechanism in hydraulic systems. The qualitative results obtained in the cavitation tunnel led to the investigation of the effect of a constant pressure gradient on the collapse of the bubble. An experimental setup is built to observe the dynamics of the bubble in water, subject to the gravity induced hydrostatic pressure gradient, and to measure the pressure fluctuation due to the shock waves. The bubbles are generated with a high energy pulsed laser and recorded with a high speed camera. The experimental setup is taken onboard parabolic flights. The parabolic manoeuvres allow the gravity level to be varied in the plane, which modulates the intensity of the pressure gradient in the liquid. The high speed movies taken during the flights reveal that vapor jets appear with the rebound bubble. An empirical law for the prediction of the volume of the jet is deducted from the experimental results. The volume of the jet, normalized with the volume of the rebound bubble, is found to be proportional to a non dimensional parameter ζ0=|∇p|Rmax/Δp, where ∇p is the pressure gradient, Rmax is the maximal bubble radius and Δp is the driving pressure. This dependance is enforced by a theoretical development based on the concept of the Kelvin impulse. Moreover, we identify a threshold for the apparition of the vapor jet: ζ > 4 · 10 − 4 . A new approach for the study of the bubble collapse is proposed: we look at how the energy in the initial cavitation bubble is partitioned between the collapse channels, namely the rebound, the shock wave, the jet, and the luminescence. The microgravity phases of the parabolic flights prevent the apparition of the jet. The collapse of the bubble, in this case, is perfectly spherically symmetric. Moreover, the energy dissipated through luminescence is negligible. Therefore, the study reduces to the energy partition between rebound and shock wave. The measurements uncover a systematic pressure dependence of the energy partition between rebound and shock. We demonstrate that these observations agree with a physical model relying on a first-order approximation of the liquid compressibility and an adiabatic treatment of the non-condensable gas inside the bubble. Using this model, we find that the energy partition between rebound and shock is dictated by a single non-dimensional parameter ξ=Δp(γ^6)/(pg0^1γ)/(ρc^2)^(1−1/γ), where γ is the adiabatic index of the non-condensable gas, pg0 is the pressure of the non-condensable gas at the maximal bubble radius, ρ is the liquid density, and c is the speed of sound in the liquid.

EPFL2013