On the hysteresis of cavitation incipience and desinence in hydraulic machines

The omnipresent vortical structures in hydraulic machines are extremely prone to the occurrence of cavitation. It is well known that besides the flow parameters, the incipience, development, and disappearance of cavitation within a vortex is very sensitive to the gas content. It is also known that the pressure threshold for vortex cavitation desinence may be significantly higher than that of its incipience. This hysteresis, which is not yet well understood, is the scope of the current work. The case study is made of an elliptical NACA 16020 hydrofoil, placed in the test section of EPFL high-speed cavitation tunnel. We have observed the inception and the desinence of tip vortex cavitation (TVC) for different flow conditions and gas contents. We found that the pressure threshold for the TVC desinence increases with the dissolved gas content. We have also found that this pressure threshold strongly depends on the flow parameters and may reach atmospheric pressure for specific conditions. We argue that the persistence of a cavity at pressure levels higher than the vapor pressure is due to an outgassing process that sucks air from of the surrounding supersaturated liquid to feed the cavity. The gas diffusion is likely enhanced when a laminar separation of the boundary layer is formed at the tip of the hydrofoil on the suction side.

Vortex shedding from blunt and oblique trailing edge hydrofoils

Philippe Ausoni, François Avellan, Mohamed Farhat, Amirreza Zobeiri

The phenomenon of vortex shedding behind a hydrofoil is an important issue from both scientific and technical point of view. The resulting fluctuating forces may lead to excessive vibrations and premature cracks in the hydraulic machines. According to previous studies, it is well known that an oblique trailing edge, also called "Donaldson cut", reduces the vibration in comparison with a blunt trailing edge; however the physics of the problem is still poorly understood. The purpose of the present work is the experimental investigation of vortex shedding dynamics in the wake of oblique and blunt trailing edge NACA0009 hydrofoils. Experiments are performed at zero incidence angle and high Reynolds numbers, ReL =5 10 5 - 2.9 10 6. The wake velocity profile is measured by two-component Laser Doppler Velocimetry. Cavitation occurrence in the core of the vortices is used as a mean of wake visualization with the help of a high speed camera. We have found that vortex induced vibration is significantly reduced for oblique trailing edge hydrofoil in comparison with the truncated one, which is in agreement with former reports. A disorganization of the Karman vortex street in the near wake is believed to be the reason of this vibration reduction. The high speed movies clearly show that the alternate shedding of the vortices turns into almost simultaneous shedding at the hydrofoil trailing edge. As a result, the upper and lower vortices pair with a significant thickening of the lower vortex core and a reduction of its strength. Consequently, the fluctuating lift, which is the cause of the structural vibration, is also reduced by the oblique truncation. We believe that this result stands for a basis to better optimize the trailing edge of turbine blades in order to further decrease the flow induced vibration.

Brno university of technology2009

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

Mind The Gap

Matthieu Dreyer

The tip leakage vortex (TLV), which develops in the clearance between the blade tip and the casing of axial turbomachines, appears in many industrial applications, such as air transportation, space rockets and hydraulic machines. In the latter, cavitation may develop in the core of the TLV, often leading to severe erosion of the runner blades and the casing. Despite the progress achieved in understanding and controlling the dynamics of this particular flow, many associated phenomena are still not sufficiently explored. It remains, for instance, unclear how the clearance size is related to the occurrence of cavitation in the TLV. The present work contributes to this research by assessing the effect of the clearance size on the TLV intensity and dynamics in a simplified case study. The vortex is generated by a two dimensional generic blade in a water tunnel, while the clearance between the blade tip and the wall is varied. The properties of the TLV are established with the help of stereo-PIV and flow visualizations for a wide range of incidence angles, inlet velocities and tip clearances. The measurements clearly reveal the existence of a specific tip clearance for which the vortex intensity is at its maximum and most prone to generate cavitation. By introducing a new dimensionless coefficient

\tau/\Gamma^*_{\infty}

, where

\tau

is the normalized clearance and

\Gamma^*_{\infty}

is the normalized circulation in the unconfined case, it is established that the TLV circulation reaches a peak intensity for

\tau/\Gamma^*_{\infty}\approx0.2

, the amplitude of which is in average 45 (

\pm

10) % higher than in the unconfined case, regardless of the operating conditions. The change in the vortex structure due to cavitation occurrence is also investigated in a different case study by means of PIV using fluorescent seeding particles. A vortex is generated by an elliptical hydrofoil and the velocity field outside the vapor phase is compared with the one in cavitation-free conditions. It is found that the cavitation does not change the vortex circulation, since the tangential velocity distribution of the cavitating vortex is identical to the non-cavitating vortex far from the vapor core. The tangential velocity close to the vapor core is however lower than in cavitation-free conditions. Moreover, the fluid is in solid body rotation in the vicinity of the liquid-gas interface. The alteration of the clearance geometry with shallow grooves to manipulate the gap flow and control the TLV intensity is evaluated in the simplified case study. The cavitation in the TLV and in the clearance region is significantly reduced with grooves located near the foil leading edge, oriented at 45

^{\circ}

or 90

^{\circ}

relative to the incoming flow. This result paves the way for further investigations, which may ultimately lead to TLV cavitation mitigation in axial turbines.

EPFL2015