Prédiction de l'érosion de cavitation

Predicting the rate and location of cavitation erosion is a complex problem that motivated an important amount of basic and applied research in the fields of hydrodynamics, mechanical science and metallurgy. Using an original approach, the so-called energetical approach, we proposed a prediction model, through the erosive power term, in an attempt to conciliate these various aspects of the cavitation erosion phenomenon. Our attention was also devoted to defining a transposition procedure in order to correctly apply this model in practical fields such as model tests. The energetical approach is based on the knowledge of the energy spectrum associated with a leading edge cavitation, also known as sheet cavitation. The collapse of vapour cavities at the rear part of the attached cavity is known to be sufficiently violent to produce damage on most types of materials, even on very high strength ones such as stellite or stainless steel. However, the experimental determination of such a spectrum has been a matter of great difficulty. As a consequence, no prediction model has received enough consensus up to now to be successfully applied. We established this energy spectrum on the basis of large experimental work performed on a hydrofoil mounted in the IMHEF-LMH high speed cavitation tunnel. We aimed at the determination of the fundamental components of a cavity potential energy : its volume and the driving pressure forcing it to collapse. The production rate of the cavities completes the set of basic parameters needed to completely define the fluid energy spectrum. We first measured the wall pressure field over the profile. This allowed us to have a measure of the overpressure in the downstream closure part of the leading edge cavity. Measuring the travelling time of vapour vortices through a laser beam allowed us to determine their individual main size. Then, we used the continuous wavelet transform to determine their shedding frequency according to this size. On a statistical basis, we found a Strouhal relationship between their main dimension, their shedding rate and the mean flow velocity. This relationship applies to both the steady and unsteady states of the cavitation behaviour. However, in this latter situation, two specific sizes were also found that are essentially defined by the main cavity length. In this case, their production rate is rather ruled by the well-known Strouhal number based on the cavity length and on the flow velocity. We introduced an original visualisation technique, called stereo-tomography, in order to take a measure of the volume of vapour vortices shed by the main cavity. Our analysis of the volume distribution and of the vapour structures morphology led us to consider that all types of vapour vortices could be seen as equivalent to spherical volumes. The characteristic volumes related to the unsteady behaviour are defined by the knowledge of the main cavity length. According to these results, we were able to define the energy spectrum as a function of the main hydrodynamic parameters.We then derived the erosive power term, taking into account the minimal damaging energy, which is a parameter depending only on the mechanical properties of the material. Moreover, we introduced the erosive efficiency in order to quantify the erosiveness of a cavitation development considering the above energy threshold. Finally, we suggested a simple model predicting the location of erosion, as a function of the material energy threshold and of the flow parameters. Considering the transposition side of the erosion problem, we introduced the erosive power coefficient as a scaling factor for the erosive potential between geometrically similar flows. The comparison between the fluid and the deformation energy spectra, carried out from former erosion tests, showed a remarkable proportionality relationship between both. This relationship is defined by the collapsing efficiency, which we found to be constant over the considered range of energies. We then managed to establish a link between the fluid and the material being damaged. This result claims the merits of the energetical approach and ensures its validity.

Détection vibratoire de l'érosion de cavitation des turbines Francis

Cavitation erosion of Francis turbines continues to impose costly repairs and loss of revenues. This erosion is primarily caused by leading edge cavitation. A revue of the literature reveals the non-existence of an absolutely validated detection technique of this cavitation in operating Francis turbines. Considering the impulsive character of the implosion of a cavitation structure, the assimilation of cavitation erosion to a process of mechanical fatigue of materials and the vibratory response at high frequencies of a linear structure to multiple random excitations whose responses add on a power basis, we have proposed that the vibratory response of a Francis turbine at high frequencies is tightly related to its cavitation erosion rate. The absolute measurement of cavitation aggressiveness on the blades can be made by the normalization of lower guide bearing vibration measurements by an average Transmissibility function measured by reciprocity with the runner underwater. The proposed method has been validated and it is now possible to state that the MSV of inferred forces at the cavitation impact rate of hydrodynamic origin is proportional to the erosion rate. The approach has been validated in excellent manner in laboratory set-ups with little or no flows by comparison to absolute cavitation aggressiveness assessment methods such as the DECER electrochemical technique and the pit counting technique on polished material samples. The validation was then pursued with laboratory homologous flows on a NACA 009 profile in the LMH high-speed cavitation tunnel with blade mounted DECER sensors as reference. Once again, impact frequencies of hydrodynamic origin, following here a Strouhal law, were observed and the MSV of the profile acceleration at high frequencies was proportional to the average erosion rate on the profile. Notwithstanding the difficulty of the measurements, the results were excellent and fared well with the erosive power of the flow in V3L2 (V= flow velocity, L= length of the attached vapour cavity). Preliminary measurements on a Francis model with blade mounted DECER sensors agreed well with the MSV of lower guide bearing acceleration at high frequencies. Later measurements on the Rapide Blanc model confirmed the damage model observed on the NACA profile. Hydrodynamic impact frequencies were however not governed by the tunnel Strouhal law but were found to be determined by the blade passage frequency. Stationary measurements at the lower guide bearing were equivalent to runner on board measurements. Reciprocity, typical to linear structures, was verfied. As on the profile, maximum aggressiveness on the runner blade occurs in the leading edge cavity closure area. This was confirmed by the application of "Prescale" pressure sensitive film on the blades for operating conditions generating maximum vibratory response at the cavitation hydrodynamic frequencies. High-speed video recordings shot at 2000 frames/s allowed detailed observation of the dynamics of the cavitation structures at the blade passage frequency. Visual observations of cavitation developments along with implosion frequencies allowed observing that the MSV of vibratory response at high frequencies at the cavitation impact occurrence rate was coherent with the calculated value of the flow erosive power inasmuch as the implosions occurred on the blades and not beyond the blade trailing edges. These results on the Francis model therefore supported the proposed vibratory detection approach. The application of the developed techniques, including the measurements of Transmissibility with the runners underwater, allowed assessing the difference in absolute cavitation aggressiveness on an existing and proposed replacement model runner for the Beauharnois power plant. The applicability of the proposed measurement and calibration methods was confirmed on prototype N°6 of the Rapide Blanc power plant. Measurements on fixed and rotating elements of the machine are equivalent and reciprocity also applies. The recurrence frequency of the cavitation impacts was however different from that of the model. The difference appears to be due to the semi-spiral case utilized on the model. It was not fully homologous to the full spiral case of the prototype. It would thus appear that on the model, the wake of the semi-spiral case tongue plays a determinant role in the generation and implosion process of cavitating structures while on the prototype the wakes of the wicket gates fill that function. The ultimate validation of the vibratory approach to the detection of erosive cavitation on Francis prototypes occurred in 1995 on unit 44 of the Manic 5 PA power plant. This was done using on board sensors (pressure, DECER and accelerometer) on severely eroded blade 4 and polished 316L stainless steel disks mounted in this same blade after removal of the pressure sensor housings. Paint removal and pit counting tests had previously correlated well in 1993 with the MSV of global modulation of high frequency acceleration at the lower guide bearing at the cavitation hydrodynamic impact occurrence rate which was for this prototype the wicket gate passing frequency for a rotating observer. The 1995 correlation of the MSV of the blade 4 high frequency acceleration modulation at the wicket gate passage hydrodynamic frequency with the volume pitting rate of the 316L stainless steel disks and the DECER erosion current was excellent. The existence in the flow of the 60Hz (rotation speed, 180 r.p.m., 20 wicket gates) hydrodynamic frequency was confirmed by dynamic pressure measurements on blade 4 and in the draft tube just below the runner. The per blade inferred forces were calculated for each set of test conditions with the average Transmissibility measured by reciprocity on five blades with the runner underwater. The MSV of high frequency inferred forces agrees better with the real aggressiveness than does the wideband acceleration but not as well as the MSV of the acceleration modulation at the hydrodynamic frequencies of the cavitation impacts. Improvements on this subject have been incorporated in the cavitation erosion monitoring system now in operation at Hydro-Québec. Tu summarize, the MSV of the vibratory response at the lower guide bearing modulated at the cavitation hydrodynamic frequencies describes well its relative aggressiveness with varying operating conditions and the use of an averaged Transmissibility measured with the runner underwater allows to estimate it on an absolute basis.

EPFL2000

Erosion vibratory fingerprint of leading edge cavitation of a NACA profile and of a Francis model and prototype hydroturbine

François Avellan

This paper summarizes the findings of CEA project No 307 G 657 entitled "Hydraulic Turbine Cavitation Pitting Detection by Monitoring Runner Vibration." The project was centered on the detection of leading edge cavitation, the main cause of erosion damage on Francis turbines. Based on a damage model proposed by EPFL and verified by EPFL and IREQ, the vibratory signature of erosive cavitation was first sought on a bi-dimensional NACA 009 profile in a high speed cavitation tunnel and then on the model and the prototype of a Francis turbine design. The main results of these investigations are presented. These show that the damage mechanism observed in the cavitation tunnel appears to also apply to the model and the prototype but its vibratory signature is modified and is determined by overall system flow characteristics that can vary from model to prototype if complete system homology is not maintained. Appropriate measurements on the fixed part of the machine were found to be equivalent to those made on the rotating part.

1993

Détection vibratoire de l'érosion de cavitation des turbines Francis

EPFL2000