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Erschienen: Auf die Merkliste Drucken Weiterempfehlung. The red contours are the cross-sections of the surface at the cutoff depths shown under each picture. Dark gray pixels not surrounded by red contours are pits shallower than the selected cutoff depths. Left, Ultrasonic G32 settings, exposure time: 1 min. Analysis of the pitting results is done in the same manner as in Sect.

The same materials tested in the tunnel were also exposed to cavitation gen- erated by the submerged cavitating jets and the ultrasonic device described in Chap. In the cavitating jet tests, The central jet impact area where maximum pitting occurred was chosen for detailed analysis.

Cavitation Erosion – Phenomenon and Test Rigs

Naval Research Laboratory. Shown here is the actual 1. Based on [6], reprinted with permission from Elsevier Optical scanning profiles of the surface of the pitted sample were obtained using an Alicona InfiniteFocus G4 scanner at the US Naval Research Laboratory. The spatial resolution of the instrument could be set to a few nanometers and an interrogation mesh size of 1.

Very little pitting overlap occurred, individual pits could be well identified, and the geometric characteristics of each individual pit could be accurately measured and used in the statistical analysis. Results from several cut- off depths were compared and the results were very similar to Fig. The cut-off depth of 0.

From the scanned profilometer measurements, an average pitting rate was cal- culated as the ratio of the cumulative number of pits per unit area to the exposure time. The cavi- tating jet pitting phenomenon follows a universal scaling law, as the pitting mea- sured in the high-speed water tunnel does in Sect. The main difference between this scaling law 3. This parameter was selected to be 1 in Eq. In all these tests, the jets were discharged into a container where the local pressure was the atmospheric pressure see Fig.

Therefore all results were for the same local pressure and this resulted in differences in the cavitation number between runs. However, in all cases the cavitation numbers were very small between 0.

Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction | SpringerLink

This difference in the procedure is responsible for some difference with the results obtained at constant cavitation number in the previous section. The effect of the jet pressure or the cavitation intensity on the pitting characterization parameters and, as a consequence, on the distribution function of pitting rate versus pit diameter is discussed in the following paragraphs. The larger pits are of particular interest as they correspond to the rare high intensity events, which would result in micro-fracture and later weight loss.

Equation 3.

Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction

Different curve fits using Eq. It is clear that the characteristic pitting rate and pit size increase with the jet pressure or jet speed, with approximately 0. Line fits correspond to the three-parameter Weibull distribution of Eq. Based on [6], reprinted with permission from Elsevier Fig. Based on [6], reprinted with permission from Elsevier characteristic pit diameter and the characteristic pitting rate are significantly dif- ferent between jet cavitation Figs.

Also, cavitation pits appear significantly smaller in the case of jet cav- itation see Fig. This may be attributed to the smaller length scale of the present jet flow, which produces smaller bubbles and consequently smaller pits see also Fig. The differences in cavitation generation methods and facilities contribute to this difference in the exponent.

Based on [6], reprinted with permission from Elsevier cavitation number for higher jet velocity tests. As mentioned earlier, to increase the local velocity at constant r one also increases the ambient pressure and this results in the bubbles experiencing much larger pressure during their collapse and thus a much stronger collapse see Chap. Another potential for discrepancy is the arbitrary use of the upstream pressures in both facilities to characterize the local velocities of interest. A better definition of the characteristic velocity may be required in the erosion region.

Finally, the different values of k used for fitting may also have an impact on the results. Since this aluminum is much softer than the stainless steel A, the jet pressures used for the pitting tests were reduced to the range 50 to 80 bars 5 to 8 MPa. Two test durations are shown in Fig. As shown in the figure the cumulative pitting rates obtained with the two exposure times are close, indicating that during the incubation period, pitting increases linearly with time.

The same scaling law 3. Comparison of the jet tests with ultrasonic cavitation tests red symbols and dotted line using the ASTM G32 alternative method Figure 3. This is consistent with other observations in terms of pressure measurements and material loss curves discussed in Chaps.

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The characteristic pit size and the pitting rate can be used as a measure of the intensity level of the cavitating field. They are key parameters for the prediction of the erosion rate by proper modeling of the material response to cavitation impact loads. It is thus essential to accurately determine impact loads and their statistical distribution in order to correlate them with the flow behavior and material damage.

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The most widely used method to detect cavitation impacts and assess their intensity is based on pressure sensitive transducers as discussed in more detail in Chap. Several kinds of such transducers have been used, in particular con- ventional commercial pressure sensors [14], piezoelectric ceramic discs [15], piezoelectric polymer PVDF Polyvinylidene fluoride films [16] as well as fiber optic sensors [17].

In spite of the progress made to improve the accuracy and reliability of pressure transducers by adapting them to impulse loading of cavi- tation see Chap. In addition, the sensor dimension is often too big compared to the microbubble size and the sensor may be rapidly damaged by cavitation. Another method to deduce the impulsive pressure is to extract it from the material itself considered as a sensor capable of detecting the spectrum of impulsive loads, which exceed its elastic limit.

From this standpoint the material itself is also a filter of the impulsive loads. Every sufficiently strong collapse beyond the elastic limit can induce a pit on the surface of a sample Fig. The basic point of this inverse procedure for evaluation of collapse pressure is the need for a proper modeling of material behavior.

A complex relation between the loading state and the material response probably occurs because of the high strain rates coupled with triaxial stress fields generated during impulsive loading. From an experimental point of view, the method consists of three steps: i perform pitting test to measure pit size, ii conduct nanoindentation mea- surements to establish stress—strain relation, and finally iii determine the impulsive loads or pressures by correlating the results of pitting test with nano- indentation test.

The principle of the inverse method is explained in detail below. The inverse method is applied to pitting tests conducted in the cavitation flow loop presented in Sect. Three alloys: aluminum Al T, nickel alu- minum bronze C, and duplex stainless steel A, were exposed to the same cavitating flows for comparative analysis. The samples were mechanically polished to obtain a metallographic surface with roughness smaller than 0. The shape of the plastic zone surrounding the pit will not necessarily have a round smooth shape because of the crystallographic orientation dependence of the plastic deformation.

However, for simplicity of calculations and modeling, we assume the cavitation pits as spherical caps char- acterized by their diameter D and depth h as illustrated in Fig. Therefore, the measurement of pit diameter D and pit depth h will allow determination of the strain e of a cavitation pit. Cavitation erosion pits are generally shallow indentations with a depth h much smaller than the diameter D.

Lec 19 Numerical Techniques for Fluid Flow: Lax-Wendroff Technique

Consequently, the mean strain of a cavitation pit 3. For materials with large values of E ry e. In this case, plastic deformation occurs mostly near the contact radius and piling up is expected. The blue region is the plastic zone surrounding the pit contact circle and the elastic deformation contributes also to the accommodation of impact deformation over a greater distance. In this case, sinking-in is more likely expected. The sketch of Fig. An example of application of the method is given in Fig. Each data point corresponds to a pit. All pits whose depth is smaller than the cutoff depth 0.

Numerical modelling of cavitation erosion

The corresponding measuring limit is represented by the black dotted line in Fig. No measurement is available below this line. The plots are very similar for the three alloys. This is because the relationship 3. Larger strains are apparently associated with impacts of smaller size. This is related partly to the aspect ratio of the small pits being far from spherical shape, and to the measurement errors in defining the profile of submicron pits by the stylus method.