This section describes a method to analyze statistically the cavitation impulses via AE. The enveloping and peak counting method presented here was the approach in Publication III. In cavitation research, the method as presented here has not been previously used, as far as the author of this thesis is aware of. The method produced statistical distributions of the impacts that were possible to connect with the cavitation pitting distributions, described in section 2.3. The relation to the statistical
distributions was not dependent of cavitation intensity, only of the AE setup and its transfer path, and probably the specimen material. This suggests that the AE peak voltage values have a direct connection to the actual impact loads induced by cavitation, but the scaling of AE voltages to impact pressures was out of the scope of this study. The results in this thesis were compared to those of (Hujer et al. 2015;
Hujer & Muller 2018), who utilized PVDF sensors for the same purpose and in the same cavitation tunnel. Additionally, the work by (Franc et al. 2011; Franc et al. 2012) provided the baseline in what to search from the AE signals in the tunnel.
The principal assumption in this thesis is that the burst signals in AE represent cavitation impulses, resulting either from single bubbles collapsing or from bubble clouds in which individual bubbles collapse virtually simultaneously. A single burst in AE lasted in the order of 0.1 to 1 ms. Therefore, a collective bubble collapse with μs timescale differences would not be differentiated in these measurements. For the purpose of impulse detection, only the results from the analysis of the resonance type sensor were used, as they were better separated in the signal.
The AE signals in the cavitation pitting tests had the same appearance than those in Figure 6. The approach in Publication III was rather simple: If a single bubble collapse induces a fairly well distinguishable burst in the AE signal, the maximum amplitude of that burst could correlate with the impact load. The AE signals were relatively long, with different burst durations, so a reliable method to detect the peaks was required. Enveloping the absolute values of the signal and then counting the envelope peaks proved effective. The envelope was a peak envelope that utilized spline interpolation, with a pre-defined minimum distance between the peaks. The minimum distance in this thesis was chosen to be 80 samples, which corresponds to 16 μs of signal. This is about 5 times the wavelength corresponding to double the resonance frequency of the sensor. As the absolute signal was calculated before the enveloping, the original wave minima turned to maxima, leading to a doubled apparent frequency. This value of minimum distance was found to properly filter out the sensor resonance effects, while still following the overall signal shape and not creating false peaks. Figure 7 presents an extract of an AE signal absolute value with a fitted envelope.
Figure 7. The enveloped signal. The peaks from the enveloped signal are detected through regular peak counting methods.
This type of approach detects the relatively high peaks extremely effectively, but it tends to create a large quantity of small peaks. These peaks are however insignificant in the final analysis, as an assumption was made that AE contains more peaks than there are pits in the pitting distributions. Therefore, it was safe to assume that voltage peaks under a certain threshold were either from noise or from events insignificant in damage accumulation. The total peak rate was in this thesis in the order of 10,000 peaks per second, dropping quickly if a threshold value was applied. Interestingly, even the assumed noise and small impacts followed the same exponential distribution in some of the measurements.
To analyze the distributions, it was chosen to display them as cumulative, as with the pitting distributions in section 2.3. The cumulative distributions for the peak voltages may be expressed similarly as for pits in equation 3:
ܰሶ=ܰሶ,݁ି
ೆ
ೆబ 5
whereܰሶ is the cumulative peak rate,ܰሶ, is the reference peak rate,U is the peak voltage andU0 is the reference peak voltage. The reference peak voltage is the mean voltage over the whole distribution and the reference peak rate is the peak rate whenU = 0, assuming the distribution is valid over the whole range of voltage values. It was found practical to define a cut-off voltageUcutoff, which is the voltage limit with only noise and non-damaging impacts below it. It was assumed that the
cut-off voltage was a material and setup dependent parameter that is essential to define for a system of this kind. Equation 5 can be expressed with the cut-off voltage applied to it:
ܰሶ =ܰሶ,௧݁ି
ೆషೆೠ
ೆబ 6
In this form, the equation is only valid for voltages above the cut-off limit. The Y-axis intersection is at ܰሶ,௧, which replaces ܰሶ, in equation 5. This formulation was found beneficial, as described in section 5.3. Figure 8 presents the peak voltage value distribution with the cut-off voltage applied. The peak voltage values were arranged to bins, such as in Figure 3 with the diameters, to improve readability.
Figure 8. Peak voltage distributions for the 2 MPa and 4 MPa upstream pressures in the cavitation tunnel. The scale is linear – logarithmic. The voltage bin size was 0.2 V.
The cut-off voltage was about 0.05 V for both upstream pressures, but it is discussed in more detail in section 5.3. The linear part in the linear – logarithmic scale was assumed to hold true globally, even for the 2 MPa case, even though Figure 8 suggests that below 0.1 V, the peak voltage data becomes less reliable. The most important data, lays in the truly exponential part, as it is assumed that the small impacts do not contribute that much in the damage accumulation. Additionally, the 4 MPa plot seems to be linear until 0 V, while the 2 MPa plot converges towards the 4 MPa value. Therefore, it was assumed that the 2 MPa plot below 0.1 V consists
mostly of noise, generated already in the sensor or in the enveloping process, and it can safely be excluded from the impulse distribution estimation.