## 5 Results and Discussion
### Time Evolution of Fluid Oscillations
When applied to scalograms, clusters containing residual noise, wavelet artifacts or non-relevant oscillations will present lower \(k\) coefficients [28]. Areas including significant oscillatory phenomena will instead present high k coefficients. Consequently, the only partitions defined by \(k=K\) were considered as meaningful regions, while other partitions were discarded. For the present analysis, the value \(K=4\) was chosen using, as a reference, the one provided by the Calinski-Harabasz criterion [47]. Since the convergence of the \(K\)-means algorithm is affected by the initial position of centroids, their initialization was replicated until an optimal final partition of scalograms, i.e., a partition capable of identifying with good accuracy the high-power regions, was obtained. In Figure 13a,b, the scalograms of Figure 8 (250 W, Ch12, BHM) and 10 (250 W, Ch12, horizontal) are proposed to clearly present, from a visual standpoint, the steps of the present peak identification procedure. In Figure 13c,d, the corresponding denoised scalograms are shown: the application of the K-means method highlights high-power peaks, while the scalograms low-power background is set to 0. Once the denoising procedure was applied, the scalograms' maximum peaks, i.e., main oscillatory phenomena, could be identified, time instant by time instant. In Figure 13e,f, the time location of frequencies referred to scalogram peaks is shown over time, together with the dominant frequencies (solid lines) and \(B_{f}\) boundaries (dotted lines). As is noticeable, time instants that do not present high-power peaks in the threaded scalograms are not assigned to any frequencies (gaps in Figure 13e,f). In addition, time periods exceeding the COIs limits are not considered. When compared to the vertical BHM (Figure 13e), the signal referring to the horizontal orientation (Figure 13f) denotes longer periods of oscillation within Bf, suggesting greater continuity over time. In particular, the continuity time \(t_{t}\), defined as the total time during which oscillations occur around the dominant frequency, was assessed to be equal to 2.14 s and 8.22 s for the vertical and horizontal orientations, respectively. This confirms the qualitative information provided in Section 5.2. On the other hand, the vertical BHM exhibits an overall longer activity, since oscillations at given frequencies are present for more time within the observation window. The channel activity time was evaluated to be equal to 17.32 s and 12.76 s for the vertical and horizontal orientations, respectively. The investigation on the continuity of fluid oscillations and channel activity was extended to all FPHP channels for average and high-power inputs to the evaporator, namely \(Q=150\) W and \(Q=250\) W. Lower heat loads were not considered since either weak or absent fluid oscillations prevented a clear discernment of high-power peaks from low-power backgrounds in scalograms. In Tables 6 and 7, \(t_{c}\) and \(t_{a}\) are listed for the mentioned study cases to present a channel-wise description of continuity and activity. It has to be stressed that the uncertainty, referring to the evaluated times, is strictly linked to the time resolution of the obtained magnitude scalograms. In fact, the time resolution determines the error made in the estimation of the time instants at which maximum powers are identified in scalograms after the denoising procedure. For the given wavelet parameters (Table 2),the time resolution equals 0.01 s, corresponding to less than 0.1 % of the total observation windows. For both heat loads in the vertical BHM (Table 6), the continuity generally assumes different values from channel to channel with respect to the horizontal orientation (Table 7), confirming that the fluid oscillatory motion is more scattered over a wider range of frequencies. For what concerns activity, the vertical BHM denotes more similar ta values, especially at high heat load, underlining that the fluid oscillations are promoted in every channel by such orientation.