3.1. Comparative Results of the Experiments Performed with PLIF40 Concerning the Spatial and Temporal Resolution

Before comparing the PLIF and conductance probe, we analyzed the differences in the temporal evolution of the film thickness using the PLIF methodology. To determine the waveform, a minimum of one pixel resolution can be considered to generate the total evolution of the film thickness during the measured time. Nevertheless, to reduce the noise introduced by the binarization during the pre-processing of the images, a moving average filter with a window of 15 pixels has been applied. Therefore, the spatial resolution is slightly increased from 1 pixel (or 0.033 mm approximately) to 15 pixels, equivalent to 0.5 mm. The conversion relation is 1 mm equivalent to 30 pixels as explained in the previous section.

Figure 20 shows a comparison of the waveform during 0.5 s between the processing of the film thickness considering 0.5 mm or 7.5 mm of spatial resolution. The reasoning behind taking 7.5 mm lies in the fact that the separation of the electrodes in the conductance probe is 6 mm with an electrode radius of 0.75 mm. Therefore, the total distance between the extremes of the emitter and received electrodes is 7.5 mm. It is possible to see in the figure that the average of 7.5 mm correctly reproduces the shape with a higher resolution but introduces subtle errors in the rugosity of the interface. As seen between 0.6 and 0.7 s in the graph, some ripple waves are neglected, reducing the capability to study them by methodologies with higher averaging.

Comparison between the evolution of the film thickness with an average of 0.5 mm and an average of 7.5 mm.

Next, the results obtained from the analysis of the spatial and temporal evolution of the liquid film thickness in annular two-phase flow are presented. As discussed earlier, the spatial evolution methodology for the data gathered using PLIF differs from the temporal evolution. Figure 21 provides a comparison between these two distinct techniques employed to analyze the waveform of the liquid film. The first approach involves reconstructing the film thickness by iteratively adding new information obtained between frames, while the second method requires tracking a single pixel in each snapshot over time. Notably, this analysis brings to light the dynamic nature of the liquid film, where a 3 s interval translates to an equivalent spatial length of approximately 6 m due to the fast motion of the film. However, it is important to clarify that the scale of the x-axis in the spatial evolution representation is not a direct reflection of the physical length of the tube. Instead, it serves as a composite extension, if both the film thickness and the waves remain unchanged over time. This abstraction allows for a focused examination of the evolving patterns and behavior of the liquid film. Upon closer examination of the comparison between the two techniques, it becomes evident that both consistently identify the waveform. They exhibit similar trends, although subtle discrepancies manifest in most of the waves. Notably, the temporal evolution analysis showcases a more uniform pattern, while the spatial evolution analysis excels in detecting the rugosity present at the liquid–gas interface. Differences in the disturbance wave height are also detected. The first explanation for these differences is that the snapshots were performed at a rate of 1940.1 Hz, so the difference in time between snapshots was 0.51×10−3 s. During this time, if the DW has a celerity, for instance, of 3 m/s, then travels 1.53 mm, which is equivalent to 45 pixels, so when capturing the temporal evolution at a given point, we are capturing points separated by approximately 45 pixels in space. This produces some differences when comparing spatial and time evolution as displayed in Figure 21.

Comparison between temporal and spatial evolution of the film thickness.

To compare the measurements between both techniques, the temporal evolution has been taken as a reference. It is important to underscore that the measurements conducted through the PLIF (planar laser-induced fluorescence) technique, and the conductivity probe were executed in not identical close regions, with a separation distance of approximately 100 mm. The measurement region using PLIF is, therefore, slightly anterior to the ROI of the probe. Figure 22 illustrates the temporal evolution of the liquid film through both techniques over a measurement period of 1.5 s. It is important to note that the spatial resolution plays an important role in the shape of the wave, as discussed before. The PLIF graph has been obtained with a spatial resolution of 0.5 mm while the conductance probe has a resolution of approximately 7.5 mm. Observable differences between the two techniques become apparent at first glance. Primarily, variations are discernible in the ripple waves. The spatial resolution of the camera allows for a much more detailed interface where a more detailed rugosity of the film is observed. Regarding the disturbance waves, subtle differences are also observed. For instance, in the latter two waves, a more pronounced dissociation is evident, meaning that even within the developed region, instantaneous interfacial characteristics continue to undergo temporal changes. It is worth emphasizing that transient statistics over time remain consistent, as explained in more detail in the following part of this discussion.

Comparison between temporal evolution of the film thickness for 1.5 s employing both techniques PLIF and conductance probe.