## 3 Results and Discussions
### Wavelet Spectrum Analysis  
The wavelet packet analysis decomposed the pressure signals into four levels. Among the wavelet decomposition methods, [PERSON] four-scale base wavelet (db4) has been used most frequently in multiphase flow time series decompaction [57]. In this study, [PERSON] four-scale base wavelet (db4) and norm entropy analysis method generated 16 wavelet packet coefficients. The pressure fluctuation signal achieved from the experimental data only yields a frequency of 100 Hz. Thus, only four-level decomposition is sufficient because the pressure signals do not have sufficiently high-frequency and high-resolution data to obtain more detailed frequency analysis. The spectrum of the packet wavelet analysis represents the time-frequency plot, which provides a coefficient of decomposed frequencies at a different level. This spectrum represents the time and location of the fluctuation of the signal. From Figure 23, it can be observed that the time-frequency plot divides the time-frequency plane into concentrated rectangles as a two-dimensional representation of signals. The pink color intensity of each box depends on the coefficient of the wavelet packet [34]. Figure 23: Spectrum for slug flow under different flow conditions. A similar plot is shown in Figure 24, which is the time-frequency plot for the bubbly flow regime for various flow conditions. The intensity of the pink shade represents the energy level of a time-frequency cell; the lower the energy content, the lighter the shade. For the bubbly flow regime, the bubbles are smaller, so the pressure fluctuation intensity is less, which means the low-frequency response has less energy content and the pink shade is light and scattered. In the slug flow, the Taylor bubble size is more prominent. Therefore, the low-frequency cells have more energy and a darker shade [34]. In addition, the repetition of the intense pink shade after a specific time interval can be evidence of the picks of the pressure signal. Thus, with a higher-resolution and better-quality sensor, where the pressure signal picks are more precise, this map can be a helpful way to understand the flow phenomena inside the pipe. When comparing the wavelet spectrum analysis of bubbly and slug flows for the same water flow rate, it has been observed that, for bubbly flow, the color intensity is comparatively less in the low-frequency response area. However, the use of a higher-resolution pressure transducer may enhance the wavelet spectrum quality with more precise fluctuation characteristics. The wavelet entropy analysis of the pressure fluctuation data represents the nonlinearity of the gas/liquid two-phase flow. After calculating the wavelet entropy of 10,000 pressure signal data points of gas/liquid two-phase horizontal flow, it was seen that the wavelet entropy increased with the increase of the pressure signal fluctuation. The entropy values of the pressure fluctuation data were compared with the gas to liquid volume flowrate ratio (GLR) and the void fraction (\(\alpha_{g}=\frac{\sigma_{g}^{\prime}}{v_{g}^{\prime}+v_{1}^{\prime}}\)). The void fraction (\(\alpha_{g}\)) is the ratio of the gas velocity and the liquid velocity. Figure 24: Spectrum for bubbly flow under different flow conditions. In Figure 25, it can also be observed that wavelet entropy increased with the increase of gas void fraction for gas/non-Newtonian fluid. This means the fluctuation of the pressure increases with the rise in the GLR for gas/water flow. Another observation is that the wavelet entropy value for gas/non-Newtonian flow is less than that for the gas/Newtonian fluid flow. This phenomenon occurred due to the viscosity effect of the non-Newtonian fluid, which means the disturbance of the pressure signals is less than that of the Newtonian fluid. Figure 26 shows that with the growth of the GLR, the norm wavelet entropy increased, which means the fluctuation of the pressure increases with the increase of the GLR. However, the norm entropy change at the low GLR is not consistent. [PERSON] et al.