## 4 Results and Discussion  
It is worth noting that the four-sensor probe can only give out local flow parameters of two-phase flow. It is unable to discriminate different two-phase flow regimes of stratified, slug, wavy, etc. Extra correlation research is required to make connections between local flow parameters to global flow regimes. Measuring local flow parameters at multiple locations is the purpose of the four-sensor probe and the validations against visual measurement are hence extended below. For cap bubble occupying almost the tube diameter from \(-4\) to \(4\) mm, ten radial locations ranging from \(-2.5\) to \(2\) mm are measured by the four-sensor probe. The numbers of total detectable bubbles and the numbers and ratios of the effective bubbles in the \(80\)-s measurement duration at each radial location are given in Table 1. It can be seen that \(350\) bubbles on average are produced in \(80\) s, resulting in a bubble frequency of \(4.375\) per second. The uncertainty of the counted bubble number changes between \(-5\) to \(6\), indicating that the steady and uniform features of the bubbly flow, which is necessary for this verification test. As expected, the effective number of bubbles recognized by the MATLAB code is lower than their total number. Meanwhile, both the effective number and the ratio of the effective number to the total number decrease, and this decrease becomes faster toward the ends of the test range. For the test location beyond \(2\) mm, the ratio can be well below \(0.5\). This is because, as the probe moves away from tube axis, the bubble interfaces become more inclined and it becomes easy for the bubble to slip away from the probe. It should be noted that the errors of the obtained local flow parameters increase with the decrease of ratio of number of effective bubbles to their total number. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Location (mm)** & \(-2.5\) & \(-2\) & \(-1.5\) & \(-1\) & \(-0.5\) & \(0\) & \(0.5\) & \(1\) & \(1.5\) & \(2\) \\ \hline \(N_{total}\) & 349 & 356 & 351 & 347 & 347 & 353 & 345 & 355 & 352 & 350 \\ \(N_{\text{eff}}\) & 107 & 202 & 252 & 29 The void fraction from four-sensor probe by Equation (2) and visual measurement by Equation (13) are compared in Figure 10. Since the void fraction from Equation (13) is an average void fraction across the whole tube diameter, it appears as a horizontal straight line in Figure 10. In view of the bubble shape shown in Figure 9c, the bubbly flow should produce a void fraction distribution with a peak value in the tube axis and decrease towards the tube wall. This trend was successfully reflected by the probe measurement, as shown by the black square dots in Figure 10. Its arithmetic mean value shown by the dashed line agrees well with the visual measurement, with an overestimation of 8.4%. The IAC from four-sensor probe by Equation (4) and visual measurement by Equation (14) are compared in Figure 11. Since the IAC from Equation (14) is an average void fraction across the whole tube diameter, it appears as a horizontal straight line in Figure 11. In view of the bubble shape shown in Figure 9c, the normal vector of bubble interface changes from vertical near the tube axis to pointing right-upwards near the tube wall, thus the angle between bubble velocity which is parallel to the tube and the normal vector of interface increase and the denominator of Equation (3) decreases. As a result, a larger IAC should be observed near the tube wall, with a minimum value emerging at the tube axis. This trend was successfully captured by the probe measurement, as shown by the black square dots in Figure 11. Its arithmetic mean value shown by the dashed line agrees well with the visual measurement, with an underestimation of 1.7%.