## 3 Experimental Facilities
### Visual Measurement Techniques  
Besides the probe measurement described in Section 2, the flow parameters can also be obtained by the visual measurement which contains image recording and processing. A series of continuous captured images is shown in Figure 7, with time intervals between each of 20 ms. It can be seen that the recorded bubbles are roughly in cap shape, and the space intervals between bubbles are roughly constant. When a bubble reached the location where the four-sensor probe was located, as shown by the red frame of Figure 7, the image was taken as one of the images constituting the visual measurement. For each of the chosen images, the subsequent bubble image processing is shown in Figures 8 and 9. For the first step of image processing (Figure 8a as an example), each bubble was cropped out, according to marked edges and converted into binary black and white image (matrix), as shown in Figure 8b-d, respectively. Five successive chosen bubbles are shown in Figure 9a, and it can be  
Figure 6: Experiment loop of the present study. (a) Schematic diagram of the experimental loop; (b) Real photo of the experiment loop. Figure 7: A series of images showing continuous captured bubbles. seen that, although the flow conditions remain unchanged during the test, the shape of cap bubbles change continuously. To obtain the interface direction and bubble chord length, the images of bubble were added up in MATLAB code and divided by the number of bubbles to get the averaged bubble shape. The resulted image (matrix) shown in Figure 9b stands for the probability of a pixel occupied by gas phase (void fraction). As the number of images \(n\) increases, the difference of the resulted images reduces to minor, and it was found that \(n=100\) is enough in this research. By binarization of the last image of Figure 9b taken with 0.5 as the threshold value, the averaged bubble and its edge are shown in Figure 9c,d, respectively. Based on Figure 9d, the time-averaged bubble interface direction \(\theta\) and bubble chord length \(C\) at different radial location can be read by MATLAB. Assuming the averaged bubble in Figure 9c is axisymmetric, the bubble volume can be obtained by integrating the bubble's cross area at each horizontal layer throughout the bottom to top of the bubble, as shown in Equation (11). The total area of the interface can be obtained by integrating the bubble's interface area at each horizontal layer throughout the bottom to top of the bubble, as shown in Equation (12):  
\[\overline{B_{V}}=\int_{bottom}^{top}\pi r(y)^{2}dy \tag{11}\]  
Figure 8: Cut out bubbles and its binarization. (**a**) Bubble series; (**b**) Bubble isolation; (**c**) Bubble cropped out; (**d**) Bubble binarization. Figure 9: Averaging of bubbles. (**a**) Five bubbles in a sequence; (**b**) Adding different number of bubbles; (**c**) Result of the averaged bubble; (**d**) Outer shape of the averaged bubble. \[\overline{B_{a}}=\int_{bottom}^{top}2\pi r(y)dy \tag{12}\]  
where \(r\), a function of vertical location, is the radius of bubble at each horizontal layer. The time-averaged void fraction across the whole diameter can be obtained through dividing \(B_{V}\) by the average interval volume between two successive bubbles, as shown in Equation (13):  
\[\overline{V_{f}}=\overline{\overline{B_{V}}}{A\overline{L}} \tag{13}\]  
where the two short lines above \(V_{f}\) indicate time-averaged and space-averaged value for the same time, A is the cross area of the test tube and \(L\) is the average distance between two successive bubbles.