## 5 Results and Analysis  
The flow profiles of the bubbles were analyzed based on the calculated results of the 3D bubble reconstruction algorithm. Figure 8c displays the size and distribution of the 3D bubbles recreated by computing and processing a certain frame from the recorded video. Stereoscopic parallax explains the following results: the bubble viewed in the mirror deviated from its actual appearance. Hence, the 3D bubble image from the back (B) side appeared to opposite left and right when compared with the mirror image of the B side in Figure 8a,b. As per the 3D reconstruction results, the bubble algorithm gave satisfying results. Even if not all bubbles were reconstructed, the results of the 3D reconstruction tallied with the original experimental images, thereby concluding with a vivid and solid reference for recreating the bubble morphology. Figure 10 illustrates the 3D reconstructed bubble flow profile of four adjacent frames from 0 ms to 0.87 ms. The time interval between two adjacent frames was the least time difference captured by the high-speed camera, which was equal to 0.29 ms. Furthermore, the 3D bubble reconstruction algorithm was stable enough to simulate and evaluate the bubble flow profile in each frame. Figure 9: Space partition of the flow field. As an example, a short experimental video which consisted of 50 frames of images was used to further analyze the characteristics of the reconstructed 3D cavitation bubble cluster. Its first four frames were the same frames in Figure 10. It is worth noting that the time of 50 frames of experimental images is only 14.5 ms, which exhibits the advantage of the high-camera camera. The number of 3D bubbles fluctuating within 50 frames of experiment images was showed in Figure 11, which can present the size of the bubbles and its number in each time interval The blue-color curve mainly floats between 40 to 70, which indicates that the generation and collapse of the cavitation bubbles can achieve a relative balance in a short time. The average number of bubble is 57.78. The cavitation volume percentage in each frame is stated as Equation (9):  
\[P_{v}=\frac{\sum\limits_{i=1}^{n}\frac{4}{3}\pi a_{i}b_{i}c_{i}}{\pi(R_{\text{ fluid}}-r_{\text{core}})h}\times 100\%, \tag{9}\]  
where \(R_{\text{fluid}}\) is the radius of the fluid field in the valve and \(r_{\text{core}}\) is the radius of the valve core. In addition, \(R_{\text{fluid}}\) and \(r_{\text{core}}\) are constants. \(a_{i}\), \(b_{i}\), \(c_{i}\) are the three semi-major sizes of the cavitation bubble on the \(x\), \(y\), and \(z\)-axes. The variation of the cavitation volume percentage \(P_{v}\) over time is shown in Figure 11. The change of the \(P_{v}\) and the number of bubbles between the adjacent frames revealed that the growth and collapse of the cavitation bubbles were recurrent and fast. While comparing the \(P_{v}\) curve with the number of bubble curve in Figure 11, an obvious positive correlation between the number of bubbles and the percentage of cavitation can be found. Moreover, the increase in the number of bubble and the \(P_{v}\) did not exactly match; at times, while the cavitation volume percentage was decreasing, the number of  
Figure 11: Change of the number of bubble and \(P_{v}\) over time. Figure 10: 3D reconstruction results of bubble flow in a short time (unit: mm). bubbles did increase. Through the analysis of both results in Figure 11 and the original experiment images, it was concluded that scattering of the bubble clusters into small bubbles increased the number of bubbles in the cavitating space. As shown in Figure 12, a short experimental video with 100 frames were analyzed. Various perspectives of the bubble clouds were presented and from the 100 th frame (at about 29 ms), 5635 cavitation bubbles were detected and reconstructed, respectively. Based on the scatter diagram, the flow pattern of the 3D bubble cluster could be inferred.