## 3 Results and Discussion
### Influence of Jet Velocity on the Erosion Performance of HBS  
In this work, to study the influence of jet velocity on water jet erosion performance, different numerical models for the water jet erosion of HBS were established with different jet velocity and standoff distance. The jet velocities used were in the range of 20 to 150 m\(\cdot\)s\({}^{-1}\). The standoff distances of 0.5 cm, 1.5 cm, and 2.5 cm were used. The nozzle diameter was set to 1.5 mm. The shape of the erosion hole of HBS at different jet velocities with a standoff distance of 1.5 cm is shown in Figure 7. The erosion depth of HBS increases when the jet velocity increases. The surface of the erosion hole is rough, and stair-step shaped when HBS is eroded at a low jet velocity, and an increase in jet velocity increases the smoothness of the crater. The analysis considers that, under the submerged condition, the momentum exchange between the water jet and the surrounding water occurs, and the jet velocity decreases gradually. When the velocity at the edge of the jet decreases to a certain extent, the HBS cannot be eroded. The higher the jet velocity, the longer the cutting ability of the water jet is maintained, and the smoother the surface of the erosion crater. The jet velocity influence on the depth of erosion and the volume of erosion is illustrated in Figure 8. In Figure 8a, the erosion depth increases linearly with the jet velocity, which is consistent with the test results of rock breaking by a jet of [PERSON] [41; 42] and [PERSON] [43]. Moreover, when the jet velocity is constant, a smaller standoff distance leads to greater depth erosion. This indicates that the increase in jet velocity is beneficial to the erosion of HBS, and the smaller the standoff distance, the better. Figure 8: Jet velocity influence on the depth of erosion and the volume of erosion. (**a**) Depth of erosion; (**b**) volume of erosion. Figure 7: Erosion hole shapes of HBS at different jet velocities. (**a**) \(V=50\) m\(\cdot\)s\({}^{-1}\); (**b**) \(V=70\) m\(\cdot\)s\({}^{-1}\); (**c**) \(V=90\) m\(\cdot\)s\({}^{-1}\). Figure 8b shows the change in erosion volume. An increase in jet velocity corresponds to an increase in erosion volume, and the erosion volume increases rapidly at high speed, which is consistent with the test results of rock breaking by a water jet of [PERSON] [41; 42]. This result indicates that the larger the jet velocity, the higher the efficiency of the jet erosion of HBS. The analysis considers the rebounding water jets that were generated in the process of jet erosion of HBS, which would entrain the surrounding water when it flowed to both sides. Then, the rebounding water jets scoured the side of the erosion hole continuously, namely, the reaming hole process; the water jet energy increased with the increase in jet velocity, which not only enhanced the vertical erosion of HBS by the jet but also enhanced the erosion of the side of the crater by the rebounding water. Thus, under jet erosion, the erosion crater expanded in the vertical and radial directions. In addition, two commonalities between Figure 8a,b can be found. In the analysis of the relation between jet velocity and erosion depth, [PERSON] [41; 42] divides the erosion depth and jet velocity curve into the incubation period and erosion period. The threshold velocity separates the two periods and only when the jet velocity is greater than the threshold velocity can the rock be eroded. Similarly, from Figure 8a,b, a critical jet velocity could be noticed at the intersection of the velocity axis and the erosion depth and the erosion volume function, which describes the minimum impact velocity required to erode the HBS. The critical velocity is considered the HBS threshold velocity. As another commonality, when the jet velocity is constant, a smaller standoff distance leads to greater depth erosion and volume erosion, and the trend of the curve does not change under different standoff distances.