## 3 Results and Discussion
### Influence of Standoff Distance on the Erosion Performance of HBS  
In this work, in order to study the influence of the standoff distance on water jet erosion performance, different numerical models for the water jet erosion of HBS were established with  
Figure 9: Stress distributions 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\({}^{-1}\).  
different standoff distances and nozzle diameters. The standoff distance in the range of 1 to 13 mm was used. The nozzle diameters of 1.2 mm, 1.5 mm, and 1.8 mm were used. The jet velocity was set to 100 m\(\cdot\)s\({}^{-1}\).  
Figure 10 illustrates the erosion depth and the erosion volume with change in standoff distance under different nozzle diameters. From Figure 10a, two features could be noticed. On one hand, the erosion depth of HBS shows a linearly decreasing trend with increasing standoff distance because the jet energy dissipation increases due to the increase in standoff distance. On the other hand, it can be seen that the effect of different nozzle diameters on the erosion depth is small, which is consistent with the sensitivity analysis in Section 3.1.1.  
The erosion volume with change in standoff distance is shown in Figure 10b. The erosion volume of HBS decreases with the increase in standoff distance, however, the trend of the curve is quite different from that of Figure 10a. The erosion process is very sensitive in the range of 3 mm standoff distance. Within this range, just a small variation in the standoff distance yields significant changes in the erosion volume. Moreover, the variation trend of the curve does not change under different nozzle diameters. The results indicate that the short standoff distance is more effective for the jet erosion of HBS. The analysis shows that, in a submerged state, the jet diffuses due to water entrainment after ejection from the nozzle, and the velocity of the jet decreases when HBS is eroded, which results in a rapid increase in the amount of water entrained by the jet and a large increase in the diffusion range. Meanwhile, because HBS has the characteristics of low cementation strength and easy fragmentation, the diffused jet can still cause strong erosion. Therefore, the shorter the standoff distance, the earlier the jet erosion of HBS occurs, the wider the jet diffusion range, and the stronger the jet erosion of HBS.  
The above conclusions can be validated by Figure 11. It shows the flow situations of the water jet erosion of HBS at different standoff distances, with a jet velocity of 100 m\(\cdot\)s\({}^{-1}\) and a nozzle diameter of 1.2 mm. As shown in Figure 11, the jet diffuses in the process of eroding HBS, and the diffusion range of the jet is largest when the standoff distance is 1 mm, which is significantly larger than that when the standoff distance is 3 mm or 9 mm. Meanwhile, the erosion is strongest at the standoff distance of 1 mm, and there is no significant difference in the erosion hole morphology between the two farther distances.  
Figure 10: The erosion depth and the erosion volume with change in standoff distance. (**a**) Depth of erosion; (**b**) volume of erosion.  
In general, a decrease in standoff distance corresponds to an increase in erosion depth and erosion volume, which is consistent with the conclusions of Sections 3.1.1 and 3.1.2, respectively. Furthermore, the decrease in standoff distance enhances the efficiency of jet erosion of HBS. Thus, in the process of using a high-pressure water jet to exploit marine NGH, it is suggested that the standoff distance be less than 3 mm to obtain a higher mining efficiency.