## 3 Results and Discussion
### Influence of Nozzle Diameter on the Erosion Performance of HBS  
In this work, in order to study the influence of the nozzle diameter on water jet erosion performance, different numerical models for the water jet erosion of HBS were established with different nozzle diameters and standoff distances. The nozzle diameters used were in the range of 0.6 to 3.0 mm. The standoff distances of 0.5 cm, 1.0 cm, and 1.5 cm were used, and the jet velocity was set to 100 m\(\cdot\)s\({}^{-1}\). The erosion depth and the erosion volume versus nozzle diameter at different standoff distances are illustrated in Figure 12. Figure 12a shows the erosion depth versus nozzle diameter. With the increase in nozzle diameter, the erosion depth of HBS increases rapidly, however, the increment rate decreases gradually, and the erosion depth reaches a maximum value. The critical line 2 in Figure 12a illustrates the maximum erosion depth and the corresponding nozzle diameter, which is 1.8 mm. Then, the erosion depth decreases slowly and finally plateaus. Furthermore, the variation trend of the curve does not change under different standoff distances. All the results show that, for the erosion depth, the optimal nozzle diameter is 1.8 mm in the process of jet erosion of HBS. The analysis considers that, within a certain range, the jet energy increases with the increase in nozzle diameter, thus the impact force of the jet on HBS increases and the erosion depth increases. However, as the nozzle diameter continues to increase, the amount of water entrained by the jet increases greatly during the HBS erosion process, resulting in water accumulation at the bottom of the erosion hole. Meanwhile, the water accumulation effect is enhanced by rebounding water, which is generated by the jet. Thus, for the erosion depth, there is an optimal nozzle diameter in jet erosion process of HBS. Figure 11: Flow situations under different standoff distances. (**a**) \(L=1\) mm; (**b**) \(L=3\) mm; (**c**) \(L=9\) mm. Figure 12b shows the erosion volume versus nozzle diameter at different standoff distances. On one hand, it can be seen that, with the increase in nozzle diameter, when the nozzle diameter is under 1.2 mm, the erosion volume increases slowly while the erosion depth increases rapidly. The critical line 3 (located at a nozzle diameter of 1.2 mm in Figure 12b) indicates the end of the slowly increasing stage of erosion volume and the beginning of a rapid increase stage, while the critical line 1 (located at a nozzle diameter of 1.2 mm in Figure 12a) separates the rapid increase stage of erosion depth and the slowly increasing stage. Thus, within the range of 1.2 mm nozzle diameter, the erosion volume of HBS in the vertical direction plays a leading role in the total erosion volume. On the other hand, when the nozzle diameter is larger than 1.2 mm, the erosion volume increases rapidly but the erosion depth increases slowly (from critical line 1) with the increase in nozzle diameter. This result indicates that the erosion volume of HBS in the radial direction plays a leading role in the total erosion volume, and the increase in the radial direction is much larger than that in the vertical direction. Moreover, it can be seen that the difference between the curves is very small when the nozzle diameter is under 1.2 mm, and the difference increases with the further increase in nozzle diameter. The above results occurred because, the jet has less energy when the nozzle diameter is small, and the energy of the rebounding water jet decays rapidly after entraining the surrounding water, resulting in the weak erosion of the side of the crater. With the increase in nozzle diameter, the energy of the rebounding water jet increases, and the amount of water entrained by the rebounding water jet increases greatly, which enhances the erosion of the side of the crater. It can be concluded that, for the erosion volume, the jet erosion efficiency of HBS can be significantly improved due to the increase in nozzle diameter.