## 5 Discussion  
From the experimental results, the nozzle configuration has significant effects on the rock erosion characteristics of the SC-CO\({}_{2}\) jet. How nozzle configuration influences rock erosion ability is likely to  
Figure 9: Effect of nozzle configuration on rock erosion volume of the SC-CO\({}_{2}\) jet under different fluid temperatures. depend on the nozzle configuration and the ratio of the inlet pressure and the ambient pressure. This is due to the fact that the pressure ratio can have large effects on the acceleration process of the SC-CO\({}_{2}\) fluid inside the different nozzles which in turn directly affects the flow characteristics as well as the impingement characteristics of the high-speed SC-CO\({}_{2}\) jet. To further understand the mechanism of effects of nozzle configuration on the rock erosion characteristics of the SC-CO\({}_{2}\) jet, a preliminary analysis was performed as follows. According to the theory of erosion of materials by jet impact, when the fluid and the rock specimens remain unchanged, the erosion intensity of the jet on the rock specimens is largely dependent on the impact velocity which determines the magnitude of the impact loading and the stress wave energy [44; 45]. Moreover, the impact velocity is affected by the pressure ratio which drives the fluid to flow in the nozzle, and the nozzle configuration which determines the acceleration of the fluid inside the nozzle [26; 27; 29]. As described in Section 2.2, when using nozzles with different configurations, the jet will have different impact velocities and structures under the same pressure condition. The impact velocity and structure of the jet can be judged and analyzed by the critical pressure ratios. According to Equation (2), the calculated critical pressure ratio, \(R_{1}\), is 0.55 for the convergent nozzle. Simultaneously, in light of Equations (3)-(5), the calculated critical pressure ratios, \(R_{2}\), \(R_{a1}\), and \(R_{a2}\) are 0.13, 0.57, and 0.92, respectively. For the experiments on the effect of nozzle configuration on the erosion ability of the SC-CO\({}_{2}\) jet under various inlet pressures, the pressure ratios were plotted in Figure 10. As shown in the figure, at inlet pressure of 20 MPa, the pressure ratio is very close to \(R_{1}\) and \(R_{a1}\). For the convergent nozzle, the flow of the jet approaches the critical state and almost no shock wave is formed at this pressure ratio; while for the Laval nozzles, this will cause strong normal shock waves formed in the jet near the nozzle exit due to compression of jet fluid by ambient fluid, resulting in the largely reduced impact velocity and the weak impingement on the specimens [26; 27; 29]. As a result, the convergent nozzle has a greater erosion capability than the Laval nozzles, as shown in Figure 6a. Besides, with the increase of inlet pressure, for the convergent nozzle, the pressure ratio is getting lower than the critical value, \(R_{1}\), resulting in more and more intense expansion of the jet ejected from the nozzle exit [26; 29]. This will make the jet cannot focus enough energy to effectively impact and erode the specimen, which is likely to be the reason for the reduction of the optimal standoff distance, as shown in Figure 6b-d. For the Laval nozzles, the pressure ratio is getting closer to the critical value, \(R_{2}\), with increasing inlet pressure. This will reduce the intensity of the shock waves in the jet flow and enhance the acceleration of SC-CO\({}_{2}\) fluid, and thus enhance erosion capability of the jet [27; 29] so that the maximum enhanced erosion volume increases when raising the inlet pressure, as described in Section 4.2. Moreover, for the experiments under various ambient pressure and constant inlet pressure, the pressure ratio grows up with increasing ambient pressure, as shown in Figure 11.  
Figure 10: Distribution of pressure ratio under different inlet pressures at constant ambient pressure of 10 MPa.