## 5 Discussion
For the Laval nozzle, the increasing pressure ratio above \(R_{2}\) will cause the stronger and stronger normal shock waves near the nozzle exit [26; 29]. Then the normal shock waves attenuate the acceleration of the SC-CO\({}_{2}\) fluid, thus, resulting in the gradually decreasing enhancement of rock erosion ability of the SC-CO\({}_{2}\) jet by the Laval nozzle, as described in Section 4.3. At an ambient pressure of 26 MPa the pressure ratio is greater than \(Ra_{1}\); the normal shock waves will locate inside the Laval nozzle and obviously reduce the impact velocity of the jet [26; 29], which results in the weaker erosion ability of the Laval nozzles than that of the convergent nozzle, as shown in Figure 7d. Furthermore, at ambient pressure of 2 MPa, the pressure ratio is less than \(R_{2}\) and far below \(R_{1}\). This leads to intense expansion of the jets ejected from the nozzles [27; 29] and the smaller optimal standoff distances than that at ambient pressures of 10, 18, and 26 MPa. Besides, for the experiments under various ambient pressure and constant \(\Delta P\), the pressure ratio increases with the growth of ambient pressure under constant \(\Delta P\), as illustrated in Figure 12.  
Similarly, the higher the pressure ratio is, the stronger the normal shock wave near the nozzle exit will be [26; 29]. As a result, the enhancement decreases with increasing ambient pressure under constant \(\Delta P\), as described in Section 4.4. Likewise, the intense expansion of the SC-CO\({}_{2}\) jet at very low pressure ratio [27; 29] results in the smaller optimal standoff distances at ambient pressure of 2 MPa, as shown in Figure 8a. In addition, for the experiments under various fluid temperatures, the pressure ratio remains constant, however, the enhancement of erosion ability of the SC-CO\({}_{2}\) jet by the Laval nozzles still shows an increasing trend when the fluid temperature rises from 310 to 350 K, as described in Section 4.5. This is mostly due to the fact that the acceleration of fluid in the divergent section of the Laval nozzle is taking advantage of the compressibility of the fluid [26; 28]. The compressibility of the SC-CO\({}_{2}\)  
Figure 11: Distribution of pressure ratio under different ambient pressure at constant inlet pressure of 40 MPa. Figure 12: Pressure ratio as a function of ambient pressure under constant pressure difference of 30 MPa. fluid increases as the temperature rises. As a result, the enhancement keeps an upward tendency with increasing fluid temperature. Furthermore, at fluid temperature of 290 K below the critical temperature (304.13 K), the Laval nozzles have weaker erosion capability than that of the convergent nozzle, as shown in Figure 9a, which seems attributed to the low compressibility of the liquid CO\({}_{2}\). Another interesting phenomenon that can be observed in Figures 6-9 is that, the SC-CO\({}_{2}\) jet issuing from the Laval-1 nozzle always has a weaker erosion ability than that discharging from the Laval-2 nozzle. This is likely due to the fact that the inner profile of the Laval-2 nozzle is much smoother than that of the Laval-1 nozzle, as shown in Figure 3. For Laval-1 nozzle, the unsmooth inner profile makes the flow inside the nozzle more turbulent and shock waves form at the corner [29], which results in more energy loss of the flow. As a result, the erosion ability is reduced.