## 5 Conclusions  
Particle acceleration and erosion models were developed and verified in this study based on the properties of abrasives and target materials. This paper describes the abrasive acceleration process through hydrodynamic analysis considering the properties of the abrasive and fluid. Based on energy conservation, a simple energy-work erosion model for a rock-like material was developed, considering energy transfer due to hardness differences between the abrasive and target. This theoretical approach was verified through comparisons to a previous theoretical brittle erosion model and numerical analyses results. The results obtained using the proposed simple and convenient model showed good agreement with those obtained using the previous erosion model and numerical analyses. Through a parametric study using the proposed acceleration model and the simple energy-work erosion model, the effects of the abrasive and target properties on erosion performance were reviewed. The following are the major findings of this study:  
* The abrasive acceleration characteristics were theoretically derived depending on the density and diameter of the abrasive particle, the density of the fluid, and the fluid flow state. Therefore, the particle velocity, exit velocity, and distance traveled by the particle could be calculated;  
Figure 11: Effects of abrasive particle parameters on erosion depth: (**a**) particle diameter and particle density; (**b**) particle diameter and particle hardness; (**c**) particle diameter and target hardness; (**d**) hardness ratio (\(H_{p}/H_{t}=R_{h}\)).  
Figure 12: Erosion rate according to abrasive and target properties.  
* A simplified erosion model was developed considering the hardness as a resistance force for energy transfer from the particle to the target. The erosion depth and volume could be calculated depending on the diameter, density, and hardness of the abrasive particle and target;
* For the erosion of rock-like materials, simultaneously occurring plastic failure and microcracking were simulated numerically. A CSCM was used for modeling the brittle material, and this numerical model was used to validate the theoretical erosion model developed in this study;
* Parametric studies were conducted to evaluate the acceleration and erosion characteristics using a wide range of abrasive particle properties (diameters, densities, and hardness values) and target hardness values. General acceleration and erosion characteristics could be identified.  
However, one limitation of this study was that the developed simple erosion model does not account for diversity in abrasive particle shapes and erosion caused by water. Therefore, further studies regarding the effects of abrasive particle shapes on targets and on erosion caused by water energy are required to overcome this limitation. Nonetheless, the results of this study can be used to estimate erosion rates based on the properties of the abrasive and target and to optimize the operation of AWJ systems.  
Conceptualization, G.-C.C. and Y.C.; formal analysis, T.-M.O. and Y.C.; investigation, Y.C.; writing--original draft preparation, T.-M.O. and Y.C.; writing--review and editing, G.-C.C. and Y.C.; supervision, G.-C.C.  
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2017R1A5A1014883).  
The authors declare no conflicts of interest.