The abrasive mixing variables, such as the abrasive and water flow rates and the focus geometry parameters, determine the profitability of an abrasive waterjet system. In this study, the mixing efficiency characteristics in abrasive waterjet rock cutting were investigated. To demonstrate comprehensively the efficiency reduction due to collision during abrasive mixing, the chance of collision was expressed as the distance between the abrasive particles in the focus. The mixing efficiency was then assessed by utilizing the empirical relationship between the experimental results and the developed model. Based on the particle density and the velocity, the closer particles showed higher chances of collision, thus yielding a reduced cutting performance. Using the distance between particles model, the optimum abrasive flow rate and the cutting performance of abrasive waterjet systems can be estimated. This developed model can be used for the design selection of abrasive flow rate and systems for the cost-effective use of abrasive waterjets.

Abrasive waterjet (AWJ) is a technology that removes a target material with an abrasive accelerated by ultra-high-pressure water. Recently, its application for rock excavations in civil and geotechnical engineering has increased. AWJ excavation performance is affected by the abrasive velocity formed by momentum transfer during mixing and acceleration. The abrasive velocity varies owing to changes in the abrasive flow rate, focusing tube diameter, and focusing tube length. In this study, the momentum transfer efficiency (MTE) according to the abrasive flow rate and focusing tube geometry was investigated by a numerical analysis to better understand the multiphase flow inside the AWJ system. The MTE was defined based on the theoretical relationship between the abrasive velocity ratio and focusing tube factor, and evaluated through the empirical relationship between the water stiffness and focusing tube length. The optimal abrasive flow rate for generating efficient MTE was approximately 15 g/s, which enabled economical and effective acceleration of abrasive particles. Accordingly, a prediction model based on the derived MTE was developed for the final abrasive velocity generated at the tip of the focusing tube. Using the prediction model, it is possible to evaluate the comprehensive relationship between various AWJ parameters. Based on the prediction model, the abrasive–water flow ratio to generate the optimal abrasive velocity was 0.83. The developed prediction model provides guidelines for selecting the optimal focusing tube geometry and applying an economical abrasive flow rate when designing an AWJ system.