Semi-empirical model for abrasive particle velocity prediction in abrasive waterjet based on momentum transfer efficiency

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.