Theoretical analysis of the particle acceleration process in abrasive water jet cutting

In this paper, a general modelling for the acceleration process of abrasive particles in a high pressure water jet is presented. For this purpose, a new mathematical method is used which consists of the analytical resolution of the differential and non-linear equation of particle motion within a high speed waterjet flowing in a mixing nozzle (mixing tube). As a result, the equations of motion reveal that the particle velocity increases while the fluid jet velocity decreases as function of the distance within the mixing tube with respect to the assumption of conservation of momentum along the acceleration process. The original method of resolution used here enabled the authors to take account of all of the interfacial forces that act on the particle such as drag and virtual mass force. Moreover, it becomes more possible to predict the particle velocity at impact considering the real conditions of jet formation where air is entrained into the jet to feed abrasive particles by the Ventury phenomenon. The experimental validation of the present theoretical modelling has been conducted successfully by means of an experimental correlation which links the estimated particle velocity at impact and the experimental depth of cut. So the theoretical modelling of particle acceleration coupled with the experimental correlation provides a good estimate for control of cutting parameters such as hydraulic pressure of water, abrasive mass flow rate, traverse rate and depth of cut.