# Waterjet And Smoothed Particle Hydrodynamics

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Particle waterjet is similar to the abrasive waterjet; however, particle waterjet uses steel and spherical particles with larger diameter (ranged from 0.5 to 5mm) and smaller particle concentration (ranged from 0.5% to 5% by volume), which is different from the abrasive waterjet [5,6]. Steel particles play an important role in the erosion of rock with a waterjet. Particles erupting from the nozzle at a high speed and frequency impact the rock within extremely short time and in an extremely small contact area. The instantaneous contact stress is significantly high, thus changing the conventional rock breaking way and greatly increasing the energy utilization

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Finite element model

2.1 SPH-FEM Method

In the SPH method, the continuous fluid is dispersed to interact with particles, and the change in particles is used to describe the change in continuous fluid by the Diffuse Element Method (DEM). The SPH method is widely used in exploring the large deformation of penetration [31–33]. In this study, SPH–FEM coupled with the algorithm method was applied to investigate the relationship between the particle waterjet parameters and the rock breaking performance (depth and volume). In addition, the SPH and FEM methods were used to establish the particle jet model and the rock model, respectively.

Both the particle and water are modeled by the SPH method, which is a pure Lagrange method and does not need a mesh based on the interpolation theory. It uses a series of uniformly distributed smoothed particles having variety of physical properties to solve the partial differential equations under various conditions. The kernel estimated value f(x) can be expressed as [34–37]: