Fundamentals of constructing particle-laden jetflow by fractal point sets and predicting 3D solid-erosion rates

A theoretical framework is established for constructing arbitrary particle-laden jetflow by means of fractal sets in the sense of average scale. This novel approach involves three main coherent components, in which one (1) searches for an appropriate original point set and confirms its intrinsic properties such as chaos, symmetry and density distribution; (2) derives governing equations for the formation of new point sets with any geometric configuration and desired normal velocity profile so that they can physically and geometrically represent particle motion on the cross-section of jetflow; and (3) develops the constitutive equations of particle-target interaction with erosion histories of particles and introduces the memory-element technique to handle the chaotic penetrating capabilities of millions of particles. Based on these results, the model is applied to predict the erosion rate in a drilling operation by abrasive waterjet. Results show that theory is consistent with experiments of drilling glass and titanium.