Mathematical modeling of separation characteristics of a coal-washing spiral

An improved mathematical model to simulate the particle and flow behavior in a coal-washing spiral has been developed. The modeling framework addresses three main components of the spiral system: (i) geometry of the spiral and its trough, (ii) fluid motion along the curvilinear path of the spiral and (iii) principal forces acting on a particle incorporating “Bagnold effect”. This effect has been addressed for both particle–inertial and macro-viscous regimes. The modeling components have been combined seamlessly by assuming that the particles eventually attain dynamic equilibrium in the forward longitudinal direction and static equilibrium in the transverse direction. The resulting force function provides a spectrum of the particle's radial location on the trough according to their size and relative specific gravity. The model predicts relative specific gravity distribution as a function of equilibrium radial position for different particle sizes. It also computes particle size variation as a function of equilibrium radial position for various values of relative specific gravity. Sensitivities of radial equilibrium distribution of particle size and relative specific gravity with respect to mean flow depth have also been investigated. Simulation results validated with the published data, are found to be reasonably consistent. The model provides an analytical tool for understanding of the separation behavior of particles in a coal-washing spiral.