Industrial modeling of spirals for optimal configuration and design: spiral geometry, fluid flow and forces on particles

Abstract

Gravity, centrifugal, drag, lift and friction forces act on a particle during its passage down the curvilinear path of the spiral. The resultant force function dictates the separation of particles on the spiral deck by their size and density. Except for gravity force, all other forces depend on the hydrodynamics prevailing on the spiral. The flow of fluid, in turn, is determined by the spiral geometry. In order to develop a tractable and working model for simulation and design of industrial spirals, we describe the spiral geometry in detail, test the suitability of various empirical power laws for different flow regimes that are available in fluvial hydrology and estimate the magnitude of forces acting on particles. It is shown that of the four laws examined, the transitional or mixed flow power law is seemingly most appropriate for simulating the flow indices, such as the water line profile, local flow velocity, flow depth and flow rate along the spiral trough. The power law involves relatively simple computations and mimics the principal features and broad trends of flows as measured experimentally or simulated by highly computationally intensive solution of the Navier-Stokes equations for spiral geometry. The magnitude of individual forces acting on a particle in most instances is less than 10^-4 N, with considerable overlap between the forces. As a consequence, in general no force overwhelms the other forces and apparently it is the rate of change of forces with size, density, velocity and radial location which drives the separation.