Thin-film flow in open helically-wound channels

Abstract

The study of flow in open helically-wound channels has application to many natural and industrial flows, including those in static spiral separators. The flow consists of a primary axial component and a secondary cross flow and, in spiral separators, the fluid depth is typically small making experimental investigation difficult. Mathematical models are therefore of great value for determining how such flows are influenced by fluid properties and geometrical parameters and, hence, for predicting and improving the performance of these separators. A thin-film approximation is appropriate and yields an explicit expression for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that can easily be solved numerically and in some cases analytically. The semi-analytic predictions of the thin-film model are found to be in good agreement with much more computationally expensive solutions of the Navier–Stokes equations.