| A multiphase flow model for the flow of dense, noncolloidal, settling slurries through horizontal pipelines, and an associated numerical scheme to carry out computer simulations based on the model, are developed. The principal elements of the theoretical slurry flow model are: equations for estimation of the velocity distributions for each component of the slurry; and equations for estimation of the concentration distributions. The governing equations for calculation of the velocity distribution are derived from the local volume-averaged, time-smoothed conservation of mass and momentum equations. In these, the total stress contains a component to account for the Coulombic friction among contacting particles and between particles and solid boundary, in addition to the viscous and turbulent components. A so-called zeroth order turbulent model with the eddy viscosity suitably modified to include the effects of the solid particles is used in the present formulation. The boundary conditions on velocities include the imposition of no-slip for all components. The governing equations for the concentration profiles are derived from the convective diffusion equation, or generalized Fick's law. The formulation entail modification of the eddy diffusivity to account for the presence of the solid particles, and requires an accurate estimate of the hypothetical vertical component of the solid velocity. The present model, which includes the associated boundary conditions, is complete, in the sense that no experimentally determined slurry pipeline flow data are required as input data. The numerical code for solving the equations for velocity and concentration consisted of applying Galerkin's method to the governing equations and solving the resulting system using the finite element method. Numerical simulations for the flow of gypsum, coal, crushed glass, sand and gravel, coverning a solid particle size range from 38.3 {dollar}mu{dollar}m to 13,000 {dollar}mu{dollar}m, and pipe diameters from 4 cm to 49.5 cm, were carried out. These slurry systems were selected because detailed experimental data pertaining to them were available. The present slurry flow model, and the associated numerical code, provide the pressure gradient and the holdup as well as the detailed in situ solid, liquid and mixture velocity distributions and concentration profiles. The agreement between model predictions and experimental measurements is excellent. |
