Slurry transport in a pipeline – Comparison of CFD and DEM models

In this paper, experimental data of solid distributions in horizontal pipelines were modelled using CFD and Discrete Element Method (DEM). Experimental data were taken from Gilles et al. (2004), Roco et al. (1983) and Hill (1996) for pipe diameter in the range from 51 mm to 103 mm, the average sand particle size from 90 m to 4400 m and average solid volume fraction from 0.092 to 0.21. Two CFD models available in STAR-CCM+ for Eulerian multiphase flows were used, the simple solid pressure model that uses the exponential formula for the solid pressure force and more sophisticated model based on the kinetic theory of granular flows that takes into account bulk, collisional, kinetic and frictional viscosities, which result from the presence of solid particles. In both models the turbulent flow was modelled using the standard k- model. The drag force acting on the particles was modelled using the Gidaspow formula. The granular flow model was compared with the DEM implemented in STAR-CCM+. The DEM formulation used in STAR-CCM+ is based on the soft-particle formulation where particles are allowed to develop an overlap. The non-slip Hertz-Mindlin contact model was used to account for particle-particle interactions and the Gidaspow drag formula for liquid-particle interaction. CFD and DEM predictions of solids concentration were compared against experimental data. The comparisons were made in terms of accuracy and computational time. NOMENCLATURE A constant in solid pressure force equation D ij A linearized drag coefficient c concentration of solid particles <c> average solid concentration CD drag coefficient CL lift coefficient d particle diameter D pipe diameter e coefficient of restitution F force   i int F internal forces g gravitational acceleration g0 radial distribution function I2D second invariant of deviator of the strain rate tensor Mi interphase momentum transfer p pressure v velocity vr relative velocity between phases  volume fraction d volume fraction of dispersed phase d,max maximum volume fraction of dispersed phase(packing limit)  angle of internal friction  dynamic viscosity p granular viscosity C p  collisional part of granular viscosity f p  frictional part of granular viscosity K p  kinetic part of granular viscosity f p max ,  maximum frictional viscosity  kinematic viscosity t c  turbulent viscosity  density  turbulent Prandtl number i stress tensor INTRODUCTION Transport of minerals like coal, copper, iron, phosphate and oil sand requires good understanding of slurry behaviour in the pipelines. This paper presents a CFD model of solid distribution in pipelines that gives better insight into the sedimentation process. In this work two approaches were used, the Eulerian multiphase model and the Discrete Element Method (DEM). The Eulerian multiphase model treats phases as interpenetrating continua. Each phase is characterized by its own physical properties, velocity and temperature. The pressure is shared by the phases and the amount of a given phase in a computational cell is given by the phase volume fraction. The DEM model is based on explicit modelling of the collisions between the particles. This modelling technique uses the Lagrangian approach. Eulerian multiphase model STAR-CCM+ solves the mass conservation equation for phase i:     0 vi     i i i i t       (1) and momentum balance takes form: