Finite element study of multi-size particulate flow in horizontal pipes

Abstract

Fully developed pseudo-homogeneous horizontal pipe flow of slurry with multi-size particles is modelled via Galerkin finite element method using nine-noded isoparametric elements. The momentum equation for the slurry mixture is based on a pseudo-fluid model. For each particle size (termed as specie), a convection-diffusion equation is solved to obtain the volumetric concentration distribution for that specie. A mixing length model, with a concentration-dependent eddy viscosity, is used to account for turbulence. Wall functions are used to prescribe mixture velocity at the wall. For any specified axial pressure gradient, the finite element code predicts the volumetric concentration distribution of each size fraction and the mixture axial velocity distribution. These are found to agree favourably with results published in the open literature. Overall mass conservation for each size fraction is satisfied to within 1%. The variations of concentration and mixture velocity along the pipe circumference are presented and possible insight into the sliding wear distribution along the pipe wall is deduced.