Scale-up Technique of Slurry Pipelines—Part 2: Numerical Integration

Abstract

A kinetic energy turbulence model has been proposed for the computer flow simulation and scale-up of slurry pipelines (in Part 1 [1]). The numerical integration is performed by using a modified finite volume technique, with application to high-convective two-phase flows in two and three dimensions (in Part 2). The mixture kinetic energy and eddy viscosity turbulence models are compared. The one-equation eddy-viscosity turbulence model (εt - model) is formulated in Part 2 and applied for the multi-species particle slurry flow in cylindrical pipes. A modified finite volume technique is proposed for high convective transport equations, for one and two-phase flows. The integral formulation per volume yields surface and volume integrals, that are stored and counted only by interfaces using a multidimensional approach. The nonlinear distributions in volumes and on interfaces are approximated employing the derivatives in the normal and tangent directions to the bounding surfaces. Linear, analytical (upwind) and logarithmic laws of interpolations are considered for internal flows. The numerical approach was tested with good results for transport equations of momentum and various contaminants (solid particles, temperature, eddy-viscosity) in pipes. Experimental data for one and two-phase flows are compared to the integral finite volume predictions. The proposed finite volume technique can economically simulate complex flow situations encountered in the slurry pipeline scale-up applications.