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.
A kinetic energy turbulence model is proposed for the flow simulation and scale-up of slurry pipelines (in Part 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 [1]). The mixture kinetic energy and eddy viscosity one-equation turbulence models are compared. The constitutive equations and model constants are tested using laboratory experiments and then employed for large-scale applications. The governing equations are derived from the space/time averaging of the momentum equations and integrated in the pipe cross section using the finite volume approach. The specific interaction stresses (liquid-liquid, liquid-solid, solid-solid and solid-wall) are expressed in the mathematical formulation. The predictions for the velocity and concentration distributions, as well as on the mean velocity-headloss correlations, have been compared to available experimental data (water-sand, water-glass, water-coal mixtures; of concentrations αS = 5 – 40 vol percent, in pipes of various diameters D = 40 – 500 mm). The suggested model can simulate multi-species particulate pipe flow for which the semiempirical methods cannot be satisfactorily applied. The numerical tests and comparison to experiments show the model capabilities to scale-up data from laboratory to real flow situations via infinitesimal two-phase flow analysis.
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