Multi-Size Particulate Flow through Rotating Channel — Modeling and Validation Using Three Turbulence Models

Abstract

A comparison of three turbulence models in modeling and validating dense multi-size particulate flow through rotating channel is presented. All the three turbulence models incoporate a rotation modification to the production term in the turbulent kinetic energy equation. In the first model, rotation-modified k-ε equations are used to compute the eddy viscosity of pure carrier which is then modified for the presence of particles. In the other two models, rotation-modified k m-ε m equations are solved for the mixture directly. The eddy viscosities are then computed from k m and ε m. The predicted results of all three models show excellent mesh independence. The coarsest mesh satisfied the mass conservation to within 0.1%. The code based on pure carrier-phase eddy viscosity (modified for concentration) is computationally 2-3 times more efficient than the other two (mixture-based) models. The predicted results using all three turbulence models are compared against applicable experimental results in the open literature. Regression between the computed and experimental results shows excellent agreement between the two.

Finite Element Prediction of Multi-Size Particulate Flow through Three-Dimensional Channel: Code Validation

“…The mathematical expressions for these stresses are straightforward extensions from the two-dimensional equations [6,7], and are not included here. Following previous procedures [1,[6][7]11], the eddy viscosity of the mixture and solid species are determined from concentration-modification of the eddy viscosity (µ t ) of the pure carrier-phase. The required turbulent viscosity, µ t , of the pure carrier phase is computed using the Spalart-Allmaras model [17], in which a transport equation is written directly for the turbulent viscosity.…”

“…The interaction force term mainly consists of the interactive drag between the solid species and the mixture [6][7][8][9][10][11]. Thus the drag force, M → k , on a solid species 'k' is ,…”

“…where C Dk is the drag coefficient, d eqk is the equivalent particle diameter (after correction for particle non-sphericity) of species 'k', and C is the local overall solids volumetric concentration. Drag coefficient, C Dk , is taken as (11) The particle Reynolds number, Re pk of species 'k' is defined as ,…”

“…Several two-dimensional studies [4][5][6][7][8][9][10][11] in the last decade examined slurry flows through pipes [4,5], horizontal ducts [6,7] and rotating channels [8][9][10][11][12] using Galerkin finite element method. In these studies, Eulerian-Eulerian (continuum) description [13,14] of the slurry consisting of the carrier fluid and the solids multi-species of different sizes was employed.…”

“…Several of the studies [8][9][10][11][12] used Galerkin finite element method with Q 1 Q 0 elements (velocities interpolated bi-linearly and pressure assumed constant over each element). Despite failing the LBB (Ladyzhenskaya-Babuska-Brezzo) condition [16], this element was shown to perform well for this type of application.…”