Multi-dimensional modelling of a spouted bed
Creators: name: Krzywanski, Romuald S.
Publisher: name: University of British Columbia
Year: 2008

description: Previous flow models of the spout and the annulus of a spouted bed were examined and their deficiencies identified. An attempt to adapt the fluidization version of the transient two-fluid model, K-FIX , to describe the flow in a spouted bed failed due to difficulties in reaching a steady state of stable spouting and unrealistic flow patterns predicted in the annulus region, probably because treatment of that zone as a two-fluid flow domain was grossly inaccurate. Two-phase flow models applied to systems having flow characteristics similar to those of the spout or the annulus were reviewed and approaches more suitable for modelling gas and particle flows in these two regions of a spouted bed were selected. A multi-dimensional model was then developed to describe the fluid and particle dynamic behaviour of cylindrical spouted beds with either conical or flat bottoms. Relationships yielding the position of the spout-annulus interface as a function of bed height were derived by a variational analysis for both two-dimensional and cylindrical spouted beds and were tested against experimental data selected from the literature. It is demonstrated that the spout diameter variation can be predicted from information about the average spout diameter and the spout expansion angle. The former can be predicted using available empirical correlations. Expressions for the latter were derived by a stress analysis, based on soil mechanics principles, of the particles in the vicinity of the spout inlet. Under most practical circumstances, this rigorous analysis yields expansion angles which are in good agreement with values calculated from a simple formula based solely on the operative bed geometry. The spout cavity obtained by this approach is superimposed on the ensuing two-region flow model. In the latter model, two-fluid equations are used to represent gas and solids motions in the spout while the vector Ergun equation and soil mechanics equations are employed to describe, respectively, gas and solids behaviour in the annulus. These give rise to a set of 11 non-linear partial differential equations which must be solved simultaneously to determine the distributions of gas and particle velocities, pressure and voidage in the spout and the annulus regions. Using numerical finite difference methods, the set of governing equations was solved subject to carefully chosen boundary conditions. A heuristic method of determining entrainment, using the minimum spouting predictions of the model, was employed. Local particle velocities, gas velocities and void fractions were obtained by marching the parabolized set of partial differential equations from the bottom of the bed while the pressure field was found from an elliptic Poisson equation applied to the whole bed. The model solution algorithm was tested for a single phase pipe flow case with both non-porous and porous walls, and good overall agreement with other computational results from the literature was obtained. The model predictions were in good qualitative agreement with available measured data selected to represent a wide range of experimental conditions in spouted beds. Even the quantitative agreement was reasonable, considering the fact that spouted-bed-specific empirical information utilized by the model was limited to the determination of an average spout diameter. The newly developed model was subsequently used to explore the fluid and particle dynamic behaviour of spouted beds as a function of controllable parameters. The results were consonant with the measured characteristics of operating spouted beds and showed some observable effects which are not predictable by more primitive models. A number of recommendations are made both to future experimenters and to future modellers of spouted beds.