| Summary: | 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.
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