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By Giuseppina Montante, University of Bologna, Bologna, Italy; and André Bakker, Fluent Inc.
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Among the various industrial applications
of stirred vessels, the agitation of solidliquid
systems is quite common. One
important aspect of solid-liquid mixing is the
distribution of solid particles inside the mixed
volume, since it may affect the apparatus performance
and process efficiency. Over the
years, novel experimental techniques for measuring
the spatial distribution of solids in solidliquid
systems have been developed by the
Mixing Research Group in the Chemical
Engineering Department of the University of
Bologna. The experiments have been used to
study a number of stirred vessels with a variety
of geometrical configurations, physical scales,
and solid-liquid mixtures. Recently, FLUENT has
been used to predict the 3D solid distribution
for a variety of mixing systems studied in the
Bologna laboratory. The aim has been to determine
a computational strategy that can be confidently
applied to any stirred vessel and any
solid-liquid system.
Solids concentration predicted by the Eulerian
granular multiphase model in FLUENT using two drag
laws, compared with experimental data
Flow field (left), solids volume fraction (right), and a comparison between the predicted solids volume
fraction and experimental data (middle) for a tall baffled vessel equipped with four Rushton turbines.
To date, most CFD simulations of solid-liquid
systems in stirred tanks appearing in the literature
are concerned mostly with baffled vessels
and single, flat blade impellers. Since one of the
goals of the present work was to demonstrate
the reliability of the CFD procedure, test cases
of considerable difficulty were selected; all of
them consisted of multiple impeller systems in
tall vessels, some made use of hydrofoil
impellers, and some were carried out in swirldominated
unbaffled vessels. Multiple impeller
vessels are often adopted in industrial practice,
but they are difficult to model because of the
exchange flows between the circulation zones
that surround each impeller. Moreover, in multiple
impeller tanks, the axial profiles of solid
concentration are often characterized by pronounced
gradients and discontinuities. While
these features are particularly helpful for pointing
out any discrepancies between the simulations
and experiments, they make the numerical
work more challenging.
Several CFD analyses were performed for
tanks of different scales, both with and without
baffles, and agitated with different impellers:
pitched blade turbines (PBT), standard Rushton
turbines (RT), and Lightnin A310 hydrofoil
impellers. In all cases, experimental solid concentration
data were available for validation of
the CFD results. The Eulerian-granular multiphase
model was used for the mixture, and the
multiple reference frames (MRF) model was
used for the rotating impellers. Different turbulence
models, all extensions of single phase turbulence
models to multiphase systems, were
tested to find out which would lead to the most
satisfactory representation of the flow field and
solid distribution for each case. The simplest,
the “k-ε mixture model,” was found to be accurate
enough for the baffled tanks. For the
unbaffled vessels, a multiphase version of the
Reynolds stress model (RSM) [1] was adopted,
since the k-ε model could not correctly capture
the strong swirling flow. Including the turbulent
dispersion force in the momentum equations
was found to be critical for all cases studied.
A comparison between experimental data and predictions using the dispersed
Reynolds stress model (left) and the local volume fraction of solids (right) for an
unbaffled stirred vessel equipped with four Rushton impellers
A comparison between experimental data and predictions using the RNG k- εεand
dispersed Reynolds stress models (left) for an unbaffled stirred vessel equipped with four
LIGHTNIN A310 impellers; the corresponding local volume fraction of solids predicted
using RSM (right)
In multiphase systems, momentum transfer
between the phases dictates the coupled flow
field. It is based on the drag coefficient, CD, and
this parameter is critically important for successful
predictions of the solid distribution. The
basic drag correlation implemented in FLUENT
(Schiller-Naumann) applies to particles falling in
a still fluid, and this correlation [2] was tested in
the simulations performed. It is well known,
however, that drag coefficients measured for
single particles settling in still fluids do not necessarily
apply to particles settling in turbulent
fluids. A modified drag law that takes into
account the increase in drag due to liquid turbulence
[3,4] was therefore tested as well.
A comparison of the drag coefficients was
performed for a baffled vessel containing water
and 675 micron glass particles, stirred with
three down-pumping PBTs [5]. Axial profiles of
the solid concentration were found to be in
excellent agreement with the experimental
data when the Magelli correlation is used, but those predicted by the Schiller-Naumann correlation
were not. The Schiller-Naumann correlation
under-predicts the drag coefficient, causing
the particles to settle more than they
should. Indeed, the superiority of the Magelli
correlation was found for all cases studied. For
a baffled vessel stirred with four RTs, the simulation
even picked up discontinuities in the distribution
above each impeller.
While solids distribution simulations in baffled
tanks are challenging, those in unbaffled
tanks, characterized by strongly swirling flow,
are even more so. One system studied makes
use of four RTs, and experiments suggest that
the mixing performance of this system is poor.
As a result of segregated circulation patterns
surrounding each impeller, most of the solids
stay near the bottom of the tank. To simulate
systems such as this, eddy-viscosity formulations
such as the k-ε family of models tend to
predict unphysical flow reversals. Meaningful
flow field results can only be obtained using
either RSM or the large eddy simulation (LES)
model. For the unbaffled Rushton system considered,
a “dispersed” Reynolds stress model,
corrected for multiphase flow, was used, and a
very good comparison with experimental
measurements was achieved. The simulation
correctly predicted an accumulation of solids
below the bottom impeller, and a rapidly
diminishing amount as the height increases.
A second unbaffled stirred tank validation
involved the same vessel, but equipped with
four LIGHTNIN A310 hydrofoil impellers, an
operating condition not recommended by the
impeller manufacturer, who recommends the
use of baffles. Indeed, when operated with baffles,
it was observed that the solids concentration
profile is relatively uniform. When operated
without baffles, however, a peculiar phenomenon
was observed. The solids were found to
slowly move upwards through the vessel and
accumulate near the top [4]. Despite this
unusual behavior, the dispersed RSM model
was found to correctly capture the axial profiles,
with the highest concentration of solid material
near the top of the vessel. Additional simulations
for this case were performed to test the
(multiphase corrected) RNG k-ε model, and the
results showed that it completely failed to capture
the observed behavior. The success of the
dispersed RSM model for both unbaffled systems
with distinctly different operating characteristics
provides a strong validation of this
capability.
The results of these simulations demonstrate
that FLUENT can be applied with confidence to
predictions of the solid distribution in solidliquid
stirred vessels using the Eulerian granular
multiphase model. Special attention must be
paid to the particle drag coefficient correlation,
however. Indeed, the drag coefficient, CD, is a
critical parameter for the correct prediction of
solid distributions in general, and the Magelli
drag correction is recommended for solid suspension
in turbulent liquids. The Reynolds stress
turbulence model for multiphase flow is also
necessary for the case of unbaffled vessels,
which are characterized by strong swirl.
References:
- D. Cokljat, M. Slack, S.A. Vasquez, A. Bakker, G.
Montante, “Reynolds Stress Model for Eulerian
Multiphase”, submitted, Progress in Computational
Fluid Dynamics, 2004.
- L. Schiller, Z. Naumann, “A Drag Coefficient
Correlation.” Z. Ver. Deutsch. Ing., 77:318, 1935.
- F. Magelli, D. Fajner, G. Nocentini, G. Pasquali, “Solid
Concentration Profiles in Slurry Reactors Stirred with
Multiple Impellers: Recent Results”, Engineering foundation
conference-Mixing XI, New England College,
Henniker N.H., USA, 1987.
- D. Pinelli, M. Nocentini, F. Magelli, “Solids
Distribution in Stirred Slurry Reactors: Influence of
Some Mixer Configurations and Limits to the
Applicability of a Simple Model for Predictions.”
Chem. Eng. Comm., 2001, Vol. 118, pp. 91-107.
- G. Montante, D. Rondini, A. Bakker, F. Magelli, “CFD
Predictions of Solid Concentration Distributions in a
Baffled Stirred Vessel Agitated with Multiple PBT
Impellers.” CHISA 2002, Prague, 25-29 August 2002.
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