Numerical Modelling of Hydrodynamics and Gas Dispersion in An Autoclave - Appa Et Al 2013-1
Numerical Modelling of Hydrodynamics and Gas Dispersion in An Autoclave - Appa Et Al 2013-1
Numerical Modelling of Hydrodynamics and Gas Dispersion in An Autoclave - Appa Et Al 2013-1
Hydrometallurgy
journal homepage: www.elsevier.com/locate/hydromet
a r t i c l e i n f o a b s t r a c t
Article history: This paper investigates the numerical modelling of hydrodynamics and gas dispersion in the first compart-
Received 1 February 2012 ment of an autoclave. A scaled down model of an 80 m 3 Sherritt Gordon horizontal autoclave agitated by a
Received in revised form 24 September 2012 radial Smith turbine was used. The CFD simulations were implemented using the commercial code, ANSYS
Accepted 6 October 2012
Fluent 13. The CFD model was validated using experimentally determined power draw, velocity flow field
Available online 12 October 2012
and bubble size data. Hydrodynamics and gas dispersion displayed unusual characteristics compared to
Keywords:
conventional stirred tanks. Fluid flow leaving the impeller was found to have a negative inclination to the
Autoclave horizontal. Mixing was found to be asymmetric and non-ideal. Gas dispersion was found to be relatively
Computational fluid dynamics poor, non-homogeneous with accumulation of oxygen gas below the impeller, asymmetric and with low
Modelling gas hold-ups.
Multiphase © 2012 Elsevier B.V. All rights reserved.
0304-386X/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.hydromet.2012.10.006
68 H. Appa et al. / Hydrometallurgy 131-132 (2013) 67–75
few studies have been focused on the CFD modelling of autoclaves 2.2. Power
(Nicolle et al., 2009).
The purpose of this research is to develop a CFD model to predict Power input was determined from the torque experienced by the
hydrodynamics and gas dispersion in the first compartment of an motor. The motor was mounted between bearings to allow free rota-
autoclave and to validate the model against experimental data. Fur- tion and any torque experienced due to the inertia on the impeller
thermore, the numerical results and experimental data will be used blades resulted in a rotation. The resultant moment on a lever arm
to illustrate key features of hydrodynamics and gas dispersion in fitted to the motor was measured by a load cell. The power was deter-
autoclaves. mined from the product of the torque and the impeller speed.
3. Computational model
CFD model. Due to the asymmetry of the vessel the fluid flow in exist between the impeller and the curved sides of the vessel as
the system was expected to be asymmetrical. Therefore, a full well as the baffles. The sliding mesh was run for 20 impeller rotations
3-dimensional geometry was simulated. The impeller and the sparger for all single phase simulations. In order to implement the MRF or the
were modelled as infinitely thin walls and the shaft was extended to SM model an impeller zone, a cylindrical region, around the impeller
the bottom of the tank to facilitate the meshing of the vessel. Standard has to be defined. According to Lee and Yianneskis (1994) this region
wall functions as proposed by Launder and Spalding (1974) were has to be of a minimum size to be able to capture the strongly period-
used to account for the viscous flow near the solid surfaces. The free sur- ic flows in a stirred system. However, due to the geometry of the ves-
face was modelled with a symmetry boundary. Two different meshes sel and the position of the sparger the dimensions suggested by Lee
were used for this study, 322,749 cells (Grid 1) and 1,061,360 cells and Yianneskis (1994) were altered. The cylindrical region used to
(Grid 2). Grid 1 had 90,054 and 232,695 cells for the impeller and describe the impeller region had a height that was 2.5 times the
bulk regions respectively. Grid 2 had 114,752 and 946,608 cells for the blade height and a width 1.5 times the impeller diameter.
impeller and bulk regions respectively.
Table 1
Experimental conditions and variables.
Experimental Conditions
Tank volume 60 l
Medium Water
Gas Oxygen
Gas flow rate 4.37 l min−1
Temperature 25 °C
Experimental Variables
k − ε model was used to model the turbulent flow regime for the 3.2.3. Discretisation scheme and pressure–velocity coupling
autoclave. Momentum and volume fraction equations were discretised
using the QUICK scheme. First order schemes were used for the
3.1.4. Discretisation scheme and pressure–velocity coupling discretisation of the turbulent kinetic energy and dissipation rate.
The order of the discretisation schemes when modelling stirred The phase-coupled SIMPLE algorithm was used for the pressure ve-
tanks has been reported to highly influence the prediction of the locity coupling.
turbulent kinetic energy (Deglon and Meyer, 2006). However, if the
grid is not too coarse the mean velocity is negligibly affected by the 4. Autoclave CFD model validation
discretisation schemes. Similar findings were made by Aubin et al.
(2004) while investigating effects of various discretisation schemes. 4.1. CFD model
Therefore, the first order upwind differencing scheme was used for
the start of the simulations to discretise the momentum and turbu- Single phase and multiphase simulations were done using an
lence equations. Then the higher order QUICK scheme was used for AMD Quad Core 2.15 GHz CPU with 8 GB of RAM and an AMD dual
the discretisation of the equations. The SIMPLE algorithm was used Quad Core 2.2 GHz CPU with 16 GB of RAM respectively. For both
for the pressure–velocity coupling. multiphase and single phase systems all cores were used, that is 8 and
4 respectively. The simulations were considered to have converged
3.2. Multiphase: water–oxygen when the scaled residuals were below 1×10−3. The average running
time for the multiphase simulations was about three weeks. The CFD
The gas–liquid system, with water and oxygen gas, was modelled models were validated against experimental power draw, velocity flow
with the commonly used Euler-Euler model (Aubin et al., 2004; field and Sauter mean bubble diameter. As indicated previously, gas
Gimbun et al., 2009; Kerdouss et al., 2008; Khopkar et al., 2005; hold-up was too low to be measured accurately and therefore could not
Morud and Hjertager, 1996; Ranade and Van Den Akker, 1994; be used for CFD validations. For the bubble size, even though as reported
Scargiali et al., 2007). The dispersed k − ε turbulence model as simi- by Laakkonen et al. (2007) a large number of classes are required to sim-
larly used by Kerdouss et al. (2008) was employed to simulate the ulate satisfactory gas liquid systems, the discrete model with 11 classes
turbulent flow. When using the k − ε model the primary phase controls accurately predicted the bubble size. Similarly, Kerdouss et al. (2008)
the motion of the secondary phase and the influence of the bubbles on found that 13 classes gave satisfactory predictions for simulating a gas–
the flow field is negligible. Therefore, to ensure that the effect of the liquid system for stirred tanks. This shows that the number of classes
secondary phase is minimised and to avoid any numerical instability used is problem dependent and a prior knowledge of the bubble size
the bubble size should be smaller than the cell size. To this end, and distribution helps in choosing the optimal number of classes.
based on the results of the single phase simulations, Grid 1 was used
to model the gas–liquid system. Turbulent dispersion is taken into ac- 4.2. Hydrodynamics
count by the dispersed k − ε turbulence model (Simonin and Viollet,
1990). The Schiller–Naumann model (Schiller and Naumann, 1933) 4.2.1. Power
was used to account for the interphase drag. The result for the power draw comparing the experimental and
numerical data is plotted in Fig. 4. Power from the CFD simulations
3.2.1. Boundary conditions was calculated from the torque experienced by the impeller and the
The boundary conditions used are similar to the ones described known impeller speed. The torque was determined from the sum of
for the single phase system. However, to account for the gas phase, moments (sum of cross product of the pressure and viscous forces
the sparger was modelled as a velocity inlet boundary and the outlet with the moment vector) on both sides of the impeller blades. The
was modelled as a degassing boundary, where a velocity boundary numerical data for the two cases for Grid 1 and Grid 2 are also com-
was used. The velocity of the gas at the sparger was based on the vol- pared. Power as expected increases as impeller speed is increased.
umetric flow rate. For the degassing boundary the velocity and the There is also a good correlation between the experimental and nu-
volume fraction of the gas at the boundary was set to the value at merical data. However, a small over-prediction is observed at 350
one cell below the boundary. A no-slip wall was used for the liquid and 395 rpm. This could be a consequence of not considering the
phase, with water only allowed to move along the boundary and
with the normal component of the velocity set to zero.
0.16
Experimental
3.2.2. Gas phase Numerical, Grid 1
Numerical, Grid 2
The dispersed phase was modelled using a population balance 0.14
model. The bubble size distribution was simulated using the discrete
method. Using this method the particle size distributions are repre- 0.12
sented in terms of classes or bins. It allows for the direct simulation
of the bubble size distribution but at the expense of extra computa- 0.1
Power (kW)
0
where v is the volume of the bubble and q is the ratio factor that can 150 200 250 300 350 400
be obtained using a geometric progression as well as the minimum Impeller speed (rpm)
and maximum bubble volumes. The Luo models (Luo and Svendsen,
1996) were used to simulate bubble breakage and coalescence. Fig. 4. Power — CFD vs Experimental.
H. Appa et al. / Hydrometallurgy 131-132 (2013) 67–75 71
Fig. 5. Velocity flow field at 150 rpm — PIV. Fig. 7. Velocity flow field at 150 rpm at Position 2 — CFD.
72 H. Appa et al. / Hydrometallurgy 131-132 (2013) 67–75
0.35
Numerical − Grid 1
Numerical − Grid 2
0.3 PIV
0.25
Position, z (m)
0.2
0.15
0.1
0.05
0
−1 −0.5 0 0.5
Velocity in y direction (ms−1)
Fig. 10. Velocity profile in y direction at 200 rpm.
5.1. Hydrodynamics
5.1.1. Power
In summary, results from the single phase simulations showed Power draw was found to increase with increasing impeller speed.
that the standard k − ε model, coupled with the sliding mesh model The Reynolds number was found to vary between 7.34 × 10 4 and
and high order discretisation schemes gave good prediction for the 1.95 × 10 5. The typical turbulent power number, Np, varies between
velocity flow field. These findings are similar to CFD methodologies 2.8 and 3.2 for the Smith turbine. For the impeller speeds investigated
used for stirred tanks. The gas–liquid system was simulated with the the power number was found to vary between 4.1 and 5.6, with the
Euler-Euler model coupled with a population balance model. Using lower power numbers at the higher impeller speeds. These power
this approach and the discrete solution method with 11 classes gave rea- numbers are higher than the typical literature values as reported for
sonably good predictions of the Sauter mean diameter. stirred tanks.
0.35 3.5
Numerical − Grid 1
Numerical − Grid 2
0.3 PIV
3
0.25
Position, z (m)
2.5
d32 (mm)
0.2
0.15
2
0.1
1.5
0.05 Impeller Experimental
Impeller Numerical
Vessel Experimental
Vessel Numerical
0 1
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 200 220 240 260 280 300 320 340 360 380 400
Velocity in y direction (ms−1) Impeller speed (rpm)
Fig. 9. Velocity profile in y direction at 150 rpm. Fig. 11. Sauter mean diameter — CFD and experimental.
H. Appa et al. / Hydrometallurgy 131-132 (2013) 67–75 73
the impeller and the bottom of the vessel is reduced (Montante et al., the flow is dependent on the impeller blade position. The asymmetry
2001; Nienow, 1968). Therefore, it can be inferred that the flow pattern of the flow field is due to the geometry of the vessel and also the
is dependent on the impeller speed. The downward inclination of the effect of the shape of the impeller blade on the flow pattern. It is
radial jet is also observed in dished bottom vessel as reported by Deen also observed that the lower recirculation loop disappears on the
et al. (2002). Therefore, the downward inflection can be due to a contri- right hand side of the vessel.
bution of the impeller clearance as well as the geometry of the vessel. The downward inflection is also observed at both Position 1 and
The effect of the curved bottom on the recirculation loop below the im- Position 2. The angle of the radial flow to the horizontal is more pro-
peller increases with impeller speed, resulting in a more or less single nounced than at 150 rpm. This is believed to be a result of a predom-
loop structure. inant axial flow at this speed such that the flow leaving the impeller is
Figs. 15 and 16 show the instantaneous predicted velocity vectors immediately entrained by the axial flow. In addition, the effect of the
on a vertical plane in the centre of the tank at 395 rpm at two differ- curved blades becomes more substantial at 395 rpm resulting in the
ent impeller positions. The impeller blade is on the plane at Position 1 fluid in the impeller discharge to have a greater angle of inflection.
and the plane is midway between two impeller blades. There are two
main observations; firstly the flow field is asymmetric and secondly
5.2. Gas dispersion
Fig. 15. Velocity flow field on vertical plane across tank at Position 1 — CFD.
Fig. 16. Velocity flow field on vertical plane across tank at Position 2 — CFD.
the large bubbles and poor dispersion of gas. The distribution of gas is 6. Conclusions
distinctly non-homogeneous and asymmetrical. Most of the gas is
trapped under the impeller and in the two large recirculating loops. The purpose of this study was to develop and validate a CFD model
There are entire regions of the vessel where there is practically no of an autoclave. The study was conducted using a scaled-down, 60 l
oxygen. model of the first compartment of an industrial autoclave.
Gas dispersion is unlikely to improve at higher superficial gas ve-
locities. Here, the overall gas hold-up would increase but the quality • CFD model: It was found that the same CFD methodology used
of gas dispersion may even deteriorate. The relatively poor gas dis- for stirred tanks was appropriate for the autoclave. For the single
persion would have an impact on mass transfer in the autoclave, phase system, the standard k − ε model with high order QUICK
with no mass transfer occurring in certain regions. scheme gave reasonable predictions of the power draw and velocity
5.53e-03 5.00e-02
5.07e-03 4.50e-02
4.62e-03 4.00e-02
4.17e-03 3.50e-02
3.72e-03 3.00e-02
3.26e-03 2.50e-02
2.81e-03 2.00e-02
2.36e-03 1.50e-02
1.91e-03 1.00e-02
1.45e-03 5.00e-02
1.00e-03 0.00e+02
Fig. 17. Local Sauter mean diameter on vertical plane at 395 rpm. Fig. 18. Volume fraction of oxygen on a vertical plane at 395 rpm.
H. Appa et al. / Hydrometallurgy 131-132 (2013) 67–75 75
flow field. For the two phase system, the Euler-Euler model with Gimbun, J., Rielly, C., Nagy, Z., 2009. Modelling of mass transfer in gas–liquid stirred
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observed in stirred tanks with radial impellers was not reproduced. The transfer coefficient prediction in stirred vessel with a CFD model. Comput. Chem. Eng.
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