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Numerical modeling of a OK rotor-stator mixing device
European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.
959
Numerical Modeling of a OK Rotor-Stator Mixing Device J. Tiitinen Helsinki University of Technology, Mechanical Process Technology and Recycling, P.O.Box 6200, FIN-02015 HUT, Finland E-mail: [email protected]
Abstract The flov^ field induced in an Outokumpu TankCell and by a OK rotor-stator mixing device in a process size flotation cell v^as simulated by cfd using two main grid types. The effects of different grid types were investigated with structured and unstructured grids. The geometry used was axisynmietric and a sector of 60 degrees of the tank with periodic boundaries was modeled. Finally, validation measurements and calculations with a laboratory size flotation cell were done. A "hybrid" grid for a laboratory size OK flotation cell with unstructured cells in the rotor domain and structured cells in the stator and tank domain was generated. Preprocessing and computational mesh generation process of complicated geometries like the OK rotor-stator mixing device can take considerably long time with regular structure type grids. This type of geometry is where meshes with irregular structure can be used much easier and with less processing time. Preprosessing and grid generation was done with the commercial Fluent Gambit 1.3. The CFD code Fluent 5.5 was used in the simulation. Standard k-e turbulence model and standard wall functions were used. Multiple reference frame method was used in all simulations instead of the computationally slower sliding mesh method. Simulations were done in one phase (/). Calculated velocity fields on horizontal and vertical planes, pressure distributions on rotor and stator surfaces and turbulent magnitudes were compared with structured and unstructured grid types. No grid dependency was found. Comparisons between velocity and turbulence results measured using the LDV (Laser Doppler Velocimetry) technique and CFD modeling were done. The predicted velocity components agreed well with the values obtained from LDV. The standard k-e model underpredicts the k level in the flotation cell compared to measured values. It was shown that a CFD model with periodicity, hybrid grid and MRF approach can be used for detailed studies on the design and operation of the Outokumpu flotation cell.
1. Introduction Froth flotation is a complex three phase physico-chemical process which is used in mineral processing industry to separate selectively fine valuable minerals from gangue. The importance of the mineral froth flotation process to the economy of the whole industrial world is important. As costs has increased in mining industry and ore grades and metal prices decreased, role of mineral flotation has become even more important. The flotation process depends among many other factors on control of the pulp aeration, agitation intensity, residence time of bubbles in pulp, pulp density, bubble and particle size and interaction and pulp chemistry. Development of flotation machines has been carried out as long as there has been minerals flotation to achieve better flotation performance and techniques. This
960 development has mainly been build from advices from practice or thumb rules. The development and research work has been mainly focused on the control of the chemistry not on the hydrodynamics of the flotation cell. This paper reviews the detailed hydrodynamics of Outokumpu flotation cells by using Computational Fluid Dynamic (CFD) modelling. This includes different computational grid type dependency defining in the CFD model and examining the flow pattern induced in the cell as well as validating the model.
2. General Outokumpu flotation cell development began in the late 1960s to satisfy company's own needs for treating complex-sulfide ores at Outokumpu's mines in Finland. Main properties for flotation machines can be defined: keep mineral grains in suspension in pulp, near ideal mixing disperse sufficient amount of fine airbubbles to the pulp make flotation environment advantageous for bubbles and minerals interaction, sufficiently turbulent conditions in the contact zone high selectivity develope a quiescent upper zone to flotation tank to avoid bubble-particle separation energy efficiency, low power and air consumption secure efficient discharge of concentrate and tailings The flotation cell mechanism by Outokumpu in general consists of: flotation tank rotor and stator air feed mechanism pulp feed- and discharge mechanism concentrate ducts pulp level regulators The Outokumpu's rotor profile was originally designed to equibalance the hydrodynamic and static pressures, allowing a uniform air dispersion over surface of the blades. The blade design also provides separate zones for air distribution and slurry pumping. Figure 1 shows Outokumpu cell desing in general. Industrial cell size can be from 5 m^ to 200 m^. Figure 2 is a close up demonstration of air distribution and slurry pumping. Mineral flotation is a three phase process where solid phase consists of mineral grains, liquid phase is mainly based on water and air as gaseos phase. In Outokumpu flotation cells air is conducted through hollow shaft to the rotating rotors direct influence. Intense eddy currents throw bubbles and pulp against the stator blades and through the gaps of the vertical blades and are distributed evenly to the flotation cell. Hydrofobic minerals attached to bubbles are lifted up to the froth area and to the concentrate duct.
Figure 1. Flotation cell.
Figure 2. OK rotor-stator close up.
961
3. CFD Modelling Mesh generation plays two main roles in CFD modelling. First, mesh generation consumes most of the total time used to analysis. Second, the quality of the computed solution is substantially dependent on the structure and quality of the computational mesh. The attributes associated with mesh quality are node point distribution, smoothness and skewness. Building a valid computational mesh is a separate species of science which can be separated to structured and unstructured grid generation. Choosing appropriate mesh type will mainly depend on the geometry of the flow problem. Figure 3 shows general 3D grid cells types accepted by most of the CFD solvers. Figure 4 shows an example of 3D multiblock structured grid and unstructured tetrahedral grid.
WamTWtdgit
Pyramid
Figure 3. 3D grid cell types.
Figure 4. Structured and unstructured grid.
When choosing appropriate mesh type for flow problem there are some issues to consider: Many flow problems involve complex geometries. The creation of a structured mesh for such geometries can be substantially time-consuming and perhaps for some geometries impossible. Preprocessing time is the main motivation for using unstructured mesh in these geometries. Computational expense can be a determinant factor when geometries are complex or the range of length scales of the flow is large. Hexahedral elements generally fill more efficiently computational volume than tetrahedral elements. A dominant source of error in calculations is numerical diffusion. Amount of numerical diffusion is inversely related to the resolution of the mesh. Also numerical diffusion is minimized when the flow is aligned with the mesh. In unstructured mesh cases with tetrahedral elements the flow can never be aligned with the grid. Using and combining different types of elements as a hybrid mesh can be a good option and bring considerable flexibility in mesh generation.
4. Computational Model 1 The flow and mixing simulations for grid type dependency calculations were carried out for the flotation tank geometry showed in figure 5. The tank is cylindrical and has six symmetrically placed vertical baffles and one horizontal baffle on the cylindrical walls.
962
Table 1. Tank specifications. Tank diameter (mm) Tank height (nmi) Shaft diameter (mm) Rotor diameter (nam) Rotor bottom clearance (nmi) Rotor speed of rotation (rpm)
3600 3600 160 825 83 100/160
Figure 5. Flotation tank geometry for CFD. Flotation tank is equipped with Outokumpu rotor and stator mixing device. The geometrical details of the tank are given in Table 1. For symmetry reasons it was sufficient to model only a part of the domain. The smallest symmetry of the geometry is 60** which contains one impeller blade and one vertical baffle. Two different type of grids were studied. Both grids were refined adaptively. After adaption both grids had about 450 000 cells. Steady state multiple reference frame approach was used in Fluent 5.5 simulations for modelling the rotor rotation in the stationary tank. Standard k-e turbulent model and standard wall functions were used. Simulations were done in liquid (water) phase. Computational model 1 results CFD simulation results, consisting of velocity vectors and distributions, pressures in rotor and stator area and turbulence quantities show similar results with both mesh types. No significant grid dependency between structured and unstructured grid types were found. Resultant velocities at two levels are shown in figure 6 and turbulent kinetic energy at rotor stator area in figure 7. ValooMy Magnttuda 0.3m
5
2
Vslocily Magnttiid* OAn
AV
\V \
0, OO
s l^^atruct
\
1
IH^ulTucI
1 3
i
V> < x — J 0,50
1.00
f9
^ 1,50
2,00
0, 00
^'^^ ^^^w— 0,50
1,00
_.• 1,50
Figure 6. Resultant velocities.
Figure 7. Turbulent kinetic energy at rotor-stator area.
2, DO
963
5. Computational Model 2 As a result from computational model 1 a hybrid grid for a laboratory size OK flotation cell with unstructured cells in the rotor domain and structured cells in the stator and tank domain was generated. The tank was a cylindrical, unbaffled tank with Outokumpu's rotor-stator mixing device. Computational geometry is shown in figure 8. Geometrical details of the tank are given in table 2. Table 2. Tank diameter (mm) Tank height (mm) Shaft diameter (mm) Rotor diameter (mm) Rotor bottom clearance (mm) Rotor speed of rotation (rpm)
1070 900 57 270 27 328
Figure 8. Computational geometry.
A 60** sector of the tank was modelled with periodic boundaries on the sides of the sector and symmetric boundary on the top of the tank to describe the free surface. Standard wall functions were employed on all wall boundaries of the computational domain. Fluent's multiple reference frame steady state approach was used with k-e turbulence model. Calculation was done in one phase (water). Computational model 2 results Results from computational model 2 were compared to Laser Doppler Velocimetry (LDV) measurements done to a similar flotation cell at CSIRO Thermal and Ruids Engineering laboratory. The velocity vectors predicted by CFD and the velocity vectors obtained from LDV are compared in figure 9. LDV is shown on the left and CFD velocity field on the right side.
0.2
0.4
0.6
0.8
1
r/R
Figure 9. Velocity vectors from LDV and CFD. Reasonable agreement is obtained between measured and calculated flow fields. Rotor creates a jet stream in the radial direction towards the cylindric wall. Two main flows circulates back to the impeller, one through the top side and second from the lower side of the stator. The comparisons of the measured and computed mean velocity components for radial direction as a function of cell height is showed in figure 10.
964 -•_r/R=024,| LDV
-•-r/FW).47,
1
f/f«.24.
I"
\
?"
V Ur(irt.)
LDV
LDV
r/fW)7S, TKKCR3|
r/FW47, TKKCFD
L ° u(^., '
5-
"'
u<:.,
"
Figure 10. Mean velocity components. Generally, the agreement is good between the measured and computed velocities. Standard k-e turbulence model suggest lower values than measured in the tank.
6. Conclusions The complex flow field in the Outokumpu's flotation cell has been studied by CFD. The flow pattern is dominated by strong radial flow from rotor towards the flotation cells cylindrical wall and two vortexes - one below the rotor and another above the rotor. The predicted velocity components agreed well with the values obtained from LDV. The standard k-s model does not predict accurately the k level in the flotation cell compared to measured values. It was shown that a CFD model with periodicity, hybrid grid and MRF approach can be used for detailed studies on the design and operation of the Outokumpu flotation cell.
7. References Matis, K.A. (Ed.), 1995. Flotation Science and Engineering, Marcel Dekker, Inc., New York, Basel, Hong Kong. Fluent Inc. 2002, Fluent manuals. Toimi Lukkarinen, 1987, Mineralprocessing part two, Insinooritieto Oy (In Finnish). Zhu, Y., Wu, J., Shepherd, I., Nguyen B. 2002, MineralsModelling of Outokumpu flotation cell hydrodynamics, CSIRO Minerals report DMR-1899.
959
Numerical Modeling of a OK Rotor-Stator Mixing Device J. Tiitinen Helsinki University of Technology, Mechanical Process Technology and Recycling, P.O.Box 6200, FIN-02015 HUT, Finland E-mail: [email protected]
Abstract The flov^ field induced in an Outokumpu TankCell and by a OK rotor-stator mixing device in a process size flotation cell v^as simulated by cfd using two main grid types. The effects of different grid types were investigated with structured and unstructured grids. The geometry used was axisynmietric and a sector of 60 degrees of the tank with periodic boundaries was modeled. Finally, validation measurements and calculations with a laboratory size flotation cell were done. A "hybrid" grid for a laboratory size OK flotation cell with unstructured cells in the rotor domain and structured cells in the stator and tank domain was generated. Preprocessing and computational mesh generation process of complicated geometries like the OK rotor-stator mixing device can take considerably long time with regular structure type grids. This type of geometry is where meshes with irregular structure can be used much easier and with less processing time. Preprosessing and grid generation was done with the commercial Fluent Gambit 1.3. The CFD code Fluent 5.5 was used in the simulation. Standard k-e turbulence model and standard wall functions were used. Multiple reference frame method was used in all simulations instead of the computationally slower sliding mesh method. Simulations were done in one phase (/). Calculated velocity fields on horizontal and vertical planes, pressure distributions on rotor and stator surfaces and turbulent magnitudes were compared with structured and unstructured grid types. No grid dependency was found. Comparisons between velocity and turbulence results measured using the LDV (Laser Doppler Velocimetry) technique and CFD modeling were done. The predicted velocity components agreed well with the values obtained from LDV. The standard k-e model underpredicts the k level in the flotation cell compared to measured values. It was shown that a CFD model with periodicity, hybrid grid and MRF approach can be used for detailed studies on the design and operation of the Outokumpu flotation cell.
1. Introduction Froth flotation is a complex three phase physico-chemical process which is used in mineral processing industry to separate selectively fine valuable minerals from gangue. The importance of the mineral froth flotation process to the economy of the whole industrial world is important. As costs has increased in mining industry and ore grades and metal prices decreased, role of mineral flotation has become even more important. The flotation process depends among many other factors on control of the pulp aeration, agitation intensity, residence time of bubbles in pulp, pulp density, bubble and particle size and interaction and pulp chemistry. Development of flotation machines has been carried out as long as there has been minerals flotation to achieve better flotation performance and techniques. This
960 development has mainly been build from advices from practice or thumb rules. The development and research work has been mainly focused on the control of the chemistry not on the hydrodynamics of the flotation cell. This paper reviews the detailed hydrodynamics of Outokumpu flotation cells by using Computational Fluid Dynamic (CFD) modelling. This includes different computational grid type dependency defining in the CFD model and examining the flow pattern induced in the cell as well as validating the model.
2. General Outokumpu flotation cell development began in the late 1960s to satisfy company's own needs for treating complex-sulfide ores at Outokumpu's mines in Finland. Main properties for flotation machines can be defined: keep mineral grains in suspension in pulp, near ideal mixing disperse sufficient amount of fine airbubbles to the pulp make flotation environment advantageous for bubbles and minerals interaction, sufficiently turbulent conditions in the contact zone high selectivity develope a quiescent upper zone to flotation tank to avoid bubble-particle separation energy efficiency, low power and air consumption secure efficient discharge of concentrate and tailings The flotation cell mechanism by Outokumpu in general consists of: flotation tank rotor and stator air feed mechanism pulp feed- and discharge mechanism concentrate ducts pulp level regulators The Outokumpu's rotor profile was originally designed to equibalance the hydrodynamic and static pressures, allowing a uniform air dispersion over surface of the blades. The blade design also provides separate zones for air distribution and slurry pumping. Figure 1 shows Outokumpu cell desing in general. Industrial cell size can be from 5 m^ to 200 m^. Figure 2 is a close up demonstration of air distribution and slurry pumping. Mineral flotation is a three phase process where solid phase consists of mineral grains, liquid phase is mainly based on water and air as gaseos phase. In Outokumpu flotation cells air is conducted through hollow shaft to the rotating rotors direct influence. Intense eddy currents throw bubbles and pulp against the stator blades and through the gaps of the vertical blades and are distributed evenly to the flotation cell. Hydrofobic minerals attached to bubbles are lifted up to the froth area and to the concentrate duct.
Figure 1. Flotation cell.
Figure 2. OK rotor-stator close up.
961
3. CFD Modelling Mesh generation plays two main roles in CFD modelling. First, mesh generation consumes most of the total time used to analysis. Second, the quality of the computed solution is substantially dependent on the structure and quality of the computational mesh. The attributes associated with mesh quality are node point distribution, smoothness and skewness. Building a valid computational mesh is a separate species of science which can be separated to structured and unstructured grid generation. Choosing appropriate mesh type will mainly depend on the geometry of the flow problem. Figure 3 shows general 3D grid cells types accepted by most of the CFD solvers. Figure 4 shows an example of 3D multiblock structured grid and unstructured tetrahedral grid.
WamTWtdgit
Pyramid
Figure 3. 3D grid cell types.
Figure 4. Structured and unstructured grid.
When choosing appropriate mesh type for flow problem there are some issues to consider: Many flow problems involve complex geometries. The creation of a structured mesh for such geometries can be substantially time-consuming and perhaps for some geometries impossible. Preprocessing time is the main motivation for using unstructured mesh in these geometries. Computational expense can be a determinant factor when geometries are complex or the range of length scales of the flow is large. Hexahedral elements generally fill more efficiently computational volume than tetrahedral elements. A dominant source of error in calculations is numerical diffusion. Amount of numerical diffusion is inversely related to the resolution of the mesh. Also numerical diffusion is minimized when the flow is aligned with the mesh. In unstructured mesh cases with tetrahedral elements the flow can never be aligned with the grid. Using and combining different types of elements as a hybrid mesh can be a good option and bring considerable flexibility in mesh generation.
4. Computational Model 1 The flow and mixing simulations for grid type dependency calculations were carried out for the flotation tank geometry showed in figure 5. The tank is cylindrical and has six symmetrically placed vertical baffles and one horizontal baffle on the cylindrical walls.
962
Table 1. Tank specifications. Tank diameter (mm) Tank height (nmi) Shaft diameter (mm) Rotor diameter (nam) Rotor bottom clearance (nmi) Rotor speed of rotation (rpm)
3600 3600 160 825 83 100/160
Figure 5. Flotation tank geometry for CFD. Flotation tank is equipped with Outokumpu rotor and stator mixing device. The geometrical details of the tank are given in Table 1. For symmetry reasons it was sufficient to model only a part of the domain. The smallest symmetry of the geometry is 60** which contains one impeller blade and one vertical baffle. Two different type of grids were studied. Both grids were refined adaptively. After adaption both grids had about 450 000 cells. Steady state multiple reference frame approach was used in Fluent 5.5 simulations for modelling the rotor rotation in the stationary tank. Standard k-e turbulent model and standard wall functions were used. Simulations were done in liquid (water) phase. Computational model 1 results CFD simulation results, consisting of velocity vectors and distributions, pressures in rotor and stator area and turbulence quantities show similar results with both mesh types. No significant grid dependency between structured and unstructured grid types were found. Resultant velocities at two levels are shown in figure 6 and turbulent kinetic energy at rotor stator area in figure 7. ValooMy Magnttuda 0.3m
5
2
Vslocily Magnttiid* OAn
AV
\V \
0, OO
s l^^atruct
\
1
IH^ulTucI
1 3
i
V> < x — J 0,50
1.00
f9
^ 1,50
2,00
0, 00
^'^^ ^^^w— 0,50
1,00
_.• 1,50
Figure 6. Resultant velocities.
Figure 7. Turbulent kinetic energy at rotor-stator area.
2, DO
963
5. Computational Model 2 As a result from computational model 1 a hybrid grid for a laboratory size OK flotation cell with unstructured cells in the rotor domain and structured cells in the stator and tank domain was generated. The tank was a cylindrical, unbaffled tank with Outokumpu's rotor-stator mixing device. Computational geometry is shown in figure 8. Geometrical details of the tank are given in table 2. Table 2. Tank diameter (mm) Tank height (mm) Shaft diameter (mm) Rotor diameter (mm) Rotor bottom clearance (mm) Rotor speed of rotation (rpm)
1070 900 57 270 27 328
Figure 8. Computational geometry.
A 60** sector of the tank was modelled with periodic boundaries on the sides of the sector and symmetric boundary on the top of the tank to describe the free surface. Standard wall functions were employed on all wall boundaries of the computational domain. Fluent's multiple reference frame steady state approach was used with k-e turbulence model. Calculation was done in one phase (water). Computational model 2 results Results from computational model 2 were compared to Laser Doppler Velocimetry (LDV) measurements done to a similar flotation cell at CSIRO Thermal and Ruids Engineering laboratory. The velocity vectors predicted by CFD and the velocity vectors obtained from LDV are compared in figure 9. LDV is shown on the left and CFD velocity field on the right side.
0.2
0.4
0.6
0.8
1
r/R
Figure 9. Velocity vectors from LDV and CFD. Reasonable agreement is obtained between measured and calculated flow fields. Rotor creates a jet stream in the radial direction towards the cylindric wall. Two main flows circulates back to the impeller, one through the top side and second from the lower side of the stator. The comparisons of the measured and computed mean velocity components for radial direction as a function of cell height is showed in figure 10.
964 -•_r/R=024,| LDV
-•-r/FW).47,
1
f/f«.24.
I"
\
?"
V Ur(irt.)
LDV
LDV
r/fW)7S, TKKCR3|
r/FW47, TKKCFD
L ° u(^., '
5-
"'
u<:.,
"
Figure 10. Mean velocity components. Generally, the agreement is good between the measured and computed velocities. Standard k-e turbulence model suggest lower values than measured in the tank.
6. Conclusions The complex flow field in the Outokumpu's flotation cell has been studied by CFD. The flow pattern is dominated by strong radial flow from rotor towards the flotation cells cylindrical wall and two vortexes - one below the rotor and another above the rotor. The predicted velocity components agreed well with the values obtained from LDV. The standard k-s model does not predict accurately the k level in the flotation cell compared to measured values. It was shown that a CFD model with periodicity, hybrid grid and MRF approach can be used for detailed studies on the design and operation of the Outokumpu flotation cell.
7. References Matis, K.A. (Ed.), 1995. Flotation Science and Engineering, Marcel Dekker, Inc., New York, Basel, Hong Kong. Fluent Inc. 2002, Fluent manuals. Toimi Lukkarinen, 1987, Mineralprocessing part two, Insinooritieto Oy (In Finnish). Zhu, Y., Wu, J., Shepherd, I., Nguyen B. 2002, MineralsModelling of Outokumpu flotation cell hydrodynamics, CSIRO Minerals report DMR-1899.