Third International Conference on CFD in the Minerals and Process Industries [607844]

Third International Conference on CFD in the Minerals and Process Industries
CSIRO, Melbourne, Australia
10-12 December 2003

NUMERICAL MODELING OF AN OUTOKUMPU
FLOTATION DEVICE

Juha TIITINEN1, Jussi VA ARNO2 and Sami GRÖNSTRA ND3

1 Helsinki University of Technology , Mechanical Process T echnology and Recy cling
P.O.Box 6200, FIN-02015 HUT , Finland
2 Outokumpu Research OY, P.O. Box 60 FIN-28101 Pori, Finland
3 Outokumpu T echnology – Minerals Processi ng, Riihitontuntie 7C FIN-02200 Espoo, Finland

ABSTRA CT
This paper reviews the detailed hydrody namics of
Outokumpu flotation cells by using CFD modeling.
Scope of this work was to build an industrial tool, based
on CFD, for modeling flow field and solids distribution in
flotation cell without air feed. Selection of tested and
validated fundamental methods for achieving optimal
cycle for analy sis was also objective. Preproces sing,
solver time and postprocessing for testing design layout
with CFD should be done in less than one week.
The combination of basic approaches was chosen by
simulating the single phase ( l) flow field in process and
laboratory scale flotation cells with different ty pe and size
computational grids and principal methods. Comparisons
between velocity and turbul ence res ults measured us ing
the LDV (Laser Doppler Velo cimetry ) technique and CFD
modeling were done. Also mi xing power and liquid phase
mixing time calculations were com pared to validating
measurem ents.
INTRODUCTION
Froth flotation is a complex three phase phy sico-chemical
process which is used in mineral processing industry to
separate selectively fine va luable minerals from gangue.
Main functions for flotation machines are to keep mineral
grains in suspension and disperse sufficient amount of fine
airbubbles to the pulp, energy efficiency and low power
and air consumption
The flotation cell by Outokumpu in general consists of
flotation tank, rotor and stator, air feed mechanism and
pulp feed- and discharge mechanism. Figure 1 shows
Outokumpu cell design in general. Industrial cell size can
be from 5m³ to 200m³. Figure 2 is a close up
demonstration of air distribu tion and slurry pumping. The
Outokumpu' s rotor profile was originally designed to
equibalance the hy drody nami c and sta tic pressure s,
allowing a uniform air dis persion over s urface of the
blades . The blade des ign als o provides separate zones for
air distribution and slurry pumping.
Development of flotation machines has earlier mainly
been build on experimental data or rules of thumb. Now a
Computational Fluid Dy nami c (CFD) based tool for
design and study of flotation cells is under development. ROLE OF GRID TYPE
Mesh generation is a signifi cant part of CFD modeling.
Mesh generation consumes most of the total tim e used to
analy sis. Moreover, the quality of the com puted solution is
substantially dependent on the structure and quality of the
computational m esh. The attributes associated with mesh
quality are node point dist ribution, sm oothness and
skewness. Building a valid computational mesh is a
separate s pecies of s cience which can be separated to
structured and unstructured grid generation.

Figu re 1: Outokumpu Flotation Cell.

Figu re 2: Rotor-stator close up.

Choosing appropriate m esh ty pe will m ainly depend on
the geometry of the flow problem. Figure 3 shows general
3D grid cells types accepted by most of the CFD solvers .
Copy right  2003 CSI RO Austr alia 167

Figure 4 shows an exam ple of 3D m ultiblock structured
grid and unstructured tetrahedral grid.

Figu re 3: 3D Cell ty pes.

Figu re 4: Grid topologies.

When choosing appropriate mesh ty pe for flow problem
there are s ome issues to cons ider:
Many flow problems involve complex geometries. The
creation of a s tructured m esh for such geom etries can be
substantially time-consuming and perhaps for some
geometries impossible. Prep roces sing time is the m ain
motivation for using unstructured mesh in these
geometries.
Computational e xpense can be a determ inant factor when
geom etries are com plex or the range of length scales of
the flow is large. Hexahedral elem ents generally fill m ore
efficiently com putational volum e than tetrahedral
elem ents.
A dominant source of error in calculations is numerical
diffusion . Amount of numerical diffusion is inversely
related to the resolution of the m esh. Also num erical
diffusion is minimized when the flow is aligned with the
mesh. In unstructured mesh cas es with tetrahedral
elem ents the flow can never be aligned with the grid.
Using and combining different ty pes of elements as a
hybrid mesh can be a good option and bring considerable
flexibility in m esh generation.
GRID TYPE DEPENDENCY A ND MIXING TIME
The grid type dependency calculations were carried out
with an industrial size Outokumpu flotation tank cell. The
geometrical details of the tank are given in Table 1.
Geom etry is rotationally symmetric and therefore it was
sufficient to model only a part of the domain. The smallest
symmetry of the geometry is 60ș which contains one
impeller blade and three stator blades. Two different ty pe
of grids (figure 5) were studied. Steady state, MRF, k- ε
turbulent model and periodi c and sy mmetric boundaries
were used in liquid phase simulations.

Figu re 5: Structured and unstructured grid ty pes.

Tank diam eter (mm) 3600
Tank height ( mm) 3600
Shaft diam eter (mm) 160
Rotor diam eter (mm) 825
Rotor bottom clearance (m m) 83
Rotor speed of r otation ( rpm) 100/160
Table 1 : Geom etrical details of the tank.

Mixing time measurem ents were done by injecting NaCl
solution to the im peller area and m easuring electrical
conductivity of the fluid as a function of time in the upper
part of the flotation cell. Mixing time calculations were
done with the same geometry and CFD-model than grid
dependency calculations. Solver approach was time
dependent, unsteady state calculation. In the CFD-model a
region in the injection area was adapted and marking
solution was patched to it.
Grid ty pe dependency and mixing time results
CFD sim ulation results, consisti ng of velocity vectors and
distributions, pressures in rotor and stator area and
turbulence quantities show sim ilar results with both mesh
types. No significant grid dependency between structured
and unstructured grid ty pes were found. Resultant
velocities at two axial levels are shown in figure 6.
Mixing time had good agreemen t between measured and
computed results. Figure 7 shows that significant change
of measured conductivity and calculated change of
average mass fraction of marker converged.
VALIDA TION WITH LDV
As a result from grid ty pe dependency model a hy brid grid
for a laboratory size Outokumpu flotation cell with
unstructured cells in the roto r domain and structured cells
in the stator and tank domain was generated. The tank was
a cy lindrical, unbaffled tank with Outokumpu' s rotor-
stator flotation device. Computational grid of the rotor-
stator area is shown in figure 8. Geometrical details of the
tank are given in table 2.
A 60ș sector of the tank was modeled with periodic
boundaries on the sides of the sector and sy mmetric
boundary on the top of the tank to describe the free
surface. S tandard wall functions were em ployed on all
wall boundaries of the computational domain. Grid was
adapted on the norm alized dis tance to the wall (Y+) during
the solution process. Fluent's m ultiple reference fram e
steady state approach was used with k-ε turbulence model.
Calculation was done in one phase (water).
168

Velocity Magnitude 0.3m
0123456
0,00 0,50 1,00 1,50 2,00
mm/sstruct
unstruct

Velocity Magnitude 0.6m
01234567
0,00 0,50 1,00 1,50 2,00
mm/sstruct
unstruct

Figu re 6: Resultant velocities at two axial levels.
Mixing time
0,12 50,130,13 50,140,14 50,150,15 5
01 0 20 30 40
Time (s)Condu ctivity
-2,00E-030,00E+002,00E-034,00E-036,00E-038,00E-031,00E-021,20 E-021,40 E-02
Average mass fractionMeasured
CFD

Figu re 7: Mixing tim e results.

Figu re 8: Com putational grid of the rotor-stator area. LDV results
Results from laboratory size Outokumpu’s flotation cell
model were compared to Laser Doppler Velocimetry
(LDV) measurements done to a similar flotation cell at
CSIRO Thermal and Fluids Engineering laboratory .
Reas onable agreem ent is obtained between m easured and
calculated flow fields . Rotor creates a jet s tream in the
radial direction towards the cy lindric wall. Two m ain
flows circulates back to the impeller, one through the top
side and second from the lower side of the stator. The
comparisons of the m easured and com puted m ean velocity
components for radial direction as a function of cell height
is showed in figures 9 and 10.
Generally , the agreement is good between the measured
and com puted velocities. Standard k-ε turbulence model
suggest lower values than measured in the tank.

Tank diam eter (mm) 1070
Tank height ( mm) 900
Shaft diam eter (m m) 57
Rotor diam eter (mm) 270
Rotor bottom clearance (m m) 27
Rotor speed of r otation ( rpm) 328
Table 2 : Geom etrical details of the LDV validation tank.

00,10,20,30,40,50,60,70,80,91
-1 0 1 2
Ur (m/s)z/Hr/R=0.47,
LDV
r/R=0.47,
TKK CFD
00,10,20,30,40,50,60,70,80,91
-1 0 1 234
Ur (m/s)z/Hr/R=0.24,
LDV
r/R=0.24,
TKK CFD

Figu re 9: Mean velocity components r/R 0.24 and 0.47.

0,000,100,200,300,400,500,600,700,800,901,00
-1 -0,5 0 0,5 1
Ur (m/s)z/Hr/R=0.75,
LDV
r/R=0.75,
TKK CFD
0,000,100,200,300,400,500,600,700,800,901,00
-1 -0,5 0 0,5 1
Ur (m/s)z/Hr/R=0.93,
LDV
r/R=0.93,
TKK CFD

Figure 10 : Mean velocity components r/R 0.75 and 0.93.
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VALIDA TION WITH POWER MEA SUREMENTS
CFD-model was compared with torque moment
measurements done by Outokumpu Research. A
laboratory size, similar to previous, flotation cell was
measured with a m oment m easuring table. One phase
calculations were done with five rotational speeds and
fluid was water.
Power measurement results
In figure 11 is com pared calculated and measured values
of Outokumpu laboratory size flotation cell power
consumption. CFD-model ha s good agreement with the
power consumption in all rotational speeds.
Grid independence was also tested in power calculations.
Grid adaptation by Y+ values was used to improve the
quality of the results from the CFD-solution.
POWER CONSUMPTION – CFD AND M EASURED
-20020406080100120
0 100 200 300 400 500 600 700 800
RPMPOWER CONSUMPTION (W)Measured
CFD
Adapted CFD

Figure 11 : Power consumption.

Similar comparation was also done to industrial size
flotation cell. Torque moment was measured s traight from
the shaft with strain-gage trans ducer. In that cas e CF D-
model underestimated more the power consumption.
Similar moment measuring me thod is not applicable for
laboratory size cells .
CONCLUSIONS
The complex flow field in the Outokumpu' s flotation cell
has been studied by CFD. It was proven that converged
solution from CFD calculations was grid ty pe
independent. Resolution of computational mesh was
sufficient when standard wall functions were valid (Y+ =
50-500). Present operation model is to perform grid
adaptation, when needed, to get valid Y+ values .
It was also shown that CFD can be used for predicting
mixing time with good accuracy . Different scale of
flotation cells caused conflict in power consumption.
Solution for this has not been found yet and results can’t
be exploited at this stage.
The predicted velocity com ponents agreed well with the
values obtained from LDV. The standard k-ε model does
not predict accurately the k level in the flotation cell
compared to m easured values .
It was proved 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 in one phase. Further studies of numerical modeling of Outokumpu
flotation device in two phase ( s,l) flows are continuing.
The work reported is part of a broad national
computational fluid dy nami cs research program .
ACKNOWLEDGEMENTS
The authors are grateful to Outokumpu Research (Pori,
Finland) and AMIRA Inte rnational Ltd (Melbourne,
Australia) for their contribution to this work. AMIRA
P9M project’s industry partners are acknowledged for
their sponsorship. CSIRO Thermal and Fluids Engineering
laboratory is acknowledged fo r the LDV measurements.
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, Mineral processing part
two, Insinööritieto Oy (In Finnish).
ZHU, Y., WU J., SHEPHERD I., NGUYEN B. 2002,
MineralsModelling of Ou tokumpu flotation cell
hydrody namics, CSIRO Minerals report DMR-1899.
VANHANEN T. 2003, Measuri ng one- and two phase
fluids in flotation cells with moment measuring table,
Outokumpu Report 03029-ORC-T.
TIITINEN J., 2003, Numerical modeling of a OK rotor-
stator mixing device, poste r presentation, ESCAPE-13
symposium, Lappeenranta, Finland.

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