1. The Dorr-Oliver Flotation cell
Six blade impeller
These are the elements of a machine that was used as a model for the calculations.
Stator with 4 large blades and 12 small

2. The three studied Configurations for Re=35000y
x or r
Three configurations were studied. The first two with an impeller at two clearances from the ground, namely 3 cm and 1 cm. In the third configuration we add the stator system. In all the charts that follow, the results are presented in terms of the three configurations, arranged in the same way.
3cm
1cm
1cm with stator

3. Normalized velocity magnitude contours
Here we present calculated streamline patterns. The color contours represent the magnitude of the velocity. In the first case two recirculation regions are observed, while in the last we have only one. The significant finding is that in the third configuration, the recirculation pattern is opposite to the first two. The flow is directed upward above the impeller. Moreover, the points of stagnation move from the inclined wall, to the floor and then it is eliminated for the three configurations respectively.

4. Normalized radial velocity contours
The radial jet is more energetic in the case where the impeller is further up. This is perhaps because with less obstruction from the bottom, more fluid volume enters the impeller region and is directed outward along the upper part of the impeller. The case with the stator has the smallest radial component.

5. Normalized TKE contours
TKE is the Turbulent Kinetic energy calculated in terms of a sum of the kinetic energy terms of the fluctuating components. Fro smooth, laminar flow, the quantity is zero. It takes large values when the turbulent agitation is high. With a flat disk covering the impeller and blocking the return of the flow from the top, and the ground blocking the return from the bottom, the edges of the impeller produce slower flow but much higher levels of turbulence. In the case where the stator is present even more turbulence is generated due to the vortices that form between the stator blades.

6. Normalized Dissipation rate contours
Dissipation is another measure of turbulent activity, representing the rate at which the energy stored in turbulent agitation is ultimately converted to heat. For the case with the stator even if high values of dissipation can be seen around
the stator, the maximum is observed inside the stator blades

7. Normalized Z-vorticity
Vorticity is a measure of the local rotation of fluid elements. Different signs of vorticity, here presented in terms of shades of blue and red, represent different sense of rotation. In the first two cases two distinct recirculation regions form while in the latter one
small structures seem to appear between the stator blades and some inside the stator but clearly smaller than in the other cases.

8. Streamlines along a horizontal plane of the impeller at
These are horizontal cuts just below the flat disk that caps the impeller. At this elevation for all three configurations the flow streams away from the impeller. In the second case an envelope of the streamlines separating those that spiral
inward from those that spiral outward can be seen. In the case with the stator, the fluid in its effort to pass through the
stator blades forms small vortices between them.

9. Y-vorticity along a horizontal plane of the impeller at
In the first case, vorticity is high around the impeller blade where an extended
vortex is formed. In the second case small vortices are very close to impeller blades
and the second one starts closer. In the last case high values of vorticity can be observed everywhere
due to the vortices that form around the stator blades.

10. TKE along a horizontal plane of the impeller at
The first case presents the lowest value of TKE
The second one has higher values because more turbulence is generated
In the last case the flow finds more resistance, passing through the stator, it creates vortices around the stator, which in turn break down into turbulent kinetic energy.

11. Dissipation rate along a horizontal plane of the impeller at
Similar conclusion with the ones for the TKE can be drawn for the Dissipation rate

12. Streamlines along a horizontal plane of the impeller at
In this and the following three charts, we present data along a cut half-way down the impeller from its plate cover. In the first two cases some of the flow is returning back from the two recirculation regions next to the impeller while some of it is still going out. In the case with the stator most of the flow is returning back from the huge recirculation region while some of it inside the stator still tries to pass through.
In the first two cases some of the flow is returning back from the two recirculation
regions next to the impeller while some of it is still going out
In the case with the stator most of the flow is returning back from the huge
recirculation region while some of it inside the stator still tries to pass through.

13. Y-vorticity along a horizontal plane of the impeller at
In the case with the stator most of the flow is returning back from the huge
recirculation region while some of it inside the stator still tries to pass through.

14. TKE along a horizontal plane of the impeller at
TKE for the first case increased while in the second the opposite happened
In the case with the stator it decreased in the boundary of it but increased in
the area close to the rotor blades.

15. Dissipation rate along a horizontal plane of the impeller at
Similar conclusion with the ones for the TKE can be drawn for the Dissipation rate

16. Streamlines along a horizontal plane of the impeller at
In this and the next three charts, we present results along a plane close to the floor of the tank. In the first two cases the ‘envelope’ separating the inward spiraling flow from the outward-spiraling flow grows, because more flow is returning back to the impeller. In the last case in the lower part of the tank, instead of sixteen stator blades there are only four and therefore they do not block as much the flow as at in the case of higher elevations

17. Y-vorticity along a horizontal plane of the impeller at
For the first two cases, even smaller values of vorticity are observed
In the case with the stator although there are not high values of vorticity between
the stator blades, high values are observed in the area of the impeller blades

18. TKE along a horizontal plane of the impeller at
Low values of TKE dominate in the first two configurations, while in the one
with the stator somewhat higher values of TKE than before appear next to the impeller blades.

19. Dissipation rate along a horizontal plane of the impeller at
As in the previous slide, turbulence is less active near the floor, because this is the region that receives the fluid at the end of its recirculation pattern, and by then most of the turbulence has dissipated.

20. Conclusions
The Fluent code can predict in many features of the flow in a flotation cell, but so far, single-phase flow was considered.
The turbulent kinetic energy and dissipation have the highest values in the immediate neighborhood of the impeller
Stators generate recirculation patterns that lead the flow upward in the center of the tank, and thus promote flotation.
Stators generate significant increases in turbulent dissipation and thus could promote the collision of bubbles and particles.

21. Future Work
Experimental predictions for the Dorr-Oliver Flotation cell
Comparisons of the studied cases with the experiments
More Re numbers and clearances for the Dorr-Oliver Cell
Higher Re numbers for both Tanks ( )
Unsteady calculations
Extension to two-phase or three phase flows