Vasileios N Vlachakis 06/16/2006

1. Turbulence Characteristics in a Rushton & Dorr-Oliver Stirring Vessel: A numerical investigation Vasileios N Vlachakis 06/16/2006

2. Outline of the Presentation • Introduction/Motivation • Background of the Flotation process • Mechanically agitated vessels • The Rushton Stirring Tank • Computational Model • Comparisons between them • The Dorr-Oliver Stirring Tank • Conclusions • Future Work

3. Introduction/Motivation The objectives of the thesis are to: • study the hydrodynamics of two stirring tanks • The Rushton mixing tank • The Dorr-Oliver • estimate accurately the velocity distribution • discuss which turbulent model is the most suitable for this type of flow (validation with the experiments) • determine the effect of the clearance of the impeller on the turbulence characteristics • Vorticity • Turbulent kinetic energy • Dissipation rate

4. Significance of the Dissipation rate • Dissipation rate controls: • Collisions between particles and bubbles in flotation cells • bubble breakup • coalescence of drops in liquid-liquid dispersions • agglomeration in crystallizers

5. Background Flotation is carried out using Mechanically agitated cells Widely Used in Industries to separate mixtures • Mining • Chemical • Environmental • Pharmaceutical • Biotechnological Principles of Froth-Flotation

6. The flotation process • The flotation technique relies on the surface properties of the different particles • Two types of particles: • hydrophobic (needs to be separated and floated) • hydrophilic • Particles are fed from a slurry located in the bottom • While the impeller rotates air is passing through the hollow shaft to generate bubbles • Some particles attach to the surface of the air bubbles and some others fall on the bottom of the tank • The floated particles are collected from the froth layer

7. The Rushton Stirring Tank Cylindrical Tank Diameter of the Tank Diameter of the Impeller Four equally spaced baffles with width Thickness of the baffles Blade height Blade width Liquid Height = Height of the Tank

8. Governing Equations Unsteady 3D Navier-Stokes equations Continuity Momentum Decomposition of the total velocity and pressure Averaging rules Time-averaged Navier-Stokes equations Continuity Momentum

9. Dimensionless ParametersScaling Laws The Reynolds number: Laminar flow: Re<50 Transitional: 50<Re<5000 Turbulent: Re>10000 The Power number: Where a=5 and b=0.8 in the case of radial-disk impellers In our case where This Power number is hold for unbaffled tanks

10. Power number versus Re number

11. Dimensionless ParametersScaling Laws Froude number: The Froude number is important for unbaffled tanks It is negligible for baffled tanks or unbaffled with Re<300 In unbaffled tanks for Re>300 Flow number: In the case of the radial-disk impellers In our case (Rushton turbine) : Fl=1.07

12. Computational Grid The computational grid consists of 480,000 cells Grid surrounding the impeller (The unsteady Navier - Stokes equations are solved) Outside grid (The steady Navier - Stokes equations are solved) Two frames of reference: The first is mounted on the Impeller and the second is stationary (MRF) View from the top 3Dimensional View The grid surrounding the impeller is more dense from the outside

13. Simulation Test matrix Three different configurations Three turbulent models Five Reynolds numbers

14. Normalized radial velocity contours The flow for the first two cases can be described as a radial jet with two recirculation regions in each side of the tank In the case of the low clearance, a low speed jet and only one large recirculation area is observed

15. Normalized dissipation rate contours In the first two cases the dissipation rate has high values around and next to the impeller’s blade while in the last is extended to the region below them too

16. Normalized TKE contours Slices that pass through the middle plane of the impeller The TKE is lower in the case of the low configuration

17. Normalized X-vorticity contours Re=35000 In the first two cases the tip vortices that form at the end of the moving blades can be observed while in the third case only one big vortex ring forms.

18. Y- Vorticity Time-averaged experimental results Trailing vortices at the next blade Trailing vortices at the 1st blade Trailing Vortices at y/Dtank=0.167 (exactly at the end of the blades)

19. Vorticity superimposed with streamlines for Re=35000 Flow can be described as a radial jet with convecting tip vortices

20. Normalized Z-vorticity contours In the first two cases the presence of the trailing vortices that form behind the rotating blades can be seen. In all cases small vortices also form behind the baffles

21. Grid Study

22. Radial Plots for Re=35000 along the centerline of the impeller Normalized radial velocity Normalized velocity magnitude The velocity magnitudes consists only of the axial and radial components in order to be validated by the experimental results where the tangential component Is not available. The low speed jet in the case of the low configuration is confirmed but a strong axial component is present as it is shown in the second plot

23. Radial Plots for Re=35000 along the centerline of the impeller Normalized tangential velocity Re=35000 Normalized X-Vorticity Experimental vorticity seems to be oscillating due to the periodicity and due to the fact that trailing vortices are present. Clearly none of the turbulent models can capture what is happening

24. Radial Plots for Re=35000 along the centerline of the impeller Normalized Dissipation rate Normalized Turbulent Kinetic Energy The RNG k-e model has a superior behavior among the studied turbulent models in predicting the Turbulent Dissipation Rate (TDR) The apparent discrepancy in TKE is due to the periodicity that characterizes the flow, since with every passage of a blade strong radial jet is created.

25. Normalized Maximum Dissipation rate For C/T=1/2 and C/T=1/15 For C/T=1/3 As the Re number increases the maximum TDR decreases for the first two configurations (agreement with the experimental data) For case of the low clearance configuration the line of the maximum dissipation levels off.

26. Velocity Profiles r/T=0.256 r/T=0.19 r/T=0.315

27. Dissipation rate profiles r/T=0.256 r/T=0.19 r/T=0.315

28. Reynolds Stresses & Isosurfaces C/T=1/3 u’w’ normalized component of the RS Isosurfaces of vorticity The higher the helicity the more the vorticity vector is closer to the velocity vector (swirl) Helicity Isosurfaces of helicity

29. Conclusions • The turbulent kinetic energy and dissipation have the highest values in the immediate neighborhood of the impeller • Good agreement with the experimental data is succeed • Most of the times the Standard k-e model predicts better the flow velocities and the turbulent quantities while in some others has poor performance and the RNG k-e is better • In the case of the low configuration model: • there is a strong tendency to skew the contours downward • the dominant downward flow is diverting the jet-like flow that leaves the tip of the impeller downward, and it convects with the turbulent features of the flow. • The axial component of the velocity has high values

30. 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 (100000-300000) • Unsteady calculations • Extension to two-phase or three phase flows