The flow field in a cylindrical container driven by a flat bladed impeller was investigated using particle image velocimetry (PIV). Three Reynolds numbers (0.02, 8, 108) were investigated for different impeller locations within the cylinder. The results showed that vortices were formed at the tips of the blades and rotated with the blades. As the blades were placed closer to the wall the vortices interacted with the induced boundary layer on the wall to enhance both regions of vorticity. Finite time lyapunov exponents (FTLE) were used to determine the lagrangian coherent structure (LCS) fields for the flow. These structures highlighted the regions where mixing occurred as well as barriers to fluid transport. Mixing was estimated using zero mass particles convected by numeric integration of the experimentally derived velocity fields. The mixing data confirmed the location of high mixing regions and barriers shown by the LCS analysis. The results indicated that mixing was enhanced within the region described by the blade motion as the blade was positioned closed to the cylinder wall. The mixing average within the entire tank was found to be largely independent of the blade location and flow Reynolds number.

References

References
1.
Connelly
,
R. K.
, and
Valenti-Jordan
,
J.
, 2008, “
Mixing Analysis of a Newtonian Fluid in a 3D Planetary Pin Mixer
,”
Chem. Eng. Res. Des.
,
86
(
12A
), pp.
1434
1440
.
2.
Jongen
,
T.
, 2000, “
Characterization of Batch Mixers Using Numerical Flow Simulations
,”
AIChE J.
,
46
(
11
), pp.
2140
2150
.
3.
Tanguy
,
P. A.
,
Bertrand
,
F.
,
Labrie
,
R.
, and
B. DeLaFuente
,
E.
, 1996, “
Numerical Modelling of the Mixing of Viscoplastic Slurries in a Twin-Blade Planetary Mixer
,”
Chem. Eng. Res. Des.
,
74
(
A4
), pp.
499
504
.
4.
Finn
,
M. D.
,
Cox
,
S. M.
, and
Byrne
,
H. M.
, 2003, “
Topological Chaos in Inviscid and Viscous Mixers
,”
J. Fluid Mech.
,
493
, pp.
345
361
.
5.
Connelly
,
R. K.
, and
Kokini
,
J. L.
, 2007, “
Examination of the Mixing Ability of Single and Twin Screw Mixers Using 2D Finite Element Method Simulation With Particle Tracking
,”
J. Food Process Eng.
,
79
(
3
), pp.
956
969
.
6.
Connelly
,
R. K.
, and
Kokini
,
J. L.
, 2006, “
3D Numerical Simulation of the Flow of Viscous Newtonian and Shear Thinning Fluids in a Twin Sigma Blade Mixer
,”
Adv. Polym. Technol.
,
25
(
3
), pp.
182
194
.
7.
Connelly
,
R. K.
, and
Kokini
,
J. L.
, 2003, “
2-D Numerical Simulation of Differential Viscoelastic Fluids in a Single-Screw Continuous Mixer: Application of Viscoelastic Finite Element Methods
,”
Adv. Polym. Technol.
,
22
(
1
), pp.
22
41
.
8.
Lindenberg
,
C.
, and
Mazzotti
,
M.
, 2009, “
Experimental Characterization and Multi-Scale Modeling of Mixing in Static Mixers. Part 2. Effect of Viscosity and Scale-up
,”
Chem. Eng. Sci.
,
64
(
20
), pp.
4286
4294
.
9.
Lindenberg
,
C.
,
Scholl
,
J.
,
Vicum
,
L.
,
Mazzotti
,
M.
, and
Brozio
,
J.
, 2008, “
Experimental Characterization and Multi-Scale Modeling of Mixing in Static Mixers
,”
Chem. Eng. Sci.
,
63
(
16
), pp.
4135
4149
.
10.
Zhou
,
G.
,
Tanguy
,
P. A.
, and
Dubois
,
C.
, 2000, “
Power Consumption in a Double Planetary Mixer With Non-Newtonian and Viscoelastic Materials
,”
Chem. Eng. Res. Des.
,
78
(
A3
), pp.
445
453
.
11.
Clifford
,
M. J.
,
Cox
,
S. M.
, and
Finn
,
M. D.
, 2004, “
Reynolds Number Effects in a Simple Planetary Mixer
,”
Chem. Eng. Sci.
,
59
(
16
), pp.
3371
3379
.
12.
Youcefi
,
A.
,
AnneArchard
,
D.
,
Boisson
,
H. C.
, and
Sengelin
,
M.
, 1997, “
On the Influence of Liquid Elasticity on Mixing in a Vessel Agitated by a Two-Bladed Impeller
,”
ASME J. Fluids Eng.
,
119
(
3
), pp.
616
622
.
13.
Bohl
,
D.
, 2007, “
Experimental Investigation of the Fluid Motion in a Cylinder Driven by a Flat Plate Impeller
,”
ASME J. Fluids Eng.
,
129
(
1
), pp.
137
146
.
14.
Jaffer
,
S. A.
,
Bravo
,
V. L.
,
Wood
,
P. E.
,
Hrymak
,
A. N.
, and
Wright
,
J. D.
, 2000, “
Experimental Validation of Numerical Simulations of the Kneading Disc Section in a Twin Screw Extruder
,”
Polym. Eng. Sci.
,
40
(
4
), pp.
892
901
.
15.
Bakalis
,
S.
, and
Karwe
,
M. V.
, 2002, “
Velocity Distributions and Volume Flow Rates in the Nip and Translational Regions of a Co-Rotating, Self-Wiping, Twin-Screw Extruder
,”
J. Food Process Eng.
,
51
(
4
), pp.
273
282
.
16.
Yoon
,
H. S.
,
Hill
,
D. F.
,
Balachandar
,
S.
,
Adrian
,
R. J.
, and
Ha
,
M. Y.
, 2005, “
Reynolds Number Scaling of Flow in a Rushton Turbine Stirred Tank. Part I - Mean Flow, Circular Jet and Tip Vortex Scaling
,”
Chem. Eng. Sci.
,
60
(
12
), pp.
3169
3183
.
17.
Utomo
,
A. T.
,
Baker
,
M.
, and
Pacek
,
A. W.
, 2008, “
Flow Pattern, Periodicity and Energy Dissipation in a Batch Rotor-Stator Mixer
,”
Chem. Eng. Res. Des.
,
86
(
12A
), pp.
1397
1409
.
18.
Haller
,
G.
, 2002, “
Lagrangian Coherent Structures from Approximate Velocity Data
,”
Phys. Fluids
,
14
(
6
), pp.
1851
1861
.
19.
Haller
,
G.
, and
Poje
,
A. C.
, 1998, “
Finite Time Transport in Aperiodic Flows
,”
Physica D
,
119
(
3–4
), pp.
352
380
.
20.
Haller
,
G.
, and
Yuan
,
G.
, 2000, “
Lagrangian Coherent Structures and Mixing in Two-Dimensional Turbulence
,”
Physica D
,
147
(
3–4
), pp.
352
370
.
21.
Haller
,
G.
, 2000, “
Finding Finite-Time Invariant Manifolds in Two-Dimensional Velocity Fields
,”
Chaos
,
10
(
1
), pp.
99
108
.
22.
Haller
,
G.
, 2001, “
Distinguished Material Surfaces and Coherent Structures in Three-Dimensional Fluid Flows
,”
Physica D
,
149
(
4
), pp.
248
277
.
23.
Shadden
,
S. C.
,
Lekien
,
F.
, and
Marsden
,
J. E.
, 2005, “
Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows
,”
Physica D
,
212
(
3–4
), pp.
271
304
.
24.
Wilson
,
M. M.
,
Peng
,
J. F.
,
Dabiri
,
J. O.
, and
Eldredge
,
J. D.
, 2009, “
Lagrangian Coherent Structures in Low Reynolds Number Swimming
,”
J. Phys. Condens. Matter
,
21
(
20
):
L12603
.
25.
Beron-Vera
,
F. J.
,
Olascoaga
,
M. J.
, and
Goni
,
G. J.
, 2008, “
Oceanic Mesoscale Eddies as Revealed by Lagrangian Coherent Structures
,”
Geophys. Res. Lett.
,
35
(
12
), Atn
204105
.
26.
Vetel
,
J.
,
Garon
,
A.
, and
Pelletier
,
D.
, 2009, “
Lagrangian Coherent Structures in the Human Carotid Artery Bifurcation
,”
Exp. Fluids
,
46
(
6
), pp.
1067
1079
.
27.
Salman
,
H.
,
Hesthaven
,
J. S.
,
Warburton
,
T.
, and
Haller
,
G.
, 2007, “
Predicting Transport by Lagrangian Coherent Structures With a High-Order Method
,”
Theor. Comput. Fluid Dyn.
,
21
(
1
), pp.
39
58
.
28.
Santitissadeekorn
,
N.
,
Bohl
,
D.
, and
Bollt
,
E.
, 2009, “
Analysis and Modeling of an Experimental Device by Finite-Time Lyapunov Exponent Method
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
,
19
(
3
), pp.
993
1006
.
29.
Santitissadeekorn
,
N.
,
Bohl
,
D.
, and
Bollt
,
E. M.
, 2009, “
Analysis and Modeling of an Experimental Device by Finite-Time Lyapunov Exponent Method
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
,
19
(
3
), pp.
993
1006
.
30.
Pan
,
C.
,
Wang
,
J. J.
, and
Zhang
,
C.
, 2009, “
Identification of Lagrangian Coherent Structures in the Turbulent Boundary Layer
,”
Sci China, Ser G
,
52
(
2
), pp.
248
257
.
31.
Franco
,
E.
,
Pekarek
,
D. N.
,
Peng
,
J. F.
, and
Dabiri
,
J. O.
, 2007, “
Geometry of Unsteady Fluid Transport During Fluid-Structure Interactions
,”
Journal of Fluid Mechanics
,
589
, pp.
125
145
.
32.
Gendrich
,
C. P.
, and
Koochesfahani
,
M. M.
, 1996, “
A Spatial Correlation Technique for Estimating Velocity Fields Using Molecular Tagging Velocimetry (MTV)
,”
Exp. Fluids
,
22
(
1
), pp.
67
77
.
33.
Bohl
,
D.
, and
Koochesfahani
,
M.
, 2009, “
MTV Measurements of the Vortical Field in the Wake of an Airfoil Oscillating at High Reduced Frequency
,”
Journal of Fluid Mechanics
,
620
, pp.
63
88
.
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