Abstract
Mixing of a shear thinning fluid was scaled-up by maintaining equal Reynolds number (Re), tip speed, and power per volume. A standard 45° four-blade pitch blade turbine (PBT) and a modified version of the same impeller (DF-PBT) which provided simultaneous upward and downward flow were used. The impellers were located eccentrically, and the effects of scale-up were determined. The distribution of a tracer solution to evaluate mixing progress, power consumption, and flow fields were analyzed to compare the three different scale-up rules. The same endpoint of mixing was achieved in all cases of PBT with noticeable differences in flow profiles. Higher power consumption and less time were necessary to complete mixing with equal power per volume compared to that with equal Re and tip speed rules. For DF-PBT, only equal Re rule resulted in values similar to that obtained at the small scale. At a scale-up ratio of 2, the selection of scale-up rule should be based on the time and power requirements of the process. As the effects of scale-up on eccentrically located impellers do not differ significantly from those of concentrically located impellers, impellers which have complex dynamics such as DF-PBT require further studies to understand scale-up effects.
Nomenclature
- C
impeller clearance from vessel bottom, m
- D
impeller diameter, m
- e
distance between the center of the vessel and the shaft, m
- E
eccentricity value, -
- F
volume force vector, N/m3
- K
consistency coefficient, Pa.sn
- Ks
Metzner-Otto constant, -
- Mc
corrected torque, N.m
- n
flow behavior index, -
- N
impeller speed, s−1
- p
pressure, Pa
- P
power, W
- Po
power number, -
- r
radius, m
- R
scale-up ratio, -
- Re
Reynolds number, -
- t
time, s
- T
vessel diameter, m
- v
velocity vector, m/s
- V
volume, m3
- Greek letters
- ρ
density, kg/m3
- η
apparent viscosity, Pa.s
- Ω
angular velocity vector, rad/s
- τ
viscous stress tensor, Pa
- µ
dynamic viscosity, Pa.s
- Subscripts
- 1
Small-scale
- 2
Large-scale
Acknowledgements
The authors would like to thank Nestle Nutrition North America for their support during set-up of the planar laser-induced fluorescence experiments.
The use of trade names in this publication does not imply endorsement by the North Carolina Agricultural Research Service of the products named nor criticism of similar ones not mentioned.
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