Heuristics
19 Oct 12
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Agitators and Mixing Equipment
•
•
•
•
•
Suspend solids
Disperse gases and liquids
Emulsify one liquid in another
Promote heat transfer
Blending two or more materials together
Overmixing maybe undesirable
• in biological application, high shear may damage organisms
• polymer molecules may be damaged by long mixing or high shear
For design or consideration of mixing process should understand:
• mechanism of mixing
• scale-up criteria
• power consumption
• flow patterns
• mixing time/rates
• types of equipment available
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
2
Agitators and Mixing Equipment
Fluid mixing
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
3
Agitators and Mixing Equipment
Fluid mixing: Baffles
Unbaffled mixing tanks often used:
• in transition region
• for sticky materials
• where perfect cleaning is required
• in large tanks where baffle effects are
small
• processes where it is not clear baffles
have an effect on mixing performance
G.B. Tatterson., Fluid Mixing and Gas Dispersion in Agitated Tanks,
McGraw-Hill, 1991
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
4
Agitators and Mixing Equipment
Fluid mixing: Baffles
Fluid mixing: off-center
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
5
Agitators and Mixing Equipment
Side mounted mixers.
Flow patterns for side-entering propeller
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
Paul, et.al., Handbook of Industrial Mixing, Wiley, 2004
6
Agitators and Mixing Equipment
Common Impellers
Figure 7.20 Commonly used impellers (a)
Three-bladed propeller (b) Six-bladed disc
turbine (Rushton turbine) (c) Simple paddle (d)
Anchor impeller (e) Helical ribbon.
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
7
Agitators and Mixing Equipment
Various Turbine Impellers
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
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Various Impeller Types
Axial Flow Impellers
Hydrofoil Impellers
High-Shear Impellers
Radial Flow Impellers
Paul, et.al., Handbook of Industrial Mixing, Wiley, 2004
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Various Impeller Types
R. Hesketh, mixing notes
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Various Impeller Types
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Agitators and Mixing Equipment
Selecting Agitator Type
Used to make preliminary agitator
selection based on tank volume and
liquid viscosity.
• Turbines, Pitched Blade
Turbines, and Propellers are
typically used at high Re and
low viscosity.
• Anchor, Helical Ribbon, and
Paddle agitators are used for
higher viscosity (more
laminar-like Re) fluids.
Coulson and Richardson’s Chemical
Engineering Volume 1, 6th ed.
12
Flow Patterns for Various Impellers
Flat Blade Turbine = FBT
Pitched Blade Turbine = PBT
Paul, et.al., Handbook of Industrial Mixing, Wiley, 2004
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Typical Dimensions for Mixing Equipment
G.B. Tatterson., Fluid Mixing and Gas Dispersion in Agitated Tanks,
McGraw-Hill, 1991
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Typical Dimensions for Mixing Equipment
G.B. Tatterson., Fluid Mixing and Gas Dispersion in Agitated Tanks,
McGraw-Hill, 1991
15
Power Consumption and Scale-up in Mixing
Consider geometry, fluid properties, flow patterns, power, and so on. Has
been considered through dimensional analysis.
 ND 2 
P

NP 
 K 
3 5
N D
  
a
b
 N 2D   T 

  
 g  D
With:
  fluid density
 
kg
m3
N  speed of impeller Hz or
d
C
  ...
D
For geometrically similar vessels,
ratios of all terms to right of the
Froude number are negligible.
N P  Power number
P  Power [W ]
c
rotations
s
D  diameter of impeller [m]
 ND 2 

  N Re  reynolds number
  
  fluid vis cos ity [ Pa  s or mkgs ]

The Froude number is only important
when significant vortex develops (in
unbaffled tanks); for baffled tanks the
NP does not depend on the Froude
number.
 N 2D 

  N Fr  Froude number
 g 
Tatterson & Colson and Richardson. 16
Power Consumption and Scale-up in Mixing
Consider low viscosity, unbaffled systems.
 ND 2 

N P  K 
  
a
 N 2D 


 g 
b
a
at N Re  300 : N P  K N Re
T 1.37

 4.57
D 0.3
H 1.37

 4.57
D 0.3
C 0.3

1
D 0.3
Colson and Richardson. 17
In-Class PS Exercise
Consider a solution of sodium hydroxide with the properties listed below.
It is agitated by a propeller mixer that is 0.5m in diameter in a 2.28m
diameter unbaffled tank. The liquid depth is 2.28m. The impeller is
located 0.5m above the bottom of the tank. If the propeller is rotated at
2 Hz, what power is required?
density  1650 mkg3
vis cos ity  50 cP
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Power Consumption and Scale-up in Mixing
Consider low viscosity, baffled systems.
 ND 2 

N P  K 
  
a
Colson and Richardson. 19
Power Consumption and Scale-up in Mixing
Consider low viscosity, baffled systems (wall baffles).
Figure 10.59 Power correlations for turbine impellers in a tank
with 4 baffles. [w, D, impeller width and diameter, respectively.]
Colson and Richardson. 20
In-Class PS Exercise
Assume you are mixing a small amount of material into water in a standard
configuration baffled tank. The diameter of the pitched blade turbine is 1
m and it is desired to operate at 84 RPM. Estimate the power required.
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Power Consumption and Scale-up in Mixing
Consider low viscosity, baffled systems (wall baffles).
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
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Power Consumption and Scale-up in Mixing
Propeller pitch:
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Other Terms in Mixing
Pumping Capacity: discharge flowrate from an impeller:
Q
[unitless ]
ND 3
where :
N Q  impeller disch arg e coefficient
NQ 
Q  volumetric disch arg e rate [ ms ]
3
Tip Speed of an impeller:
ut  ND [ ms ]
P
N P N 2 D 5

[W  s ]
Torque: “twist” force acting on agitator shaft: Tq 
2N
2
Power per unit volume:
P N P N 3 D 5
  2
V
4T H
 
W
m3
Blend time (estimation to within 5% desired concentration):
0.33  TD  0.5
1.5
0.5
5.40  T   H 
C
 95  13     s 
T  0.33
NP N  D   D 
0.50  HT  1.0
N Re  10,000
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Discharge Coefficient
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
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Mixing Time
t m   90
Ni  N
Blend time (estimation to within
10% desired concentration):
P.M. Doran, Bioprocess Engineering Principles, 2nd Ed., Academic Press 2012
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Mixing Time
Doran suggests that for turbulent mixing conditions, irrespective of the
impeller type, that (baffled vessel, single impeller, H=T):
 V   T 
t m  5.9T 
  
 P  D
1
2
3
1
3
3
Verified under aerated conditions also (impeller not flooded) and for:
D
 0.7
T
D  2.7 m
0.2 
P.M. Doran, Bioprocess Engineering Principles, 2nd Ed., Academic Press 2012
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In-Class PS Exercise
A fermentation broth with properties as given below, is agitated in a 2.7 m3
baffled tank using a Rushton turbine with a diameter of 0.5 m and a stirred
speed of 1 Hz. Estimate the mixing time.
density  1000 mkg3
vis cos ity  10 2 Pa  s
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Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
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Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
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Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
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Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
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Heuristics
Questions?
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