Heuristics
19 Oct 12
1
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.
8
Various Impeller Types
Axial Flow Impellers
Hydrofoil Impellers
High-Shear Impellers
Radial Flow Impellers
Paul, et.al., Handbook of Industrial Mixing, Wiley, 2004
9
Various Impeller Types
R. Hesketh, mixing notes
10
Various Impeller Types
11
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
13
Typical Dimensions for Mixing Equipment
G.B. Tatterson., Fluid Mixing and Gas Dispersion in Agitated Tanks,
McGraw-Hill, 1991
14
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
18
Heuristics
22 Oct 12
19
Power Consumption and Scale-up in Mixing
Consider low viscosity, baffled systems.
 ND 2 

N P  K 
  
a
Colson and Richardson. 20
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. 21
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.
22
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
23
Power Consumption and Scale-up in Mixing
Propeller pitch:
24
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
25
Discharge Coefficient
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
26
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
27
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
28
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
29
Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
30
Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
31
Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
32
Additional Plots for Non-Standard Mixing
N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000
33
Heuristics in Mixing
34
Heuristics in Mixing
Colson and Richardson. 35
In-Class PS Exercise
A pilot-plant vessel that is 0.3 m in diameter is agitated by a six-bladed
turbine impeller (Rushton) that is 0.1 m in diameter. With the impeller NRe
at 104, the blending time of two miscible liquids is found to be 15 s. The
power per unit volume is 0.4 kW/m3. The mixing vessel is to be scaled-up to
a vessel diameter of 1.8 m. Assume that the new vessel is geometrically
similar to the pilot-plant vessel. You may assume the NRe in the larger vessel
is still 104 or larger.
a) For the scaled-up vessel, what is the power/volume required to keep the
blending time the same (15 s)? Comment on your results.
b) For the scale-up, assume that the power/volume required is kept the
same as the pilot-plant vessel. What will be the new blending time in the
larger tank?
36
Heuristics
Questions?
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