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Heuristics19 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.

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Agitators and Mixing Equipment

Fluid mixing

Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

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Agitators and Mixing Equipment

Fluid mixing: Baffles

Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

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

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Agitators and Mixing Equipment

Fluid mixing: off-center

Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

Fluid mixing: Baffles

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Agitators and Mixing Equipment

Side mounted mixers.

Paul, et.al., Handbook of Industrial Mixing, Wiley, 2004Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

Flow patterns for side-entering propeller

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Agitators and Mixing Equipment

Common Impellers

Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

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.

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Agitators and Mixing Equipment

Various Turbine Impellers

Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

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Various Impeller Types

Paul, et.al., Handbook of Industrial Mixing, Wiley, 2004

Axial Flow Impellers

Radial Flow Impellers

Hydrofoil Impellers

High-Shear Impellers

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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

Coulson and Richardson’s Chemical Engineering Volume 1, 6th ed.

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.

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Flow Patterns for Various Impellers

Flat Blade Turbine = FBTPitched 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

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Power Consumption and Scale-up in Mixing

Consider geometry, fluid properties, flow patterns, power, and so on. Has been considered through dimensional analysis.

Tatterson & Colson and Richardson.

...22

53

dcba

P D

C

D

T

g

DNNDK

DN

PN

With:

numberFroudeNg

DN

orsPaityvisfluid

numberreynoldsNND

mimpellerofdiameterD

orHzimpellerofspeedN

densityfluid

WPowerP

numberPowerN

Fr

smkg

srotations

m

kg

P

2

Re

2

][cos

][

][

3

For geometrically similar vessels, ratios of all terms to right of the Froude number are negligible.

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.

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Power Consumption and Scale-up in Mixing

Consider low viscosity, unbaffled systems.

Colson and Richardson.

ba

P g

DNNDKN

22

aP NKNNat ReRe :300

57.43.0

37.1

D

T57.4

3.0

37.1

D

H1

3.0

3.0

D

C

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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?

cPityvis

densitym

kg

50cos

1650 3

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Power Consumption and Scale-up in Mixing

Consider low viscosity, baffled systems.

Colson and Richardson.

a

P

NDKN

2

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Power Consumption and Scale-up in Mixing

Consider low viscosity, baffled systems (wall baffles).

Colson and Richardson.Figure 10.59 Power correlations for turbine impellers in a tank with 4 baffles. [w, D, impeller width and diameter, respectively.]

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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:

][arg

arg

:

][

3

3

sm

Q

Q

rateedischvolumetricQ

tcoefficienedischimpellerN

where

unitlessND

QN

Tip Speed of an impeller: ][ sm

t NDu

Torque: “twist” force acting on agitator shaft: ][22

52

sWDNN

N

PT P

q

Power per unit volume: 324

53

mWP

HT

DNN

V

P

Blend time (estimation to within 5% desired concentration):

sD

H

D

T

NNP

5.05.1

953

1

40.5

000,10

0.150.0

33.0

5.033.0

Re

NTH

TC

TD

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Discharge Coefficient

N.P. Cheremisinoff, Handbook of Chemical Processing Equipment, B-H, 2000

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Mixing Time

P.M. Doran, Bioprocess Engineering Principles, 2nd Ed., Academic Press 2012

NN

t

i

m

90

Blend time (estimation to within 10% desired concentration):

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Mixing Time

P.M. Doran, Bioprocess Engineering Principles, 2nd Ed., Academic Press 2012

31

31

32

9.5

D

T

P

VTtm

Doran suggests that for turbulent mixing conditions, irrespective of the impeller type, that (baffled vessel, single impeller, H=T):

Verified under aerated conditions also (impeller not flooded) and for:

mDT

D

7.2

7.02.0

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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.

sPaityvis

densitym

kg

210cos

1000 3

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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?