Agitator
Mihir P.Shah
DDU
22-Sep-18 MPS,DDU 1
AGITATION & MIXING OF LIQUIDS
“Many processing operations depend for their success on the effective
agitation & mixing of fluids” ……McCabe
Agitation
It is an induced motion of a material in a specified way.
the pattern is normally circulatory.
it is normally taken place inside a container.
Mixing
Random distribution, into & through one another
of two or more initially separate phases
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Why to go for mixing?
• Heart of the chemical industry
• Uniformity of composition
• Desired flow pattern
• To control the quality of the product
• To maintain the heat transfer at highest
possible rate.
• To separate two phase mixture effectively.
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Where is it required?
• Blending of miscible liquids
• Solid suspension
• Gas absorption
• Dispersion
• Dissolution
• Crystallization
• Heat transfer
• Chemical Reaction
• Extraction
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A good mixing should achieve
• Minimum power requirement.
• Efficient mixing in optimum time.
• Best possible economy.
• Minimum maintenance, durable and trouble
free operation.
• Compactness.
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Factors affecting the designing of the
agitator
• Type of vessel
• Circulation pattern.
• Location of the agitator
• Shape and size of the vessel
• Diameter and width of the agitator
• Method of baffling
• Power required
• Shaft overhang
• Type of stuffing box or seal, bearing, drive system etc
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Types of agitator
– Paddle
– Propeller
– Turbine
– Helical
– Toothed / disc type
– Cone
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Impeller Technology
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Vortex
If solid particles present within tank; it tends to
throw the particles to the outside by centrifugal
force.
Power absorbed by liquid is limited.
At high impeller speeds, the vortex may be so deep
that it reaches the impeller.
Method of preventing vortex
- baffles
- impeller in an angular off-center position
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Flow Around Baffles
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(ii) Impeller in an angular off-center position
Mount the impeller away from the center of the vessel & tilted in the direction
perpendicular to the direction of flow.
Flow pattern with off-center propeller
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Agitator Drive system
• Electric motor supplies the power.
• If rpm of motor shaft and agitator shaft is
similar then gear box is not required.
• Gear box transmits power of electric motor
shaft to agitator shaft directly or sometimes to
the other shaft which is attached to agitator
shaft.
• Coupling is used to connect two shafts.
• This power transmission system creates power
losses up to 20% of agitator power
consumption.
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Drive
(Motor-Gearbox)
Assembly
Shaft seals
• During the process, liquid vapors or gases should not leak
through agitator shaft nozzle.
• There should not be any exchange either from inside to outside
or vise versa.
• Like in case of vacuum reaction
• Most common method for sealing shaft is with stuffing box
and gland.
• If P > 10kgf/cm2, T > 120C and N > 300rpm, one can not use
stuffing box.
• Mechanical seal will be preferred in above conditions.
• The losses occurred to loose type of fitting between shaft and
seal is considered to be 10% of agitator power consumption.
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Stuffing box
Bolt Gland sleeve
Gland
Packing
Stuffing box
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Mechanical Seal
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Power consumption in agitated vessels
For an effective mixing, the volume of fluid
circulated in a vessel via an impeller must be
sufficient to sweep out the entire vessel in a
reasonable time.
Stream velocity leaving the impeller must be
sufficient to carry currents to the remotest part
of the vessel.
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POWER REQUIREMENT
Factors affecting power requirement
• Properties of fluid to be agitated
• Height of the liquid
• Tank size and dimensions
• Agitator type and size
• Speed of agitator
Power number is ratio of drag force acting on unit area of impeller
to internal stress
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Power Number
Pg c
NP 3 5
n Da
• Where
– P = Power required for agitation
– = Density of liquid solution agitated
– N = rotational speed of agitator in rps.
– Da = diameter of agitator
N P f ( N Re , N Fr , S )
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Dimensionless Numbers
• Reynolds's Number = Inertial stress/Viscous Stress
Da2 n
N RE
• Froude Number = Inertial stress to gravitational stress
n 2 Da
N Fr
g
• Shape Factor is related to linear dimension of vessel.
For turbine type agitator,
Dt E L W J H
S1 ; S2 ; S3 ; S4 ; S5 ; S5
Da Da Da Da Dt Dt
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Froude Number
• Considered when vertex is formed.
• In baffled tank, no vertex formation, so Np (NFr).
• In un-baffled tank with Nre < 300, no vertex
formation, so Np (NFr).
• In un-baffled tank with Nre > 300, vertex formation
takes place so Np =(NFr).
a log 10 N Re
m
N P ( Corrected) N P N m
Fr b
Turbine a b
Three blades 1.7 18
22-Sep-18 Six blades MPS,DDU 1 40 25
Dimensionless Correlations
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Fig 1
Curve A = vertical blades, W/Da = 0.2 Curve C = pitched blade
Curve B = vertical blades, W/Da = 0.125 Curve D = unbaffled tank
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Power number NP vs. Reynolds number Re for turbines and impellers
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Power number NP vs. Reynolds number Re for marine propellers and helical ribbons
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Power correlation for a 6-blade turbine in pseudoplastic liquids
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Power required for complete suspension of solids
in agitated tanks using pitched-blade turbines
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Example
A flat-blade turbine with six blades is installed
centrally in a vertical tank. The tank is 1.83 m in
diameter, the turbine is 0.61 m in diameter & is
positioned 0.61 m from the bottom of the tank.
The turbine blades are 127mm wide. The tank is
filled to a depth of 1.83m with a solution of 50%
caustic soda at 65.6oC, which has a viscosity of
12cP and a density of 1498 kg/m3. The turbine
is operated at 90 rpm. What power will be
required to operate the mixer if the tank was
baffled?
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Solution (a) baffled
n = 90rpm / 60 s = 1.5 r/s
Da = 0.61m
µ = 12cP = 12x10-3 kg/ms
N RE
Da2 n
0.61 (1.5)(1498)
2
69600
1210 3
For Re > 10000, Np = KT = 5.8 from curve A for baffle (NRe = 69600),
NP = 5.8 (or from table 2 given before)
NPn 3
Da
5
P
gc
3 5
(5.8)(1.5) (0.61) (1498) 2476.6 mN / s
2476.6W
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Solution (b) unbaffled n = 90rpm / 60 s = 1.5 r/s
Da = 0.61m
From Fig 1, curve D (NRe =
µ = 12cP = 12x10-3 kg/ms
69600), NP = 1.07
Froude number,
N RE 69600
n 2 Da (1.5) 2 (0.61)
N Fr 0.14
g 9.81
From Table 1, the constants a & b are 1.0 & 40.0 respectively
a log 10 N Re 1.0 log10 69600
m 0.096
b 40
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From curve D, the power number for NRe = 69600 is 1.07
So the corrected value of NP,
N P (Corrected) N P N Fr
m
1.070.140.096 1.29
Thus power,
N P n3 Da5
P (1.29)(1.5)3 (0.61)5 (1498)
gc
550mN / s 550 W
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SHAFT DESIGN
Shaft can be attached to the vessel in vertical,
horizontal or angular positions.
It is preferable to use the bearing either at top of
the vessel or at bottom. It can be placed externally
or internally to the vessel.
DESIGNING CAN BE DONE BY 3 WAYS
• Based on torque
• Based on Bending moment calculations
• Based on the critical speed of the agitator.
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Design properties of shaft
• Sufficient strength
• Low sensitivity to stress concentration
• Ability to withstand heat, wear resistance
• Good machinability
Fabrication method
Hot rolling
Cold drawing
Turning
Grinding from through bars
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Shaft Design
• Two loads
– Torsonal load
– Bending load
• Shafts are generally made from carbon steel and is
heat treated to impart high mechanical strength up
to 8000kg/cm2.
• Total power required for agitator (X)= power
required for shaft + transmission losses + fitting
losses
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hp X 1.11.2
MPS,DDU 39
Loadings on shaft
• During start up the shaft has to withstand higher torque.
• During running condition, other than torque, forces like
hydraulic force due to turbulence in liquid or
asymmetrical construction of agitator and baffles.
• Centrifugal force will also present if agitator is not
balanced.
• Possibilities of agitators being chocked when tipping bags
or containers added to vessel.
• Worst possible conditions are assumed to be equivalent
to those in which agitator blade will be jammed at 75%
of its length.
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Based on torque (shear stress)
• Continuous average rated torque on shaft
hp * 750 * 60 hp * 60
Tc N.m kgf.m
2N 2N
where N speed in rpm
• Maximum torque developed in shaft
Tm 1.5 to 2.5 TC
• Polar modulus of section of shaft cross section
Tm
Zp d 3
s fs s ,allow
16 Zp
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Based on Moment Calculation
Worst possible conditions are assumed to be equivalent to those in which agitator
blade will be jammed at 75% of its length.
M Fm where shaft length
Tm
Fm where R b width of blade
0.75Rb
1
M e M M 2 TM2
2
Me
fb fJ Z d 3
s
32
Z
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Based on Critical Speed
• It is difficult to calculate the unbalanced forces due
to asymmetric construction of agitator.
• Fixing certain counter balance weight in the opposite
direction to it can easily eliminate this.
• It is necessary to control the deflection of shaft by
adequate support
• The speed at which the shaft vibrates violently is
called as the critical speed of the shaft.
• Range of 70% to 130% of critical speed should be
avoided
• Diameter should be so chosen that the normal
working speed should not fall in this range.
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Based on Critical Speed
3
Fm
, cm
3EI
60 * 4.987
d 4
Nc rpm
I s
12
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64 MPS,DDU 44
HUB & BLADES
• Hub is attached to shaft by Keys & Bolts.
• The load on the blade is assumed to act as
75% of the agitator radius.
• This will create a bending moment in blade,
which will be maximum at the point where
the blade is attached to the hub.
M max F m(0.75Rb Rh )
max B.M Fm 0.75Rb Rh Tm
f 2
2
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Z b
MPS,DDU
t * bw / 6 bt * bw /6 45
HuB
• The hub is fixed to the shaft by key, which
transmits the shaft torque to the impeller.
• The hub is subjected to the bending moment
due to force on the blade and to shear force
due to the torque.
• It is assumed the outside hub diameter as
twice the shaft diameter and check the shear
stress due to torque.
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Impellers
Pitched Blade Turbine (PBT) Rushton Turbine (RT
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Impeller with Shaft, Hub and Key
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Hub and key
• Hub diameter = 2 * shaft diameter
• Hub length = 2.5*shaft diameter
• Key length (ℓ) = 1.5*shaft diameter
Tm t
bf s f c
ds 2 2
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Other parts
• Stuffing box
• Gland
• Coupling
• Stabilizer
• Bearing
• Shaft seals
• Drives for agitator
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