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CHE C 213
Fluid Flow OperationsLecture Notes/Slides on
Agitation and Mixing
Dr. ASHISH M GUJARATHIBirla Institute of Technology and Science, Pilani
Email: [email protected]
You may give your course related feedback.
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
A Typical Chemical Plant
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Lecture Plan
• Agitation and Mixing
– Introduction
– Applications
– Agitated Vessels
– Impellers
• Propeller
• Turbines
• High efficiency impellers
• Anchor Agitator
• Helical and Ribbon type impellers
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Lecture Plan
• Agitation and Mixing
– Turbine Design
– Flow Patterns
– Vortex formation and Prevention
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Agitation and Mixing
• Applications
– Many operations in Process industries depend on
effective agitation and mixing of fluids
– Mass transfer and multi-phase processes
• Gas-Liquid Mass Transfer
• Liquid-Liquid Mass Transfer
• Liquid –Solid Mass Transfer
• Solid –Solid Mass Transfer
– Agitation and mixing are not synonymous
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Agitation and Mixing
• Agitation:
– Agitation refers to forcing a fluid by mechanical
means to flow in a specified way usually in
circulatory pattern.
• Mixing
– Mixing refers to random distribution between
separate phases
• E.g. A tankful of cold water can be agitated, but it cannot be
mixed until some other material (i.e., salt or hot water) is
added to it
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• Mixing term is applied to a variety of
operations (differing in degree of
homogeneity)
– Two gases that are brought together and
thoroughly blended and
– Sand, gravel, cement, and water tumbled in a
rotating drum for a long time
• Though products are not equally homogeneous ,
– In both the cases product is said to be mixed
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Agitation and Mixing
• Purposes of agitation
– Suspending solid particles in liquid
– Blending miscible liquids
– Dispersing a gas through the liquid in the form of
small bubble
– Dispersing second liquid, immiscible with first to
form an emulsion or suspension of fine drops
– Promoting Heat Transfer between the liquid and a
heating coil or jacket
Often one Agitator serves purposes at the same time
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Agitated Vessel (with agitator)
Inlet Connection
Rounded Bottom (Not Flat)
Top of vessel
(Either Open
Or Sealed with
Gasket in between
Tank and rounded
top)Proportions of tank
Vary widely,
depending on
the nature of
agitation problem Impeller causes liquid
to circulate through
the vessel and return
to impeller
Baffles used to reduce
tangential motion
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Agitation Equipments
• Agitation Equipments
– Gas Sparger, Jet Mixer, Bubble Column
• Mixing of gas with liquid
– Agitator, Centrifugal pump
• Agitation of Liquid with Liquid
– Double cone mixer or concrete mixer , Screw
Conveyer
• Mixing of solids with solid
– Colloid Mills, Mixing rolls, Pan mixer or putty
chasers for clay mixing
• Mixing of solids with liquids
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Selection of Agitator
• Impeller Agitator
– Axial Flow impeller (a)
Those that generate
currents parallel with
the axis of the
impeller shaft
– Radial flow impeller (b)
Those that generate
currents in a radial (a) (b)
or tangential direction
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Selection of Impellers
• The selection of impeller depends on viscosity
– Low to moderate viscous liquids
• Propellers (Viscosity < 3 Pa-s)
• Turbines (Viscosity < 100 Pa-s)
• High efficiency impellers
– Very Viscous liquids
• Anchor Agitator ( 50 < Viscosity < 500 Pa-s)
• Helical and Ribbon type impellers (Viscosity > 500 Pa-s)
Each type includes many variations and subtypes
which are not discussed here
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers: Propeller
• Propeller (for Viscosity < 3 Pa-s)
– Axial flow, high speed impeller for liquids
– 400-1750 rpm motor speed
– Two, three, four bladed propeller are generally
used
– Three bladed turbine are common with square
pitch
– Propeller with a pitch 1.0 is : Square pitch
diameterPropeller
bladepropeller ofn inclinatio of anglecertain at
revolution onein liquid by the moved distance alLongitudin
Pitch =
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers: Propeller
• Propeller
– The direction of rotation is usually chosen to force
the liquid downward, and the flow currents
leaving the impeller continue until deflected by
floor of the vessel.
Three Blade marine propeller
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers: Propeller
• Propeller
– Propellers rarely exceeds 18 in. in diameter
– In deep tanks two or more propellers may be
mounted on same shaft, usually directing the
liquid in the same direction
– Because of persistence of flow currents
• Propellers are effective in very large vessels
Six Blade propeller and Shaft
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers: Turbines
• Simple straight blade turbine (Visco. < 100 Pa-s)
– Pushes liquid radially and tangentially with almost
no vertical motion at the impeller
– Also called as paddles: 2-4 bladed paddles are
common
– In Process vessels they turn at 20 – 150 rpm
– Length of Paddle : 50-80% of vessel diameter
– Width of blade: 1/6 – 1/10 of the length
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers: Turbines
• Turbine (continued..)
– Anchor Agitator:
• Blades conform to the shape of dished or hemispherical
vessel, so that they scrap the surface. Useful in
prevailing deposits on a heat transfer surface
– Baffles
• Necessary to reduce swirl around the vessel
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers: Turbines
• Disc turbines
– Multiple straight blades mounted on a horizontal
disc (Fig. c):
• Creates a zone of higher shear rate
– Especially useful for dispersing a gas in a liquid
– Concave blade turbine is also used when good
overall circulation is important (Fig. d)
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers for high viscosity liquids
• High efficiency impellers
– Pitched Blade turbine (Fig. e)
• Used when good overall
circulation is important, because
it provides some axial flow in
addition to radial flow
High efficiency impeller HE3
A 310 fluid foil impeller
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Impellers : Turbines
• Impellers for highly viscose liquids
– Double flight helical ribbon (a)
• Used widely in Polymerization reactors
– Anchor Impellor (b) (Bottom mixing)
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Turbine Design:Typical Dimensions
3
1=
t
a
D
D1=
tD
H
12
1=
tD
J
3
1=
aD
E
5
1=
tD
W
4
1=
aD
L
The Designer of Agitated vessels has an unusually large number of choices
to make as to Type and Location of Impeller, Proportions of vessels, number
And proportions of baffles, Motor Speed, Speed of Agitator, etc.
Side View
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Flow Patterns
• The way liquid moves in an agitated vessel
depends on
– Characteristics of liquid i.e. viscosity, size and
properties of the tank, baffles and impeller
• The velocity at any point in the tank depends
on three components and the flow pattern in
tank depends upon variations in these
components
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Flow Patterns
• Velocity components
– Radial and acts in a direction perpendicular to shaft
of impeller
– Longitudinal and acts in a direction parallel to the
shaft
– Tangential or rotational and acts in a direction
tangent to a circular path around the shaft
• Overall flow pattern in the tank/vessel depends on
variations in these 3 Velocity Components
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Flow Patterns
• Velocity components and Vortex Formation
– In usual case of vertical shafts, the radial and
tangential components are in horizontal plane and
the longitudinal component are in a vertical
– Radial and longitudinal components are useful
and provide the flow necessary for mixing action
– When shaft is vertical and located at central,
tangential component is disadvantageous
– Tangential flow follows a circular path around the
shaft and creates a vortex
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Vortex in a reactor
• Unbaffled vessel with vortex
• At high impeller speeds, Vortex may touch
impeller: Undesirable
Top View
Shaft
Side View
Cylindrical Vessel
Swirling flow pattern with radial-flow turbine in an unbaffled vessel
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Prevention of Swirling
• Circulatory flow or swirling can be prevented
by
– Mounting impeller off-center (in small tanks)
– Moving shaft away from the centerline of tank,
then tilted in plane perpendicular to the direction
of move
– In larger tank, the agitator may be mounted in the
side of the tank, with a horizontal plane but an
angle with a radius
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Prevention of Swirling
Fig. Flow Pattern with off-center propeller
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Draft Tubes
• Draft Tubes
– When direction and velocity of flow to the section
of the impeller are to be controlled, draft tubes
are used.
– This devices are useful when high shear at the
impeller is desired.
– Loop Reactor??
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Draft tubes
• Draft tubes for propellers are mounted around the
impeller, and those for turbines are mounted
immediately above the impeller
Turbine Draft tube Propeller draft tube
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Circulation velocities and Power
Consumption• Circulation and velocity gradient of fluid inside the
agitator resulted from turbulence created by impeller
(propeller).
• Circulation and turbulence generation both consume
energy
• The power input is related to the design parameters
like
– Speed of propeller,
– Diameter of propeller
– Properties of fluid, etc.
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• The volumetric flow rate, q, is the total flow
leaving the impeller, as measured at the tip of
impeller
• K is constant that allows for the fact that the radial
velocity is not actually constant over the width of
blade. For geometrically similar impellers W is
proportional to Da, K, k, Bita2’ are approximately
constant.
( ) '
2
22 tan1 βπ knWDKq a −=
3
anDq ∝
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• The ratio of these quantities is called the flow
number
• This eqn. indicates that flow number is
constant for each type of impeller. NQ values
– For marine propellers (Square Pitch) = 0.5
– For four blade 450 turbine (W/Da=1/6)= 0.87
– For disc turbine = 1.3
– For HE-3-high efficiency turbine = 0.47
3
a
QnD
qN =
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Velocity Pattern in turbine agitator
Number in Fig. indicate the scalar
magnitude of the fluid velocity at
various points as fractions of the
velocity of the tip of the impeller blades.
Velocity in the jet quickly drops from the
tip velocity to about 0.4 times the tip
velocity near the wall.
Fluid leaves the impeller in a radial
direction, separates into longitudinal
streams flowing upward and downward
over the baffle, flows inwards towards
the impeller shaft and ultimately returns
to impeller intake.
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Power Consumption (P. C.)
• P.C. is an important consideration in design of
an agitated vessel
• When the flow is turbulent in the tank, Power
required can be estimated as
eunit volumper )(Eenergy Kinetic (q)impeller in produced rate Flow k×=P
2
2'3 VNnDP Qa
ρ×=
2
)( 23 a
Qa
nDNnDP
απρ×=
tipblade
impeller ofVelocity
bladeimpeller
at velocity Actual2'
==u
Vα
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
=
2
22
53 Q
a
NDnP
παρ
43421321essDimensionl
Q
essDimensionl
a
N
Dn
P
=
2
22
53
πα
ρ
NumberPower called is 53
"
321essDimensionl
aDn
PNP
ρ=
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• For standard 6-bladed turbine NQ=1.3 and if
α=0.9 ;Np=5.2
NumberPower called is 53
"
321essDimensionl
aDn
PNP
ρ=
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Typical Dimensions
3
1=
t
a
D
D1=
tD
H
12
1=
tD
J
3
1=
aD
E
5
1=
tD
W
4
1=
aD
L
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Power Correlations
• By Dimensional Analysis
),,,,,,,,,,( LJEWHDtgDanfP ρµ=
{ { { {{
=
4444 34444 21321321321321
rShapeFacto
SSSSSSN
a
N
a
N
a Dt
H
Dt
J
Da
W
Dt
L
Dt
E
Dt
Da
g
DnnDf
Dn
P
Frp
354321
22
5,,,,,,,,
3
Re
µ
ρ
ρ
( ),..,,,, 321FrRe SSSNNfN p =
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• Simplified example
– The three dimensionless groups can be
represented as, consider the group . Since
the impeller tip speed u2 equals (ПDan)
– This group is proportional to a Reynolds number calculated from the
diameter and peripheral speed of the impeller. This is the reason for the
name of the group
– At low Reynolds No. (Re<10) viscous flow prevails throughout the
vessel, and at Re>104, the flow is turbulent everywhere, A transition
region exists at intermediate Re.
µρ2
anD
( )µ
ρ
µ
ρ
µ
ρ aaaa DuDDnnD 2
2
Re ∝==
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• The power Number is analogous to a friction factor or a drag
coeff.
– It is proportional to the ratio of the drag force acting on a unit area of
the impeller and the inertial stress, i.e., the flow of momentum
associated with the bulk motion of the fluid.
• The Froude No. is a measure of the ratio of the inertial stress
to the gravitational force per unit area acting on the fluid.
– It appears in fluid dynamic situations where there is significant wave
motion on liquid surface. It is especially important in ship design.
– It is important when baffles are used or when Re<300
– Unbaffled vessels are rarely used at high Reynolds numbers, hence the
Froude number is not included in unbaffled correlations
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Power corelations
• For Baffled tanks
• For Unbaffled tanks
– Where a and b are constants
( ),..,,,, 321FrRe SSSNNfN p =
( ),..,,, 321Re SSSNfN
Nm
Fr
p=
b
Nbam Re10log−
=
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Power Correlations• Power No. Np Vs. Re for turbines and HE3
impellers; log –log plot
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Calculation of Power consumption
• Power delivered to the liquid is computed
after a relationship for Np is specified
• At low Reynolds No. (Re<10), lines of Np Vs Re for both baffled
and unbaffled tanks coincide
;
• If Re>10000 ;
• KL and KT constant, which depends on type of impeller (Values
are given in Table 9.2 of McCabe Text book)
ρ53
ap DnNP =
e
L
R
KNp = µ32
aL DnKP =
TKNp = ρ53
aT DnKP =
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Power consumption
(Np Vs NRE plot)
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Problem Exercise
• Study : Power Consumption in non-newtonian
fluids:
– Fig. 9.15 and Table 9.3 to be used
– Viscosity estimation using Eq. 9.24-9.26 and table
9.3
• Practice Solved Ex. 9.1, 9.2 and 9.3
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Blending and Mixing
• Mixing is much more difficult operation to
study and describe than agitation
• The patterns of fluid flow and velocity in an
agitated vessel are complex but reasonably
definite and reproducible.
• Often criteria for good mixing is visual
– Color change, or blending of gases in duct
• Other criteria include: Rate of decay of
concentration, temperature, pressure,etc.
with time/length
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Blending of miscible solids
• Miscible solids are blended in relatively small
process vessels by propellers, turbines, or
high-efficiency impellers, usually centrally
mounted,
– and in large storage and waste treatment tanks by
side-entering propellers or jet mixers.
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• In large storage tank, the agitator may be idle
much of the time and be turned on only to
blend the stratified layers of liquid that were
formed as the tank was being filled
• Stratified blending is often very slow
– To form, arrange, or deposit in layers
(Stratified:Meaning)
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Blending in process vessels
• The impeller in a process vessel produces a
high velocity stream, and the liquid is well
mixed in the region close to the impeller
because of the intense turbulence.
• As the stream slows down while entraining
other liquid and flowing along the wall, there
is some radial mixing, as large eddies break
down to smaller ones, but there is probably
little mixing in the direction of flow.
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Mixing Time
• Complete Mixing (99%) should be achieved if
the contents of the tank are circulated about
five times.
• Considering the average circulation, the
mixing time can be predicted as
– Where V= Volume of tank
– q= total flow for six bladed turbine
q
VtT
5=
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
•
=
t
aa
tT
D
DnD
HDt
3
2
092.0
1
45
π
=
Dt
H
Da
DttT
2
3.4
4.3 Constant
2
==
H
D
D
Dnt t
t
aT
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• Mixing time factor ntT depends on Reynolds
number for specific Da/Dt , Dt/H
• For Da/Dt=1/3; Dt/H=1 , ntT=36 for NRE>2000
(From Fig. 9.16)
• From Eq. ntT= 9 x 4.3 = 38.7
• The mixing time using baffled turbines varies
as about 5.1−∝ ntT
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Mixing times in agitaed vessels
– Dashed Lies are for unbaffled tanks
– Solid lines are for babbled tanks
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Let us solve
• A pilot plant vessel 1 ft (305 mm) in diameter is agitated by a
six blade turbine impeller 4 in (102 mm) id dia. When the
impeller Reynolds No. is 10000, the blending time of two
miscible liquids is found to be 15 s. The Power required is 2 hp
per 1000 gal (0.4 kW/m3) of liq.
• A) What power input would be required to give the same
blending time in a vessel 6 ft (1830 mm) in dia.
• B) What would be the blending time in the 6 ft (1830 mm)
vessel if the power input per unit volume were the same as
the pilot plant vessel.
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
• Study
• Agitator Selection and Scaleup
– Scaleup
– Scaling down
– Scaleup of non-newtonian fluids
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Jubail United Petrochemical - JUPC
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Dow F-9 Furnace Start-up
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Thai Olefins Start-up
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
Daqing Furnaces Start-up
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
BP Innovene Distinctive
Compliance Project
Dr. Ashish M Gujarathi
BITS Pilani© ASHISH GUJARATHI, BITS PILANI
All the Very Best
for
Comprehensive
Exam.