FF0 Agitation Mixing [Compatibility Mode]

CHE C 213

Fluid Flow OperationsLecture Notes/Slides on

Agitation and Mixing

Dr. ASHISH M GUJARATHIBirla Institute of Technology and Science, Pilani

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Dr. Ashish M Gujarathi

BITS Pilani© ASHISH GUJARATHI, BITS PILANI

A Typical Chemical Plant



Lecture Plan

• Agitation and Mixing

– Introduction

– Applications

– Agitated Vessels

– Impellers

• Propeller

• Turbines

• High efficiency impellers

• Anchor Agitator

• Helical and Ribbon type impellers



Lecture Plan

• Agitation and Mixing

– Turbine Design

– Flow Patterns

– Vortex formation and Prevention




• 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




• 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



• 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




• 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



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



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



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



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)


– 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



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 =




• 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




• 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



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



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



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)



Impellers for high viscosity liquids


– 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



Impellers : Turbines

• Impellers for highly viscose liquids

– Double flight helical ribbon (a)

• Used widely in Polymerization reactors

– Anchor Impellor (b) (Bottom mixing)



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



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



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



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



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



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



Prevention of Swirling

Fig. Flow Pattern with off-center propeller



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??



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



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.



• 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 ∝



• 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 =



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.



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



=

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=



• For standard 6-bladed turbine NQ=1.3 and if

α=0.9 ;Np=5.2

NumberPower called is 53

"

321essDimensionl

aDn

PNP

ρ=



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



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 =



• 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 ∝==



• 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



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−

=



Power Correlations• Power No. Np Vs. Re for turbines and HE3

impellers; log –log plot



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 =



Power consumption

(Np Vs NRE plot)



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



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



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.



• 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)



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.



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=



•

=

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



• 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



Mixing times in agitaed vessels

– Dashed Lies are for unbaffled tanks

– Solid lines are for babbled tanks



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.



• Study

• Agitator Selection and Scaleup

– Scaleup

– Scaling down

– Scaleup of non-newtonian fluids



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All the Very Best

for

Comprehensive

Exam.

FF0 Agitation Mixing [Compatibility Mode]

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