agitation and mixing-h4 class-tkmce

04/11/23 1

AGITATION AND MIXING OF FLUIDS

Dr.K.B. RADHAKRISHNAN

DEPARTMENT OF CHEMICAL ENGINEERING, TKMCE, KOLLAM

04/11/23 2

AgitationAgitation It is an induced motion of a material in a specified way.It is an induced motion of a material in a specified way. the pattern is normally circulatory.the pattern is normally circulatory. it is normally taken place inside a container.it is normally taken place inside a container.

MixingMixing Random distribution, into & through one another Random distribution, into & through one another of two or more initially separate phasesof two or more initially separate phases

CHAPTER 9CHAPTER 9

AGITATION & MIXING OF LIQUIDSAGITATION & MIXING OF LIQUIDS

“Many processing operations depend for their success on the effective agitation & mixing of fluids” ……McCabe

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Purposes of agitation of liquidsPurposes of agitation of liquids

Suspending solid particles.Suspending solid particles. Blending miscible liquids e.g. methyl alcohol Blending miscible liquids e.g. methyl alcohol

& water.& water. Dispersing gas through liquid in the form of Dispersing gas through liquid in the form of

small bubbles.small bubbles. Promoting heat transfer between liquids & Promoting heat transfer between liquids &

a coil/jacket.a coil/jacket.

04/11/23 4

AGITATORSAGITATORS

Multi-bladed paddle Multi-bladed paddle agitators with short agitators with short bladesblades– Turn at high speed on Turn at high speed on

centrally-mounted centrally-mounted shaftshaft

– Smaller diameter; 30-Smaller diameter; 30-50% of diameter of 50% of diameter of vesselvessel

– Effective over wide Effective over wide range of viscositiesrange of viscosities

Simple straight-blade turbine

Disk turbine

Pitched-blade turbine

Concave-blade CD-6 impeller

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Agitation vesselAgitation vessel

Liquids are agitated in a tankBottom of the tank is roundedImpeller creates a flow pattern.Small scale tank (less than 10 litres) are constructed using Pyrex glass. For larger reactors/tank, stainless steel is used. Speed reduction devices are used to control the agitation speed.Mixing Flow : 3 patterns (axial, radial, tangential flow)

Typical agitation process tank

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Mixing Flow patterns (3Mixing Flow patterns (3 types):

(i) Axial flow. Impeller makes an angle of less than 90o with the plane of rotation thus resultant flow pattern towards the base of the tank (i.e. marine impellers).More energy efficient than radial flow mixing. More effective at lifting solids from the base of the tank.

e.g. Propellers

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(ii) Radial flow. Impellers are parallel to the axis of the drive shaft.The currents travel outward to the vessel wall & then either upward or downward. Higher energy is required compared to axial flow impellers.

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(ii) Tangential flow. The currents acts in the direction tangent to the circular path

around the shaft. Usually, it produce vortex (disadvantageous) & swirling the

liquid.

vortex

Unbaffled vessel

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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

Vortex

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Preventing vortex(i) Baffles on the tank walls

Flow pattern for an axial flow propeller (baffled vessel)

Flow pattern for a radial flow turbine/paddle

vortex

Baffles are vertical plates (typically about 10% of the tank diameter) that stick out radially from the tank wall

04/11/23 11

Without baffles, the tangential flow (swirling) occurred in a mixing tank causes the entire fluid mass to spin (more like a centrifuge than a mixer).

With baffles, most impellers show their true flow characteristics.

Most common baffles are straight flat plates of metal (standard baffles).

Most vessels will have at least 3 baffles. 4 is most common and is often referred to as the "fully baffled" condition.

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Agitation in an unbaffled vessel leads to swirling flow with vortex formation & poor distribution

Standard baffling promotes flow that results in good solids distribution

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Flow pattern with off-center propeller

(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.

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Impeller:Impeller:Three main types of impellers :(i) Propellers; (ii) paddles & (iii) turbines

(i) Propellers:Create an axial-flow (flow of

currents is pushed in downward direction).

High speed for low viscosity liquid.Effective in very large tanks. In a deep tank, 2 or more propellers

may be mounted on the same shaft.

04/11/23 17

(ii) Paddles:Suitable for stirring simple liquids at low to

moderate speeds (between 20-150 rpm).Paddles push the liquid radially (radial flow).Anchor is one type of paddle agitator. Ratio of paddles diameter to the vessel

diameter is typically 50-80%. Dia >o.6 DtWidth of blade is 1/6 to 1/10 of its length.

Anchor

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(iii)Turbine:Diameter ~ 30-50% of vessel diameter.Suitable for wide range of viscosity.For low viscosity, it generates strong currents which

continue throughout vessel.Principal currents produced: radial & tangential.

6 blades

5 blades 4 blades 3 blades

12 blades 8 blades Disc Turbines

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Standard turbine designStandard turbine designDimension of a vessel & turbine impeller is :

12

11

3

1

ttt

a

D

J

D

H

D

D

4

1

5

1

3

1

aat D

L

D

W

D

E

Da = impeller diameterDt = tank diameter

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Draft tubesDraft tubes

Turbine Propeller

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Circulation, Velocities, and Power Circulation, Velocities, and Power ConsumptionConsumption

Volume of fluid circulated by impeller must be Volume of fluid circulated by impeller must be sufficient to sweep out entire vessel in reasonable sufficient to sweep out entire vessel in reasonable timetime

Velocity of stream leaving impeller must be sufficient Velocity of stream leaving impeller must be sufficient to carry current to remotest parts of tankto carry current to remotest parts of tank

In mixing, also need turbulenceIn mixing, also need turbulence– Results from properly directed currents and large velocity Results from properly directed currents and large velocity

gradients in liquidgradients in liquid Circulation and generation of turbulence both Circulation and generation of turbulence both

consume energyconsume energy Large impeller + medium speed = flowLarge impeller + medium speed = flow Small impeller + high speed = turbulenceSmall impeller + high speed = turbulence

04/11/23 22

Power consumption in agitated vessels 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.

04/11/23 23

(i) Flow number, NQ

a

taT D

DnDq 392.0

NQ is constant for each type of impeller.For flat-blade turbine (FBT), in a baffled vessel, NQ may be taken as 1.3; For marine propellers (Square pitch), NQ = 0.5; For four blade 45o turbine, NQ = 0.87;

For HE impeller- NQ=0.47

------ (2)

n = speed (rotation/s)Da = impeller diameterDt = tank diameter

3a

Q nDq

N 3

aDnqWhere q is the volumetric flow rate, measured at the tip of the blades, n is the rotational speed (rpm), Da is the impeller diameterTotal flow was shown to be

04/11/23 24

(ii) Power consumption

Power required to drive the impeller.

Power number,

53a

cP Dn

PgN

Power requirement is

c

aP

g

DnNP

53

or from Fig 1

Power no.- Analogous to f or Cd.

It is proportional to the ratio of the drag force acting on a unit area of the impeller

and the inertial stress (ie the total momentum associated with the bulk motion of the

fluid

04/11/23 25

(iii) Dimensionless Group

nD

N aRE

2

The Froude number, NFr

g

DnN a

Fr

2

The Reynolds number, NRe

------ (5)

------ (6)

nDau

auD

Re Froude No. is a measure of the ratio of the inertial stress to Froude No. is a measure of the ratio of the inertial stress to

the gravitational force per unit area acting on the fluid. It the gravitational force per unit area acting on the fluid. It appears in the dynamic situations where there is significant appears in the dynamic situations where there is significant wave motion on a liquid surface. Important in ship design. wave motion on a liquid surface. Important in ship design. Unimportant when baffles are not used or Re< 300Unimportant when baffles are not used or Re< 300

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Why Dimensionless Numbers?Why Dimensionless Numbers?

Empirical correlations to estimate the power Empirical correlations to estimate the power required to rotate a given impeller at a give required to rotate a given impeller at a give speed, with respect to other variables in speed, with respect to other variables in systemsystem– Measurements of tank and impellerMeasurements of tank and impeller– Distance of impeller from tank floorDistance of impeller from tank floor– Liquid depthLiquid depth– Dimensions of bafflesDimensions of baffles– Viscosity, density, speedViscosity, density, speed

04/11/23 27

(iv) Power Correlation

Typical plots of NP versus NRe is shown in Fig. 1 below

Curve A, B, & C for baffles; Curve D for unbaffled

For unbaffeld tanks, at high NRe (higher than 10,000), a vortex forms & NFr has an effect. So empirically,

The NP(corrected) must be corrected by multiplying NP by NFrm

b

Nam Re10log

mFrPCorrectedP NNN )(

04/11/23 28

Curve C = pitched bladeCurve D = unbaffled tank

Curve A = vertical blades, W/Da = 0.2Curve B = vertical blades, W/Da = 0.125

Fig 1

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Determination of power

Reynolds

number NP (Fig. 1)

Froude number

nD

N aRE

2

g

DnN a

Fr

2

c

aP

g

DnNP

53

baffled

Unbaffled(curve D)

Constants a & b (Table 9.1)

mFrPCorrP NNN )(

Power numberPower

b

Nam Re10log

TurbineTurbine aa bb

Three blades

1.71.7 1818

Six blades

11 4040

Table 1- Constants for unbaffled tank

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Dimensional analysis for fluid agitation systemsDimensional analysis for fluid agitation systems

Characteristic length: Impeller diameter D (m)

Characteristic time: Inverse impeller speed: 1/N (s)

Characteristic mass: Liquid density

Basic quan

and cube

tities

3 of impeller diameter: D (kg)

Characteristic velocity: Impeller diameter and speed: DN (m/s)

Characteristic pressure: De

Derived q

nsity and

u

velocity

antities

2 2

3 3

square: D N (Pa)

Characteristic flow rate: Velocity and area ND m /s

04/11/23 31

Dimensionless numbersDimensionless numbers

2brake

Re Po 3 5

2 3 2

We Fr

iQ 3

N D WReynolds N = ; Power N =

N D

N D N DWeber N = ; Froude N =

g

QFlow N =

ND

04/11/23 32

Dimensionless CorrelationsDimensionless Correlations

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P = P = (n, D(n, Daa, g, gcc, , , g, , g, ))

Where NWhere NReRe is Reynold’s no.; N is Reynold’s no.; NFr Fr is the Froude no.is the Froude no.

nDnDaa22// is proportional to an N is proportional to an NReRe calculated from the diameter and calculated from the diameter and

speed of the impellerspeed of the impeller NNPP is analogous to a friction factor or a drag coefficient associated is analogous to a friction factor or a drag coefficient associated

with the bulk motion of the fluidwith the bulk motion of the fluid NNFrFr is a ratio of the inertial stress to the gravitation force per unit is a ratio of the inertial stress to the gravitation force per unit

area acting on the fluidarea acting on the fluid

),...,,,,(

,...,,,2

,

21Re

21

2

53

nFrP

naa

a

c

SSSNNN

SSSg

nDnD

Dn

Pg

POWER CORRELATIONS-DIMENSIONAL ANALYSIS

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Shape FactorsShape Factors

Various linear measurements Various linear measurements – Base measurements of DBase measurements of Daa (diameter of impeller) and D (diameter of impeller) and Dtt

(diameter of tank)(diameter of tank)

Calculate remaining shape factors by dividing by Calculate remaining shape factors by dividing by magnitude of Dmagnitude of Daa or D or Dtt

– SS11, S, S22, S, S33, …, S, …, Snn

Two mixers of the same geometrical proportions but Two mixers of the same geometrical proportions but of different sizes will have identical shape factors, but of different sizes will have identical shape factors, but differ in magnitude of Ddiffer in magnitude of Daa

Geometrical similarityGeometrical similarity

04/11/23 35

Power Correlations for Specific Power Correlations for Specific ImpellersImpellers

Given in plots of NGiven in plots of NPP vs. N vs. NReRe for various for various

types of impellers, propellers, and turbinestypes of impellers, propellers, and turbines

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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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Power ConsumptionPower Consumption

Power required to drive impellerPower required to drive impeller

V’V’2 2 slightly less than tip speed, uslightly less than tip speed, u22

Power RequirementPower Requirement

ck

Qa

g

VE

NnDq

2

)( 2'2

3

2'

2 / uV anDV '2

Q

c

a Ng

DnP

2

2253

04/11/23 41

Calculation of Power ConsumptionCalculation of Power Consumption

At low NAt low NReRe (<10), density is no longer a (<10), density is no longer a

factor factor

c

aP

g

DnNP

53

c

aL

LP

g

DnKP

N

KN

32

Re

04/11/23 42

Calculation of Power ConsumptionCalculation of Power Consumption

At NAt NReRe>10,000 in baffled tanks, P is >10,000 in baffled tanks, P is independent of Nindependent of NReRe and viscosity is not a and viscosity is not a factorfactor

KKLL and K and KTT are constants for various types of are constants for various types of impellers and tanksimpellers and tanks

c

aT

TP

g

DnKP

KN

53

04/11/23 43

Type of ImpellerType of Impeller KKLL KKTT

Propeller, 3 bladesPropeller, 3 blades

Pitch 1.0Pitch 1.0

Pitch 1.5Pitch 1.5

4141

5555

0.320.32

0.870.87

TurbineTurbine

6-blade disk (S6-blade disk (S33=0.25 S=0.25 S44=0.2)=0.2)

6 curved blades (S6 curved blades (S44=0.2)=0.2)

6 pitched blades (456 pitched blades (45, S, S44=0.2)=0.2)

4 pitched blades (454 pitched blades (45, S, S44=0.2)=0.2)

6565

7070

--

44.544.5

5.755.75

4.804.80

1.631.63

1.271.27

Flat paddle, 2 blades (45Flat paddle, 2 blades (45, S, S44=0.2)=0.2) 36.536.5 1.701.70

AnchorAnchor 300300 0.350.35

Table:2

04/11/23 44

Power ConsumptionPower Consumption

In generalIn general

P = NP = NPPnn33DDaa55

For Re < 10For Re < 10

NNPP = K = KLL/Re/Re

P = KP = KLLnn22DDaa33

For Re > 10,000For Re > 10,000

NNPP = K = KTT

P = KP = KTTnn33DDaa55

04/11/23 45

Power ConsumptionPower Consumption3 5

PP N N D

3

1P K ND

2

2P K D

04/11/23 46

A disc turbine with six blades is installed centrally in a vertical baffled tank 2 m in diameter. The turbine is 0.67 m in diameter & is positioned 0.61 m above the bottom of the tank. The turbine blades are 134mm wide. The tank is filled to a depth of 2m with a solution of 50% caustic soda at 65.oC, which has a viscosity of 12cP and a density of 1500 kg/m3. The turbine is operated at 90 rpm. What power will be required?

Example

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ExampleA 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?

04/11/23 48

For Re > 10000, Np = KT = 5.8 from curve A for baffle (NRe = 69600), NP = 5.8 (or from table 2 given before)

Solution (a) baffled

n = 90rpm / 60 s = 1.5 r/s

Da = 0.61m

µ = 12cP = 12x10-3 kg/ms

69600

1012

)1498)(5.1(61.03

22

nD

N aRE

c

aP

g

DnNP

53

W

smN

6.2476

/6.2476)1498()61.0()5.1)(8.5( 53

04/11/23 49

Solution (b) unbaffled n = 90rpm / 60 s = 1.5 r/s

Da = 0.61m

µ = 12cP = 12x10-3 kg/ms

69600REN

From Fig 1, curve D (NRe = 69600), NP = 1.07

Froude number,

14.081.9

)61.0()5.1( 22

g

DnN a

Fr

From Table 1, the constants a & b are 1.0 & 40.0 respectively

096.040

69600log0.110log 10Re

b

Nam

04/11/23 50

From curve D, the power number for NRe = 69600 is 1.07

So the corrected value of NP,

29.114.007.1 096.0)( m

FrPCorrectedP NNN

Thus power,

WsmN

g

DnNP

c

aP

550/550

)1498()61.0()5.1)(29.1( 5353

04/11/23 51

ProblemProblem

The agitation system mentioned above is to The agitation system mentioned above is to be used to mix a rubber latex compound be used to mix a rubber latex compound having a viscosity of 120 Pa.s and density having a viscosity of 120 Pa.s and density 1120 kg/m1120 kg/m3. 3. What power will be required?What power will be required?

(K(KLL= 65 – from table 2 given before)= 65 – from table 2 given before)

21.5120

11205.161.0Re

2

P = KP = KLLnn22DaDa33

WDanKP L 5.398312061.05.165 32

32

04/11/23 52

Blending and MixingBlending and Mixing

More difficult to study and describe as More difficult to study and describe as criterion for “good mixing” is often visual criterion for “good mixing” is often visual observationobservation– Interference phenomena to follow blending of Interference phenomena to follow blending of

gases in a ductgases in a duct– Color change of acid-base indicator Color change of acid-base indicator – Rate of decay of concentration or temperatureRate of decay of concentration or temperature

04/11/23 53

Mixing Using a Standard 6-Blade Mixing Using a Standard 6-Blade Turbine: Mixing time modelsTurbine: Mixing time models

For a given tank and impeller or geometrically For a given tank and impeller or geometrically similar systems, mixing time, tsimilar systems, mixing time, tTT, varies , varies

inversely with stirrer speedinversely with stirrer speed

ttTT is much greater when N is much greater when NReRe is 10-1000, even is 10-1000, even

though power consumption is comparable to though power consumption is comparable to the turbulent rangethe turbulent range

a

ta D

DnDq 392.0

3.4

92.0

1

45

5

2

2

2

constH

D

D

Dnt

DnD

HD

q

Vt

t

t

aT

ta

tT

04/11/23 54

Mixing times in agitated vessels Dashed lines for unbaffled tanks, solid lines for baffled tanks

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Mixing time predictions - Norwood-Metzner Mixing time predictions - Norwood-Metzner General correlation for turbine impellersGeneral correlation for turbine impellers

When NWhen NReRe>10>1055, Da/Dt , Da/Dt

= 1/3, Da/Dh=1;f= 1/3, Da/Dh=1;ftt 5 5

6/1

2

2/12

2/32/1

2/16/13/22 )(

a

t

t

aT

t

aaTt Dn

g

H

D

D

Dnt

DH

DgnDtf

ft is the blending time factor

Correlation of blending times for miscible liquids in a turbine-agitated baffled vessel

04/11/23 56

Mixing time for a high efficiency Mixing time for a high efficiency impeller (Turbulent regime)impeller (Turbulent regime)

5.067.1

9.16

DtH

DaDt

nTT

04/11/23 57

ProblemProblem

An agitated vessel 1.83 m in dia contains a six –An agitated vessel 1.83 m in dia contains a six –blade straight-blade turbine 0.6 m in diameter, set blade straight-blade turbine 0.6 m in diameter, set one impeller diameter above the vessel floor, and one impeller diameter above the vessel floor, and rotating at 80 rpm. It is proposed to use this vessel rotating at 80 rpm. It is proposed to use this vessel for neutralizing a dilute aqueous solution of NaOH for neutralizing a dilute aqueous solution of NaOH at 70 at 70 00F with a stoichiometrically equivalent F with a stoichiometrically equivalent quantity of concentrated HNO3. The final depth of quantity of concentrated HNO3. The final depth of the liquid in the vessel is 1.83 m. Assuming that the liquid in the vessel is 1.83 m. Assuming that all the acid is added to the vessel at one time, how all the acid is added to the vessel at one time, how long will it take for the neutralization to be long will it take for the neutralization to be complete?complete?

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SolutionSolution

Dt = 1.83 m Da = 0.61 m E = Dt = 1.83 m Da = 0.61 m E = 0.61 m0.61 m

n = 80 /60 = 1.333 /s, density of n = 80 /60 = 1.333 /s, density of liquid (given) = 1000 kg/m3, liquid (given) = 1000 kg/m3, viscosity of liquid (given)viscosity of liquid (given)

Find Re = n Find Re = n Da^2.density/viscosity = Da^2.density/viscosity = 503000503000

Find ntFind ntT T from figure and thenfrom figure and then ttT.T.

3.42

const

HD

DD

nt t

t

aT

04/11/23 59

Mixer SelectionMixer Selection

Choice of impeller can also affect mixing timeChoice of impeller can also affect mixing time Propellers typically require longer mixing times Propellers typically require longer mixing times

compared to turbinescompared to turbines– Propellers have lower power consumptionPropellers have lower power consumption

Gas bubbles, liquid drops, or solid particles also Gas bubbles, liquid drops, or solid particles also increase blending timeincrease blending time

No direct relation between power consumed and No direct relation between power consumed and amount or degree of mixingamount or degree of mixing

When mixing time is critical, best mixer is one that When mixing time is critical, best mixer is one that mixes in required time with least amount of powermixes in required time with least amount of power– Mixing time is a compromise arrived at by considering Mixing time is a compromise arrived at by considering

energy cost for mixing and capital cost of equipmentenergy cost for mixing and capital cost of equipment

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Suspension of SolidsSuspension of Solids

Produce a homogeneous mixtureProduce a homogeneous mixture Dissolve solidsDissolve solids Catalyze a chemical reactionCatalyze a chemical reaction Promote growth of a crystalline product Promote growth of a crystalline product

from a supersaturated solutionfrom a supersaturated solution

04/11/23 61

Critical Stirrer SpeedCritical Stirrer Speed

13.0

45.0

2.01.085.0 BgDSvDn pac

Where nc = critical stirrer speed

Da = agitator diameter

S = shape factor

v = kinematic viscosity

Dp = average particle size

G = gravitational acceleration

= density difference

= liquid density

B = 100 x weight of solid/weight of liquid

04/11/23 62

Shape Factor, SShape Factor, S

Impeller typeImpeller type DDtt/D/Daa DDtt/E/E(E is height of impeller (E is height of impeller

above vessel floor)above vessel floor)

SS

6-blade turbine6-blade turbine

DDaa/W = 5/W = 5

NNPP = 6.2 = 6.2

22

33

44

44

44

44

4.14.1

7.57.5

11.511.5

2-blade paddle2-blade paddle

DDaa/W = 4/W = 4

NNPP = 2.5 = 2.5

22

33

44

44

44

44

4.84.8

88

12.512.5

3-blade propeller3-blade propeller

NNPP = 0.5 = 0.5

33

44

44

44

44

2.52.5

6.56.5

8.58.5

9.59.5

04/11/23 63

For the same geometry, critical speed is about For the same geometry, critical speed is about the same for standard turbine and paddlethe same for standard turbine and paddle

However, turbine requires twice as much However, turbine requires twice as much power as paddle, and 15-20 times as much power as paddle, and 15-20 times as much power as propellerpower as propeller

Sole purpose to suspend solids – use propellerSole purpose to suspend solids – use propeller For good gas dispersion or high shear – use For good gas dispersion or high shear – use

turbineturbine

04/11/23 64

(i) Nearly complete suspension with filletingLow stirrer speed, small amount of solid not in motion & rest on the bottom of the tank.

(ii) Complete particle motionAll solids are either suspended or moving along the tank bottom.

(iii) Complete suspension (complete off-bottom suspension)All solids are suspended off the tank bottom (not stay at bottom more than 2 seconds). All the surface of the solids is exposed to the fluid (all the solid surface area is available for chemical reactions).

Different processes require different degree of suspension.

Defining the suspension condition in the order of increasing power input or stirrer speed;

04/11/23 65

(iv) Uniform suspension (homogeneous suspension)Higher stirrer speed, no longer any clear liquid near the top of the tank & the suspension appears uniform.The impeller speed is called as critical impeller speed.Beyond this speed, any increase in the impeller speed does not improve the quality of suspension

04/11/2366

SCALE UP OF AGITATORS

The conditions in the large vessel are close as possible to the pilot scale/lab scale unit

Criterion (i) Constant Mixing Time

When the volume of the vessel is increased the length of the flow path for bulk also increases. To keep mixing time constant, the velocity of the fluid in the larger tank should be increased in proportion to the size. Power input per unit volume is proportional to the square of the velocity. So large power is needed to maintain constant mixing time and so this is not feasible. So this criterion for scale up cannot be used.

04/11/2367

Criterion (ii): Constant power input per Unit Volume

c

aP

g

DnNP

53

HDV t

2

4

HD

DnN

VP

t

ap

2

53

4

1a

t

D

D

2tD

H

at DD 1

tDH 2 aDH 12

04/11/2368

aa

ap

DD

DnN

V

P

12

22

1

53

4

3

2

3

1

53

4 a

ap

D

DnN

V

P

2

3

1

23

4

ap DnN

V

P

23aDKn

V

P 23

lablablab

DKnV

P

23

plantplantplant

DKnV

P

If

04/11/2369

3/2

laba

aplant

plant

lab

D

D

n

n

=

If

labVP

=

plantVP

thenIf

23

plantplant DKn =

23

lablab DKn

04/11/2370

Criterion (iii) Same impeller tip sped

ntm- dimensionless no. represents the number of

stirrer rotations required to homogenize the liquid. At

high Re, nitm is independent of Re.

354.1

am

D

Vnt

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Problem:

A fermentation liquid of viscosity 0.1 poise and density of volume 2.7 m3 using

Rushton turbine impeller with 1000 kg/m3 is agitated in a baffled tan Estimate the mixing timek a dia of 0.5 m and stirring at a sped of 600 rpm. Estimate the mixing time.

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Solution:

3

54.1

a

miD

Vtn

3

54.1

ai

mDn

Vt

stm 32.3min055.05.0600

7.254.13

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Problem:

A pilot plant vessel 1 ft (305 mm) in dia is agitated by a six blade turbine impeller 4 in (102 mm) in dia. When the impeller Re no. is 10000, the blending time of two immiscible liquids is found to be 15 s. The power required is 2 Hp/1000 gal (0.4 kW/m3

. (a) What power input is 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 in the pilot plant vessel?

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At high Re no’sc

aT

TP

g

DnKP

KN

53

233 ' DanK

D

P

a

For a given densitySubscript a and b represents 1 ft dia and 6ft dia vessel

na= nb (given)

The ratio of the power inputs per unit volume in the two vessels are

361

622

23

23

aa

ab

aaa

abb

a

a

b

b

D

D

Dn

Dn

VP

VP

23DanV

P

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3/4.144.03636 mkWV

P

V

P

a

a

b

b

(b) If the power input per unit volume is same then

23

aa

a

a DnV

P

23

bb

b

b DnV

P

(For constant blending time)

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ssvesselftintimeblendingThe

D

D

n

n

DnDnthenV

P

V

P

b

a

a

b

abaa

b

b

a

a

5.49153.36

3.31

6

,

3/23/2

2323

04/11/2377

A vertical tank 2.4 m dia is provided with a flat blade turbine impeller (6 blades) mounted centrally in the tank at a height of 0.8 m from bottom. The turbine is 0.8 m in dia and the blades are 167 mm wide. The tank is filled to a depth of 2.4 m With rubber latex compound having density 1120 kg/m3

and viscosity 120 kg/m.s. If the tank is baffled and turbine is Rotated at 90 rpm, what is the power consumption in hP?Take Np. Re = 65 for laminar flow and 5.75 for turbulent flow.

04/11/2378

)min(

1096.812060

11209082.0Re

2

arlaSo

nDa

Np x Re = 65; Np = 65 /8.96 = 7.25

P = NP = NP. P. NN3 3 DaDa5 5 = 8980 W= 12hP= 8980 W= 12hP

04/11/23 79

Newtonian and non-Newtonian Fluids

Newtonian fluids: Fluids which obey the Newton's law of viscosity are called as Newtonian fluids. Newton's law of viscosity is given by

Non-Newtonian fluids: Fluids which do not obey the Newton's law of viscosity are called as non-Newtonian fluids. Generally non-Newtonian fluids are complex mixtures: slurries, pastes, gels, polymer solutions etc.

There is also one more - which is not real, it does not exist - known as the ideal fluid. This is a fluid which is assumed to have no viscosity. This is a useful concept when theoretical solutions are being considered - it does help achieve some practically useful solutions.

,where A, B and n are constants. For Newtonian fluids A = 0, B = and n = 1.

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Type of fluidsType of fluids

– Newtonian Newtonian

– Non-Newtonian (Shear Non-Newtonian (Shear thinning - Shear thickening)thinning - Shear thickening)

xy v

yx

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Toothpaste

Latex Paint

Corn Starch

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Power law fluidsPower law fluids

Newtonian fluid:Newtonian fluid:

x xv v:

dy dyxy

d d

Power Law Fluid:

1: xyn nxy aK K

When n<1, viscosity decreases with shear

When n>1, viscosity increases with shear

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Power Consumption in Power Consumption in Non-Newtonian LiquidsNon-Newtonian Liquids

Non-Newtonian liquids – viscosity varies with Non-Newtonian liquids – viscosity varies with shear rateshear rate

Use apparent viscosity, Use apparent viscosity, aa

For a straight-blade turbine in pseudoplastic For a straight-blade turbine in pseudoplastic liquidsliquids

1'

'

2

Re,

n

av

a

a

an

dy

duK

nDN

ndy

du

av

11

04/11/23 86

Types of CompressorsTypes of Compressors

ReciprocatingReciprocatingRotaryRotaryCentrifugalCentrifugalAxialAxial

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TYPES OF COMPRESSORSTYPES OF COMPRESSORS

http://en.wikipedia.org/wiki/Gas_compressor

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§9-1.The Types of gas compressors§9-1.The Types of gas compressors

There are two general types compressorsThere are two general types compressors Reciprocating compressorReciprocating compressor

For high pressures and low-volume flow rates.For high pressures and low-volume flow rates... Rotative compressorRotative compressor

For lower pressures and high-volume flow For lower pressures and high-volume flow ratesrates..

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Air compressor

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Reciprocating compressor

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Refrigerator compressor

Motor

Compressor

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Refrigerator compressor

Motor

Compressor

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Icebox compressor

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Centrifugal rotative compressor

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Centrifugal rotative compressor

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Axis flow rotative compressor

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§9-2. The principle of reciprocating compressors§9-2. The principle of reciprocating compressors

1.The principle1.The principle

Wc

H1

H2

Q≈?

V

p

P1 1

P2 2

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v

p

P1 1

P22T

2s2n

s

T

P1

1P2

2s

2n

2T

x

KBR

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Notice that there will be a difference between the work necessary to compress the gas from states 1 to state 2 and the total work of process.

Wcs>Wcn>WcT

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§9-2. The principle of reciprocating §9-2. The principle of reciprocating compressorscompressors

2.The work of compressor2.The work of compressor Adiabatic compressorAdiabatic compressor

11

)(1

1

1

21112212,

k

k

gsc p

pTR

k

kvpvp

k

khhw

04/11/23 109

§9-2. The principle of reciprocating §9-2. The principle of reciprocating compressorscompressors

2.The work of compressor2.The work of compressor Isothermal compressorIsothermal compressor

1

21

1

21, lnln

p

pTR

v

vTRw ggTc

04/11/23 110

§9-4. Multilevel compress with intercoolers§9-4. Multilevel compress with intercoolers 1.System

Cooling water

Low pressure gas

1st-stage compression

2nd-stage compression

Intercooler

High pressure gas

122’3’

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§9-4. Multilevel compress with intercoolers§9-4. Multilevel compress with intercoolers 2.Diagram

V

p

P1 1

P2

2

3

e

g

f 2’

3’

Pm

3T

agitation and mixing-h4 class-tkmce

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