Agitation and Mixing-H4 Class-TKMCE
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Transcript of 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
04/11/23 3
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
04/11/23 5
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
04/11/23 6
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
04/11/23 7
(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.
04/11/23 8
(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
04/11/23 9
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
04/11/23 10
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.
04/11/23 12
Agitation in an unbaffled vessel leads to swirling flow with vortex formation & poor distribution
Standard baffling promotes flow that results in good solids distribution
04/11/23 13
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.
04/11/23 14
04/11/23 15
04/11/23 16
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
04/11/23 18
(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
04/11/23 19
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
04/11/23 20
Draft tubesDraft tubes
Turbine Propeller
04/11/23 21
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
04/11/23 26
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
04/11/23 29
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
04/11/23 30
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
04/11/23 33
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
04/11/23 34
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
04/11/23 36
Power number NP vs. Reynolds number Re for turbines and impellers
04/11/23 37
Power number NP vs. Reynolds number Re for marine propellers and helical ribbons
04/11/23 38
Power correlation for a 6-blade turbine in pseudoplastic liquids
04/11/23 39
Power required for complete suspension of solids in agitated tanks using pitched-blade turbines
04/11/23 40
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
04/11/23 47
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
04/11/23 55
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?
04/11/23 58
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
04/11/23 60
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
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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
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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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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Air compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Reciprocating compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Refrigerator compressor
Motor
Compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Refrigerator compressor
Motor
Compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Icebox compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Centrifugal rotative compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
Centrifugal rotative compressor
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§9-1.The Types of gas compressors§9-1.The Types of gas compressors
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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§9-2. The principle of reciprocating compressors§9-2. The principle of reciprocating compressors
1.The principle1.The principle
v
p
P1 1
P22T
2s2n
s
T
P1
1P2
2s
2n
2T
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§9-2. The principle of reciprocating compressors§9-2. The principle of reciprocating compressors
1.The principle1.The principle
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
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§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