engg 199 reacting flows spring 2006 lecture 1 process response blending and motion … · ·...

Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRocheAll rights reserved.

ENGG 199 Reacting FlowsSpring 2006

Lecture 1Process Response

Blending and MotionMix Time

Power Calculations

ENGG 199 Lecture 1 Slide 2Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved.

Handbook of Industrial Mixing


Handbook of Industrial MixingTable of Contents and Authors

Introduction Edward L. Paul, Victor Atiemo-Obeng, Suzanne M. KrestaChapter 1: Residence Time Distributons E. Bruce NaumanChapter 2: Turbulence in Mixing Applications Suzanne M. Kresta and Robert S. BrodkeyChapter 3: Laminar Mixing: A Dynamical Systems Approach Edit S. Szalai, Mario M. Alvarez, Fernando J. MuzzioChapter 4: Experimental Methods Part A: Measuring Tools and Techniques for Mixing and Flow Visualization Studies David A.R. Brown, Pip N. Jones, John C. Middleton Part B: Fundamental Flow Measurement George Papadopoulos and Engin B. ArikChapter 5: Computational Fluid Mixing Elizabeth Marden Marshall and André BakkerChapter 6: Mechanically Stirred Vessels Ramesh R. Hemrajani and Gary B. TattersonChapter 7: Mixing in Pipelines Arthur W. Etchells III and Chris F. Meyer Chapter 8: Rotor-Stator Mixing Devices Victor A. Atiemo-Obeng and Richard V. Calabrese Chapter 9: Blending of Miscible Liquids Richard K. Grenville and Alvin W. NienowChapter 10: Solid-Liquid Mixing Victor A. Atiemo-Obeng, W. Roy Penney, Piero ArmenanteChapter 11: Gas-Liquid Mixing in Turbulent Systems John C. Middleton and John M. Smith Chapter 12: Immiscible Liquid-Liquid Systems Douglas E. Leng and Richard V. Calabrese Chapter 13: Mixing and Chemical Reactions Gary K. Patterson, Edward L. Paul, Suzanne M. Kresta, Arthur W. Etchells III Chapter 14: Heat Transfer W. Roy Penney and Victor A. Atiemo-ObengChapter 15: Solids Mixing Part A: Fundamentals of Solids Mixing Fernando J. Muzzio, Albert Alexander, Chris Goodridge, Elizabeth Shen, Troy Shinbrot Part B: Mixing of Particulate Solids in the Process Industries KonanurManjunath, Shrikant Dhodapkar Karl Jacob Chapter 16: Mixing of Highly Viscous Fluids, Polymers, and Pastes David B. Todd Chapter 17: Mixing in the Fine Chemicals and Pharmaceutical Industries Edward L. Paul, Michael Midler, Yongkui Sun Chapter 18: Mixing in the Fermentation and Cell Culture Industries Ashraf Amanullah, Barry C. Buckland, Alvin W. NienowChapter 19: Fluid Mixing Technology in the Petroleum Industry Ramesh R. HemrajaniChapter 20: Mixing in the Pulp and Paper Industry Chad P.J. Bennington Chapter 21: Mechanical Design of Mixing Equipment David S. Dickey and Julian B. FasanoChapter 22: Role of the Mixing Equipment Supplier Ronald J. WeetmanCD-ROM: Visual Mixing Suzanne M. Kresta and Keith Boyle


Different Design Criteria at Different ScalesBlendtime

Solids Suspension

Gas-Liquid Mass Transfer

Maximum Turbulent Energy Dissipation

Maximum Shear

Liquid-Liquid Mass Transfer

Feed Addition Micromixing/Mesomixing with Competitive Reactions

Solid-Liquid Mass Transfer

Why is Scale-Up/Scale-Down of Stirred Tank Reactors So Difficult?


Laminar and Turbulent Flow

All fluid motions seem to consist of two zonesLaminar - linear zone

proportional to viscosity

Complex turbulent zone

not much affected by viscosity


Dimensional Analysis - Pipe Flow

Variablesvelocity, V

pipe diameter, D

pipe length, L

fluid density,

fluid viscosity,

Output (Quality)volumetric flow rate, Q

pressure drop, p

Dimensionless GroupsReynolds Number

Fanning Friction Factor

VDRe

2

24 V

g

L

pDf c


Log f vs. Log Re for Pipe Flow


Dimensional Analysis - Rotational Mixer Flow

Variablesrotational speed, N impeller clearance from bottom, C

impeller diameter, D impeller blade width, Dw

tank diameter, T liquid height, Z

fluid density, fluid viscosity,

Output (Quality)power, mix time, heat & mass transfer coefficients

Dimensionless GroupsReynolds Number

Froude Number

Power Numberor Newton Number (Ne)

Geometric Ratios

g

DNFr

2

2

ReND

53DN

PPo

D

D

D

C

D

T

D

Z w,,,


Log Po vs. Log Re for Standard Flat Paddles


Usefulness of the Power Number

Estimate power imparted to the fluid by the impellers

Many engineers may use Power per Tank Volume as a scale-up criterion

Better Approach: - local power/mass (not average)In stirred tanks, use power per impeller swept volume for ballpark estimate

Can be calculated directly from CFD

Local is an important parameter in solids breakup, gas bubble breakup, mass transfer, cell damage?

23232

53

2

53

444

DNDNP

DD

DNP

DD

DNP

V

PAssume oo

w

o

imp


Mixing Tank Equipment

Tanks/VesselsRight Cylinder most common

height-to-diameter ratio - 0.8 to 1.5

dish bottom and flat bottom

Top Entering Shaftsrotational, vertical

Excellent source of impeller datahttp://www.postmixing.com/mixing%20forum/impellers/impellers.htm

http://www.postmixing.com/mixing%20forum/impellers/impellers.htm


Turbine Impellers

radial flow patternsflat 90° blades

4-12 blades (4 most common)

discharge through cylindrical heightdraw suction flow from top and bottomsets up jet with velocity decay away from turbine


Axial Flow Impellers

Axial (Pitched Blade) Turbine4 to 6 blades angled at 45° (some at 30°)

cheaper to make than marine impeller on large scale because of weight

pushes liquid off at an angle - axial and horizontal (radial) components

Hydrofoil (Airfoil) Impellersturbines with twisted blades like airplane propellers

variable pitch

Marine Propeller


Mixing Tank Baffles

Mixing Tank without bafflespredominantly rotational flow (solid-body rotation)

no interchange between top and bottom

Vertical Baffles turn rotational component into vertical component

increase top to bottom flow

always specify baffles for turbulent flow

Alternatives to Baffles (for small vessels)angle mount shaft

off-center vertical mount shaft

side-entering shaft


Standard Baffle Configuration

Full Baffling4 Vertical Baffles at full length of straight side of tank

Baffle Width, Bw = T/12

Offset from Wall = T/72 (or Bw/6)

Partial Baffling Alternatives1/2 Height, 1/2 Width, 2 Baffles

Results in some surface vortex

Po (Baffled) is greater than Po (Unbaffled) by 20-50%


Unbaffled Tank Flow Patterns

Surface VortexOccasionally need to know vortex depth

draw down of light material

Balance of forcesKinetic Energy

Potential Energy

X = liquid height above quiet liquid level

Suggests Fr for correlations rather than Re

Xg

DNFr

22

22 )NDV

gX


Turbine Impellers as Pumps

Flow Devices

Tip Speed = ND2-6 m/s

Defines maximum velocity

How Much Flow? - Need MeasurementsPitot tubes, Laser Doppler Velocimetry

Integrate Velocity Field over Impeller Outflow Area (Faces)

Pumping NumberRe > 104, NQ constant

NQ weak function of D/T

Flow from Impeller Entrains More Flow than Impeller Pumps

3ND

QNQ


How Reliable is CFD as a Process Engineering Tool?

Validation Efforts in the mid-to-late 90 s

45° PBTTank Diameter, T = 14.5 cmLiquid Height, Z = TOff-bottom Clearance, C = 0.5TImpeller Diameter, D = 0.35T

Laminar Re = 20.4Turbulent Re = 21505

Courtesy Dow Chemical and Cray Research


Laminar Flow in a Stirred Tank

R. D. LaRoche & D. ChoudhuryMIXING XV - Banff, Alberta, Canada, June 18-25, 1995

Velocity Field Comparison for Re = 20.4


Turbulent Flow Validation


Pumping Numbers

Impeller Type Pumping Number, NQ

Radial (4 blades) 0.6

Radial (6 blades) 0.7 0.85

Axial (4 blades) 0.8

Axial (6 blades) 0.9

Propeller 0.5

A310 Hydrofoil 0.56


Pumping & Head Generation

Axial Flow Impeller - High Capacity/Low Head Pump

Head is proportional to the square of the tip speed

Pumping Capacity Example - How much head is generated?10000 gallon tank filled with water using Radial-4 impeller

T=4m, H=4m, N=30rpm=0.5sec-1, D=2m, P=7.5HP=5593watts

Typical centrifugal pump generates 30m head

533 DNPPNDNQ oQ

2

3

53

NDgN

P

NDgN

DNP

gQ

PHHead

Q

o

Q

o

mmssmmkg

smkg

NDgN

PHead

Q

24.025.06.081.91000

55933123

32

3


Some Characteristic Velocities

Tip Speed = NDThrust Velocity - Flow/Area

Axial Impeller

Radial Impeller

Bulk Velocity - Chemineer Concept

NDND

QQ

4

4

2

D

DNDN

DD

Q wQ

w

24

T

DNDN

QQ

3ND

QNQ


Chemineer Blend Scale Method

Need Way to Rate Motion in TanksUse Bulk Velocity as Criteria for Describing Motion

Combines Tank Size and Impeller Effect

Little Turbulence is Required with Homogeneous LiquidsBulk Flow or Pumping is preferred

Standardize45° Axial-4 Impeller (45° Pitched Blade Turbine)

Off-bottom Clearance, C

Rate Bulk Velocity on 1-10 ScaleLow: 1 = 6 ft/min, 5 = 30 ft/min

High: 10 = 60 ft/min

Correct for Re effectCrude method but often good enough

24

T

DNDN

QQ


Mixing Time

How fast to get to Homogeneity?Measurements - Batch Stirred Tank

Color Change - somewhat arbitrary

Conductivity or pH - approach to steady state

Acid/Base Indicator Reactions

Approach to Average Uniformity

95% approach (or 5% of steady state)

Extrapolation along exponential decay curve


Blend Time Techniques

Transport of a tracer Small amount of liquid tracer added near liquid surface

Concentration of tracer monitored as a function of time

Similar to experimental techniques

Particle trajectoriesRelease large number of Lagrangian particles

Monitor particle concentration at specified location

Use Particle Tracking


Influence of Measurement Location

0.00

1.00

2.00

0 10 20 30 40 50

Point 1

Point 2

Point 3

Point 4

U

Time, s

t99= 20s

t99= 21.4s

t99= 27.4s

t99= 55.8s


95% Mixing Time when c=0.05

Turbulent Mixing Correlation (Ruzkowski & Grenville)Based on a wide range of impeller types and tank sizes

Height effect

kec

Mixing Time Correlations

kkck 3)05.0ln()ln(

6404Re4.5 31

2

31 oo

PforD

T

PN

0.121

T

Hfor

T

H


Mixing Time Correlations (cont.)

Laminar Mixing Correlation

Defining a Fourier Number, Fo

And rearranging to give

Can also be rearranged in this form

Note that Mix Time goes laminar before Po is in laminar region

6404Re34600 314232

2123

oo

PforDNP

HT

2123 HTFo

11861186

Re31

oo

o Ffor

FP

Re

1N


Power Correlations

Experience suggests fixing geometry (C, Z, Bw, Dw, pitch) as a function of D or TExperimentally measure effects of L/D, T/D, Z/D and Fr with baffles - not significantMeasure Effects of Re, pitch/D, Dw/D, C/D to get Po vs. Re plots


Power Correlations (cont.)

Laminar Region

Power proportional to viscosity

Power independent of density

N up 10% => P up 21%

D up 10% => P up 33%

Turbulent Region

Power independent of viscosity

Power proportional to density

N up 10% => P up 33%

D up 10% => P up 61%

32253Re

1DNP

NDDN

PPo

5353

DNPconstDN

PconstPo


Power (P), Speed (N) and Impeller Diameter (D)

Power, P, quantified by motor sizes3, 5, 7.5, 10, 20, 30, 50, 75, 100 HP

Speed, N, quantified by American Gear Manufacturers Assoc.

25, 30, 45, 56, 68, 84, 100, 125 min-1 (rpm) based on 1750 rpm output motor speed

alternative motor speeds: 1150, 1750, 3500 rpm (60 Hz in U.S.)

Process responds to fluid velocity generated by impellerspecifying two variables sets the third

given P and N, know D

given N and D, know P

Power Units1 HP = 550 ft-lbf/sec = 745.7 watts

1 watt = 1 joule/sec = 1 kg-m2/s3

Need gc with English unitsc

o

g

DNPP

53

2sec17.32

f

mc lb

ftlbg


Power and Flow

Combine to get

In Turbulent Region, NQ and Po are constant for a given impeller type, therefore:

For a given Q, a larger D results in P decreasing

For a given Q, a smaller N results in P decreasing

353 NDNQandDNPP Qo

54

53

53

53

334

31

313

31

5N

P

P

N

NP

PNNQorD

P

P

ND

DP

PNQ

o

Q

oQ

o

Q

oQ

54

53

34

31

NP

QorDP

Q


Mixer Design

Should be designed to run at low speedsHence gear boxes save energy by allowing the system to run at lower speeds than the electric motor

Gear boxes are clockwork mechanisms that take motor speed and reduce it to operating speed without a change in power transmitted

To Increase Flowrate (Q) at constant impeller diameter (D)

To Increase Flowrate (Q) at constant impeller speed (N)

353 NDNQandDNPP Qo

33 QPNQandNP

3535 QPDQandDP


Power Numbers under Turbulent ConditionsShuie & Wong, Can. J. Chem. Engg., 62 (1984)

ImpellerType

BladeAngle

Numberof Blades

Dw/D Po

FBT 90 6 0.2 5.0

CBT 90 6 0.269 4.0

CBT 90 4 0.154 4.6

PBT 45 4 0.231 1.74

PBT 45 2 0.231 1.2

Propeller -- 3 -- 0.67

FBT 90 4 0.20 3.0

PBT 45 4 0.20 1.0

FBT-Flat Blade Turbine, CBT-Curved Blade Turbine, PBT-Pitched Blade Turbine


Power Numbers under Laminar & Turbulent ConditionsProf. J.M. Smith, Univ. Surrey

ImpellerType

BladeAngle

Numberof Blades

A B C

FBT 90 6 67 3.2 1.8

CBT 90 6 67 2.6 2.2

PBT 45 4 49 1.5 0.3

PBT 60 4 50 4.0 1.0

Propeller -- 3 47 0.9 0.3

FBT 90 4 50 4.0 1.0

FBT-Flat Blade Turbine, CBT-Curved Blade Turbine, PBT-Pitched Blade Turbine

Re1000Re

CB

APo

A=Kp or NeRe (Laminar Power Number)

B~Po (Turbulent Power Number)


Pumping Efficiency

NQ/PoPropeller - 0.5/0.67 = 0.75

Axial - 0.8/1.74 = 0.46

Radial - 0.6/3.0 = 0.20

Where does the extra Power go? TurbulenceHigh (Pumping) Efficiency Impellers use Low Power

Lightnin A310

Prochem

Ekato

Can get High Efficiency at Constant NQ and Po by increasing Impeller Diameter, D


Power Number and Drag Coefficient

Drag Coefficient, CD

Po contains Dw/D effect, therefore:

Po is proportional to CD

wDDdrag DDND

CAV

CF22

22

D

DDNCNTorqueP

lFTorque

wD

bladedrag

5332

Doo CPDNPP 53

engg 199 reacting flows spring 2006 lecture 1 process response blending and motion … · ·...

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