engineering data on mixing

Japan, 4,66 1971 Tomographic Observations of the Flow Around Agitator Impeller Number of blades on impeller: 8 Width of impeller blade parallel to shaft: 34 nun Off-bottom clearance:

Engineering Data on Mixing

by Reiji Mezaki, Masafumi Mochizuki, Kohei Ogawa

• Publisher: Elsevier Science & Technology Books

• Pub Date: January 2000

Preface

This book is a compilation of the engineering data on mixing, which have appeared in the major technical journals of chemical engineering and bioengineering since 1975 That year marked the beginning of a period of rapid advancement in the science and technology of mixing, with rather reliable results for both theoretical and experimental studies In addition,

we have included some important earlier articles which have been and are still being referred

to

Mixing is a basic technology important in a wide variety of industries Many numbers of tanks equipped with various types of agitators have been used for mixing all kinds of materials since ancient times Yet designs of both agitators and tanks still depend primarily on art and experience In the light of this fact we felt that the data on mixing should be compiled and presented in a systematic manner for assistance in design and analysis of agitated tanks , and

to provide easier access to mixing data for various engineering activities Of course, aided searches of pertinent data bases can be of assistance to chemical engineers and bioengineers in their studies However, computer surveys of data bases are sometimes time- consuming and often costly Furthermore inadequate selection of key words can jeopardize the searches In view of these objections, we offer this book in the hope that it will be useful to those who desire to conduct an efficient and accurate survey of the mixing data of interest to them

computer-No attempts were made to verify the mixing data given by the various investigators We have simply indicated the limitations of correlations and data when they are available The use

of uniform units might have been appreciated by users of this book However, we have elected

to use the original units as given by the various authors, lest errors be introduced in the conversion process

In Chapter 1 we present a variety of results for the experimental measurements of flow patterns in stirred tanks Most of the measurements were made by using modem Laser- Doppler techniques This chapter is useful for the prediction of flow patterns in tanks with many different geometries, various types of agitators, and fluids of diverse physical and rheological properties Here can also be found valuable data for the validation of results obtained by CFD simulations Chapters 2 through 5 deal with data for traditional chemical engineering subjects In Chapter 6 we sununarize a number of scale-up relations developed over the years for various systems They include liquid, solid-liquid, liquid-liquid, gas-liquid, and solid-liquid-gas systems Chapter 7 provides data related to multiphase processes We wish to call attention to two sections:

Section 7.4.1 Drop size and drop-size distributions Section 7.4.2 Bubble size and bubble-size distributions These two subjects have not been treated systematically either in text books or in handbooks

on stirred-tank mixing, although the results of both experimental and theoretical investigations have been reported on many occasions Chapter 8 deals with gas-inducing mechanically agitated systems The applications of this type of agitation system will become increasingly attractive from the standpoint of rationahzation of stirred-tank operations as well

as environmental protection

A review of this book will reveal many important research subjects that fall in the domain

of stirred-tank mixing We examined over nine hundred technical articles published since

1950 From this activity we could draw two important conclusions: (1) First, about 95% of the results reported in those articles were obtained by employing vessels whose diameters were less than 0.5 m In industry, vessels with appreciably greater diameters are in daily use, and many more vessels will be designed and fabricated for future use In view of this fact, much of the accumulated data and associated theory based on small- scale experiments will probably be

inadequate for prediction of the performance of industrial-scale vessels More data are undoubtedly needed to narrow the gap originating from this mismatch of equipment sizes More specifically, advanced scale-up techniques, not rules, should be developed for precise prediction In this respect it would be of great help if industries were cooperative in furnishing unsuccessful, as well as successful, examples of scale-up (2) Secondly, there is a striking shortage of mixing data for systems in which highly viscous, non-Newtonian fluids are studied

It may be true that conventional agitated tanks are not satisfactory for such fluids However, the authors of this book feel that many challenges still exist in this area

In this book we have excluded from consideration two important subjects related to mixing: reactions and crystallization in stirred tanks Most of the articles treating those subjects were found to place more emphasis on the development of rate expressions for the reactions or crystallization Here, we have aimed to compile data correlating process parameters with agitated-tank geometry and the physical properties of the relevant fluids For this reason we feel that reactions and crystallization should be treated differently

It should be noted that several important journals issued in Russia, in Eastern Europe, and in the People's Republic of China were not considered in our search for mixing data This

is mainly because of difficulties in obtaining the original journals as well as the language versions However, the authors sincerely hope that the pubhcation of this book will encourage other interested persons to compile mixing data published in the geographical regions mentioned above Perhaps in this way some collaborative efforts will result in a substantially more complete compilation of engineering mixing data

English-It is inevitable that errors, omissions, and misunderstandings will arise in a work of this type The authors will be grateful if readers would take the time and trouble to point these out

to us

The authors would like to thank Professor R B Bird of the University of Wisconsin, who aided with advice and suggestions in reviewing and editing the title and preface to this book Acknowledgment is also made to the staff members of Shinzan Sha, in particular, to Mr K Shinoe for his constructive advice during the preparation of the manuscript of this book, and

to Ms H Tomita for the preparation of the camera-ready manuscript Without their efforts this book could not have become a reality

August, 1999

Reiji Mezaki Masafumi Mochizuki Kohei Ogawa

Table of Contents

Preface, Pages v-vi

Chapter 1 - Flow patterns, Pages 1-84

Chapter 2 - Mixing time, Pages 85-115

Chapter 3 - Power draw and consumption, Pages 117-238

Chapter 4 - Heat transfer, Pages 239-304

Chapter 5 - Mass Transfer, Pages 305-468

Chapter 6 - Scale-up rules, Pages 469-512

Chapter 7 - Other subjects related to multi-phase systems, Pages 513-731 Chapter 8 - Gas-inducing mechanically agitated systems, Pages 733-764 Author index, Pages 765-769

Chapter 1 Flow patterns

1.1 Single phase

Peters, D C and Smith, J M., Ttans Instn Chem Engrs., 45, T360 (1967)

Fluid Flow in the Region of Anchor Agitator Blades

Width of agitator blade: 1.0 in

Wall/blade clearance: runs2A 0.125 in runs2C 0.50 in

Working fluids and their physical properties

perpendicular to radii, along

normal to, and at 30*^ to

agitator blade

^ (poise) 1.5 - 2.5 6.8 - 10.4 5.6 - 9.75

125 - 131

290 ~ 318

n

0.7 0.46 - 0.54 0.30 - 0.38

p (g/cm^) 0.865 0.885 1.25 0.96 0.98

/j(gs" Vcm) p(g/cm^)

2.12 - 2.57 1.01 40.4 - 50.4 1.02

3 0 8 - 4 6 0 1.04 using temperature-corrected viscosity data

1 ' 1 ' '

t

- -

Chapter 1 Flow pattoms

33.4 p.p.s and 63.4 p.p.s

i\^(/?e)=143.4, Run3-2C-60 Flow patterns with glycerol

k usual power law characterization parameter

n usual power law characterization parameter

N rotational speed of stirrer

p density of fluid

/i viscosity of fluid

Note: Cxeneralized Reynolds numbers are based on a power law (expression for the shear rate/shear stress relationship as used by Beckner)

Flow patterns with 2% aqueous polyacrylamide, 1 in blade, 0.5 in clearance

The normal Reynolds number:

NiHe)=N^Dpln

The Reynolds nimiber for power-law fluids:

N*{Re)=N^~''D^p/[k[a(\-n)Y'\

a=37-120 C/DT

Chapter 1 Plow patterns

Cooper, R C and Wolf, D., Can J ofChem Eng., 46,94 (1968)

Velocity Profiles and Pumping Capacities for Turbine Type Impellers

Blade length

in

0.75 1.0 1.25 1.5 2.25 2.25 1.0 1.0 1.0 1.0 1.0 1.0

Water and air

Flow measurement technique

Hot-wire anemometry and three-directional pressure measurement

1.1 Siiigl* phas«

Results

Normalized radial velocity profiles for various turbine

sizes and various rotational speeds in water

Radial velocity profiles at different radial distances (4-in turbine in water)

Notation

VR radial velocity component

W turbine blade width

Z vertical distance

Chapter 1 Flow patterns

Bourne, J R and Butler, H., Trans Instn Chem Engrs., 47, Til (1969)

An Analysis of the Flow Produced by Helical Ribbon Impellers

The geometry of the helical ribbon mixer

Summery of principal dimensions Impeller number

d

D

0.889 0.952 0.962 0.981 0.954

h

D

1.06 1.06 1.06 1.06 1.06

W

D

0.108 0.108 0.108 0.108 0.104

s

D

0.345 0.345 0.345 0.345 0.345

Zo

D

1.22 1.2L' 1.22 1.22 1.22

Working fluids and their physical properties

•f20 _

Y l

YS X20

X20 X20

1 J ,„-J., J

^

y /

X

xAxo / X / + / X X^

/x+

Xf + Xo +

o o x+

X X ^

O y ^ -»ox /

X X + X + \ + X + X ^ X+ X + X + X + X X

The distribution of axial fluid velocities in the core

for impeller 2 pumping upwards The distribution of axial fluid velocities in the core for impeUers 1,2 and 5 (6 gal and 160 gal tanks)

pumping downwards

Notation

d outside diameter of ribbon

D inside diameter of tank

Chapter 1 Flowpatt«ms

Takashima, I and Mochizuki, M.J Chem Eng Japan, 4,66 (1971)

Tomographic Observations of the Flow Around Agitator Impeller

Number of blades on impeller: 8

Width of impeller blade (parallel to shaft): 34 nun

Off-bottom clearance: 260 mm

Results

Flow profile in each sectional zone of various types of 8 blades turbine agitator

1.1 Single phas«

Double helical flow model for agitator blade

Notation

u tangential velocity at blade tip

V absolute velocity of flow observed on the fixed coordinate

Vr radial velocity of flow

w relative velocity of flow observed on the rotating coordinate

*P angle of the blade (see attached figure)

Fb circulation of bound vortex around the blade

0 Vr/u flow coefficient

CD angular velocity of impeller

Subscript

2 outer point of flow from the impeller

10 Chapter 1 Flow patterns

Murakami, Y., Fujimoto, K., Shimada, T, Yamada, A and Asano, K.,/ Chem

Eng Japan, 5,297 (1972)

Evaluation of Performance of Mixing Apparatus for High Viscosity Fluids

Vessel and impeller geometry

Impellers and vessels (a) anchor (b) paddle (c) helical ribbon (d) mixing apparatus with two agitator axes having multidisks

Z>=12.2cm, H=D, rf=0.90D and 0.95A 6=0.1Z), 1)^=6.0 and 9.0 cm, /=0.5/)rf and 0.22Drf

Working fluids and their physical properties

Liquid: aqueous solutions of com syrup

Viscosity: about 200 poise

Flow measurement technique

1.1 Single phase 11

Mixing apparatus with two agitator axes having multidisks (velocity profiles at a section 6 mm apart from the disk at 15 mm space intervals)

^CIRCULAR ANNULUS KEILSPALT MASCHINEN CIRCULAR ANNULUS (ROTATING CYLINDER) ECCENTRIC CYLINDERS HELICAL RIBBON WITH SCRAPE MIXER WITH TWO AGITATOR AXES HAVING DISKS EXTRUDER

gr gravitational conversion factor, g cm/G sec^

/ distance between disks, cm

n rotational speed, 1/sec

Pv power consumption/unit volume, Gcm/seccm^

Vb, V2 tangential and axial velocity, cm/sec

77 liquid viscosity, poise

K ratio of impeller diameter to vessel diameter

12 Chapter 1 Flow pattoms

Ito, S., Ogawa, K and Yoshida, N.,/ Chem Eng Japan, 8,206 (1975)

Turbulence in Impeller Stream in a Stirred Vessel

Number of blades on impeller: 6

Length of impeller blade (perpendicular to shaft): 26 nrni

Width of impeller blade (parallel to shaft): 20.8 nmi

Off-bottom clearance: 156 mm

Working fluids and their physical properties

an aqueous solutions of K4Fe (CKk and KaFe (CN)6 The kinematic viscosities of the solutions

are the same as that of water

Flow measurement technique

Measurement of diffusional mass transfer rate using a multi-electrode

Ui mean velocity of i component, cm/sec

UT impeller tip velocity, cm/sec

1.1 13

Van't Riet, K and Smith, J M., Chem Eng ScL, 30,1093 (1975)

The Trailing Vortex System Produced by Rushton Turbine Agitators

Number of blades on impeller: 6

Length of impeller blade (perpendicular to shaft): Z)/4

Width of impeller blade (parallel to shaft): D/5

Working fluids and their physical properties

Fluid: tap water and water/glycerin solutions

Tracer: polystyrene particles (diameter 0.5 mm)

Flow measurement technique

14 Chapter 1 Flow patterns

N stirrer speed, 1/sec

NRt Reynolds number, pND^/j], dimensionless

1.1 Single phase 15

Gunkel, A A and Weber, M E.,AIChE Journal, 21,931 (1975)

Flow Phenomena in Stirred Tanks Part I The Impeller Stream

Number of blades on impeUer: 6

Length of impeller blade (perpendicular to shaft): //Z)=0.25

Width of impeller blade (parallel to shaft): w/D=0.2

2 - 0 , 0 - 0 ' N - 6 0 0 r p m , s - 1 cm

2—0.5 In , 0 - 0

N - 2 0 0 r p m , $-1cm,

2 - 0 ^ 0 - 4 3 ' probe in vertical plane

16 Chapter 1 Flow pattoms

Hiraoka, S., Yamada, I and Mizoguchi, K.,/ Chem Eng Japan, 12,56 (1979)

IWo Dimensional Model Analysis of Flow Behavior of Highly Viscous Non-Newtonian Fluid in Agitated Vessel with Paddle Impeller

Dimension of vessel and impeller

K fluid consistency, k g / m (sec)^"**

n flow behavior index

J? radial coordinate, m

Re Reynolds number, DVp/fi, dimensionless

V rotational velocity of vessel wall, m / s e c

p non-Newtonian viscosity, N s e c / m ^

/Xar apparent viscosity, N s e c / m ^

ft* dimensionless non-Newtonian viscosity, fi/po,

NN non-Newtonian fluid

N Newtonian fluid

w vessel wall

Aqueous solutions of com syrup containing solid-particles as tracers

Flow measurement technique

VB tangential velocity of blade tip

Re Reynolds number, d ^Nl v, dimensionless

V kinematic viscosity

18 Chapter 1 Flow patterns

Mochizuki, M and Takashima, I., Kagaku Kougaku Ronbunshu, 8,487 (1982)

The Flow around Turbine Type Impellers

Number of blades on impeller: 6

Length of impeller blade (perpendicular to shaft): 56 mm

Width of impeller blade (parallel to shaft): 28,46,56, 75, and 112.5 mm

Velocity profiles at impeller tip

Tomograms with rotating cameraB/D=l/5, 62.5 rpm

Notation

B width of impeller blade

D impeller diameter

U2 tangential velocity

V absolute velocity of flow

z vertical distance along z-axis

0 normalized velocity, v/u2

(p angle of polar coordinate

Q) angular velocity of impeller

Subscripts

1 inner area of impeller

2 outer area of impeller

3 top and bottom area of impeller

r radial component

z axial component (p tangential component

20 Chapter 1 Flow patterns

Mochizuki, M and Takashima, L, Kagaku Kougaku Ronbunshu, 10,399

Number of blades on impeller: 6

Length of impeller blade (perpendicular to shaft): 56 nmi

Width of impeller blade (paraUel to shaft): B/Z)=l/2,1/5, and 1/8

1.1 Single phase 21

Kuboi, R and Nienow, A W, Chem Eng Sci., 41,123 (1986)

Intervortex Mixing Rates in Viscosity Liquids Agitated by Speed Dual Impellers

A schematic diagram of the equipment

Working fluids, their physical properties and experimental conditions

Physical properties and experimental conditions

(a) Tunnel G140 com syrup/saturated benzoic acid (mass ratio = 5.7:1)

p =1,347 kg/m^ n =1.00 Pas (221C): ^ =1.35 Pas (20^:)

Re range: 70^140; speed range =3.3—6.7 rev/s

(b) 0.30% by wt Goodrich Carbopol in water (pH 4.4)

p =1,000 kg/m', T =22.27°-^ ; Ui=1.54r°" ; To=20.0 Pa

Re range: 85 ~ 150 ; speed range=6.3-^7.5 rev/s

(c) 1.4% by wt Hercules 7H4C CMC in water (neutral)

p = 1,000 kg/m', T= 12.2 f"^; t;i=9.82r''

Re range: 72^190; speed range=4.3~8.0 rev/s

Flow measurement technique

Photographs of solid-particle tracers

22

Results

Chapter 1 Plow patterns

Flow patterns with com syrup: (a) upward pumping

combination (5 rev/s); (b) downward pumping (three

gross vortices (3,33 rev/s)); (c) downward pumping

showing the additional fourth small vortex (5 rev/s)

Flow patterns with Carbopol: (a) upward pumping combination (5.3 rev/s); (b) downward pumping combination (5.3 rev/s)

1.1 Single phas* 23

Yianneskis, M., Popiolek, Z and Whitelaw, J E.J Fluid Mech., 175,537

(1987)

An Experimental Study of the Steady and Unsteady Flow

Characteristics of Stirred Reactors

55.12 73.5 110.25

14.7 19.6 29.4

18.37 24.5 36.75 Off-bottom clearance: 7/4, 7/3 and 7/2

Flow measurement technique

Image sensor velocimetry

Distribution of flow velocity expressed by dimensional components (D=0.2 m, «=6.88 s *)

three-0

a:

[-{U -0.6

26 Chapter 1 Flow patterns

Winardi,S., Nakao, S and Nagase, Y.,/ Chem Eng Japan, 21,503, (1988)

Pattern Recognition in Flow Visualization around a Paddle Impeller

Number of blades on impeller: 4

Width of impeller blade (parallel to shaft): 40 mm

(c) Asymmetric Discharge patten, UD (d) Illustration of Weak Discharge patten, WD

(e) Illustration of Weak Cross-pass patten, WP

1.1 Single phas« 27

Komori, S and Murakami, Y.,AIChE Journal, 34,932 (1988)

Turbulent Mixing in Baffled Stirred Tanks with Vertical-Blade

Number of impellers: 1 and 2

Number of blades on impeller: 4

Velocity vectors and flow patterns in a double-impeller tank, H-2D, «=150 rpm (group A)

(a) with lowest mixing efficiency, (b) with highest mixing efficiency

1.1 Single phase 29

Velocity vectors and flow patterns in a double-impeller tank, H=2D, «=150 rpm (group B)

(a) with lowest mixing efficiency, (b) with highest mixing efficiency

Ettox maximum value of mixing efficiency

hb vertical distance between bottom of a tank and center of lower impeller

H water depth

L vertical distance between double impellers

n impeller rotational speed

P' 6 energy consumption

P- 6mn minimum value of energy consumption P- 6

30 Chapter 1 Flow patterns

Wu, H and Patterson, G K., Chem Eng Scu, 44,2207 (1989)

Laser-Doppler Measurements of Turbulent-Flow

Parameters in a Stirred Mixer

Number of blades on impeller: 6

Length of impeller blade (perpendicular to shaft): D/4

Width of impeller blade (parallel to shaft): D/5

Mean radial velocity profiles

at various radial positions

0.1 02 0.3 0.4 09 0.$ 07 0 8

Ua/U,ip

Mean tangential velocity profiles

at various radial positions

Profile of tangential turbulence

intensity near the impeller tip

Uiip impeller tip velocity

w impeller blade width

32 Chapter 1 Flow patterns

Ranade, V V and Joshi, J B., Ttam Instn Chem Engrs., 68, Pirt A 19 (1990)

Flow Generated by a Disc Turbine: Part I Experimental

mm

67

117

Disc thickness,

mm

2.7 3.7

Blade thickness

mm

2.0 2.7

Blade width=i)/5 Blade length=Z)/4 Hub diameter=25 mm

Hub height=25 mm Shaft diameter=19 mm

OIMCMSIONLESS RAOIAL COOHOINATE , ( r- R,)/(l^fl, I

Radial profile of maximum mean radial velocity in the impeller stream

270

89

300

101.6 101.6 96.7 333.3 93.0 30.4 100.0

Streak photography Hot wire anemometer Laser Doppler anemometer Hot film anemometer Laser Doppler anemometer Laser Doppler anemometer Laser Doppler anemometer

1 Cutter, L A \9&I,AIChEJ, 4:485

2 Cooper, R G and Wolf, D., 1968, CanJCkem EngScu 46:96

3 Van der Molen, K and Van Maanen, H R E., 1978, Chem Eng Sci, 33:1161

4 Drbohlav, J., Fort, L, Maca, K and Placek, J., 1978, CoU Czech Chem Commun, 43:3148

5 Wu, H and Patterson, G K., 1987 Private Communications

6 Chen, K Y, Hajduk, J C, and Johnson, J W 1988, Chem Eng Commun, 72:141

0»% 0*2 0«} 0>4 0*f 0«« ••? 0*ft

OtMCHSIOMLKSS RADIAL COOHOINATE f r - l t | ] / | l | f l , |

Radial profile of maximum mean tangential velocity in the impeller stream

Notation

D impeller diameter, m

H height of vessel, m

N impeller rotational speed, 1/sec

Q flow rate, mVsec

r radial coordinate, m

R tank radius, m

Ri impeller radius, m

T tank diameter, m

U mean velocity, m/sec

Utip impeller tip velocity, m/sec

V tangential mean velocity, m/sec

2 axial coordinate, m

0 0.1 0-2 OO 0*4 0*S 0*1 MMCNStOflLESS RADIAL COORDINATE ( r - R | | / ( R - R | )

Radial profile of radial pumping capacity

34 Chapter 1 Flow pattoms

Kaminoyama, M., Saito, F and Kamiwano, M.J Chem Eng Japan, 23,214

(1990)

Flow Analogy of Pseudoplastic Liquid in Geometrically Similar Stirred Vessels Based on Numerical Analysis

Experimental apparatus

Dimensions of vessel and impeller

Vessel type: flat-bottomed

(2) paddle (3) anchor (2) 1 (3) 1 onolysed region

.Ks21

H/D«1.0

h 70=0.5 ds/0 = 0.0^

Schematic diagrams of mixers and analyzed regions: (a) turbine impeller mixer;

(b) paddle impeller mixer;

(c) anchor impeller mixer

Velocity vector distributions in turbine mixer (Z)=0.2m,«=3.33s"'):

(a) on r-z plane a t / = l and 4; (b) on r-0 plane at/C=l and 11

Velocity vector distributions in paddle mixer (Z>=0.2 m, «=3.33 s *):

(a) on r-z plane a t / = l and 4; (b) on r-d plane at ^ = 1 1 and 21

36 Chapter 1 Flow patterns

Velocity vector distributions in anchor mixer (Z)=0.2 m, «=0.83 s *):

(a) on r-z plane a t / = l , 5 and 9; (b) on r-0 plane at/C=l, 11 and 20

/ mesh number in Q direction

K mesh number in z direction

0) rotational speed