engineering data on mixing

Engineering Data on Mixing
by Reiji Mezaki, Masafumi Mochizuki, Kohei Ogawa




• ISBN: 0444828028
• 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,

computer-
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.
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
VI
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 English-
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.
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
Experimental apparatus
Vessel
Type: flat-bottomed
Diameter: 12.08
in
Height: 18 in
Liquid contained
Height:
14
in
Impeller
Type: anchor
Width of agitator
blade:
1.0 in
Wall/blade
clearance:
runs2A 0.125 in runs2C 0.50 in
Working fluids and their physical properties

No.
1 lubricating oil
2 lubricating oil
3 glycerol
(3%
water)
4 silicone oil (MS200)
5 silicone oil (MS200)
6
1%
polyacrylamide (aq.)
7
2%
8
4%
Reynolds numbers were computed
Flow measurement technique
Photography
Results
Tank:
22.9 cm
diameter
Anchor:
19.5 cm
diameter,
2.5 cm
wide,
90
rev/min
Fluid:

Silicone
oils,
60
poise
and
180
poise
Velocity
components
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
308-460
1.04
using temperature-corrected viscosity data.

1
'
1
' '
t-
t«-
-
t-
1
8
«
'
' ' LJ-' f
^^^-^^V^J
Hi))
^^^Sr/w/y
feCX^^^y^vy*!?^^^^
IS^^^^^r^'^^'
Velocity
profiles and
flow
patterns (Beckner, J.
L., Ph. D.
Thesis,
1965.
University of Wales)
Chapter
1.
Flow pattoms
\'

X
y
16 p.p.s. (some points at 8 p.p.s.)
NiRe)=21A, Run3-2C-10
25.4 p.p.s. (some points at 12.7 p.p.s.)
iV(i?«)=105.3, Run3-2C-30
33.4 p.p.s. and 63.4 p.p.s.
i\^(/?e)=143.4, Run3-2C-60
Flow patterns with glycerol
1.1 Single phas«
^"
•
. -^A*
• . 7
• '. •M-Ji'.i'V^ ••• y
/f •
r'' *
. >r;*, .
/
32.0p.p.s.
N*(Me)=l2.9, Run7-2C-40
64.0 p.p.s (some points at 32
p.p.s.)
iV*(/?^)=25.5, Run7-2C-80
'- -r - ^ *
/
64.0 p.p.s (some points at 32
p.p.s.)
N*(Jie)=3lA,
Run7-2C-100

Notation
a geometrical constant
c clearance between blades
and wall
D paddle diameter
DT
tank diameter
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
Experimental apparatus
Vessel
Type:
flat-bottomed
Diameter:
15
in
Height:
20
in
Baffle
Number: 4
Width:
IV2
in
Impeller
Type:
6
and
10
bladed turbines

Dimension:
Turbine
No.
1
2
3
4
5
6
7
8
9
10
11
12
Blade diameter
in.
3
4
5
6
9
9
4
4
4
4
4
4
Blade width

in.
0.6
0.8
1.0
1.2
1.8
3.6
0.6
1.0
1.2
1.4
1.6
0.8
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
No of Blades
6
6

6
6
6
6
6
6
6
6
6
10
Working fluids
Water and air
Flow measurement technique
Hot-wire anemometry
and
three-directional pressure measurement
1.1 Siiigl* phas«
Results
J
2
.4 .« .B LO
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
Experimental apparatus
Dimensions of vessels and impellers
Type:
flat-bottomed
Volume:
(1) 6 gals
(2)
160
gals
Geometry
The geometry of the helical
ribbon

mixer
Summery of principal dimensions
Impeller number
1
2
3
4
5
d
(in)
10.303
11.030
11.142
11.370
34.34
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
Pseudoplastic fluids:
aqueous solutions of
sodium
carboxy methyl cellulose
(CMC)
and hydroxypropyl methyl
cellulose (Celacol)
apparent viscosities 1 ~
500 poise

at concentrations
up
to
3
w/w%
and shear rates of 1 -
3001/s
1.1 Single phase
Flow-measurement technique
Observations of solid tracers and cine-photography
Results
0-15
0-03 L
p-
y
Y
Y
Y
U
[T
T" \" II 1
i
xa
A*
Y4 4*0
D20
20A X40 i^AO
20 XS YCO
X20 Y40
Y

X O30
SX20
•
A80
^20
AAO
O30
e+goao
3p V,
•''J,
Y20
V«0 O30
V20
30
X
a oso aso
vioo
oso
30o3o
^30 YIO
030
lOOA
S^OW VW
20X O60
vco 0*0
AID
vso
1
1 1 1 i i
I i 1

+ 30
_
X«0
•f20
_
Yl
YS
X20
X20
X20
1 J
,„-J., J
^
y
/
/
o
7
/
/
0-A 0-6
NOTE
>
No
values
of r^/Ni
bclwtcn
0
ondOOS
X: Howflex SP

D:2'95<
Celacol
y;2'65%Celacol
+
:2-3%
Celacol
A;
2-0% Celacol
Y: 1-65% Celacol
o-iep-
0-15
0-09 h
0-03
Y
Y
Y
Y
Y
V
Y
Y
Y
Is
Y
Y
Y
Y
y
V
z

1 1 ' i
X-t-
X
xAxo
/ X
/+
/ X X^
/x+
Xf + Xo
+
oo x+
X
X^
O
y^
-»ox /
x^l
X X
/
/
/ . .
i 1 !
r T—
X
-t-
X+
X+ XO X \
xj
X XX +x\
Ox

\
+
X X X X \
X+
X
O X
+ \
X
X +X + \
+
X+ X ^
X+
X
+
X + X
+
XX
X X +
X
J
l_ .1 1 J
• r-—
1
\ "H
X
\
H
X
X
H

\
\
_LAI
0-A 0-6
+
:
impeller I
X: impeller 2
o: impellers
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
h height of ribbon
N rotational speed of impeUer
r radial coordinate
Ri inside radius of ribbon
5 pitch of ribbon
Vt axial fluid velocity
W width of ribbon
Zo static height of liquid in 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
Experimental apparatus
Vessel
Type: flat-bottomed
Diameter: 450 mm
Height: 600 mm
Liquid contained
Height: 520 mm
Baffle
Number: 4
Width: 45 mm
Impeller
Type: radial flow turbine
Diameter: 150 mm
Number of

impellers:
1
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
Photography
Results
t " I I h t I t I
0 0.5 1.0
*' VQ XTTnd
Anchor-tangential velocity

ll-H'
h
I
i i
I
MM I
0 0.5 1.0
*"•* VQ ^Tind
Paddle-tangential velocity
RE
- 0.07
[ol
1 XjlfUlDK
1 Lfflll^
W?nfK
11
j
•
I
Sg
/S>KP1
/"^
0 0.5 1.0
"adn
Helical ribbon (velocity profiles)
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
\-
C
& R
REACTOf
|CL>
s
Q
0.01 0.02 0.0^ 0.1 0.2
1 -K , C/D, I/D^
Shear characteristics
ELICAL SCREki
(NAGATA)
HELICAL SCREW
(GRAY)
Notation

b
blade width of helical ribbon, cm
d impeller diameter, cm
D vessel diameter, cm
Dd disk diameter, cm
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
Experimental apparatus
Vessel
Type:
flat-bottomed
Diameter:
312
mm
Liquid contained
Height: 312 mm
Baffle
Number: 4
Width:
10.4 mm
Impeller
Type:
a standard six-bladed turbine
Diameter:
104
nmi
Number of
impellers:
1
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
Experimental conditions
Impeller
speed:
60,90
and 120
rpm
Results

Notation
r_ radial position, mm
Ui mean velocity of i component, cm/sec
UT
impeller
tip
velocity,
cm/sec
2
axial
position,
mm
Subscript
r,
z,
G
radial,
axial,
tangential component
65 75 85 95 105 t15 125
r, mm
Turbulence intensity
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
Experimental apparatus
Vessel
Type: flat-bottomed
Diameter: (1)
44 cm
(2)
120 cm
Baffle
Number: 2
Impeller
Type: six-bladed
disc
turbine
Diameter: (1) 17.6 (2)
48
cm
Number
of
impellers:
1
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
Photography
Experimental conditions
Impeller
speed:
5
rps Direction
of
Results rototion
Schematic thee dimensional view of
the
trailing vortex pair.
Dirtetion
Schematic two dimensional view of
the
flow
in the stirrer
blade
region.

S, stagnation point.
14
Chapter 1. Flow patterns
,
Blode
>^<A{»,<9xlO'
500
A/ff,«300
The vortex axis position at different
iV)?,.
0
o
\
%
I
.1
(A
c
E
o
lOh
' ' ' 1
\
I »
^ l-5xlO*</V^,<9xlO*
/V/?,*500
%5-300
Slopc-2
0
5

-1 M I I
I
J I I I
The dimensionless angular velocity distribution.
#, Averages for 1.5X 10^<
NR,
>
9X
10^;
O, Measuring points for 7V)?,=300 ; Z)=17.6cm
10
Dimensionleis rodius from vortex axis.
r/Oin\0
Notation
D stirrer diameter,
m
N stirrer speed, 1/sec
NRt Reynolds number,
pND^/j],
dimensionless
r radial distance,
m
7}
dynamic
viscosity,
Nsec/m^
p density, kg/m^
(o angular
velocity,
1/sec

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
Experimental apparatus
Vessel
Type:
flat-bottomed
Diameter:
45.7 cm
Height:
45.7 cm
Baffle
Number: 4
Width:
0.17
Impeller
Type:
standard six-bladed disk turbine
Diameter:
22.8
cm
Number of
impellers:
1
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
Off-bottom
clearance:
T/2
Working fluid
Air
Flow measurement technique
Hot-wire anemometry
Experimental conditions
Impeller
speed:
200,400,600 and
950
rpm ^^
Results
Notation
D
E,(n)
I
n

N
T
w
impeller diameter
one-dimensional energy
spectrum in the frequency
space
length of impeller blade
j&requency
rate of rotation of impeller
tank diameter
impeller
blade
width
10
10"
10'
10"'
10"
10
10-
10
^4-400
rpm,
s-lcm,
z-0 . O-O
N-800rpm, s-7cm^
2-0 , 0-0
' N-600rpm, s-
1

cm.
2—0.5
In ,0-0
N-200rpm, $-1cm,
2-0
^
0-43'
probe in vertical
plane
23468
10"
lrf 10^ 10^ 10*
n (H2)
One dimensional energy spectra in the impeller
stream.
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
0.3
^d/D<
0.9
Computational conditions
10 <

Re
{=^DVp/fi)
Computational results
d/D
>
0.5
n «o.e
Rcf 0
(p/>*.v)
Non-Newtonian viscosity distribution
for paddle of rf/2>=0.5
Notation
d
impeUer diameter,
m
D vessel diameter,
m
K fluid consistency, kg/m (sec)^"**
n flow behavior index
J? radial coordinate,
m
Re Reynolds number, DVp/fi, dimensionless
V rotational velocity of vessel wall, m/sec
p non-Newtonian viscosity, Nsec/m^
/Xar apparent viscosity, Nsec/m^
ft* dimensionless non-Newtonian viscosity, fi/po,
dimensionless
p fluid density, kg/w?
(o dimensionless vorticity
Non-Newtonian viscosity distributions for different size

impellers
^^^\w^^m^
I {(cDw+2)}.
N
J
^-^mv/DT
Superscript
—
averaged value
Subscript
NN non-Newtonian fluid
N Newtonian fluid
w vessel wall
1.1 SingI* phase
17
Kuriyama, M., Inomata, H., Aral, K. and Saito, S.,AIChEJoumaU 28,385
(1982)
Numerical Solution for the Flow of Highly Viscous Fluid in Agitated
Vessel with Anchor Impeller
Experimental apparatus
Vessel
Type: flat-bottomed
Diameter:
128 mm
Liquid contained
Height:
128 mm
Impeller
Type: anchor
Diameter: about

128
mm
Height:
115 mm
Number of
impellers:
1
Working fluids
Aqueous solutions of
com
syrup containing solid-particles as tracers
Flow measurement technique
Photography
Experimental conditions
Results
i
: C«tcuUt«d
• : ExptrimtnUI
Tangential velocity distributions
(Be
= 1)
(K 07
0.91.0
r/R H
—: CatcuUted
• :Exp«rim«nU(
Radial velocity distributions
{Re
= 1)
Notation

d impeller diameter
N rotational speed of impeller
U,
V velocity components
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
Experimental apparatus
Vessel
Type:
flat-bottomed
Diameter:

450 mm
Liquid contained
Height:
450 mm
Impeller
Type:
six-bladed disk turbine
Diameter:
225
mm
Disk diameter:
150 mm
Number of impellers: 1
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
Off-bottom
clearance:
225 mm
Working fluid

Tap
water
Flow measurement technique
Photography
Experimental conditions
Impeller
speed:
62.5
and
99.4
rpm
Results
ry piong
V, V,
Velocity diagram of
the
flow
around impeller
1.1 Single phas«
19
I
2/D Part0 (2)
0.250
j , 1 r
0235
^ 9
lil L
T~l r
^-h
O

T-n «-
^T
^^
T~1 r-
®
i_ai L_
f"
•f^f
j<JiJ
J L.
4
upper edge
btade
B/Ort/2
0 10 0 ^0 0 10 0 10 0 1-0 0 10
Center of
B/0^1/5
B/DrI/8
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
(1984)
Distribution of Pressure on the Surface of Blade of Turbine Impeller
Experimental apparatus

Vessel
Tjrpe: flat-bottomed
Diameter:
450 mm
Liquid contained
Height:
450 mm
Baffle
Number: 4
Width:
45 mm
Impeller
Type: six-bladed disk turbine
Diameter:
225
mm
Number of
impellers:
1
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

Off-bottom
clearance:
225 mm
Working fluid
Tap water
Flow measurement technique
Visualization
Experimental conditions
Impeller rotational velocity:
82,104
and
106 rpm
Results
Sock surface
Front surface
Notation
B width of impeller
blade,
m
D impeller diameter,
m
N impeller rotational speed,
1/min
!cl B/D»1/8 N*106rpm
Visualization
of
flow on the surface of blade with oil film method
1.1 Single phase
21
Kuboi,

R.
and
Nienow,
A.
W,
Chem.
Eng.
Sci.,
41,123 (1986)
Intervortex Mixing Rates in High-Viscosity Liquids Agitated by High-
Speed Dual Impellers
Experimental apparatus
Vessel
Type:
flat-bottomed
Diameter: 0.29
m
Liquid contained
Height: 0.29
m
Impeller
Type:
(1)
angled blade
(2)
disk turbine
Number of
impellers:
2
Number of

blades
on impeller:
(1) 6
(2) 6
Ct>N
T^
,x
i>
Boffins. 0-lT.
:s].
HD»T/2 H l|
6 Blodts
45»
-*4DMI
MA OH T
6 Blodts
JL
0/5
T-0-29in
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