DRAWDOWN OF FLOATING SOLIDS IN LIQUID
BY MEANS OF MECHANICAL AGITATION:
EFFECT OF SYSTEM GEOMETRY
Thesis
Submitted to
The School of Engineering of the
UNIVERSITY OF DAYTON
In Partial Fulfillment of the Requirements for
The Degree of
Master of Science in Chemical Engineering
By
Anand Kumar Pandit
Dayton, OH
May, 2013
DRAWDOWN OF FLOATING SOLIDS IN LIQUID BY MEANS OF
MECHANICAL AGITATION: EFFECT OF SYSTEM GEOMETRY
Name: Pandit, Anand Kumar
APPROVED BY:
______________________
Kevin J. Myers, D.Sc., P.E.
Advisory Committee Chairman
Research Advisor & Professor
Chemical & Materials Engineering
________________________
Eric E. Janz, P.E.
Research Advisor
Research & Development Manager
Chemineer, Inc.
________________________
Robert J. Wilkens, Ph.D., P.E.
Committee Member
Program Director & Professor
Chemical & Materials Engineering
_______________________
John G. Weber, Ph.D.
Associate Dean
School of Engineering
________________________
Tony E. Saliba, Ph.D.
Dean, School of Engineering
& Wilke Distinguished Professor
ii
ABSTRACT
DRAWDOWN OF FLOATING SOLIDS IN LIQUID BY MEANS OF
MECHANICAL AGITATION: EFFECT OF SYSTEM GEOMETRY
Name: Pandit, Anand Kumar
University of Dayton
Research Advisors: Kevin J Myers
Eric E. Janz
This research focuses on drawdown of floating solids with up-pumping agitators
in a batch vessel equipped with baffles for solid–liquid system. Up-pumping agitators
incorporate floating solids via a combination of different mechanisms turbulence
engulfment, mean drag and vortices formed behind baffle. After screening five different
baffle arrangements, standard full length baffle was found to work well with up-pumping
agitators. The use of standard baffling for solids drawdown lead to better understanding
of power and torque. The optimum design of the up-pumping agitator for drawdown of
floating solids requires understanding effects of various design parameters, such as
impeller type, diameter, and submergence and their effect on drawdown speed, torque
and power. This study considers comparing two types of impeller Pitched Blade Turbine
(P-4) and Chemineer HE-3. Totally nine different impeller to tank diameter ratios ranging
from twenty to fifty percentage of tank diameter with submergences varying from ten to
iii
seventy percent of the liquid height which is equal to tank diameter were tested to find
optimum design.
The drawdown speed for P-4 and HE-3 increased with increase in submergence
and decreased with increase in the impeller diameter. The drawdown speed of P-4 and
HE-3 are related to impeller to tank diameter ratio by a power-law relation. The
drawdown speed of P-4 and HE-3 are also related to impeller submergence by a powerlaw relation. The power correlations are given below.
P-4
HE-3
Njd
(D/T) -1.39
Njd
(D/T) -1.60
0.2 < D/T < 0.5 and 0.1 < S/T <0.7
Njd
(S/T) 0.32
Njd
(S/T) 0.15
0.2 < D/T < 0.5 and 0.1 < S/T <0.4
Njd
(S/T) 1.45
Njd
(S/T) 0.47
0.2 < D/T < 0.5 and 0.4 < S/T <0.7
The drawdown power for P-4 impeller has a minimum value at D/T=0.33 and for
D/T=0.4 and above the power is very high.
HE-3 drawdown power has a broad
minimum between D/T of 0.23 to 0.44. The torque of both impellers increases with
increase in impeller diameter and submergence.
iv
ACKNOWLEDGEMENTS
I sincerely thank Dr. Kevin J. Myers, my research advisor, for all the help he has
given me during my study over three years. I have obtained a great deal of support,
encouragement and approval from Dr. Myers that helped me to deal with the difficulties
and burdens of study as well as daily life. He has offered me great opportunity to further
understand how as a chemical engineer I can do things differently for the development of
society and industry. Dr. Myers also helped me to improve my computer skills and
writing skills related with research. Dr. Myers even helped me in the journey from
research place to university place. I would like to thank Eric Janz, my research advisor,
for providing me all the equipment at Chemineer’s R&D Lab for carrying out
experiments for my thesis research. I am grateful to Department of Chemical and
Material Engineering at University of Dayton for giving all the knowledge and making
me capable of doing my research.
I would also like to thank everyone else who gave me support: my family who
encouraged me to study M.S in Chemical Engineering; Tianxin Bao, my classmate, who
helped me in the lab; I also thank Michael Adams and Erin Duff from Chemineer R&D
Lab for their help with taking pictures and technical support while doing my research. I
also thank my friends who helped at home for being nice and calm.
v
TABLE OF CONTENTS
ABSTRACT ....................................................................................................................... iii
ACKNOWLEDGEMENTS ................................................................................................ v
LIST OF FIGURES ......................................................................................................... viii
LIST OF TABLES ............................................................................................................. xi
NOMENCLATURE ........................................................................................................ xiii
CHAPTER 1 INTRODUCTION AND OBJECTIVE ........................................................ 1
1.1 Background and Literature ........................................................................................ 2
1.2 Objective of Current Research .................................................................................. 5
CHAPTER 2 EXPERIMENTAL APPARATUS AND PROCEDURE ............................. 6
2.1 Experimental Apparatus ............................................................................................ 6
2.2 General Experimental Procedure............................................................................... 8
2.3 Experimental Details ................................................................................................. 9
2.3.1: Baffle Configuration Study ............................................................................... 9
2.3.1.1 Standard Baffles .......................................................................................... 9
2.3.1.2 Angled Baffles ........................................................................................... 10
2.3.1.3 Partial Baffles (1)....................................................................................... 10
2.3.1.4 Partial Baffles (2)....................................................................................... 10
2.3.1.5 Narrow Baffles .......................................................................................... 11
2.3.2: Up-Pumping with Standard Baffles Study ...................................................... 14
CHAPTER 3 RESULTS AND DISCUSSION - BAFFLE CONFIGURATION ............. 16
3.1 P-4, Up-Pumping, Standard Full Length Baffles .................................................... 17
3.2 HE-3, Up-Pumping, Standard Full Length Baffles ................................................. 17
3.3 P-4 - HE-3 Comparison for Up-Pumping with Standard Full Length Baffles ........ 18
3.4 P-4, Up-Pumping and Down-Pumping Comparison for Standard Full Length
Baffles ........................................................................................................................... 19
3.5 HE-3, Up-Pumping and Down-Pumping Comparison for Standard Full Length
Baffles ........................................................................................................................... 20
vi
3.6 P-4, Comparison of Angled-Baffles and Standard Full Length Baffles with UpPumping ........................................................................................................................ 21
3.7 HE-3, Comparison of Angled Baffles and Standard Full Length Baffles with UpPumping ........................................................................................................................ 22
3.8 P-4, Comparison of Partial Baffles (1) and Standard Full Length Baffles with UpPumping ........................................................................................................................ 23
3.9 HE-3, Comparison of Partial Baffles (1) and Standard Full Length Baffles with UpPumping ........................................................................................................................ 24
3.10 P-4, Comparison of Partial Baffles (1) with Down-Pumping and Standard Full
Length Baffles with Up-Pumping ................................................................................. 25
3.11 HE-3, Comparison of Down-Pumping with Partial Baffles (1) and Up-Pumping
with Standard Full Length Baffles ................................................................................ 26
3.12 P-4, Comparison of Down-Pumping with Partial Baffles (2) and Up-Pumping with
Standard Full Length Baffles ........................................................................................ 27
3.13 HE-3, Comparison of Down-Pumping with Partial Baffles (2) and Up-Pumping
with Standard Full Length Baffles ................................................................................ 28
3.14 P-4, Comparison of Up-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles ........................................................................................ 29
3.15 HE-3, Comparison of Up-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles ........................................................................................ 30
3.16 P-4, Comparison of Down-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles ........................................................................................ 31
3.17 HE-3, Comparison of Down-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles ........................................................................................ 32
3.18 Summary ............................................................................................................... 33
CHAPTER 4 RESULTS AND DISCUSSION - EFFECT OF IMPELLER DIAMETER
AND SUBMERGENCE ................................................................................................... 34
4.1 P-4 Drawdown Speed .............................................................................................. 34
4.2. HE-3 Drawdown Speed .......................................................................................... 42
4.3 P-4 and HE-3 Comparison ...................................................................................... 49
CHAPTER 5 CONCLUSIONS ........................................................................................ 52
BIBLIOGRAPHY ............................................................................................................. 54
APPENDIX A RAW AND CALCULATED DATA FOR THE P-4 IMPELLER .......... 55
APPENDIX B RAW AND CALCULATED DATA FOR THE HE-3 IMPELLER........ 59
vii
LIST OF FIGURES
Figure 2.1a: Pitch Blade Turbine (P-4)............................................................................. 7
Figure 2.1b: High-Efficiency Impeller (HE-3) .................................................................. 7
Figure 2.2a: Green Acrylic Particle Dimensions ............................................................... 8
Figure 2.2b: Green Acrylic Particles ................................................................................. 8
Figure 2.3a: Top View of Standard Full Length Baffles ................................................. 11
Figure 2.3b: Side View of Standard Full Length Baffles ................................................ 11
Figure 2.3c: Top View of Angled Baffles (impeller rotates clockwise) .......................... 12
Figure 2.3d: Side View of Angled Baffles ...................................................................... 12
Figure 2.3e: Side View of Partial Baffles (1)................................................................... 12
Figure 2.3f: Side View of Partial Baffles (2) ................................................................. 13
Figure 2.3g: Top View of Narrow Baffles ....................................................................... 13
Figure 2.3h: Side View of Narrow Baffles ...................................................................... 13
Figure 3.1: Drawdown speed for up-pumping P-4 with Standard Full Length Baffles ... 17
Figure 3.2: Drawdown speed for up-pumping HE-3 with Standard Full Length Baffles18
Figure 3.3: Comparison of up-pumping drawdown speeds for P-4 and HE-3 with
Standard Full Length Baffles (D/T = 0.3) ......................................................................... 19
Figure 3.4: Comparison of up-pumping and down-pumping drawdown speed for P-4
with Standard Full Length Baffles .................................................................................... 20
Figure 3.5: Comparison of up-pumping and down-pumping drawdown speed for HE-3
with Standard Full Length Baffles .................................................................................... 21
Figure 3.6: Comparison of P-4 up-pumping drawdown speed for Angled Baffles and
Standard Full Length Baffles ............................................................................................ 22
Figure 3.7: Comparison of HE-3 up-pumping drawdown speed for Angled Baffles and
Standard Full Length Baffles ............................................................................................ 23
viii
Figure 3.8: Comparison of P-4 up-pumping drawdown speed for Partial Baffle (1) and
Standard Full Length Baffles ............................................................................................ 24
Figure 3.9: Comparison of HE-3 up-pumping drawdown speed for Partial Baffles (1) and
Standard Full Length Baffles ............................................................................................ 25
Figure 3.10: Comparison of P-4 down-pumping drawdown speed for Partial Baffles (1)
with up-pumping drawdown speed for Standard Full Length Baffles .............................. 26
Figure 3.11: Comparison of HE-3 down-pumping speed for Partial Baffles (1) with uppumping drawdown speed for Standard Full Length Baffles ........................................... 27
Figure 3.12: Comparison of P-4 down-pumping drawdown speed for Partial Baffles (2)
with up-pumping drawdown speed for Standard Full Length Baffles .............................. 28
Figure 3.13: Comparison of HE-3 down-pumping speed for Partial Baffles (2) with uppumping drawdown speed for Standard Full Length Baffles ........................................... 29
Figure 3.14: Comparison of P-4 up-pumping drawdown speed for Narrow Baffles and
Standard Full Length Baffles ............................................................................................ 30
Figure 3.15: Comparison of HE-3 up-pumping speed for Narrow Baffles and Standard
Full Length Baffles ........................................................................................................... 31
Figure 3.16: Comparison of P-4 down-pumping drawdown speed for Narrow Baffles
with up-pumping drawdown speed for Standard Full Length Baffles .............................. 32
Figure 3.17: Comparison of HE-3 down-pumping drawdown speed for Narrow Baffles
with up-pumping drawdown speed for Standard Full Length Baffles .............................. 33
Figure 4.1: Linear plot of the P-4 impeller drawdown speed as a function of D/T for
various S/T ........................................................................................................................ 34
Figure 4.2: Logarithmic plot of the P-4 impeller drawdown speed as a function of D/T at
various S/T ........................................................................................................................ 35
Figure 4.3: Linear plot of P-4 drawdown speed as a function of S/T for various D/T .... 37
Figure 4.4: P-4 tip speed as a function of D/T for various S/T ........................................ 39
Figure 4.5a: P-4 power as a function of D/T for the submergences of 0.1 to 0.4 ............ 40
Figure 4.5b: P-4 power as function of D/T for various S/T............................................. 41
Figure 4.6a: P-4 torque as a function of D/T for the submergences of 0.1 to 0.4 ........... 41
Figure 4.6b: P-4 torque as a function of D/T for various submergences ......................... 42
Figure 4.7: Linear plot of HE-3 drawdown speed as a function of D/T for various
submergences .................................................................................................................... 43
ix
Figure 4.8: Logarithmic plot of HE-3 drawdown speed as a function of impeller diameter
to tank diameter ratio (D/T) for various S/T ..................................................................... 43
Figure 4.9: Linear plot of HE-3 drawdown speed as function of S/T for various D/T .... 45
Figure 4.10: HE-3 tip speed as function of D/T for the submergences of 0.1 to 0.7 ...... 46
Figure 4.11a: HE-3 power as a function of D/T for submergences of 0.1 to 0.5 ............ 47
Figure 4.11b: HE-3 power as a function of D/T for various S/T ..................................... 48
Figure 4.12: HE-3 torque as a function of D/T for the submergences of 0.1 to 0.7 ........ 49
Figure 4.13: Comparison of P-4 and HE-3 power as a function of D/T for submergence
of 0.1 and 0.4 .................................................................................................................... 50
Figure 4.14: Comparison of P-4 and HE-3 torque as a function of D/T for submergence
of 0.1 and 0.4 .................................................................................................................... 50
x
LIST OF TABLES
Table 2.1: Description of Baffle Configurations ................................................................ 9
Table 2.2: Details of Baffle Type and Pumping Mode Study .......................................... 14
Table 4.1: P-4 drawdown speed D/T power law correlation parameters ......................... 36
Table 4.2: P-4 drawdown speed power law correlation parameters for various D/T over
two submergence ranges ................................................................................................... 38
Table 4.3: HE-3 drawdown speed D/T power law correlation parameters ...................... 44
Table 4.4: HE-3 drawdown speed power law correlation parameter for various D/T over
two submergence ranges ................................................................................................... 45
Table 4.5: Speed, torque and power ratio P-4 to HE-3 averaged over 0.23 ≤ D/T ≤ 0.44 51
Table A.1: Raw and Calculated Data of P-4 impeller with D/T=0.200 ........................... 55
Table A.2: Raw and Calculated Data of P-4 impeller with D/T=0.228 ........................... 55
Table A.3: Raw and Calculated Data of P-4 impeller with D/T=0.271 ........................... 56
Table A.4: Raw and Calculated Data of P-4 impeller with D/T=0.300 ........................... 56
Table A.5: Raw and Calculated Data of P-4 impeller with D/T=0.329 ........................... 56
Table A.6: Raw and Calculated Data of P-4 impeller with D/T=0.371 ........................... 57
Table A.7: Raw and Calculated Data of P-4 impeller with D/T=0.400 ........................... 57
Table A.8: Raw and Calculated Data of P-4 impeller with D/T=0.443 ........................... 57
Table A.9: Raw and Calculated Data of P-4 impeller with D/T=0.500 ........................... 58
Table B.1: Raw and Calculated Data of HE-3 impeller with D/T=0.200 ........................ 59
Table B.2: Raw and Calculated Data of HE-3 impeller with D/T=0.228 ....................... 59
Table B.3: Raw and Calculated Data of HE-3 impeller with D/T=0.271 ........................ 60
Table B.4: Raw and Calculated Data of HE-3 impeller with D/T=0.300 ........................ 60
xi
Table B.5: Raw and Calculated Data of HE-3 impeller with D/T=0.329 ........................ 60
Table B.6: Raw and Calculated Data of HE-3 impeller with D/T=0.371 ........................ 61
Table B.7: Raw and Calculated Data of HE-3 impeller with D/T=0.400 ........................ 61
Table B.8: Raw and Calculated Data of HE-3 impeller with D/T=0.443 ........................ 61
Table B.9: Raw and Calculated Data of HE-3 impeller with D/T=0.500 ........................ 62
xii
NOMENCLATURE
A
Logarithmic intercept
B
Logarithmic intercept
C
Impeller off-bottom clearance, m
D
Impeller diameter, m
m
Power law exponent
n
Power law exponent
M
Torque, N·m
N
Impeller rotational speed, s-1 or rpm
Njd
Just-drawdown speed, s-1 or rpm
NP
Dimensionless impeller power number
P
Impeller power draw, W
S
Impeller submergence, m
T
Tank diameter, m
W
Blade width, m
Z
Liquid level, m
ρ
Density, kg m-3
xiii
CHAPTER 1
INTRODUCTION AND OBJECTIVE
Drawdown of floating solids in agitated liquid phase is required by many
industrial processes involving the processing of powders that have the tendency to clump,
additives that must be dumped on the surface, and floating solids such as rubber crumb.
These solids, without adequate agitation, will float on the liquid surface. There are three
kinds of floating solids: those with density lower than liquid (A), those in which the
solids are not wetted with the liquid (B), and those in which solids float because of low
bulk density (C). This study considers case A where the primary reason for the solids to
float is that their density is less than the liquid. For solids heavier than the liquid there are
many correlations to calculate the minimum impeller speed for the off-bottom suspension
of the particles. But limited results on the drawdown of floating particles in agitated
vessel have been published up to the present. The following is a review of some literature
studies that are pertinent to the current work.
This study considers different baffle arrangements with two different impeller
types. After finding standard full length baffles with up-pumping impellers as
appropriate, further studies are carried out with these baffles considering nine different
impeller to tank diameter ratios ranging from twenty to fifty percent over submergences
of ten to seventy percent of the tank diameter.
1
1.1 Background and Literature
Siddiqui (1993) studied incorporation of buoyant solids in a tall vessel. He studied
two types of partial baffles, the full length narrow baffles (T/48) and partially immersed
rectangular baffles. The impellers used were pitch blade turbine with 45 degree angle and
marine propeller. He used long cylindrical tank with aspect ratio varying from 1 to 3 and
experimented with more than twenty-five different combinations of baffle position,
length, and spacing. He did not consider the drawdown of floating particle as the
important criteria in his research and dealt more with the homogeneity of particles as the
main point. According to Siddiqui’s research the vortex formation was considered to be
key to incorporate the buoyant particles. The optimum pitch blade turbine diameter and
blade width were found to be T/2 and T/8, respectively. The optimum baffle
configuration was rectangular partial baffles placed from the top and separated at 90, 180
and 270 degrees on the periphery of vessel.
Hemrajani et al. (1988) studied the drawdown of floating solids in stirred tanks.
They varied the size of the vessel and there is nothing mentioned about the impeller size.
They tested four different types of baffles configuration: full length, rectangular finger
held in surface flow, rectangular finger baffle attached to the tank wall and triangular
finger baffles. They also varied the concentration of the solid in the vessel. The impeller
used was a pitch blade turbine with 45 degree angle but there was no study with respect
to the submergence of the impeller. This study was mainly focused on the formation of
controlled surface vortex. They found that the rectangular finger baffles are suitable for
constant level tanks since the baffles work well only when positioned just below the
2
liquid surface. They also found that for variable level tanks floating finger baffles and
T/50 wide baffles were more effective in the drawdown of the solids.
Karcz and Mackiewicz (2008) studied the effects of vessel baffling on the
drawdown of floating solids. The experiments were carried out for twelve different baffle
configurations. They tested partial and standard full length baffle, and varied number of
baffles like four, three, two and one. The different impeller types used were pitched blade
turbine, Rushton turbine and propeller. Two impeller submergences were tested, 0.33 and
0.67 T. The operating mode up-pumping or down-pumping of the impeller had great
effect on the drawdown of floating particles. They observed that narrow deep vortex
intensifies the immersion and dispersion of floating particles from free surface of the
liquid to the liquid volume when having only single baffle. It was found that there was
very little effect on the drawdown speed due to the symmetry or asymmetry of two or
three baffles in the vessel. They found that the up-pumping pitched blade turbine
positioned at a submergence of 0.33 T is more energy efficient in drawing down the
particles than down pumping operation with a standard full baffle configuration.
Khazam and Kresta (2009) studied three different baffle types with respect to
baffle length immersed in the liquid: full, half, and surface. They tested two different
types of impeller, pitch blade turbine with diameters of T/2 and T/3, and LIGHTNIN
A340 with impeller diameter equal to 4T/9.
The LIGHTNIN A340 is three-blade
hydrofoil impeller with wide blades. Two mechanisms for drawdown of floating solids in
the baffled stirred tanks were observed: turbulent engulfment and mean drag. The
performance of the baffle configurations was compared based on just drawdown speed
and cloud depth. They found that the four half baffles offered no advantage compared to
3
the fully baffled configuration. In case of the half baffles the circulation of particles was
weak and distribution was poor. In case of surface baffles, the lower 80% of the tank
axial flow was suppressed and formation of multiple strong circulations occurred which
helped to enhance performance because the tangential flow in the bottom of the tank
gives good distribution of particles compared to either half or full baffles in the
drawdown of floating solids. The up-pumping mode was more sensitive to the baffle
configuration than down-pumping showing more stable operation with the use of surface
baffles. They also found that larger diameter impellers performed better by consuming
less power and providing more stable operation as the submergence increased.
Bakker and Frijlink (1989) studied the drawdown and dispersion of floating solids
in aerated and un-aerated stirred vessels. They considered two different types of impeller,
disc turbine and pitch blade turbine with two variations of 45 degree and 60 degree angle.
Two submergence levels, 0.35 and 0.5 T, were considered with both up-pumping and
down-pumping mode. They found that pitch blade impeller with 45 degree angle and uppumping mode of operation performed efficiently, with low drawdown speed and power.
However, they found that the particles tended to concentrate in the upper half of the
vessel and the suspension was not homogenous in all cases.
Ozcan-Taskin and Wei (2003) studied the effect of impeller-to-tank diameter ratio
on drawdown of solids using two different impeller types, a pitched-blade turbine and a
narrow blade hydrofoil. The impeller to tank diameter ratios (D/T) considered were 1/2
and 1/3 at impeller submergences of T/3, T/2, 2T/3 and 3T/4. They found that when a
down–pumping impeller is mounted closer to the base of the vessel, the solids are drawn
down by recirculation loops close to the wall. When the impeller is mounted closer to the
4
surface, vortices are formed around the shaft, drawing the solids into the liquid. When
pumping up, the impeller discharge flow appeared to act on the liquid surface by
entraining the solids, and the drawdown speeds were found to be lower for the larger
diameter impeller while the power draw was higher.
Decreasing the impeller
submergences led to decrease in the drawdown speed and power draw. When pumping
down the opposite was found, as the impeller was mounted closer to the liquid surface,
both the drawdown speed and power draw increased. The flow pattern of particles at the
very large submergence with up-pumping mode was found to be more radial leading to
poor drawdown performance.
1.2 Objective of Current Research
This research is concerned with the minimum drawdown speed for floating solids in
liquid–solid stirred tank where the particles rest no more than 2-4 seconds on the liquid
surface. Like many other studies, the first portion of this study focused on finding the
best baffle configuration based on screening many different baffle arrangements. The
results of this portion of the study are described in Chapter 3. The second portion of the
study focused on drawdown of floating solids by applying the up-pumping mode for two
impeller types, P-4 and HE-3, with standard full length baffle configuration. The study
involved impeller to tank diameter ratios from twenty to fifty percent over submergences
ranging from ten to seventy percent of the tank diameter. The results of this portion of
study are described in Chapter 4.
The novelty of this work is its focus on studying a sufficient range of geometries
(impeller to tank diameter ratio and impeller submergence) for industrial design purposes.
5
CHAPTER 2
EXPERIMENTAL APPARATUS AND PROCEDURE
2.1 Experimental Apparatus
All experiments were performed in a clear acrylic circular cross section tank with
a flat bottom. The tank had a 17.5 inches inner diameter and 22.5 inches height. Four
baffles of different configuration such as height, width and angle to vessel wall were
attached to the inner surface of the tank separated by 90 degrees. The details for the
baffle type are given later. Two different types of impeller, pitched blade turbine, referred
to as the P-4, and the Chemineer HE-3, were employed with different diameters relative
to tank diameter (D/T). The impellers are shown in Figure 2.1. The P-4 blade angle was
45 degree with W/D ratio of 0.2 and Chemineer HE-3 impeller blade was of standard
construction. The impeller was kept on the centerline of the vessel, with the drawdown
speed measured at various submergences (S/T = 0.1, 0.2 ... 0.7). Three hundred grams of
green color acrylic solid particle (refer to Figure 2.2) with a density of 1.049 gm/cc was
used in the salt water solution with a density of 1.10 gm/cc.
This solid mass
corresponded to 0.43 mass percent solids in the slurry. The characteristic length of solid
was 3 mm and shape of the solid particle was approximately cubic. An electric motor was
used as power source to rotate the shaft and impeller by means of gear head connected to
the agitator drive. The variable speed gear box allowed rotational speed to be changed
6
until the drawdown speed was achieved in the stirred vessel, and then the speed was
measured with direct contact tachometer with digital display.
Figure 2.1a: Pitch Blade Turbine (P-4)
Figure 2.1b: High-Efficiency Impeller (HE-3)
7
Figure 2.2a: Green Acrylic Particle Dimensions
Figure 2.2b: Green Acrylic Particles
2.2 General Experimental Procedure
A reference tank was used to get consistent results in the test tank by matching the
solid particle behavior on the liquid surface, particularly the time that particles resided on
the liquid surface. Like the test tank, the reference tank was acrylic with a flat bottom
having inner diameter of 17.5 inches and height of 22.5 inches. The liquid level (Z) in the
reference tank was 17.5 inches (such that Z/T=1). The reference tank had an up-pumping
P-4 impeller of 5.75 inches diameter (D/T=0.329) kept at a submergence to tank diameter
ratio of thirty percent (S/T=0.3). .The drawdown speed of the solids was measured when
the solids particles did not stay more than 2 to 4 seconds on the liquid surface. The uppumping drawdown speed of P-4 impeller in the reference tank was found to be 86 rpm.
8
Drawdown speed (Njd) in the test tank was measured for all different baffle
configurations, impeller type, various impeller diameter and various submergences.
2.3 Experimental Details
2.3.1: Baffle Configuration Study
The purpose of the study was to find the right kind of baffle type leading to
optimum torque and power for the best performance in the mixing operation. A number
of experiments were performed using different baffle configurations by changing baffle
height, width and angle to the vessel wall. The general description of these baffles is
given below in Table 2.1.
Table 2.1: Description of Baffle Configurations
Baffle Type
Height
Width
Wall Angle
Z/T
Standard Baffle
>Z
T/12
90
1
Angled Baffle
>Z
T/12
135
1
Partial Baffle (1)
0.7 Z
T/12
90
1
Partial Baffle (2)
0.58 Z
T/12
90
1.2
Narrow Baffle
>Z
T/23
90
1
Descriptions of the different types of baffles are as follows while the baffle
configurations are illustrated in Figure 2.3.
2.3.1.1 Standard Baffles
These baffles are typically full length baffles immersed in the liquid. Their width
is one-twelfth of the tank diameter, and they are attached to the tank wall at four points
9
on the internal tank periphery. They are separated by 90 degree on the periphery of the
tank. The baffles have wall clearance of T/72 and are made of acrylic.
2.3.1.2 Angled Baffles
These baffles are typically full length baffle angled at 135 degrees in the direction
of impeller rotation, their width is one twelfth of the tank diameter, and they are attached
to the tank at four points on the internal periphery. They are separated by 90 degrees on
the periphery of the tank. The baffles are made of acrylic.
2.3.1.3 Partial Baffles (1)
These baffles have height 70% of the tank diameter. They touch the bottom of the
tank and are immersed completely in the liquid. This leaves the upper thirty percent of
the liquid unbaffled. The baffles have width one twelfth of the tank diameter and they are
attached at four different points on the tank internal periphery. They are also separated by
90 degree on the periphery of the tank. The baffles are made of acrylic.
2.3.1.4 Partial Baffles (2)
These baffles also have height 70% of the tank diameter. They touch the bottom
of the tank and are immersed completely in the liquid. However, in this case the liquid
level was 1.2 times the tank diameter (Z/T = 1.2). This left a liquid depth equal to fifty
percent of the tank diameter unbaffled (compared to the thirty percent unbaffled with the
first partial baffles). These baffles’ width is one-twelfth of the tank diameter and they are
attached at four different points on the tank internal periphery. The baffles are made of
acrylic.
10
2.3.1.5 Narrow Baffles
These baffles are full length baffles immersed in the liquid. They have width one
twenty-third of the tank diameter, approximately half the width of standard baffles. They
are attached at four different points on the tank internal periphery. They are also
separated by 90 degree on the periphery of the tank. The baffles are made of stainless
steel.
Figure 2.3a: Top View of Standard Full Length Baffles
Figure 2.3b: Side View of Standard Full Length Baffles
11
Figure 2.3c: Top View of Angled Baffles (impeller rotates clockwise)
Figure 2.3d: Side View of Angled Baffles
Figure 2.3e: Side View of Partial Baffles (1)
12
Figure 2.3f: Side View of Partial Baffles (2)
Figure 2.3g: Top View of Narrow Baffles
Figure 2.3h: Side View of Narrow Baffles
13
The baffle configuration study was done on all the above baffle types with P-4
and HE-3 impellers with impeller to tank diameter ratios of 0.3 and 0.4 (D/T = 0.3 and
0.4), with submergences of ten, twenty, thirty, …, and seventy percent of the tank
diameter (S/T = 0.1, 0.2, 0.3, …, 0.7). In Table 2.2 the details of baffle type and pumping
mode are discussed. Up-pumping mode was applied to all the baffles types except Partial
Baffles (2), whereas down pumping was applied only for Standard Full Length Baffles,
Partial Baffles (1), Partial Baffles (2) and Narrow Baffles types.
Table 2.2: Details of Baffle Type and Pumping Mode Study
Baffle Type
Up-Pumping Down-Pumping
Standard Baffle
Yes
Yes
Angled Baffle
Yes
No
Partial Baffle(1)
Yes
Yes
Partial Baffle(2)
No
Yes
Narrow Baffle
Yes
Yes
2.3.2: Up-Pumping with Standard Baffles Study
The study on standard baffles with up-pumping mode of operation was done after
finding it to be the best baffle configuration when compared to other configurations. Then
complete characterization was done based on various impeller diameter and
submergences for drawdown speed with two different impellers types, P-4 and HE-3, for
the industrial design purpose. Many experiments were done with an up-pumping impeller
using Standard Full Length Baffles. For both impeller types the impeller diameter was
varied from 20% to 50% of the tank diameter (0.2 < D/T < 0.5). The impeller
14
submergence was varied from ten to seventy percent of the tank diameter (0.1 < S/T <
0.7).
15
CHAPTER 3
RESULTS AND DISCUSSION
BAFFLE CONFIGURATION
In this chapter different types of baffle configuration are discussed. The different
types of baffle used for the study are:
a) Standard Full Length Baffles
b) Angled Baffles
c) Partial Baffles (1)
d) Partial Baffles (2)
e) Narrow Baffles.
The study of these different types of baffle configuration will determine the best
baffle configuration for the desired purpose of incorporating floating solids. All the raw
experimental data in this study is tabulated in the appendices. The experimental data is
taken for two impeller types, P-4 and HE-3, for impeller diameter to tank diameter ratios
of 30 and 40%. The other variables include mode of operation (up and down pumping)
and the impeller submergence that varies from 10 to 70% of the tank diameter. The
condition for the drawdown is solid particles should not stay more than 2-4 seconds on
the liquid surface. As discussed in the experimental chapter, a reference tank was used to
aid in consistent determination of the drawdown speed.
16
3.1 P-4, Up-Pumping, Standard Full Length Baffles
Figure 3.1 illustrates the up-pumping drawdown speed trend of P-4 impeller for
various submergences. From the plot it is found that the up-pumping drawdown speed of
P-4 impeller increases relatively linearly for submergence from 0.1 to 0.4 (0.1<S/T<0.4)
and increases dramatically for submergence greater than 0.4 (S/T > 0.4). This behavior is
due to the fact that the P-4 discharge flow at greater submergences impinges on the tank
wall instead of the free liquid surface. The drawdown speed for smaller impeller is high
and it decreases with the increase in the impeller size.
Figure 3.1: Drawdown speed for up-pumping P-4 with Standard Full Length Baffles
3.2 HE-3, Up-Pumping, Standard Full Length Baffles
Figure 3.2 illustrates the up-pumping drawdown speed trend of HE-3 impeller
with varying submergence. From the plot it is found that the up-pumping drawdown
speed of HE-3 increases relatively linearly with increasing submergence (0.1<S/T<0.7).
The increase in the drawdown speed is relatively linear due to the fact that the discharge
17
flow from the impeller blade is axial in nature and reaches upward towards free liquid
surface directly without impinging on the tank wall, even at higher submergences.
Drawdown speed is higher for the smaller impeller, and it decreases with the increase in
impeller diameter, similar to the P-4 impeller.
Figure 3.2: Drawdown speed for up-pumping HE-3 with Standard Full Length
Baffles
3.3 P-4 - HE-3 Comparison for Up-Pumping with Standard Full Length Baffles
Figure 3.3 illustrates the comparison of up-pumping P-4 and HE-3 drawdown
speed for Standard Full Length Baffles. From the plot it is found that the P-4 drawdown
speeds are lower than HE-3 for submergence of 0.1 to 0.4 (0.1< S/T<0.4), but drawdown
speeds for P-4 are higher than HE-3 for submergences greater than 0.4 (S/T > 0.4). This
is due to the fact that the P-4 discharge flow impinges on the tank wall at greater
submergences, while the HE-3 has a highly axial flow that reaches upward towards free
liquid surface without impinging on tank wall even at greater submergence.
18
Figure 3.3: Comparison of up-pumping drawdown speeds for P-4 and HE-3 with
Standard Full Length Baffles (D/T = 0.3)
3.4 P-4, Up-Pumping and Down-Pumping Comparison for Standard Full Length
Baffles
Figure 3.4 illustrates comparison of P-4 up-pumping and down-pumping
drawdown speeds with the Standard Full Length Baffles. From the plot it is found that the
P-4 down-pumping drawdown speeds are significantly higher compared with P-4 uppumping drawdown speeds for all submergences (0.1< S/T<0.6). The drawdown speed
for P-4 down pumping are higher as the discharge flow from the impeller blade is
directed downwards away from the free liquid surface and the suction created behind the
impeller blades is not strong enough at lower speeds for the drawdown of solid particles.
Thus down-pumping requires higher speeds when compared with that of up-pumping. It
is observed that the speed tends to slow down or remain relatively same as the
submergence increases for down-pumping as shown in the plot. From the data it shows
that the P-4(D/T=0.3) drawdown speeds ratio (down/up) varies from 1.46 to 3.38, while
19
P-4(D/T=0.4) drawdown speeds ratio varies from 1.37 to 2.24, and the down-pumping
speed averages 2.5 times the up-pumping for D/T=0.3 and 1.87 times for D/T=0.4.
Figure 3.4: Comparison of up-pumping and down-pumping drawdown speed for P-4
with Standard Full Length Baffles
3.5 HE-3, Up-Pumping and Down-Pumping Comparison for Standard Full Length
Baffles
Figure 3.5 illustrates the comparison of up-pumping and down-pumping HE-3
drawdown speed with Standard Full Length Baffles. From the plot it is found that the
drawdown speeds for HE-3 down-pumping are significantly higher when compared to
HE-3 up-pumping drawdown speeds for the submergences (0.1< S/T<0.7). It is due to the
fact that the strong discharge flow from the impeller does not incorporate solids but the
weak suction created behind the impeller blades leads to drawdown of solids. It is also
found that for larger impeller the drawdown speeds first increase and then decrease as the
submergence increases in the downward pumping mode. The HE-3(D/T=0.3) drawdown
speeds ratio (down/up) varies from 1.97 to 3.53 and for HE-3(D/T=0.4) it varies from
20
2.32 to 2.69. The average down-pumping speed is 2.76 times the up-pumping for
D/T=0.3 and 2.55 for D/T=0.4.
Figure 3.5: Comparison of up-pumping and down-pumping drawdown speed for HE-3
with Standard Full Length Baffles
3.6 P-4, Comparison of Angled-Baffles and Standard Full Length Baffles with UpPumping
Figure 3.6 illustrates the comparison of P-4 up-pumping Angled-Baffles with uppumping Standard Full Length Baffles. From the plot it is found that the drawdown
speeds are sometimes similar, sometimes lower and sometimes higher, for the AngledBaffles when compared to the Standard Full Length Baffles for submergences of 0.1 to
0.7 (0.1<S/T<0.7). It is found that the Angled Baffle has no effective advantage over
Standard Full Length Baffles due to the fact that although the vortices formed behind the
angled baffle visually appear stronger, lot of solids still remain on the surface between
the baffles. The P-4(D/T=0.3) drawdown speed ratio (Angled Baffles/Standard Baffles)
21
varies from 0.98 to 1.08, and for P-4(D/T=0.4) the drawdown speed ratio varies from
0.90 to 1.11. The average for the Angled Baffles is about 1.01 times higher than Standard
Full Length Baffle for D/T=0.3 and about 0.99 for D/T=0.4.
Figure 3.6: Comparison of P-4 up-pumping drawdown speed for Angled Baffles and
Standard Full Length Baffles
3.7 HE-3, Comparison of Angled Baffles and Standard Full Length Baffles with UpPumping
Figure 3.7 illustrates the up-pumping drawdown speed comparison of AngledBaffle with full length baffles for HE-3 impeller. From the plot it is found that the HE-3
up-pumping drawdown speeds are almost same as the speeds for the standard full length
baffles for submergences of 0.1 to 0.5 (0.1< S/T<0.5), but higher for submergence higher
than 0.5 (S/T > 0.5). The HE-3(D/T=0.3) drawdown speeds ratio (Angled
Baffles/Standard baffles) varies from 0.97 to 1.24 and for HE-3(D/T=0.4) the ratio varies
from 1 to 1.21. It is found that the angled baffle has no effective advantage over Standard
Full Length Baffles because although the formation of vortices behind the angled baffles
22
appears stronger but lot of solid particles still remain between the baffles. The average for
the Angled Baffles is about 1.06 times higher than Standard Full Length Baffles for both
D/T=0.3 and D/T=0.4.
Figure 3.7: Comparison of HE-3 up-pumping drawdown speed for Angled Baffles and
Standard Full Length Baffles
3.8 P-4, Comparison of Partial Baffles (1) and Standard Full Length Baffles with
Up-Pumping
Figure 3.8 illustrates the comparison of P-4 impeller up-pumping Partial Baffles (1)
with Standard Full Length Baffles. From the plot it is found that the P-4 up-pumping
drawdown speeds for Partial Baffles (1) are relatively higher than Standard Full Length
Baffles for submergences of 0.1 to 0.4 and relatively less for submergences greater than
0.4. This is due to the fact that at lower submergence the flow is tangential which does
not incorporate solids and as the submergence increases the effect of baffling helps for
the drawdown of solids. The P-4(D/T=0.3) drawdown speeds ratio (Partial Baffles
(1)/Standard Baffles) varies from 0.89 to 1.12 and for (D/T=0.4) the ratio varies from
23
0.91 to 1.08. The average drawdown speed compared with standard baffles is 1.03 times
for D/T=0.3 and 1.01 times for D/T=0.4.
Figure 3.8: Comparison of P-4 up-pumping drawdown speed for Partial Baffle (1) and
Standard Full Length Baffles
3.9 HE-3, Comparison of Partial Baffles (1) and Standard Full Length Baffles with
Up-Pumping
Figure 3.9 illustrates the comparison of up-pumping HE-3 impeller drawdown
speed for Partial Baffles (1) and Standard Full Length Baffles. From the figure it is found
that the HE-3 up-pumping drawdown speeds for Partial Baffles (1) are slightly higher
than Standard Full Length Baffles for all submergences 0.1 to 0.7 (0.1<S/T<0.7). This is
due to the fact that without baffling near the liquid surface, there is increased ineffective
tangential circulation, no vortices formed behind the baffles, and reduced downward axial
flow at the wall. The HE-3(D/T=0.3) drawdown speeds ratio (Partial Baffles (1)/Standard
Baffles) varies from 1.07 to 1.13 and for HE-3(D/T=0.4) drawdown speed ratio varies
24
from 1.03 to 1.15. The average drawdown speed when compared with standard baffles
for both D/T=0.3 and D/T=0.4 is 1.09.
Figure 3.9: Comparison of HE-3 up-pumping drawdown speed for Partial Baffles (1) and
Standard Full Length Baffles
3.10 P-4, Comparison of Partial Baffles (1) with Down-Pumping and Standard Full
Length Baffles with Up-Pumping
Figure 3.10 illustrates the comparison of P-4 down-pumping with Partial Baffles
(1) and Up-Pumping with Standard Full Length Baffles. From the plot it is found that the
P-4 down-pumping speeds are significantly higher than for Standard Full Length Baffles
for the submergence 0.1 to 0.7 (0.1<S/T<0.7). The speeds were found to be double the
standard full length baffles for the submergence of 0.1 to 0.5 (0.1<S/T<0.5). The
P-4(D/T=0.3) drawdown speeds ratio (Partial Baffles (1) Down/Standard Full Length
Baffles Up) varies from 1.07 to 3.55 and for P-4(D/T=0.4) it varies from 1.37 to 2.26.
The average drawdown speed compared with Standard Full Length Baffles is 2.41 times
for D/T=0.3 and 1.78 times for D/T=0.4.
25
Figure 3.10: Comparison of P-4 down-pumping drawdown speed for Partial Baffles (1)
with up-pumping drawdown speed for Standard Full Length Baffles
3.11 HE-3, Comparison of Down-Pumping with Partial Baffles (1) and Up-Pumping
with Standard Full Length Baffles
Figure 3.11 illustrates the comparison of HE-3 down-pumping drawdown speed
for Partial Baffles (1) with up-pumping for Standard Full Length Baffles. From the plot it
is found that the HE-3 down-pumping speeds are significantly higher for Partial Baffles
(1) when compared with Standard Full Length Baffles for the submergences of 0.1 to 0.7
(0.1<S/T<0.7). The HE-3(D/T=0.3) drawdown speeds ratio (Partial Baffles (1)
Down/Standard Full Length Baffles Up) varies from 2.2 to 3.5 and for HE-3(D/T=0.4) it
varies from 1.94 to 2.72. The average drawdown speed when compared with standard
baffles is 3.02 times for D/T=0.3 and 2.48 times for D/T=0.4.
26
Figure 3.11: Comparison of HE-3 down-pumping speed for Partial Baffles (1) with uppumping drawdown speed for Standard Full Length Baffles
3.12 P-4, Comparison of Down-Pumping with Partial Baffles (2) and Up-Pumping
with Standard Full Length Baffles
Figure 3.12 illustrates the comparison of P-4 down-pumping drawdown speed for
Partial Baffles (2) with up-pumping with Standard Full Length Baffles. From the plot it is
found that the P-4 down-pumping drawdown speeds are significantly higher than for
Standard Full Length Baffles for the submergence of 0.1 to 0.7 (0.1< S/T<0.7). The P4(D/T=0.3) drawdown speeds ratio (Partial Baffles (2) Down/Standard Baffles Up) varies
from 2.08 to 3.43 and for P-4(D/T=0.4) it varies from 1.46 to 2.0. The average drawdown
speed compared with the Standard Full Length Baffles is 2.58 times for D/T=0.3 and for
D/T=0.4 it is 1.68 times.
27
Figure 3.12: Comparison of P-4 down-pumping drawdown speed for Partial Baffles (2)
with up-pumping drawdown speed for Standard Full Length Baffles
3.13 HE-3, Comparison of Down-Pumping with Partial Baffles (2) and Up-Pumping
with Standard Full Length Baffles
Figure 3.13 illustrates the comparison of HE-3 down-pumping for Partial Baffles
(2) and up-pumping with Standard Full Length Baffles. From the plot it is found that the
drawdown speeds with Partial Baffles (2) are more than double for up-pumping with
standard full length baffles for submergence of 0.1 to 0.7 (0.1<S/T<0.7). The HE-3
down-pumping speeds ratio (Partial Baffles (2) Down-Pumping /Standard Full Length
Baffles Up-Pumping) for D/T=0.3 varies from 2.87 to 3.98 and for D/T=0.4 it varies
from 2.3 to 3.0. The average drawdown speed when compared to Standard Full Length
Baffles for D/T=0.3 is 3.55 times and 2.79 times for D/T=0.4.
28
Figure 3.13: Comparison of HE-3 down-pumping speed for Partial Baffles (2) with uppumping drawdown speed for Standard Full Length Baffles
3.14 P-4, Comparison of Up-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles
Figure 3.14 illustrates the comparison P-4 up-pumping drawdown speed with
Narrow Baffles with up-pumping Standard Full Length Baffles. From the plot it is found
that the P-4 up-pumping drawdown speeds for Narrow Baffles are slightly higher than for
the Standard Full Length Baffles for submergences of 0.1 to 0.7 (0.1<S/T<0.7). This is
due to the fact that relatively weaker vortices are formed behind the baffle and the vortex
at the center of vessel is stronger with tangential bulk flow between baffles. The P4(D/T=0.30) drawdown speeds ratio (Narrow Baffles/Standard Baffles) varies from 0.84
to 1.26 and for P-4(D/T=0.4) it varies from 1.07 to 1.47. The average speed compared to
the Standard Full Length Baffles is 1.05 times for D/T=0.3 and for D/T=0.4 it is 1.15
times.
29
Figure 3.14: Comparison of P-4 up-pumping drawdown speed for Narrow Baffles and
Standard Full Length Baffles
3.15 HE-3, Comparison of Up-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles
Figure 3.15 illustrates the comparison of HE-3 up-pumping drawdown speed for
Narrow Baffles and up-pumping with Standard Full Length Baffles. From the plot it is
found that the HE-3 up-pumping drawdown speeds with Narrow Baffles are slightly
higher for submergence of 0.1 to 0.4 (0.1<S/T<0.4) but the speeds are significantly
higher at greater submergences. The HE-3(D/T=0.3) drawdown speeds ratio (Narrow
Baffles/ Standard Baffles) varies from 1.03 to 1.32 and for HE-3(D/T=0.4) it varies from
1.02 to 2.08. The average speed when compared to the Standard Full Baffles is 1.16 times
for D/T=0.3 and for D/T=0.4 it is 1.32 times.
30
Figure 3.15: Comparison of HE-3 up-pumping speed for Narrow Baffles and Standard
Full Length Baffles
3.16 P-4, Comparison of Down-Pumping with Narrow Baffles and Up-Pumping with
Standard Full Length Baffles
Figure 3.16 illustrates the comparison of P-4 down-pumping with Narrow Baffles
and up-pumping for Standard Full Length Baffles. From the plot it is found that the P-4
down-pumping drawdown speeds for the Narrow Baffles are significantly higher than the
up-pumping Standard Full Length Baffles for the submergences of 0.1 to 0.7 (0.1<
S/T<0.7). The P-4(D/T=0.3) drawdown speeds ratio (Narrow Baffles/Standard Full
Length Baffles) varies from 1.16 to 2.79 and for P-4(D/T=0.4) it varies from 1.16 to 1.77.
The average drawdown speeds when compared to Standard Full Length Baffles for
D/T=0.3 is 2.18 times and for D/T=0.4 it is 1.50 times.
31
Figure 3.16: Comparison of P-4 down-pumping drawdown speed for Narrow Baffles
with up-pumping drawdown speed for Standard Full Length Baffles
3.17 HE-3, Comparison of Down-Pumping with Narrow Baffles and Up-Pumping
with Standard Full Length Baffles
Figure 3.17 illustrates the comparison of HE-3 down-pumping drawdown speed
with Narrow Baffles and up-pumping for Standard Full Length Baffles. From the plot it
is found that the HE-3 down-pumping drawdown speeds for Narrow Baffles are
significantly higher than up-pumping Standard Full Length Baffles for submergences of
(0.1<S/T<0.7). The HE-3(D/T=0.3) drawdown speeds ratio (Narrow Baffles DownPumping/Standard Full Length Baffles Up-Pumping) varies from 2.30 to 3.79 and for
HE-3(D/T=0.4) it varies from 2.65 to 3.17. The average drawdown speed for D/T=0.3
when compared to Standard Full Length Baffles is 3.04 times and for D/T=0.4 it is 2.94
times.
32
Figure 3.17: Comparison of HE-3 down-pumping drawdown speed for Narrow Baffles
with up-pumping drawdown speed for Standard Full Length Baffles
3.18 Summary
Totally five different baffle configuration were tested. P-4 & HE-3 impeller with
Standard Full Length Baffles and up-pumping mode were compared with all the other
baffle types and it was found that Standard Full Length Baffles with up-pumping mode
had relatively lower drawdown speeds .Based on this result, a detailed study was done to
chracterize not only drawdown speed, but also power and torque by varying impeller
diameter and submergence as dicussed in Chapter 4.
33
CHAPTER 4
RESULTS AND DISCUSSION
EFFECT OF IMPELLER DIAMETER AND SUBMERGENCE
4.1 P-4 Drawdown Speed
Figure 4.1 illustrates how the up-pumping P-4 drawdown speed varies with
impeller diameter and submergence (expressed in dimensionless form as D/T and S/T,
respectively). The drawdown speed decreases with an increase in the diameter and
increases with an increase in the submergence.
Figure 4.1: Linear plot of the P-4 impeller drawdown speed as a function of D/T for
various S/T
34
Figure 4.2 illustrates how the P-4 drawdown speed data of Figure 4.1 varies with
D/T logarithmically. The data exhibits relatively linear trend indicating that the following
power law correlation can describe the relation between drawdown speed (Njd) and
impeller to tank diameter ratio (D/T).
Njd = A (D/T)n
Table 4.1 presents the power-law correlation parameters A, n, and R2 (A is the
logarithmic intercept, n is slope or exponent of power law equation and R2 is coefficient
of determination). Table 4.1 indicates that the average value of the exponent is -1.39 with
coefficient of variation of 10% (coefficient of variation = standard deviation/average).
Figure 4.2: Logarithmic plot of the P-4 impeller drawdown speed as a function of D/T
at various S/T
35
Table 4.1: P-4 drawdown speed D/T power law correlation parameters
S/T
A
N
R2
0.1
13.83
-1.59
0.99
0.2
15.80
-1.16
0.94
0.3
19.87
-1.43
0.99
0.4
27.25
-1.33
0.94
0.5
46.28
-1.44
0.94
0.6
47.18
-1.15
0.97
0.7
45.53
-1.51
0.97
Average
-1.39
Using the data of Figure 4.1, the drawdown speed is plotted as a function of
submergence (S/T) at various impeller to tank diameter ratios (D/T). Figure 4.3 shows
that the drawdown speed of the P-4 impeller increases with an increase in submergence.
For the submergence from 0.1 to 0.4 (0.1 < S/T < 0.4), the drawdown speed increase is
steady and small; however, for the submergence of 0.4 to 0.7 (0.4 < S/T < 0.7), the
drawdown speed increase with increasing submergence is more rapid. This is because
the discharge flow from the P-4 impeller does not reach the surface.
Rather, the
discharge flow impinges on vessel wall and leads to lower velocities at the surface which
is not conducive to drawdown of the solid particles.
36
Figure 4.3: Linear plot of P-4 drawdown speed as a function of S/T for various D/T
Table 4.2 presents the power-law correlation parameter values (Njd = B (S/T)m)
over the two submergence ranges of 0.1 to 0.4 (0.1<S/T<0.4) and 0.4 to 0.7
(0.4<S/T<0.7).
The average value of exponent for the submergence 0.1 to 0.4
(0.1<S/T<0.4) is 0.32 with coefficient of variation 16%, and the average value of
exponent for the submergence 0.4 to 0.7 (0.4<S/T<0.7) is 1.45 with coefficient of
variation of 15%. The drawdown speed increases drastically for submergences greater
than 0.4 (S/T>0.4). This is because the discharge flow from the impeller blade hits the
surface directly at submergence below 0.4 (S/T<0.4), and for the submergence greater
than 0.4 (S/T>0.4) it impinges on vessel wall before reaching the surface.
37
Table 4.2: P-4 drawdown speed power law correlation parameters for various D/T over
two submergence ranges
D/T
S/T exponent
S/T exponent
0.1 ≤ S/T ≤ 0.4
0.4 ≤ S/T ≤ 0.7
0.20
0.32
1.51
0.23
0.27
1.61
0.27
0.31
1.50
0.30
0.28
1.75
0.33
0.31
1.63
0.37
0.32
1.48
0.40
0.31
1.35
0.44
0.38
1.24
0.50
0.44
1.01
Average
0.33
1.45
Figure 4.4 illustrates the drawdown tip speed (= π Njd D) as a function of impeller
to tank diameter ratio (D/T) at various S/T. From the figure it is found at lower
submergences of 0.1 to 0.4, the tip speed is high for smaller D/T and then remains
approximately constant or increases slightly for D/T greater than 0.33. For submergence
of 0.5, the drawdown tip speed is higher for larger D/T, while for the highest
submergences, S/T = 0.6 and 0.7, the drawdown tip speed continually decreases with
increasing D/T.
38
Figure 4.4: P-4 tip speed as a function of D/T for various S/T
The power (P) of the impeller can be found indirectly from power number (Np)
which is a function of impeller type, geometry and Reynolds number. The P-4 impeller
turbulent power number has an approximate value of 1.25 neglecting the effect of system
geometry (D/T and S/T). The equation given below illustrates how the power can be
computed using the power number.
P= Np ρ D5 Njd3
Figure 4.5a illustrates how the P-4 impeller drawdown power varies as a function
of impeller to tank diameter ratio (D/T) for the submergence of 0.1 to 0.4. The power is
found to be a minimum at D/T=0.33 for submergences of 0.1 to 0.4. The power required
is slightly higher for smaller impeller and significantly higher for much larger impeller
when compared with D/T=0.33. Figure 4.6b illustrates how the power depends on the
impeller diameter to tank diameter ratio (D/T) for all submergences that were studied (0.1
< S/T < 0.7). From Figure 4.5b it is found that the power at submergences greater than
39
0.4 (S/T>0.4) is quite high and does not exhibit such clear trends as at lower
submergences because the discharge flow from impeller does not reach the surface as the
flow pattern is radial in nature and impinges on the vessel wall before reaching the
surface.
Figure 4.5a: P-4 power as a function of D/T for the submergences of 0.1 to 0.4
40
Figure 4.5b: P-4 power as function of D/T for various S/T
P-4 Torque delivered to the fluid by the impeller can be computed from the impeller speed
(Njd) and power draw (P) from the equation given below.
Torque= P/(2πNjd)
Figure 4.6a: P-4 torque as a function of D/T for the submergences of 0.1 to 0.4
41
Figure 4.6b: P-4 torque as a function of D/T for various submergences
Figure 4.6a and 4.6b above illustrate how the drawdown torque increases as a
function of D/T over various S/T. From these figures it is found that the torque increases
with both the increase in impeller diameter and impeller submergence.
4.2. HE-3 Drawdown Speed
Figure 4.7 below illustrates how the HE-3 drawdown speed depends on impeller
to tank diameter ratio (D/T) over various S/T. From Figure 4.7 we find that drawdown
speed decreases with an increase in the diameter and increases with an increase in the
submergence.
42
Figure 4.7: Linear plot of HE-3 drawdown speed as a function of D/T for various
submergences
Figure 4.8: Logarithmic plot of HE-3 drawdown speed as a function of
impeller diameter to tank diameter ratio (D/T) for various S/T
Figure 4.8 above illustrates the HE-3 drawdown speed data of Figure 4.7 as a
function of D/T logarithmically. The data exhibits relatively linear trend, but the
43
magnitude of the slope decreases with increasing impeller diameter to tank diameter.
Despite this more complex behavior, a single power law correlation at a given
submergence will be used to describe the relation between drawdown speed (Njd) and
impeller to tank diameter ratio (D/T).
Njd = A (D/T)n
Table 4.3 presents the power-law correlation parameters A, n, R2 for the HE-3
impeller. The average value of the exponent is -1.60 with coefficient of variation of
7.0%; however, variation in the exponent is not random, with the magnitude of the slope
decreasing with increasing submergence.
Table 4.3: HE-3 drawdown speed D/T power law correlation parameters
S/T
A
N
R2
0.1
15.31
-1.79
0.97
0.2
17.90
-1.71
0.97
0.3
21.83
-1.60
0.98
0.4
25.77
-1.53
0.98
0.5
27.78
-1.54
0.98
0.6
31.16
-1.52
0.96
0.7
35.12
-1.49
0.96
Average
-1.60
Figure 4.9 illustrates how the HE-3 drawdown speed depends on the submergence
of impeller. From the plot it is found that the drawdown speed increases with the increase
in submergence of the impeller.
44
Figure 4.9: Linear plot of HE-3 drawdown speed as function of S/T for various D/T
Table 4.4 presents the power-law correlation parameter values (Njd = B(S/T)m)
over the two submergence ranges of 0.1 to 0.4 and 0.4 to 0.7. The power law relation
exponent value for submergence varying from 0.1 to 0.4 has an average value equal to
0.15 with a coefficient of variation of 44%. Similarly for the submergences varying from
0.4 to 0.7 the average value of exponent is equal to 0.47 with a coefficient of variation of
19%.
Figure 4.10 illustrates the HE-3 drawdown tip speed (=πNjdD) as a function of
impeller to tank diameter ratio (D/T) for various submergences, and it is found that the tip
speed decreases for impeller to tank diameter ratio (D/T) between the values of 0.2 and
0.3 and remains relatively constant for values greater than 0.3 to 0.4.
45
Table 4.4: HE-3 drawdown speed power law correlation parameter for various D/T over
two submergence ranges
D/T
S/T exponent
S/T exponent
0.1≤S/T≤0.4
0.4≤S/T≤.7
0.20
0.02
0.47
0.23
0.14
0.59
0.27
0.15
0.32
0.30
0.12
0.37
0.33
0.15
0.42
0.37
0.22
0.44
0.40
0.17
0.48
0.44
0.27
0.58
0.50
0.19
0.55
Average
0.15
0.47
Figure 4.10: HE-3 tip speed as function of D/T for the submergences of 0.1 to 0.7
46
Like P-4 the HE-3 power (= NpρD5Njd3) is estimated from the turbulent power
number, which has an approximate value of 0.3 neglecting the effect of system geometry
(D/T and S/T). Figure 4.11a illustrates the HE-3 impeller drawdown power as a function
of impeller diameter to tank diameter ratio over the submergence range of 0.1 to 0.5
(0.1<S/T<0.5) and Figure 4.11b illustrates how the HE-3 impeller power varies with the
impeller diameter over the submergence of 0.1 to 0.7 (0.1<S/T<0.7). From these figures
we find that the power required is high for smaller and very large impellers, but for
impeller to tank diameter ratios (D/T) of 0.271 to 0.4 the magnitude of the power is
approximately same for smaller submergences. For larger submergences the power of the
HE-3 impeller has a minimum at D/T=0.3. The HE-3 power also increases with the
increase in the submergence of impeller.
Figure 4.11a: HE-3 power as a function of D/T for submergences of 0.1 to 0.5
47
Figure 4.11b: HE-3 power as a function of D/T for various S/T
Like P-4, HE-3 impeller Torque (=P/(2πNjd) delivered is computed from power
draw (P) and drawdown speed (Njd). Figure 4.12 illustrates the drawdown torque as a
function of impeller to tank diameter ratio (D/T) with the increase in the submergence.
Figure 4.12 indicates that the torque increases with the increase in impeller diameter and
with the increase in submergence.
48
Figure 4.12: HE-3 torque as a function of D/T for the submergences of 0.1 to 0.7
4.3 P-4 and HE-3 Comparison
Figure 4.13 illustrates the comparison of P-4 and HE-3 power for the
submergence of 0.1 and 0.4. From Figure 4.14 the average ratio of power for D/T ranging
from 0.23 to 0.44 for P-4 compared with HE-3 at 0.1 submergence is 1.24 and at 0.4
submergence is 2.55.
Figure 4.14 illustrates the comparison of torque for different impeller diameters of
P-4 and the HE-3 for the submergence of 0.1 and 0.4. From Figure 4.15 we find that the
average torque ratio for the P-4 compared with HE-3 impeller for the submergence of 0.1
is 1.39 and for submergence of 0.4 is 2.99.
49
Figure 4.13: Comparison of P-4 and HE-3 power as a function of D/T for submergence
of 0.1 and 0.4
Figure 4.14: Comparison of P-4 and HE-3 torque as a function of D/T for submergence
of 0.1 and 0.4
Table 4.5 presents the speed, torque and power ratio (P-4 to HE-3) over
submergence of 0.1 to 0.7 (0.1<S/T<0.7), averaged for D/T between 0.23 and 0.44
50
(0.23<D/T<0.44). From Table 4.5 it is seen that P-4 has lower drawdown speed
compared to HE-3 at submergence less than 0.4 and for submergence greater than 0.4, P4 has higher drawdown speed compared to HE-3. P-4 has higher torque compared to HE3, for lower submergence about twice that of HE-3 but for higher submergence the ratio
is much higher. P-4 requires higher power compared to HE-3, ranging from forty percent
higher at the smallest submergence studied to many times higher at greater
submergences. These trends are observed since P-4 is strongly affected by increasing
submergence, particularly for submergence greater than 0.4, whereas for HE-3 increase in
submergence has little effect in comparison.
Table 4.5: Speed, torque and power ratio P-4 to HE-3 averaged over 0.23 ≤ D/T ≤ 0.44
S/T
Speed Ratio
Torque Ratio
Power Ratio
0.1
0.69
2.0
1.4
0.2
0.71
2.1
1.5
0.3
0.75
2.4
1.8
0.4
0.85
3.0
2.6
0.5
1.1
5.5
6.4
0.6
1.4
8.0
11
0.7
1.5
9.4
14
51
CHAPTER 5
CONCLUSIONS
The purpose of this work was to study the drawdown of floating particles based
on different geometrical aspects of the vessel. The basis for drawdown speed was solid
particles should not stay more than 2-4 seconds on the surface of liquid. The three main
mechanisms to incorporate the floating solids are via combination of turbulence, bulk
flow and vortices formed behind the baffles near the vessel wall. In this study five
different baffle configurations were tested and it was found that Standard Full Length
Baffles with an up-pumping impeller is a good configuration since it had relatively lower
drawdown speeds. Standard baffling worked better and lead to understanding of
important agitator design parameters such as power draw and torque. In this research nine
different impeller to tank diameter ratios over seven different submergences were studied.
The P-4 impeller has a mixed flow pattern: at lower submergence the flow
reaches to the surface directly whereas at higher submergence the discharge flow from
the impeller impinges on the vessel wall and then directs towards the liquid surface. The
HE-3 impeller discharge is more axial and the flow from the impeller discharges towards
liquid surface directly without impinging on the vessel wall. The P-4 and HE-3
drawdown speed decreased with increasing impeller diameter. From the experimental
52
work it is found that drawdown speed of P-4 and HE-3 impellers are related to impeller to
tank diameter ratio (D/T) by a power-law relation, Njd = A (D/T)n, having exponent
value -1.39 and -1.60, respectively. The P-4 impeller drawdown speed drastically
increased for submergence of 0.4 and above whereas for HE-3 the increase was linear
and steady. The P-4 impeller dependence on submergence was described by a power law
relation, Njd = A (S/T)n, and has the exponent value of 0.33 for submergence from 0.1 to
0.4 (0.1<S/T<0.4) and 1.45 for submergences between 0.4 to 0.7 (0.4<S/T<0.7).
Similarly, for HE-3 impeller, the values of exponent are 0.15 for submergence 0.1 to 0.4
(0.1<S/T<0.4) and 0.47 for submergence of 0.4 to 0.7 (0.4<S/T<0.7). The P-4 power was
found to be minimum for D/T=0.33 for submergences of 0.1 to 0.4 (0.1<S/T<0.4). The
power for submergence greater than 0.4 (S/T>0.4) was much higher and does not have an
easily described behavior. For HE-3 impeller the power was approximately same for D/T
ratios of 0.271 to 0.4 (0.271<D/T<0.4) for lower submergences. The power for HE-3 was
found to be minimum at D/T=0.3 for higher submergences. The power increased with
submergence for HE-3 impeller. The torque for P-4 and HE-3 increased with increase in
impeller diameter and impeller submergence.
53
BIBLIOGRAPHY
Bakker, A. and J. J. Frijlink., “The drawdown and dispersion of floating solids in aerated
and un-aerated stirred vessels”, Chemical Engineering Research and Design, Volume 67,
pages 208-210, March 1989.
Hemrajani, R. R., D. L. Smith., R. M. Koros and B. L. Tarmy, “Suspending floating
solids in stirred tanks - mixer design, scale-up and optimization”, presented at 6th
European Conference on Mixing”, Pavia, Italy, May 24-26, 1988.
Karcz, J. and B. Mackiewicz, “Effects of vessel baffling on the drawdown of floating
solids”, presented at the 35th International Conference of the Slovak Society of Chemical
Engineering, Tatranske Matliare, May 26-28, 2008.
Khazam, O and S. M. Kresta., “A novel geometry for solids drawdown in stirred tanks”,
Chemical Engineering Research and Design, Volume 87, pages 280-290 (2009).
Ozcan-Taskin, G. and H. Wei., “The effect of impeller-to-tank diameter ratio on
drawdown of solids”, Chemical Engineering Science, Volume 58, pages 2011-2022
(2003).
Siddiqui, H., “Mixing technology for buoyant solids in a nonstandard vessel”, AIChE
Journal, Volume 39, Number 3, pages 505-509 (1993).
54
APPENDIX A
RAW AND CALCULATED DATA FOR THE P-4 IMPELLER
Table A.1: Raw and Calculated Data of P-4 impeller with D/T=0.200
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
168
0.782
0.167
0.00952
0.2
189
0.880
0.239
0.0120
0.3
226
1.052
0.408
0.0172
0.4
263
1.224
0.643
0.0233
0.5
353
1.644
1.554
0.0420
0.6
488
2.272
4.108
0.0803
0.7
603
2.808
7.750
0.123
Table A.2: Raw and Calculated Data of P-4 impeller with D/T=0.228
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
141
0.750
0.193
0.0130
0.2
154
0.819
0.251
0.0156
0.3
179
0.952
0.395
0.0210
0.4
209
1.112
0.629
0.0287
0.5
257
1.368
1.170
0.0434
0.6
391
2.081
4.120
0.0100
0.7
498
2.650
8.511
0.163
55
Table A.3: Raw and Calculated Data of P-4 impeller with D/T=0.271
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
95
0.600
0.139
0.0140
0.2
110
0.695
0.216
0.0188
0.3
124
0.783
0.310
0.0239
0.4
151
0.954
0.560
0.0354
0.5
199
1.257
1.282
0.0615
0.6
283
1.788
3.688
0.0124
0.7
340
2.148
6.396
0.180
Table A.4: Raw and Calculated Data of P-4 impeller with D/T=0.300
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
83
0.579
0.153
0.017
0.2
90
0.628
0.195
0.0207
0.3
106
0.740
0.319
0.0287
0.4
123
0.859
0.499
0.0387
0.5
164
1.145
1.183
0.0689
0.6
254
1.774
4.398
0.165
0.7
316
2.207
8.469
0.255
Table A.5: Raw and Calculated Data of P-4 impeller with D/T=0.329
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
66
0.505
0.122
0.0175
0.2
76
0.581
0.185
0.023
0.3
86
0.658
0.269
0.0298
0.4
105
0.803
0.489
0.0445
0.5
165
1.262
1.900
0.1100
0.6
224
1.713
4.754
0.2026
0.7
257
1.966
7.180
0.2667
56
Table A.6: Raw and Calculated Data of P-4 impeller with D/T=0.371
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
59
0.510
0.160
0.0259
0.2
64
0.553
0.204
0.0305
0.3
75
0.648
0.329
0.0419
0.4
95
0.521
0.669
0.0672
0.5
147
1.271
2.480
0.161
0.6
188
1.626
5.188
0.263
0.7
216
1.868
7.869
0.347
Table A.7: Raw and Calculated Data of P-4 impeller with D/T=0.400
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
55
0.512
0.188
0.0326
0.2
61
0.568
0.256
0.0401
0.3
70
0.652
0.388
0.0529
0.4
87
0.810
0.745
0.0817
0.5
145
1.350
3.448
0.227
0.6
169
1.574
5.459
0.308
0.7
187
1.741
7.396
0.377
Table A.8: Raw and Calculated Data of P-4 impeller with D/T=0.443
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
49
0.505
0.221
0.0431
0.2
55
0.567
0.313
0.0543
0.3
67
0.690
0.566
0.0806
0.4
85
0.876
1.155
0.1297
0.5
129
1.330
4.0392
0.2988
0.6
154
1.588
6.872
0.426
0.7
171
1.763
9.408
0.525
57
Table A.9: Raw and Calculated Data of P-4 impeller with D/T=0.500
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
44
0.512
0.294
0.0638
0.2
51
0.594
0.458
0.0857
0.3
65
0.757
0.948
0.1392
0.4
82
0.954
1.903
0.221
0.5
108
1.257
4.348
0.384
0.6
129
1.0501
7.410
0.548
0.7
144
1.676
10.307
0.683
58
APPENDIX B
RAW AND CALCULATED DATA FOR THE HE-3 IMPELLER
Table B.1: Raw and Calculated Data of HE-3 impeller with D/T=0.200
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
318
1.48
0.273
0.00819
0.2
324
1.509
0.288
0.0085
0.3
313
1.457
0.260
0.00793
0.4
336
1.564
0.322
0.00914
0.5
374
1.741
0.444
0.0113
0.6
411
1.913
0.589
0.0137
0.7
436
2.030
0.703
0.0154
Table B.2: Raw and Calculated Data of HE-3 impeller with D/T=0.228
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
200
1.0643
0.132
0.00631
0.2
213
1.133
0.160
0.00716
0.3
228
1.213
0.196
0.00820
0.4
242
1.288
0.234
0.00924
0.5
270
1.436
0.325
0.0115
0.6
303
1.612
0.460
0.0145
0.7
337
1.793
0.633
0.0179
59
Table B.3: Raw and Calculated Data of HE-3 impeller with D/T=0.271
Pjd(watt)
S/T
Njd(rpm)
Tjd(m/s)
Mjd(N.m)
0.1
153
0.967
0.140
0.00872
0.2
164
1.036
0.172
0.0100
0.3
178
1.125
0.220
0.0118
0.4
190
1.201
0.268
0.0134
0.5
201
1.270
0.317
0.0150
0.6
213
1.346
0.377
0.0169
0.7
228
1.441
0.463
0.0194
Table B.4: Raw and Calculated Data of HE-3 impeller with D/T=0.300
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
126
0.880
0.129
0.00976
0.2
132
0.922
0.148
0.0107
0.3
139
0.971
0.173
0.0119
0.4
150
1.048
0.217
0.0138
0.5
162
1.131
0.274
0.0161
0.6
173
1.208
0.333
0.0184
0.7
185
1.292
0.408
0.0210
Table B.5: Raw and Calculated Data of HE-3 impeller with D/T=0.329
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
106
0.811
0.121
0.0109
0.2
111
0.849
0.139
0.0119
0.3
120
0.918
0.175
0.0139
0.4
131
1.002
0.228
0.0166
0.5
144
1.101
0.303
0.0200
0.6
155
1.185
0.378
0.0232
0.7
167
1.277
0.472
0.0270
60
Table B.6: Raw and Calculated Data of HE-3 impeller with D/T=0.371
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
85
0.735
0.115
0.0129
0.2
94
0.813
0.155
0.0158
0.3
106
0.916
0.223
0.0201
0.4
116
1.003
0.292
0.0240
0.5
126
1.089
0.375
0.0284
0.6
137
1.184
0.482
0.0335
0.7
148
1.28
0.607
0.0391
Table B.7: Raw and Calculated Data of HE-3 impeller with D/T=0.400
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
80
0.745
0.139
0.0166
0.2
85
0.791
0.167
0.0187
0.3
93
0.866
0.218
0.0224
0.4
102
0.950
0.288
0.0270
0.5
111
1.034
0.371
0.0319
0.6
121
1.127
0.481
0.0379
0.7
134
1.248
0.653
0.0465
Table B.8: Raw and Calculated Data of HE-3 impeller with D/T=0.443
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
60
0.618
0.0974
0.0155
0.2
68
0.701
0.142
0.0199
0.3
78
0.804
0.214
0.0262
0.4
88
0.907
0.307
0.0333
0.5
98
1.010
0.424
0.0413
0.6
111
1.144
0.617
0.053
0.7
121
1.247
0.799
0.063
61
Table B.9: Raw and Calculated Data of HE-3 impeller with D/T=0.500
S/T
Njd(rpm)
Tjd(m/s)
Pjd(watt)
Mjd(N.m)
0.1
63
0.733
0.207
0.031
0.2
69
0.803
0.272
0.037
0.3
74
0.861
0.336
0.043
0.4
84
0.978
0.491
0.0558
0.5
91
1.059
0.624
0.0654
0.6
102
1.187
0.879
0.0822
0.7
114
1.327
1.227
0.1027
62