-
OPTIMIZATION OF DISSOLVED AIR FLOTATION FOR
DRINKING WATER TREATMENT
THROUGH CFD MODELING
by
Babak Lakghomi
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Civil Engineering
University of Toronto
© Copyright by Babak Lakghomi (2015)
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ii
OPTIMIZATION OF DISSOLVED AIR FLOTATION FOR DRINKING
WATER TREATMENT THROUGH CFD MODELING
Babak Lakghomi
Doctor of Philosophy, 2015
Graduate Department of Civil Engineering
University of Toronto
0B0BABSTRACT
The dissolved air flotation (DAF) process is known for its
efficiency in the removal of low-
density particles from water. The performance of the system
depends, in part, on the
hydrodynamics of the flow. Whereas experimental flow measurement
methods for DAF can be
very challenging due to the presence of bubbles and particles,
computational fluid dynamics
(CFD) can be applied as an alternative approach for improving
the understanding of the
hydrodynamics, but would still require validation.
In this study, two-phase and three-phase analytical and CFD
models of DAF were developed to
evaluate the formation of stratified flow (back and forth
horizontal flow layers in the separation
zone) and its impact on bubble and particle removal. By
including the effects of bubble
aggregation and bubble-particle aggregation, the models were
able to predict the formation of
stratified flow under different air fractions, bubble sizes, and
loading rates.
The CFD model showed that stratified flow improved bubble
removal as well as particle
removal, demonstrating that up to 130% higher loading rates can
be achieved in the presence of
stratified flow. An increase in air fraction and bubble size was
shown to improve bubble
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removal, but particle removal began to decrease when air
fractions and bubble sizes increased
beyond optimum levels.
The CFD model was then validated with a pilot-scale DAF system
by comparing measurements
of residence time distribution (RTD), bubble layer position and
bubble-particle contact
efficiency. In general, the CFD model was able to represent the
pilot-scale DAF flow at different
loading rates with very good accuracy (R2 values higher than
0.75).
Finally, the validated model was applied to evaluate the effect
of the addition of different
configurations of baffles in the separation zone. The results
suggested that baffles in the
separation zone can enhance stratification of the flow and allow
up to 86% higher loading rates.
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1B1BACKNOWLEDGMENTS
This research was financially supported by Walkerton Clean Water
Centre, the Natural Sciences
and Engineering Research Council of Canada, and Corix Water
Systems.
I would like to express my deepest gratitude to my supervisors,
Professor Ron Hofmann, and
Professor Yuri Lawryshyn, for their guidance and encouragement
in my research and my
professional life. I would also like to thank Professors Bob
Andrews and Markus Bussmann for
being on my supervisory committee and offering their
constructive and insightful suggestions.
I would like to appreciate Stephen Tang for his great help in
set-up of the pilot system.
Finally, I would like to thank my dear parents and my dearest
wife, Sara, for their endless
support and encouragement along the way.
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2B2BTABLE OF CONTENTS
0B0BABSTRACT
....................................................................................................................................
ii
1B1BACKNOWLEDGMENTS
.............................................................................................................
iv
2B2BTABLE OF CONTENTS
................................................................................................................
v
3B3BLIST OF TABLES
.........................................................................................................................
ix
4B4BLIST OF FIGURES
........................................................................................................................
x
1. 5B5BIntroduction
.............................................................................................................................
1
1.1. 12B12BBackground
......................................................................................................................
1
1.2. 13B13BObjectives
.........................................................................................................................
2
1.3. 14B14BThesis Chapters
................................................................................................................
3
1.4. 15B15BAssociated Journal Publications
.......................................................................................
4
1.5. 16B16BReferences
........................................................................................................................
4
2. 6B6BLiterature
review......................................................................................................................
6
2.1. 17B17BImportance of stratified flow
............................................................................................
6
2.2. 18B18BBubble-particle attachment models
..................................................................................
7
2.3. 19B19BPrevious attempts at CFD modelling
.............................................................................
10
2.4. Research gaps
.................................................................................................................
14
2.5. 21B21BReferences
......................................................................................................................
14
3. 7B7BImportance of flow stratification and bubble aggregation
in the separation zone of a
dissolved air flotation tank 0F0F
........................................................................................................
18
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3.1. 22B22BIntroduction
....................................................................................................................
18
3.2. 23BMethodology
..................................................................................................................
20
3.3. 24B24BA conceptual model for bubble removal in the
separation zone .................................... 21
3.4. 25B25BResults and Discussions
.................................................................................................
26
3.5. 26B26BConclusions
....................................................................................................................
32
3.6. 27B27BReferences
......................................................................................................................
33
4. 8B8BA model for optimization of particle removal in a
dissolved air flotation tank: importance
of stratified flow and bubble size1F1F
..............................................................................................
35
4.1. 28B28BIntroduction
....................................................................................................................
35
4.2. 29BMethodology29B
..................................................................................................................
37
4.4. 30B30BResults and Discussions
.................................................................................................
47
4.5. 31B31BSummary and Conclusions
.............................................................................................
57
4.6. 32B32BReferences
......................................................................................................................
58
5. 9B9BEvaluation of flow hydrodynamics in a pilot-scale
dissolved air flotation tank: a
comparison between CFD and experimental measurements 2F2F
.................................................... 60
5.1. 33B33BIntroduction
....................................................................................................................
60
5.2. 34B34BMethodology
..................................................................................................................
62
5.3. 35B35BResults
............................................................................................................................
68
5.4. 36B36BConclusions
....................................................................................................................
76
5.5. 37B37BReferences
......................................................................................................................
76
6. 10B10BCFD Applications: Effect of geometric modifications and
3D modelling ............................ 78
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6.1. 38B38BIntroduction
....................................................................................................................
78
6.2. 39B39BMethodology
..................................................................................................................
78
6.3. 40B40BResults
............................................................................................................................
81
6.4. 41B41BConclusion
......................................................................................................................
85
7. 11B11BConclusions and Recommendations for Future Research
..................................................... 86
7.1. 42B42BConclusions
....................................................................................................................
86
7.2. 43B43BResearch Contributions
..................................................................................................
86
7.3. 44B44BRecommendations for Future Research
.........................................................................
87
Appendix A:
..................................................................................................................................
89
A.1 62B62BModel set up and convergence
.......................................................................................
89
A.2 63B63BTwo-phase flow model
...................................................................................................
90
A.3 64B64BPopulation balance model for bubble coalescence and
break-up ................................... 90
A.4 Three-phase flow model
.................................................................................................
92
A.5 65B65BReferences
......................................................................................................................
94
Appendix B:
..................................................................................................................................
95
B.1 66B66BUser defined function (UDF) for degassing
...................................................................
95
B.2 67B67BUser defined function (UDF) for aggregation
................................................................
95
B.3 68B68BMATLAB code for analytical particle removal model
.................................................. 98
Appendix C:
................................................................................................................................
101
C.1 Analytical bubble and aggregate distribution
...............................................................
101
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C.2 CFD bubble distribution and collision frequency
........................................................ 102
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3B3BLIST OF TABLES
Table 2.1 Governing equations for bubble-particle aggregation
rates ............................................ 8
Table 2.2 A comparison of two phase CFD models for DAF
...................................................... 11
Table 3.1 Bubble size groups for each inlet bubble size
...............................................................
21
Table 4.1 Particle removal efficiency for varying air fractions
and bubble sizes.. ....................... 53
Table 4.2 Particle removal efficiency for varying air fractions
and bubble sizes.. ....................... 54
Table 4.3 Percentage of particle aggregation occurring in the
separation zone at different air
fractions and bubble sizes..
.........................................................................................
55
Table 5.1 Particle size ranges (bins) measured by the particle
counter ........................................ 64
Table 5.2 Inlet bubble size distribution in the contact zone.
....................................................... 67
Table 5.3 Comparison between CFD predictions and experimental
measurements. .................. 70
Table 5.4 Effect of attachment efficiency on CFD predictions.
................................................... 74
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4B4BLIST OF FIGURES
Figure 1.1 Schematic diagram of the dissolved air flotation tank
.................................................. 1
Figure 3.1 Configuration of the modeled DAF
system.................................................................
20
Figure 3.2 The conceptualized flow models for separation zone,
reverse flow on top and plug
flow at bottom
.............................................................................................................
22
Figure 3.3 Velocity vectors (0-0.03 m/s), a) Single phase, b)
Air fraction 0.005, c) Air fraction
0.02
..............................................................................................................................
27
Figure 3.4 Velocity vectors (0-0.03 m/s), a) Air fraction 0.005,
b) Air fraction 0.01, c) Air
fraction 0.02.
...............................................................................................................
27
Figure 3.5 Effect of air inlet fraction on bubble removal at
different loading rates. .................... 28
Figure 3.6 Effect of air inlet fraction on bubble removal in
presence of bubble aggregation at
different loading rates, a) Inlet bubble size 80 µm, b) Inlet
bubble size 20 µm. ........ 29
Figure 3.7 Velocity vectors (0-0.03 m/s) in the presence of
bubble aggregation, a) Air fraction
0.005, b) Air fraction 0.008, c) Air fraction 0.01..
...................................................... 30
Figure 3.8 Velocity vectors (0-0.05 m/s) in the presence of
bubble aggregation, a) Air fraction
0.01, b) Air fraction 0.035, c) Air fraction 0.05.
......................................................... 30
Figure 3.9 Comparison of air content in the separation zone from
Lundh et al. (2001) and the
present model.
.............................................................................................................
31
Figure 3.10 Velocity vectors (0-0.03 m/s) in presence of bubble
aggregation, a) 11.8 m/hr, b)
23.6 m/hr, c) 47.2 m/hr.
..............................................................................................
32
Figure 4.1 The conceptual model for stratified flow in the
separation zone ................................ 39
Figure 4.2 Configuration of the modeled DAF
system.................................................................
45
Figure 4.3 The effect of air fraction and bubble size on
particle removal calculated from the
analytical model, a) in the absence of stratified flow, b) in
the presence of stratified
flow.
............................................................................................................................
48
Figure 4.4 Loading rates at 60% particle removal in the absence
and presence of stratified
flow.
............................................................................................................................
48
Figure 4.5 The effect of air fraction and bubble size on
particle removal from the theoretical
model, a) loading rate 11.8 m/hr, b) loading rate 23.6 m/hr
....................................... 49
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xi
Figure 4.6 The effect of particle and bubble size on particle
removal, a) loading rate 11.8
m/hr, air fraction 0.005, b) loading rate 11.8 m/hr, air
fraction 0.01, c) loading rate
23.6 m/hr, air fraction 0.005, d) loading rate 23.6 m/hr, air
fraction 0.01 (in
presence of stratified flow layer).
...............................................................................
50
Figure 4.7 Velocity vectors (0-0.1 m/s) at different air
fractions, a) 0.008, b) 0.01, c) 0.02. ....... 52
Figure 4.8 The velocity vectors (0-0.1m/s) at different bubble
sizes, a) 40 µm, b) 80 µm, c)
120 µm.
.......................................................................................................................
52
Figure 4.9 The effect of air fraction and loading rate on
particle removal from the CFD model,
a) bubble size 40 µm, b) bubble size 80 µm.
..............................................................
53
Figure 4.10 The effect of air fraction and bubble size on
particle and bubble removal from the
CFD model, a) bubble removal, loading rate 11.8 m/hr, b) bubble
removal 23.6
m/hr, c) particle removal 11.8 m/hr, d) particle removal 23.6
m/hr. .......................... 55
Figure 4.11 The effect of particle and bubble size on particle
removal from the CFD model ..... 57
Figure 5.1 A schematic diagram of the DAF pilot system
........................................................... 63
Figure 5.2 Geometry of the modeled DAF system
.......................................................................
67
Figure 5.3 RTD comparison between experimental and CFD results.
......................................... 70
Figure 5.4 The normalized position of bubble layer (hb/H) in the
separation zone at different
loading rates.
...............................................................................................................
71
Figure 5.5 The effect of loading rate on the residence time
distribution. ..................................... 73
Figure 5.6 Velocity vectors (0-0.1 m/s) at different loading
rates.. .............................................. 73
Figure 5.7 The effect of attachment efficiency on the residence
time distribution ...................... 75
Figure 5.8 Contact efficiency at different particle sizes from
particle counts, CFD and
analytical model
..........................................................................................................
76
Figure 6.1 The geometry of pilot system with different baffle
configurations, a) baffle 1, b)
baffle 2, c) baffle 3, d) baffle 4.
..................................................................................
79
Figure 6.2 Schematic diagram of Peekskill DAF tank
.................................................................
80
Figure 6.3 Air volume fraction in the tank for different baffle
configurations, a) no baffle, b)
baffle 1, c) baffle 2, d) baffle 3.
..................................................................................
81
Figure 6.4 Velocity vectors for primary phase (water) in the
tank for different baffle
configurations, a) baffle 1, b) baffle 2, c) baffle 3.
..................................................... 82
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Figure 6.5 Air volume fraction in the tank for a) porous (baffle
3), and b) non-porous
horizontal baffles (baffle 4).
.......................................................................................
82
Figure 6.6 The effect of loading rate on bubble removal for
different baffle configurations ...... 83
Figure 6.7 Velocity vectors (0-0.2 m/s) on the symmetry plane
showing the position of the
bubble layer (air volume fraction 0.0001), a) 2D model, b) 3D
model. Flow rate
2.8 mgd, air concentration of 9 g/m3, inlet bubble size of 40
µm. .............................. 84
Figure 6.8 Velocity vectors (0-0.2 m/s) on the xz plane (top
view) at the baffle overflow
height
...........................................................................................................................
85
Figure C.1 The effect of bubble size on bubble volume fraction
distribution α1,0. a) inlet
bubble size 20 µm, b) inlet bubble size 80 µm.
........................................................ 101
Figure C.2 The effect of bubble size on aggregate N3,3/N0,1
distribution. a) inlet bubble size 20
µm, b) inlet bubble size 80 µm.
................................................................................
101
Figure C.3 The effect of bubble size on bubble number
concentration. a) inlet bubble size 80
µm, b) inlet bubble size 120 µm.
..............................................................................
102
Figure C.4 The effect of bubble size on collision frequency
(m3/s). a) inlet bubble size 80 µm,
b) inlet bubble size 120 µm.
......................................................................................
102
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1. 5B5BIntroduction
1.1. 12B12BBackground
Dissolved air flotation (DAF) is a process for the separation of
solid particles from water by the
injection of air bubbles. DAF has been used in water treatment
for over 40 years (Edzwald,
1995) and is especially known as a good process for removing
particles with low specific gravity
(Kwon et al., 2006). A schematic diagram of a DAF tank can be
observed in Figure 1.1. The
DAF basin consists of two zones: a contact zone, and a
separation zone. A baffle separates the
contact zone from the separation zone. A water-bubble mixture is
injected through a nozzle at the
bottom of the contact zone, and the influent water is introduced
into the basin close to the floor
of the contact zone. Air bubbles adhere to the particles and
form particle-bubble aggregates.
Aggregates have lower specific gravity than the surrounding
liquid and as a result rise to the
surface. The particles on the surface form a discrete layer of
solids that is usually removed from
the surface by means of a scraper.
Figure 1.1 Schematic diagram of the dissolved air flotation
tank
Historical hydraulic loading rates (flow rate per unit surface
area of the separation zone) for DAF
systems have been in the order of 5-10 m/hr. However, recently
DAF systems have been
operated at loading rates as high as 20-40 m/hr (Edzwald, 2007).
Experimental measurements by
Lundh et al. (2000 and 2001) suggested the presence of back and
forth horizontal flow layers at
the top of the separation zone (stratified flow) under certain
conditions. Edzwald (2007) used the
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concept of stratified flow to qualitatively explain the higher
surface loading rates that have been
achieved.
The demonstration of the horizontal flow patterns known as
stratified flow has been so far
limited to two phase flow (i.e. air-liquid flow, with no
particles present), and only in pilot-scale
DAF systems (Lundh et al., 2001, Hague et al., 2001). As such,
there is uncertainty about the
importance of stratified flow in real DAF systems. There is also
a lack of a quantitative measure
of the impact of stratified flow on DAF performance.
Computational fluid dynamics (CFD) can
be a useful tool to better understand the flow behavior, which
can be easily applied to a variety
of conditions. However, previous CFD models (Ta et al., 2001;
Hague et al., 2001; Bondelind et
al., 2010) of DAF systems have not accurately simulated
conditions under which stratified flow
occurs, and have not evaluated the effect of stratification of
the flow on bubble and particle
removal. In addition, very few of these models have incorporated
bubble-particle attachment
(Kostoglou et al., 2007; Bondelind et al., 2012), nor have they
accounted for bubble aggregation
and the effects of the particles and aggregates on the flow
pattern in a complete DAF unit.
Moreover, there has been a lack of experimental validation in
the presence of the solid particles
(Edzwald, 2010).
There is a need for developing a CFD model that can predict the
formation of stratified flow and
removal efficiency in the presence of bubbles, particles and
aggregates. After validation, the
model can be applied as a tool in the optimization of the design
and operation of DAF.
1.2. 13B13BObjectives
The main objective of this study is to develop a CFD model of a
DAF system to better
understand and optimize operating and design conditions. The
more detailed objectives are as
follows:
1. Investigate the effect of back and forth horizontal flow
layers (stratified flow), air fraction
and bubble size on bubble removal (Chapter 3)
2. Investigate the effect of stratified flow, air fraction and
bubble size on particle removal
(Chapter 4)
3. Validate the predictions of the CFD model for two-phase and
three-phase conditions
(Chapter 5)
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4. Apply the developed CFD model to optimize the geometric
features of DAF by enhancing
stratified flow (Chapter 6)
1.3. 14B14BThesis Chapters
Chapter 2 provides a literature review of previous experimental
and modeling studies of
flow hydrodynamics and bubble-particle attachment in DAF.
Chapter 3 presents a two-phase (bubble-liquid) model of DAF that
is able to predict
formation of stratified flow under different operating
conditions by including the effect of
bubble aggregation. A conceptual model of stratified flow is
utilized to show the effect of
stratified flow on bubble removal under simplified conditions.
The developed CFD model
is then applied to study the quantitative effect of air
fraction, loading rate and bubble size
on the formation of stratified flow and bubble removal.
Chapter 4 presents an analytical model as well as a three-phase
CFD model of overall
particle removal in DAF. The models extend the previous models
by including bubble-
particle aggregation, the effect of particles and formed
aggregates on the flow, clustering
(attachment of aggregates with multiple bubbles and particles),
and the presence of
stratified flow. First, the analytical model is applied to
provide a better understanding of
the effect of stratified flow, bubble size and air fraction on
particle removal for simplified
scenarios. Then, the developed CFD model is used to study the
effect of these parameters
under more realistic conditions.
Chapter 5 evaluates the predictions of the developed two-phase
and three-phase CFD
models in the previous chapters by comparison with data obtained
from a pilot-scale
DAF tank. The residence time distributions (RTD) from tracer
testing, position of the
bubble layer in the tank, and particle count data are used to
validate the predictions of the
CFD model.
Chapter 6 applies the validated model in Chapter 5 to evaluate
the effect of modifications
in DAF geometry and addition of different internal baffles on
the formation of stratified
flow and bubble removal.
Chapter 7 summarizes the main conclusions and contributions of
the research, and
provides recommendations for future research.
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1.4. 15B15BAssociated Journal Publications
Chapter 3 waspreviouslypublishedas“B. Laghomi, Y. Lawryshyn, R.
Hofmann, 2012. Effect
of stratified flow and bubble aggregation in the separation zone
of a dissolved air flotation tank.
Water Research, 46 (14), 4468-76”.
Chapter 4 was published inWaterResearchas“B. Lakghomi, Y.
Lawryshyn, R. Hofmann, 2014.
A model for particle removal in a dissolved air flotation tank:
importance of stratified flow and
bubble size, In Press”.
Chapter 5 has been submitted to Water Science and Technology as
“B. Lakghomi, Y.
Lawryshyn, R. Hofmann, 2014. Evaluation of flow hydrodynamics in
a pilot-scale dissolved air
flotation tank: a comparison between CFD and experimental
measurements”.
The first two manuscripts have been reproduced in this thesis
with permission of the publisher.
The third manuscript is still under review, and copyright
permission will be obtained once the
publication is finalized.
1.5. 16B16BReferences
Bondelind, M., Sasic, S., Kostoglou, M., Bergdahl, L., Thomas,
J.R.P., 2010. Single and two-
phase numerical models of dissolved air flotation: comparison of
2D and 3D simulations.
Colloids and Surfaces A: Physicochemical and Engineering
Aspects, 365(1-3), 137-144.
Bondelind, M., Ström, H., Sasic, S. and Bergdahl, L., 2012.
Eulerian modelling of the formation
and flow of aggregates in dissolved air flotation. The 15th
International Conference on Fluid
Flow Technologies, Budapest, Hungary, September 4-7, 2012.
Edzwald, J.K., 1995. Principles and applications of dissolved
air flotation, Water Science and
Technology,31(3),1−23.
Edzwald, J.K., 2007. Developments of high rate dissolved air
flotation for drinking water
treatment. Journal of Water Supply: Research and
Technology-Aqua, 56(6-7), 399-409.
Hague, J., Ta, C.T., Biggs, M.J, Sattary, J.A., 2001. Small
scale model for CFD validation in
DAF application. Water Science and Technology, 43(8),
167-173.
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Kostoglou, M., Karapantsios, T.D., Matis, K.A., 2007. CFD model
for the design of large scale
flotation tanks for water and wastewater treatment. Industrial
Engineering and Chemistry
Research, 46(20), 6590-6599.
Kwon, S.B., Lee, S.J, Ahn, H.W, Wang, C.K., 2006. Examining the
effect of length/width ratio
on the hydrodynamic behavior in a DAF system using CFD and ADV
techniques. Water Science
and Technology, 53(7), 141-149.
Lundh, M., Jonsson, L., Dahlquist, J., 2000. Experimental
studies of the fluid dynamics in the
separation zone in dissolved air flotation. Water Research,
34(1), 21-30.
Lundh, M., Jonsson, L., Dahlquist, J., 2001. The flow structure
in the separation zone of a DAF
pilot plant and the relation to the bubble concentration. Water
Science and Technology, 43(8),
185-194.
Ta, C.T., Beckley, J., Eades, A., 2001. A multiphase CFD model
of DAF process. Water Science
and Technology, 43(8), 153-157.
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2. 6B6BLiterature review
2.1. 17B17BImportance of stratified flow
Previous researchers have investigated the hydraulics in DAF
systems in an effort to understand
how to optimize its efficiency. Early design of traditional DAF
systems (Haarhoff and Vuuren,
1995) assumed vertical plug flow in the separation zone. Based
on these models, free bubbles
and particle-bubble aggregates are removed if their rise
velocity exceeds the velocity of the
downward plug flow (loading rate), which was traditionally in
the range of 5-10 m/h.
Development of DAF systems at high loading rates in early 2000s
and pilot plant tests by
Edzwald (1999) showed that such simple models are not able to
represent the hydrodynamics of
high rate DAF systems (Edzwald, 2007).
An experimental study of the hydrodynamics of the air-water flow
using a pilot-scale DAF
system was performed by Lundh et al. (2000) using acoustic
Doppler velocimetry (ADV)
measurements. This study showed that when bubbles were added at
a surface loading of 10 m/hr
and a 10% recycle-rate, the flow features changed significantly
compared to bubble-free flow.
The water reaching the far wall in a horizontal flow layer at
the top of the tank turned around and
started to flow horizontally back towards the inlet baffle in a
layer underneath the top flow layer.
Only beneath the horizontal flow layers the water moved downward
in a plug-like flow towards
the collection pipes. The back and forth flow layers at top of
the tank was referred to as stratified
flow by the authors. When increasing the hydraulic loading rate
beyond a certain point, the
stratified flow pattern started to become unstable, leading to
short-circuiting of the flow towards
the outlet. The authors suggested that the stratified flow at
the top of the tank is probably due to
lower water density due to the high bubble concentration, which
does not allow the flow enough
momentum to penetrate the higher density water layer below. High
loading rate and low recycle
rate would decrease the stability of the stratified layer and
shift the flow toward short-circuiting.
In another study, Lundh et al. (2001) measured the air
concentration profile in the tank and found
a higher concentration of air in the upper part of the tank.
Based on this observation, they
approved that the stratification of the flow can be explained by
the density gradients caused by
differences in the air concentration in the tank.
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7
Hague et al. (2001) used laser Doppler velocimetry (LDV) to
study flow in a laboratory-scale
DAF tank. LDV is a non-invasive high resolution laser technique,
and was used to measure
velocity for both single phase (water) and two phase (air/water)
conditions. The authors observed
that vertical recirculation currents that were present in
single-phase flow changed when air was
added to the system. Although LDV would be more precise than ADV
for flow measurements in
the presence of bubbles, it cannot be applied to measure flow at
full-scale due to the restricted
penetrating power of the laser.
The studies reported by both Lundh et al. (2001) and Hague et
al. (2001) suggested that the
presence of bubbles changed the vertical recirculation currents
relative to flow without air
injection. As a result, the simple assumption of completely
vertical plug flow in the separation
zone would not be able to fully represent the hydrodynamics of
air-water flow.
Edzwald (2007) analyzed a simplified form of stratified flow
with two back and forth horizontal
layer, and suggested that such flow triples the clarification
separation area, and as a result, the
theoretical acceptable surface loading in the tank. This
analysis was purely theoretical, however.
It was also assumed that each additional horizontal layer below
the first is of equal importance.
Edzwald (2010) suggested that research is needed on the
hydraulic flow characteristics of the
separation zone and their incorporation into a performance model
for DAF. The experimental
work by Lundh et al. (2001), although providing very useful
information on the relationship
between the recycle rate (air fraction), hydraulic loading, and
the flow pattern in the separation
zone, was limited to a specific DAF tank depth and length to
width ratio and could not be
extended to all conditions. A detailed hydrodynamic model of the
separation zone and a better
characterization of the possible flow patterns based on the
various parameters such as air fraction
(recycle rate), surface loading rate, and bubble size, needs to
be established for optimization of
the system.
2.2. 18B18BBubble-particle attachment models
While hydraulics of the DAF system have been shown to be of
great significance, another
important phenomenon in a DAF tank would be bubble-particle
attachment, which can have an
effect on the hydraulics as well. Although a variety of
analytical models have been developed to
address the bubble-particle collision and attachment in the DAF,
they have mostly assumed a
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8
simple flow pattern in the tank independent of the operating
conditions. In addition, the models
have considered that the bubble-particle aggregation only
happens in the contact zone and have
neglected aggregations in the separation zone (Edzwald, 2010).
Bubble-particle attachment
models for DAF can be divided into two main groups (Edzwald,
2006 and 2010): turbulent
flocculation models and single collector collision models. A
summary of main collision models
and their governing equations is given in Table 2.1.
Table 2.1 Governing equations for bubble-particle aggregation
rates
Model Equations
Fukushi et al. (1995)
Rate equation for particles without previously attached
particles:
𝑑𝑛𝑃0𝑑𝑡
= −3
2𝜋𝛼𝑝𝑏 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑛𝑏𝑛𝑃0 (2.1)
Rate equation for particles with previously attached particles
from 𝑖 to 𝑁𝑏,𝑚𝑎𝑥:
𝑑𝑛𝑝,𝑖𝑑𝑡
= −3
2𝜋 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑛𝑏(𝛼𝑝𝑏,𝑖𝑛𝑝,𝑖
− 𝛼𝑝𝑏,𝑖−1𝑛𝑓,𝑖−1)
(2.2)
𝑁𝑏,𝑚𝑎𝑥 = 𝜋 (𝑑𝑝𝑑𝑏
)
2
(2.3)
Edzwald et al. (1990)
𝑛𝑝,𝑒𝑛𝑝,𝑖
= (𝑒𝑥𝑝 (−3
2𝛼𝑝𝑏𝜂𝑇𝜙𝑏𝑣𝑏𝑡𝑐𝑧 𝑑𝑏⁄ )) (2.4)
𝜂𝑇 = 𝜂𝐷 + 𝜂𝐼 + 𝜂𝑆 (2.5)
Yoon and Luttrell
(1989)
Koh and Schwartz
(2003)
𝑑𝑛𝑃𝑑𝑡
= −3
2𝜋𝛼𝑝𝑏 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑛𝑏𝑛𝑝𝑃𝑐 (2.6)
𝑃𝑐 = (1.5 +4
15𝑅𝑒𝑏
0.72)𝑑𝑝
2
𝑑𝑏2 (2.7)
Kostoglou et al. (2007)
𝑑𝑛𝑃𝑑𝑡
= −𝐾𝑛𝑏𝑛𝑝 (2.8)
𝐾 = 𝐾𝐵 + 𝐾𝐺 + 𝐾𝑇 (2.9)
𝐾𝐵 = 𝑃𝑐𝐵𝑈𝑏(𝑅𝑝 + 𝑅𝑑)2 (2.10)
𝑃𝑐𝐵 = (1.5 +4
15𝑅𝑒𝑏
0.72 + 37.5𝜑)𝑑𝑝
2
𝑑𝑏2 (2.11)
𝐾𝐺 = 𝜋𝑢𝑝(𝑅𝑝 + 𝑅𝑑)2 (2.12)
𝐾𝑇 = 3
2𝜋 (
𝜖015𝜇
)
12⁄
(𝑑𝑝 + 𝑑𝑏)3
𝑃𝑐𝑇 (2.13)
𝑃𝑐𝑇 = (1.5 +4
15𝑅𝑒0.72 + 37.5𝜑)
𝑑𝑝2
𝑑𝑏2 (2.14)
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9
The turbulent flocculation model is developed based on a
population balance in turbulent flow
(Fukushi et al., 1995) and assumes that turbulent diffusion is
the only significant mechanism in
the attachment of the particles to bubbles. The turbulent
flocculation model equations are
summarized in Table 2.1. Equation (2.1) is the rate equation
that applies to the collision of
bubbles with particles without any previously attached bubbles.
Equation (2.2) represents
collision rates between bubbles and particles containing
attached bubbles, and Equation (2.3)
considers the maximum possible number of bubbles that can attach
to a particle, where 𝑑𝑝 and
𝑑𝑏 represent particle and particle diameters, 𝑛𝑝,𝑖 and 𝑛𝑏 are
particle and bubble number
concentrations, and 𝜇 and 𝜖0 are viscosity and turbulence
dissipation rate. The authors tried to
verify their model by coupling the model with separation zone
rise velocities and comparisons to
the overall flotation with experimental data. However, their
experimental work addressed
particles of about 100-1000 µm, larger than the typical particle
size of 10-100 µm usually found
in dissolved air flotation.
The single collector collision model was first developed by
Edzwald et al. (1991) and assumed
that air bubbles collect the particles through different
transport mechanisms including Brownian
motion, interception and settling. The single collector
efficiency model can be presented by
Equations (2.4) and (2.5) where 𝜂𝑇 is single collector
efficiency and can be calculated by
summing up collision efficiencies from diffusion (𝜂𝐷),
interception ( 𝜂𝐼), and settling (𝜂𝑆)
mechanisms. 𝛼𝑝𝑏 is the attachment efficiency, and 𝜙𝑏, 𝑣𝑏 and 𝑑𝑏
are the bubble volume
concentration, bubble rise velocity and diameter, and 𝑡𝑐𝑧
represents the contact zone detention
time. The model is based on the plug flow assumption in the
contact zone and neglects the effect
of turbulent mixing.
Both modeling approaches show restrictions in terms of including
the effects of different
transport mechanisms on bubble-particle collision. They also
assume a simple flow pattern in the
tank independent of the operating conditions, and assume that
bubble-particle aggregation only
happens in the contact zone. In addition, these models do not
take the effects of the attachment
between aggregates including multiple bubbles and particles
(clustering) as shown by Leppinen
and Dalziel (2004).
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10
2.3. 19B19BPrevious attempts at CFD modelling
Previously, a variety of CFD models have been developed to study
the flow hydrodynamics of
DAF tanks. Most of these models have focused on the water-air
flow and neglected the solid
phase interaction with the bubbles. To model the two-phase flow,
Eulerian-Lagrangian and
Eulerian-Eulerian approaches have been used. An overview of the
CFD DAF models can be
observed in Table 2.2.
Hague et al. (2001) simulated the flow in a small-scale DAF
system using a three-dimensional
(3D) single-phase CFD model. The single-phase CFD model was not
able to predict the vertical
recirculation zones (stratified flow pattern) as shown by LDV
measurements. The presence of the
bubbles changed the flow importantly indicating that a
single-phase model cannot capture the
hydrodynamics of flow in a DAF tank completely.
Ta et al. (2001) built a CFD model of a full-scale tank and
evaluated the capability of their model
by ADV measurements. They used a 3D grid and applied an
Eulerian-Eulerian multiphase
approach for the air/water flow. The particles were then
introduced and tracked in the air/water
flow in a Lagrangian frame of reference. The k-epsilon
turbulence model was used for both
air/water phases as it showed better convergence behavior in
comparison with laminar or other
turbulence methods. It was assumed that particles have minor
effects on the main flow and that
their effect can be neglected. In addition, bubble-particle
collisions and the changes in the
particle size and properties were not included in the model. The
stratified flow just below the
water surface measured by ADV was not predicted by CFD. The
authors suggested that
formation of stratified flow observed from ADV could be because
of lower density of the bubbly
layer at the top.
Kwon et al. (2006) used a two phase (water-air)
Eulerian-Eulerian approach and a 3D grid to
investigate the effect of L/W (length/width ratio) on the
hydrodynamic behavior of a full-scale
DAF tank, and compared their modeling results to experimental
measurements using ADV. The
experimental validation of CFD results was limited to the bottom
region of the tank, and no flow
measurements were performed at the top bubbly layer. Considering
the inability of previous CFD
models in the prediction of the stratified flow at the top
bubbly layer (Ta et al., 2001), and
importance of this phenomenon in operation of DAF (Lundh et al.,
2000), verification of the
-
11
CFD results at this region might be of importance. The CFD model
showed that at L/W ratios of
1:1 and 2:1 no dead zone between the outlet pipe and slope
baffle was observed, but when L/W
ratio increased from 3:1 to 4:1 and 5:1, a significant dead zone
could be seen in the upper side of
the outlet part. As a result, it was suggested to design the
flotation tanks with L/W ratios smaller
than 2:1, but no elaboration or quantitative data on the effect
of presence of dead zones on
bubble or particle removal was provided.
Table 2.2 A comparison of two phase CFD models for DAF
Model Multiphase model Number of phases 2D/3D Scale
Validation
Fawcett (1997) Eulerian-Eulerian 2 2D Full-scale -
Hague et al. (2001) - 1 2D Small-
scale LDV
Hague et al. (2002) Eulerian-Eulerian 2 3D Small-
scale
LDV &
PIV
Kwon et al. (2006) Eulerian-Eulerian 2 3D Full-scale ADV
Emmanouil et al.
(2007) Eulerian-Lagrangian 2 2D Full-scale
_
Kostoglou et al. (2007) Eulerian-Eulerian 3 2D Full-scale -
Amato and Wicks
(2009) Eulerian-Eulerian 2
2D,
3D Full-scale -
Bondelind et al. (2010) Eulerian-Lagrangian 2 2D,
3D Pilot-scale -
Bondelind et al. (2012) Eulerian-Eulerian-
Lagrangian 2
2D,
3D Pilot-scale -
Strom et al. (2013) Eulerian-Euleian-
Lagrangian 3 2D - -
Bondelind et al. (2010) used an Eulerian-Lagrangian approach and
compared the ability of both
2D and 3D models to predict the experimental measurements
presented by Lundh et al. (2000).
They suggested that the distribution of the bubble layer in the
separation zone could be observed
from both their 2D and 3D simulations, although the 3D model
showed better agreement.
However, the predictions were not able to capture the horizontal
flow layers at the top of the
-
12
separation zone. As the effect of bubbles on the main flow are
important in DAF, with a
Lagrangian model, the number of bubbles must be close to reality
and a two-way coupling
should be applied to include the effects of bubbles on the
primary phase flow. This would
dramatically increase the numerical costs for the solution of
the problem. However, Bondelind et
al. (2010) did not model the total number of bubbles and used an
uncoupled solver.
The effect of bubble aggregation is not taken into account in
any of the two-phase CFD models
of DAF. The previous CFD studies in the field of bubble columns
have tried to improve the
prediction of the local recirculation zones and the gas volume
fraction in the columns by
including bubble aggregation by means of a population balance
model (Chen et al., 2004). In the
case of DAF that bubble aggregation are reported be of
significance (Hedberg et al., 1998;
Amato et al., 2001), taking bubble aggregation into account may
have an effect in better
prediction of the stratified flow.
The effect of solid particles and bubble-particle aggregation is
also rarely included in the
previous CFD models of DAF. The first study to employ the
flotation kinetic concepts in CFD
modeling was by Koh and Schwartz (2003) on a flotation cell with
external mixing, typical in
mineral processing, using a three-phase Eulerian-Eulerian
approach. The local bubble-particle
collision rates were calculated based on the local turbulent
velocities, and the size and number of
particles and bubbles obtained from CFD modeling. The flotation
effect was modeled as three
sub-steps involving collision, attachment and detachment based
on the model of Yoon and
Luttrell (1989). The only mechanism that they accounted for was
turbulent diffusion. The
governing equations of their model are shown in Table 2.1.
A study to adapt this model for CFD modeling of DAF was
performed by Kostoglou et al.
(2007) by linear addition of the collision frequencies from
settling (𝐾𝐺) and buoyancy (𝐾𝐵) to
collision frequencies from turbulence (𝐾𝑇) (Equations 2.8 and
2.9). As Equation (2.7) was
developed for a single bubble-particle collision, to account for
the presence of other bubbles, the
37.5𝜑 term was added to the buoyancy and turbulence frequency
terms, where 𝜑 was the gas
hold-up in the system (Equations 2.11 and 2.14). It was assumed
that the particle mass loading is
low, so the saturation limit of the bubbles is never reached and
the amount of attached particles is
not enough to change the bubble properties (e.g effective
density). In drinking water DAF
-
13
systems, unlike mineral processing flotation systems, the number
of solid particles is not in a
range that saturates the bubbles because of the much smaller
concentration of solids. However,
previous studies have shown that higher solid concentrations
(Lundh et al, 2001) or addition of a
coagulant to the system (Haarhoff and Edzwald, 2004) can have an
impact on the position of the
bubble layer (white milky layer). These phenomena show that the
bubble-particle aggregation
can affect the flow pattern as a result of the change in the
rise velocity of the aggregates and their
effect on the primary phase flow. As a result, the CFD model
needs to account for the effect of
the particles and the formation of the aggregates on the flow
pattern.
In addition, in the model of Kostoglou et al. (2007), it is
assumed that all the particles colliding
with the bubbles attach to them, while in reality,
bubble–particle attachment efficiency is a
function of the properties of the particle and bubbles, such as
surface charge. Han et al. (2001)
developed a collision–efficiency diagram based on the size of
particles and bubbles and the zeta
potential using trajectory analysis. Their work could show the
importance of pretreatment on
collision efficiency. Fukushi et al. (1995) reported that the
attachment efficiency of 0.4 provided
agreement between their modeling and experimental results for
aluminum dosage of 5 mg/L and
pH of 6.7. The importance of pre-treatment (ionic strength,
contact angle and particle size) was
also investigated by Hewitt et al. (1993).
Bondelind et al. (2012) attempted to include the effects of the
aggregates on the flow pattern, but
limited their Eulerian model to water and aggregate phases to
reduce the computational cost. In
addition, the developed model was only applied to model the
contact zone.
Strom et al. (2013) developed a hybrid scheme for modeling
general three-phase flow conditions
with bubbles, particles and aggregate formation. An
Eulerian-Eulerian model was applied for
water (primary phase) and aggregates, whereas bubbles were
tracked in a Lagrangian frame of
reference. The interaction of the bubbles with the primary phase
was modeled through a
momentum source term. Particles were modeled as passive scalars
and their effect on the flow
pattern was neglected. The developed model was only applied in a
rectangular geometry, and
was not utilized to study a DAF unit, and no verification of the
modeling results was provided.
The CFD models including particles and aggregates are based on
multiple simplifying
assumptions and are not applied to evaluate the performance of a
complete DAF unit; there is
-
14
also in general a lack of validation when the solid and
aggregate phases are present in the system
(Edzwald, 2010).
2.4. Research gaps
A better characterization of the stratified flow under various
conditions and its effect on bubble-
particle aggregation and DAF performance is needed. Previous CFD
models have not
represented conditions under which the stratified flow pattern
in the DAF tanks occur (Hague et
al., 2001, Ta et al., 2001, Bondelind et al., 2010). The
experimental work by Lundh et al. (2000),
although providing very useful information on the relationship
between the recycle rate,
hydraulic loading and the flow pattern in the separation zone,
was limited to specific DAF tank
geometry in the absence of the particles. The effect of bubble
aggregation is critical but is not
modeled. In addition, the effects of flow pattern on
bubble-particle aggregation and particle
removal are not quantified in any of the previous models.
The previous models accounting for bubble-particle aggregation
do not take the effects of the
aggregates and particles on the flow pattern into account in a
DAF unit, and do not evaluate the
effect of stratified flow in the separation zone on bubble and
particle removal. There is also a
general lack of validation when the solid phase is present in
the system (Edzwald, 2010).
The effects of bubble aggregation, solid particles, and
bubble-particle aggregation need to be
included in DAF models for more accurate representation of the
flow and DAF performance.
The developed model should be applied to characterize the
effects of stratified flow, air fraction
and bubble size on bubble and particle removal under different
conditions. The model
predictions also need to be validated in presence of the solid
particles. Once validated, the
developed model can be used as an optimization tool for DAF
under different conditions.
2.5. 21B21BReferences
Amato, T., Edzwald, J.K., Tobiason, J.E., Dahlquist, J.,
Hedberg, T., 2001. An integrated
approach to dissolved air flotation. Water Science and
Technology, 43(8), 19-26.
Amato, T., Wicks, J., 2009. Dissolved air flotation and
potential clarified water quality based on
computational fluid dynamics modeling. Journal of Water Supply:
Research and Technology-
AQUA, 58(1), 65-73.
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15
Bondelind, M., Sasic, S., Kostoglou, M., Bergdahl, L., Thomas,
J.R.P., 2010. Single and two-
phase numerical models of dissolved air flotation: comparison of
2D and 3D simulations.
Colloids and Surfaces A: Physicochemical and Engineering
Aspects, 365(1-3), 137-144.
Bondelind, M., Ström, H., Sasic, S. and Bergdahl, L., 2012.
Eulerian modelling of the formation
and flow of aggregates in dissolved air flotation. The 15th
International Conference on Fluid
Flow Technologies, Budapest, Hungary, September 4-7.
Chen, P., Sanyal, J., Dudukovic, M.P., 2004. CFD modeling of
bubble columns flows:
implementation of population balance. Chemical Engineering
Science, 59(22), 5201-5207.
Crittenden, J.C., Trussell, R.R., Hand, D.W., Howe, K.J.,
Tchobanoglous, G., 2005. Water
treatment: Principles and Design. John Wiley & Sons, Inc.,
Hoboken, New Jersey.
Edzwald, J.K., Malley, J.P, Yu, C., 1991. A conceptual model for
dissolved air flotation in water
treatment, Water Supply, 9(1), 141-150.
Edzwald, J.K., 1995. Principles and applications of dissolved
air flotation. Water Science
Technology,31(3),1−23.
Edzwald, J.K., Tobiasen, J.E., Amato, T., Maggi, L.J., 1999.
Integrating high rate dissolved air
flotation technology into plant design. Journal of American
Water Work Associations, 91(12),
41-53.
Edzwald, J.K., 2007. Developments of high rate dissolved air
flotation for drinking water
treatment. Journal of Water Supply: Research and
Technology-Aqua, 56 (6-7), 399-409.
Edzwald, K., 2010. Dissolved air flotation and me. Water
Research, 44(7), 2077-2106.
Emmanouil, V., Skaperdas, E.P., Karapantsios, T.D. and Matis,
K.A., 2007. Two-phase
simulations of an off-nominally operating dissolved-air
flotation tank, International Journal of
Environment and pollution, 30(2), 213–230.
Fawcett, N.S.J, 1997. The hydraulics of flotation tanks,
computational modeling. Proceedings of
the International conference charted institute of Water and
Environmental Management, London,
51-71.
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Fukushi, K., Tambo, N., Matsui, Y., 1995. A kinetic model for
dissolved air flotation in water
and wastewater treatment. Water Science and Technology, 31(3),
37-47.
Haarhoff, J., 2008. Dissolved air flotation: progress and
prospects for drinking water treatment.
Journal of Water Supply: Research and Technology-AQUA, 57(8),
555-567.
Haarhoff, J., Van Vuuren, L., 1995. Design parameters for
dissolved air flotation in South
Africa. Water Science and Technology, 31(3-4), 203-212.
Haarhoff, J., Edzwald, J.K., 2004. Dissolved air flotation
modelling: insights and shortcomings.
Journal of Water Supply: Research and Technology-AQUA, 53(3),
127-150.
Hague, J., Ta, C.T., Biggs, M.J, Sattary, J.A., 2001. Small
scale model for CFD validation in
DAF application. Water Science and Technology, 43(8),
167-173.
Han, M., Kim, W., Dockko, S., 2001. Collision efficiency factor
of bubble and particle in DAF:
theory and experimental verification. Water Science and
Technology, 43(8), 139-144.
Hedberg, T., Dahliquist, J., Karlsson, D., Sorman, L.O., 1998.
Development of an air removal
system for dissolved air flotation. Water Science and
Technology, 37(9), 81-88.
Hewitt, D., Fornasiero, D., Rulston, J., 1994. Bubble-particle
attachment efficiency. Mineral
Engineering, 7(5-6), 657-665.
Koh, P.T.L, Schwarz, M.P., 2003. CFD modeling of bubble-particle
collision rates and
efficiencies in a flotation cell. Mineral Engineering, 16 (11),
1055-1059.
Koh, P.T.L, Schwarz, M.P., 2008. Modeling attachment rates of
multi-sized bubbles with
particles in a flotation cell. Mineral Engineering, 21 (12-14),
989-993.
Kostoglou, M., Karapantsios, T.D., Matis, K.A., 2007. CFD model
for the design of large scale
flotation tanks for water and wastewater treatment. Industrial
Engineering and Chemistry
Research, 46(20), 6590-6599.
Kwon, S.B., Lee, S.J, Ahn, H.W, Wang, C.K., 2006. Examining the
effect of length/width ratio
on the hydrodynamic behavior in a DAF system using CFD and ADV
techniques. Water Science
and Technology, 53(7), 141-149.
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17
Leppinen, D.M., Dalziel, S.B., 2004. Bubble size distribution in
dissolved air flotation tanks.
Journal of Water Supply: Research and Technology-AQUA, 53(8),
531-543.
Lundh, M., Jonsson, L., Dahlquist, J., 2000. Experimental
studies of the fluid dynamics in the
separation zone in dissolved air flotation. Water Research, 34
(1), 21-30.
Lundh, M., Jonsson, L., Dahlquist, J., 2001. The flow structure
in the separation zone of a DAF
pilot plant and the relation to the bubble concentration. Water
Science and Technology, 43(8),
185-194.
Strom, H., Bondelind, M., Sasic, S., 2013. A novel hybrid scheme
for making feasible numerical
investigations of industrial three-phase flows with aggregation.
Industrial Engineering and
Chemistry Research, 52(29),10022−10027.
Ta, C.T., Beckley, J., Eades, A., 2001. A multiphase CFD model
of DAF process. Water Science
and Technology, 43(8), 153-157.
Yoon, R.H., Luttrell, G.H., 1989. The effect of bubble size on
fine particle flotation. Mineral
processing and Extractive Metallurgy Review, 5(1-4),
101-122.
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18
3. 7B7BImportance of flow stratification and bubble aggregation
in the separation
zone of a dissolved air flotation tank 0F0F1
ABSTRACT
The importance of horizontal flow patterns and bubble
aggregation on the ability of dissolved air
flotation (DAF) systems to improve bubble removal during
drinking water treatment were
explored using computational fluid dynamics (CFD) modeling. Both
analytical and CFD
analyses demonstrated benefits to horizontal flow. Two
dimensional CFD modeling of a DAF
system showed that increasing the amount of air in the system
improved the bubble removal and
generated a beneficial stratified horizontal flow pattern.
Loading rates beyond a critical level
disrupted the horizontal flow pattern, leading to significantly
lower bubble removal. The results
also demonstrated that including the effects of bubble
aggregation in CFD modeling of DAF
systems is an essential component towards achieving realistic
modeling results.
Keywords dissolved air flotation, bubble, stratified flow,
computational fluid dynamics, CFD,
DAF
3.1. 22B22BIntroduction
Dissolved air flotation (DAF) is growing in popularity as a
method of drinking water treatment
(Haarhoff, 2008). Early models of flow in the separation zone of
DAF systems assumed vertical
plug flow from the surface to the underdrain system. Based on
this assumption, the maximum
surface loading rate to avoid bubble washout was calculated to
be in the order of 5-10 m/hr
(Haarhoff and Vuuren, 1995). More recent pilot plant testing
demonstrated that higher loading
rates were possible, with excellent particle removal efficiency
at rates as high as 41 m/hr, but
with increased bubble carryover to downstream processes (Edzwald
et al., 1999). Based on the
experimental results of Lundh et al. (2000 and 2001), Haarhoff
and Edzwald (2004) and Edzwald
(2007) attributed the concept of stratified flow to explain the
higher loading rates observed in
practice. Stratified flow was explained as water travelling in a
horizontal flow layer along the top
1 ThisChapterispublishedas“B.Laghomi,Y.Lawryshyn, R. Hofmann,
2012. Effect of stratified flow and bubble
aggregation in the separation zone of a dissolved air flotation
tank. Water Research, 46 (14), 4468-76”.
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19
of the tank to the far end, and then traveling back towards the
front in a second horizontal layer
below the first layer. However, based on the study by Lundh et
al. (2000 and 2001), the stratified
flow was only present at certain flow conditions, and the second
horizontal layer was disrupted
as the loading rate increased or as the air fraction decreased,
leading to short-circuiting of the
flow. Several studies using computational fluid dynamics (CFD)
models of DAF systems have
also predicted stratified flow, however, they did not identify
limiting conditions required to
create the desirable stratified flow conditions, and did not
predict the quantitative impact of the
stratification on bubble removal (Ta et al., 2001; Hague et al.
2001; Bondelind et al., 2010).
While flow stratification is one important phenomenon that
should be better understood to
improve bubble removal efficiency in DAF systems (and hence,
implicitly, particle removal),
bubble aggregation is another factor that may be associated with
better bubble removal.
Empirical studies by Hedberg et al. (1998) and Amato et al.
(2001) suggested that increasing
bubble aggregation in the separation zone by means of adding
internal plates (such as lamella
plates) can improve removal of free bubbles in the separation
zone by producing larger bubbles
that have a larger rise velocity. Leppinen and Dalziel (2004)
also reported that large bubble
aggregates (clusters) in the separation zone improved removal
efficiency. Previous CFD models
of DAF, such as those reported by Kwon et al. (2006) and Amato
and Wicks (2009 and 2010),
were based on the assumption of a uniform bubble size and
neglected bubble aggregation. CFD
studies from other applications have included bubble coalescence
and break-up models by using
a population balance algorithm (Chen et al., 2004), and it is
hypothesized that implementation of
bubble aggregation in a CFD model of a dissolved air flotation
system would make the model
more accurate.
In this work, a simple theoretical model was first developed to
understand the effect of horizontal
flow layers on bubble removal; with and without bubble
aggregation. Then, CFD was used to
predict conditions under which the flow stratification pattern
happens and its effect on bubble
removal. The model was then enhanced with a population balance
model to account for bubble
aggregation and break-up. The enhanced model was used to
understand how changes in air
fraction and flow rate affect bubble removal by affecting bubble
aggregation and creating a
stratified flow. It was expected that the optimal air fraction
and maximum flow rate could be
determined for a prototype DAF system based on the developed
model.
-
20
Note that the effects of solid particles and the presence of a
coagulant on bubble aggregation
were not included in this chapter.
3.2. 23BMethodology
The geometric dimensions of the pilot DAF tank used by Lundh et
al. (2001) were chosen for
modeling, so that obtained CFD results could be compared
qualitatively to their observations.
The configuration of the flow domain modeled in CFD is shown in
Figure 3.1. A two-
dimensional model, capable of representing the flow
characteristics in the separation zone
(Bondelind et al., 2010), was used to reduce the computational
demand. The two dimensional
model did not allow for complete modeling of the recycle
air/water injection system, so a pre-
blended mixture of air/water was introduced into the contact
zone through the water flow inlet.
All of the simulations were performed for a water temperature of
20°C. The governing equations
and details of the modeling set-up can be found in Appendix
A.
Figure 3.1 Configuration of the modeled DAF system.
For the case with no bubble aggregation, a uniform bubble size
of 80 µm was used (average
bubble size in the contact zone is reported to be in the range
of 40-80 µm; Edzwald, 2010). For
models that included bubble aggregation and break-up, a discrete
population balance (fixed
pivot) model was used. The governing equations and details of
the applied population balance
model can be found in Appendix A.
-
21
Two different initial inlet bubble sizes (i.e. at the inlet to
the contact zone) of 20 and 80 µm
were tested in the presence of bubble aggregation based on the
lower and upper limits of bubble
sizes in the contact zone reported in Edzwald (2010). These
initial bubble sizes were then
allowed to grow in the model as the bubbles aggregated. The
bubble size distribution was
divided into four discrete groups (bins) for each inlet bubble
size, as shown in Table 3.1.
Generally, a greater number of bins would provide a more precise
representation of the bubble
size distribution, but the effect of different bin sizes and
numbers of bins were not evaluated in
this study due to the high numerical cost.
Table 3.1 Bubble size groups for each inlet bubble size
Bubble size groups (bins) Group 1 (µm) Group 2 (µm) Group 3 (µm)
Group 4 (µm)
Inlet bubble size 20 µm 20 40 80 160
Inlet bubble size 80 µm 80 160 320 640
3.3. 24B24BA conceptual model for bubble removal in the
separation zone
A study by Edzwald (2007) commented on the importance of
horizontal flow layers on bubble
removal. Edzwald (2007), however, assumed that each additional
horizontal layer is of equal
importance in improving bubble removal (i.e. the presence of two
horizontal layers triples the
maximum loading rate), and did not evaluate the importance of
bubble aggregation. In this
section, a similar conceptual model of flow in the separation
zone is followed, but bubble
removal from each horizontal layer is evaluated independently by
also looking at the effects of
bubble aggregation. This simple model will show that in the
absence of bubble aggregation,
bubble removal only occurs from the first layer. In the presence
of bubble aggregation, the
addition of multiple layers will be demonstrated to be
beneficial, but with diminishing returns for
each subsequent horizontal layer.
3.3.1. 45B45BBubble removal model in the absence of bubble
aggregation
The importance of the horizontal flow layers is first assessed,
starting with a simplistic scenario
with two perfect plug flow horizontal back-and-forth layers as
shown in Figure 3.2.
-
22
Figure 3.2 The conceptualized flow models for separation zone,
reverse flow on top and plug
flow at bottom
The bubble removal efficiency of the top layer (with length 𝐿
and thickness of 𝐻) for a bubble
rise velocity of 𝑉𝑏 can be calculated based on Hazen theory
using a similar approach to
calculating particle removal in sedimentation basins (Crittenden
et al., 2005):
𝐵𝑢𝑏𝑏𝑙𝑒 𝑟𝑒𝑚𝑜𝑣𝑎𝑙 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = (𝐿
𝑈) (
𝑉𝑏𝐻
) = (𝐿
𝑄 (𝑤𝐻)⁄) (
𝑉𝑏𝐻
) = (𝐿𝑤
𝑄) 𝑉𝑏 =
𝑉𝑏𝑉𝑠
(3.1)
where 𝑈 is the horizontal velocity, 𝑤 is the tank width, 𝑄 is
the flow rate and 𝑉𝑠 is the surface
loading rate.
For any bubble, the vertical travel in the first layer is (𝐿
𝑈) (𝑉𝑏). If this vertical travel is not
enough to reach the surface, then the bubble will not be removed
and will descend to the second
layer. If the same bubble reaches the top of the second layer
and re-enters the first layer, its
horizontal travel in the first layer will be smaller than 𝐿 this
time: so its vertical travel will be
even smaller than (𝐿
𝑈) (𝑉𝑏). Thus, the bubble cannot reach the surface this time
either. Based on
this theory, bubbles can only be removed from the top horizontal
layer in the absence of bubble-
bubble aggregation, and the formation of a second horizontal
layer is not beneficial. This theory
is based on the assumption of a uniform bubble size, uniform
horizontal velocity and uniform
-
23
mixing of bubbles in each layer. In addition, the effects of
turbulence and bubble-bubble
aggregation are neglected.
3.3.2. 46B46BBubble removal model in the presence of bubble
aggregation
The effect of bubble aggregation on bubble removal is now
assessed for cases of both perfect
plug flow (no horizontal flow layers), and the conceptual model
of Figure 3.2. In the presence of
bubble aggregation, assuming second order rate kinetics for
bubble-bubble collision, the
population balance for original bubble size can be written
as:
𝑑𝑛𝑏0𝑑𝑡
= −𝑘00𝑛𝑏0𝑛𝑏0 (3.2)
where 𝑛𝑏0 is the number concentration of the original bubble
size per unit volume, and 𝑘𝑖𝑗 is the
attachment frequency between the bubble sizes of groups 𝑖 and 𝑗.
The larger bubbles formed
(group 1) can coalesce with smaller bubbles from group 0, or the
bubbles with the same size in
group 1. Therefore, the population balance for the bubbles in
group 1, with the bubble
concentration of 𝑛𝑏1, can be written as:
𝑑𝑛𝑏1𝑑𝑡
=1
2𝑘00𝑛𝑏0𝑛𝑏0 − 𝑘01𝑛𝑏0𝑛𝑏1 − 𝑘01𝑛𝑏1𝑛𝑏1 (3.3)
Following the same pattern, the above equation can be extended
for n groups of bubble sizes. An
analytical solution that incorporates 𝑛 > 2 population
balance equations and realistic
(complicated) fluid mechanics is not feasible. Instead, a
simplified conceptual model is presented
to highlight the important theoretical aspects.
If two bubbles, with the same diameter, ∅𝑏0, attach together,
the diameter of the formed bubble
can be calculated as:
∅𝑏1 = 213∅𝑏0 (3.4)
and therefore the bubble rise velocity after attachment can be
calculated as:
𝑉𝑏1 = 223𝑉𝑏0 = 1.587𝑉𝑏0 (3.5)
-
24
where 𝑉𝑏0 is the rise velocity of the original bubbles.
For a DAF system with complete vertical plug flow throughout the
separation zone (i.e. no
horizontal layers), the total number of bubbles removed can be
calculated as the number of
bubbles in each of the size groups that have a rise velocity
greater than the loading rates. For the
plug flow case, if 𝑉𝑏0 < 𝑉𝑠 < 1.587 𝑉𝑏0, only bubbles that
were attached to other bubbles would
be removed. The ratio of bubbles converted to larger bubbles
(and removed in this case), α, can
be derived by integrating Equation (3.2):
α = 1 −𝑛𝑏0,𝑜𝑢𝑡
𝑛𝑏0= (1 −
1
1 + 𝑘00𝜏𝑛𝑏0) (3.6)
where 𝜏 = (2𝐻+𝑠
𝑉𝑠−𝑉𝑏0) is the bubble residence time in the separation zone. For
plug flow, the
residence time can be calculated as 𝜏 = (2𝐻+𝑠
𝑉𝑠−𝑉𝑏0), where 𝐻 and 𝑠 are the thicknesses of the
horizontal and vertical plug flow layers as shown in Figure 3.2.
This simple model shows that
even for a plug flow system, bubble-bubble attachment can add to
bubble removal and, as the
bubble-bubble contact time and bubble concentration increase,
more bubble removal is expected.
In the case where horizontal flow segments and bubble
aggregation both exist, the ratio of
bubbles that are converted to larger bubbles, 𝛽, can be
calculated using Equation (3.7), but the
residence time for this case will be estimated differently as 𝜏
= (𝐿
𝑈). If bubble aggregation occurs
at a distance 𝛾𝐿 from the inlet (0 < 𝛾 < 1), the total
vertical travel distance, Y, of a bubble in the
first layer can be derived by adding its vertical travel before
and after attachment. Applying the
same principle as used to derive Equation (3.1), the vertical
travel distance becomes,
𝑌 =𝛾𝐿
𝑈𝑉𝑏0 +
(1 − 𝛾)𝐿
𝑈𝑉𝑏1 =
𝛾𝐿
𝑈𝑉𝑏0 +
(1 − 𝛾)𝐿
𝑈1.587𝑉𝑏0 = (1.587 − 0.587𝛾)
𝐿
𝑈𝑉𝑏0 (3.7)
and the average vertical travel for all of the bubbles can be
calculated by averaging 𝑌 for all
values of between 0 and 1 to get 1.293𝐿
𝑈𝑉𝑏0. As a result, if the total number of bubbles is 𝑛𝑏0,
the number of converted bubbles will be 𝛽𝑛𝑏0, from which a
fraction of 1.293(𝐿
𝑈)(
𝑉𝑏0
𝑡) or
1.293(𝑉𝑏0
𝑉𝑠) can be removed based on the calculated average vertical
travel. Therefore, the
-
25
number of original bubbles removed after coalescence can be
estimated as 1.293(𝑉𝑏0
𝑉𝑠)𝛽𝑛𝑏0.
From the number of bubbles remaining at their original size,
equal to(1 − 𝛽)𝑛𝑏0, a fraction of
𝑉𝑏0
𝑉𝑠 can be removed based on Equation (3.1). As a result, the
total bubble removal can be
calculated as follows:
𝐵𝑢𝑏𝑏𝑙𝑒 𝑟𝑒𝑚𝑜𝑣𝑎𝑙 =(1 − 𝛽)
𝑉𝑏0𝑉𝑠
𝑛𝑏0 + 1.293𝛽𝑉𝑏0𝑉𝑠
𝑛𝑏0
𝑛𝑏0= (1 − 𝛽)
𝑉𝑏0𝑉𝑠
+ 1.293𝛽𝑉𝑏0𝑉𝑠
= (1 + 0.293𝛽)𝑉𝑏0𝑉𝑠
(3.8)
The removal ratio from Equation (3.8) is larger than the removal
ratio without bubble
aggregation shown in Equation (3.1).
In addition, there will be a chance for the removal of bubbles
that aggregate and form larger
bubbles in the second horizontal layer. Assuming that
bubble-bubble attachment occurs at a
distance 𝛾𝐿 from the right wall, the total vertical travel, 𝑌𝑡,
of a bubble can be calculated as the
sum of the vertical travel in the second layer before and after
attachment, and the vertical travel
in the first layer:
𝑌𝑡 = (𝛾𝐿
𝑈) 𝑉𝑏 + (
(1 − 𝛾)𝐿
𝑈) (1.587𝑉𝑏) + (
𝐿
𝑈) 1.587 𝑉𝑏 = (
𝐿
𝑈) 𝑉𝑏(3.174 − 0.587𝛾) (3.9)
As a result, for all 𝛾 values where the total vertical travel as
calculated in Equation (3.9) is larger
than the thickness of the back and forth horizontal layers (2𝐻
as shown in Figure 3.2), i.e. for
2𝐻 < (𝐿
𝑈) 𝑉𝑏(3.174 − 0. 587𝛾), the bubbles will be able to reach the
surface and be removed.
The addition of a second horizontal flow layer can therefore be
of benefit for additional bubble
removal in the presence of bubble aggregation, unlike the case
where bubble aggregation was
absent. In general, it can be shown based on Equation (3.6) that
increasing the residence time can
increase bubble aggregation (the denominator in Equation (3.6)
becomes larger, and bubble
aggregation becomes larger as a result) leading to the formation
of larger bubbles with greater
rise velocities that are removed more easily. Multiple
horizontal flow layers can help to achieve
this objective by increasing the residence time and
bubble-bubble contact. However, it is
-
26
expected that as the concentration of the bubbles decreases
deeper in the tank, the possibility of
bubble-bubble contact becomes less (the denominator in Equation
(3.6) becomes smaller) and
additional horizontal flow layers will have a less important
effect on bubble removal.
The described theory was used to conceptually show the
importance of bubble aggregation and
horizontal stratification of flow on bubble removal. The theory
showed that under idealized flow
conditions, bubble aggregation, in general, can help to improve
bubble removal, and is of
additional benefit when multiple horizontal flow layers are
present. In practice, however, flows
are not perfectly stratified and there is an important coupling
between the bubble aggregation and
flow pattern. A CFD model can be used to estimate under what
conditions stratified horizontal
flow may be present in a typical DAF system, and characterize
its effects on bubble removal in
the presence of bubble aggregation.
3.4. 25B25BResults and Discussions
3.4.1. 47B47BEvaluation of the CFD model in the absence of
bubble aggregation
The effect of volume air fraction and loading rate on flow
pattern and bubble removal was first
evaluated in the absence of bubble aggregation. The main
objective of this step was to evaluate
whether a CFD model that neglects bubble aggregation would be
able to describe realistic flow
patterns in a DAF separation zone, and would therefore be useful
for characterizing DAF
performance. Figure 3.3 shows the CFD generated velocity vectors
for increasing air fraction in
the absence of bubble aggregation at a loading rate of 11.8 m/hr
(flow rate of 10 m3/hr). The
chosen loading (flow) rates were based on those of Lundh et al.
(2001), and similar to their
study, only velocity vectors in the range of (0-0.03 m/s) are
shown to allow comparison with
their results. As can be seen, a top horizontal flow layer was
present even without air in the
system. As air was added, however, a back flow layer (travelling
from right to left in the figure)
was formed underneath the top layer, returning the water toward
the baffle. The horizontal back
flow continued to be present when the air fraction was increased
to 0.02. At a loading rate of
23.6 m/hr (flow rate of 20 m3/hr), as shown in Figure 3.4, the
flow pattern did not change
significantly as the air fraction increased. This observation,
however, was not in agreement with
the results of Lundh et al. (2001). Experimentally, Lundh et al.
(2001) observed that at this
loading rate the flow pattern shifted from short-circuiting flow
to stratified flow as the air
fraction increased from 0.005 to 0.01. The discrepancy between
the results of Lundh et al. (2001)
-
27
and model predictions at this loading rate may be related to the
formation of bubble aggregates
that was not accounted for in the CFD model.
Figure 3.5 plots bubble removal as a function of air fraction at
different loading rates, based on
the CFD model (with no bubble aggregation) and the theoretical
approach (i.e. Equation (3.1)).
The results demonstrate a good agreement between CFD and the
theoretical approach for both
assumed bubble sizes. In addition, CFD results confirm that an
increase in the loading rate
reduces the bubble removal efficiency as suggested by Equation
(3.1).
Figure 3.3 Velocity vectors (0-0.03 m/s), a) Single phase, b)
Air fraction 0.005, c) Air fraction
0.02. Loading rate 11.8 m/hr, bubble size = 80 µm.
Figure 3.4 Velocity vectors (0-0.03 m/s), a) Air fraction 0.005,
b) Air fraction 0.01, c) Air
fraction 0.02. Loading rate 23.6 m/hr, bubble size = 80 µm.
-
28
In the absence of bubble aggregation, bubble removal showed only
a weak dependence on air
fraction. In addition, no relationship between the presence of a
second horizontal layer (reverse
flow) and bubble removal was observed in the absence of bubble
aggregation. The theoretical
model in Equation (3.6) suggested that the reverse flow layer
may become important when
bubbles collide and coalesce. Bubble aggregation therefore needs
to be modeled for more
realistic results.
0
0.2
0.4
0.6
0.8
1
0.004 0.006 0.008 0.01
Bu
bb
le r
em
ova
l
Air fraction
11.8 m/hr-CFD no aggregation
23.6m/hr- CFD no aggregation
47.2m/hr-CFD no aggregation
11.8m/hr-Theoretical
23.6m/hr-Theoretical
47.2m/hr-Theoretical
Figure 3.5 Effect of air inlet fraction on bubble removal at
different loading rates. Bubble size
80 µm.
3.4.2. 48B48BEffects of operating conditions on bubble removal
in the presence of bubble aggregation
The theory demonstrated that, in principle, the formation of
horizontal flow layers in the
separation zone would help to improve bubble removal in a real
DAF system, and that bubble
aggregation would enhance the beneficial effects of the
horizontal flow layers. The CFD model
was used to explore these phenomena under more realistic flow
conditions by including a bubble
population balance model that allowed bubble aggregates to form.
The bubble removal rates
calculated at different air fractions and loading rates from CFD
modeling accounting for bubble
aggregation and break-up are shown in Figure 3.6.
-
29
0
0.2
0.4
0.6
0.8
1
0.004 0.006 0.008 0.01
Bu
bb
le r
em
ova
l
Air fraction
a) Inlet bubble size 80 µm
11.8 m/hr
23.6 m/hr
47.2 m/hr
0
0.2
0.4
0.6
0.8
1
0.01 0.02 0.03 0.04 0.05
Bu
bb
le r
em
ova
l
Air fraction
b) Inlet bubble size 20 µm
11.8 m/hr
23.6 m/hr
47.2 m/hr
Figure 3.6 Effect of air inlet fraction on bubble removal in
presence of bubble aggregation at
different loading rates, a) Inlet bubble size 80 µm, b) Inlet
bubble size 20 µm.
The CFD results in Figure 3.6 showed that bubble removal
increased with increasing air fraction
in the system. This is because a larger air fraction increases
bubble aggregation and, as a result,
forms larger bubbles that have larger rise velocities and can be
more easily removed.
In addition, similar to the case with no bubble aggregation,
increasing the loading rate reduced
bubble removal. For an inlet bubble size of 80 µm, perfect
removal was observed for loading
rates up to 23.6 m/hr at an air fraction of 0.008, and for
loading rates up to 47.2 m/hr at an air
fraction of 0.01. For a smaller inlet bubble size of 20 µm and
an air fraction of 0.035, perfect
removal could be observed at loading rates up to 23.6 m/hr.
An important factor that may be associated with the bubble
removal is the presence of reverse
(stratified) flow. The CFD results demonstrated that this
reverse flow is strengthened with
increasing air fraction. This is demonstrated in Figure 3.7 and
Figure 3.8, which show the
velocity vectors at different air fractions for a loading rate
of 23.6 m/hr and inlet bubble sizes of
80 µm and 20 µm, respectively. For both initial bubble sizes,
there was little observed stratified
flow at the lowest air fractions, but the stratified flow became
more evident at an air fraction of
about 0.01 (for the 80 µm bubbles) and 0.035 (for the 20 µm
bubbles). These results indicate that
a certain minimum air fraction is required before flow
stratification can be observed and is in
agreement with the experimental results of Lundh et al. (2001).
The CFD model also suggests
that as the initial bubble sizes increase, the minimum air
fraction that must be applied to create
the horizontal stratified flow is lower. This suggests that the
introduction of larger bubbles, for
-
30
the same total amount of air, might help to encourage horizontal
stratified flow, thereby
improving the efficiency of the separation zone of a DAF
tank.
Figure 3.7 Velocity vectors (0-0.03 m/s) in the presence of
bubble aggregation, a) Air fraction
0.005, b) Air fraction 0.008, c) Air fraction 0.01. Loading rate
23.6 m/hr, inlet bubble size 80
µm.
Figure 3.8 Velocity vectors (0-0.05 m/s) in the presence of
bubble aggregation, a) Air fraction
0.01, b) Air fraction 0.035, c) Air fraction 0.05. Loading rate
23.6 m/hr, inlet bubble size = 20
µm.
The observation that an increasing air fraction helps to
encourage horizontal stratified flow was
explained by Lundh et al. (2001). Their measurements of the air
concentration at different depths
led them to propose that the reverse flow was due to a lower
density top layer with a higher air
fraction that does not have enough momentum to push through the
higher density lower layer.
-
31
The air fractions calculated from the CFD model show a
distribution of air that is in relatively
good agreement with the experimental results of Lundh et al.
(2001) (Figure 3.9). However, the
CFD model slightly over predicts the air concentrations shown by
Lundh et al. (2001) for the
loading rate of 11.8 m/hr. This may be due to a discrepancy
between the applied inlet bubble size
based on Edzwald (2010) with the bubble size distribution in the
pilot system used by Lundh et
al. (2001).
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8
He
igh
t (m
)
Air content (mL air/L water)
CFD-11.8 m/hr
CFD-24m/hr
Lundh et al.(2001)-11.8m/hr
Lundh et al.(2001)-24m/hr
Figure 3.9 Comparison of air content in the separation zone from
Lundh et al. (2001) and the
present model. Inlet air fraction 0.005 (air content at 1.35 m
from left wall).
While a larger a