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)

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

iii

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.

iv

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.

v

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

vi

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

vii

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

viii

C.2 CFD bubble distribution and collision frequency ........................................................ 102

ix

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

x

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

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

xii

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

1

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

2

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)

3

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.

4

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.

5

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.

6

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.

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

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)

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).

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.

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.

16

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.

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.

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”.

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