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Extension and further validation of a 3D two-phase
flow model for flow, transport and mass transfer in
sewer systems
vorgelegt von
Master of Science
Abhinav Dixit
an der Fakultät VI - Planen Bauen Umwelt
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktorin der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
Promotionsausschuss:
Vorsitzende: Prof. Dr. habil. Irina Engelhardt
Gutachter: Prof. Dr.-Ing. Reinhard Hinkelmann
Gutachterin: Prof. Dr.-Ing. Katharina Teuber
Gutachter: Prof. Dr.-Ing. Ilhan Özgen-Xian
Gutachter: Prof. Dr.-Ing. Frank Molkenthin
Tag der wissenschaftlichen Aussprache: 30. Oktober 2023
Berlin 2024
i
“Water, the Hub of Life. Water is its mater and matrix, mother and medium.
Water is the most extraordinary substance! Practically all its properties are
anomalous, which enabled life to use it as building material for its machinery."
- Albert Szent-Györgyi
ii
Preface
I would like to express my heartfelt gratitude to all those who have contributed to the successful
completion of my PhD thesis. This research was conducted at the Chair of Water Resources
Management and Modeling of Hydrosystems at TU Berlin, as part of the DFG funded Research Training
Group "Urban Water Interfaces" (UWI). First and foremost, I am deeply grateful to my supervisor,
Reinhard (Phillip) Hinkelmann, for his invaluable guidance, expertise, and unwavering support
throughout this journey. Your mentorship since we met in 2014 has been instrumental in shaping my
research and academic growth. I would also thank Katharina firstly as a colleague and later for her
supervision and support throughout this research.
I would like to extend my sincere appreciation to Ralf Duda for his technical assistance and his
exceptional kindness in every aspect. Your expertise and willingness to help have been truly invaluable,
and I am grateful for the collaborative atmosphere you fostered. I would also like to acknowledge
Tosca Piotrowski for her administrative support, which has greatly facilitated the smooth progress of
my research. Your efficient and dedicated assistance has been greatly appreciated.
Special thanks go to the student assistants who have been an essential part of my research. Nicholas
R. Bowsher, your support in the beginning stages of my thesis laid a strong foundation, and Mary Lidya,
your contributions towards the end of the thesis were invaluable. I am grateful for your hard work and
dedication.
I am indebted to Micaela Pacheco Fernández, a valued project partner, for her fruitful
collaborations, which have enriched my research and provided valuable insights. I would like to express
my gratitude to my colleagues and friends: Vahid Sobhi Gollo, Christian Marx, Fatima, Yangwei,
Lennart, and Franziska. Your camaraderie, stimulating discussions, and support have made this
academic journey more enjoyable and rewarding.
I would like to offer my deepest appreciation to my parents and my sister Irshita, for their
unwavering support, encouragement, and belief in me. Your love and encouragement have been a
constant source of strength. Lastly, I want to express my profound gratitude to my wife, Sonali, for her
unending support, understanding, and encouragement. Your love and patience have been my anchor
throughout this challenging endeavor. Thank you for standing by my side and believing in me.
To all those mentioned above, and to any others who have contributed in any way, large or small,
I am truly grateful. Your support has played a significant role in the successful completion of my PhD
thesis.
Berlin, February 12, 2024
iii
Acknowledgement
This contribution was developed as part of project S2 titled “Extension and further validation of a
3D two-phase flow model for flow, transport and mass transfer in sewer systems within the
interdisciplinary Research Training Group "Urban Water Interfaces" (UWI, RTG 2032/1+2), funded by
the Deutsche Forschungsgemeinschaft (DFG). The project is based at the Technische Universität Berlin
(TUB) and the Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB).
From chapter 3 to 6, the modeling work was performed using high-performance computers (HPC)
at the Technische Universität Berlin and the North-German Supercomputing Alliance (HLRN), which
both provided computational resources.
The experimental data in chapter 6 was provided as part of collaboration within the Common topics
group on Interfaces in sewer systems of UWI. A special mention to project S1 with the title “On the
application of online monitoring for hydrogen sulphide in sewer systems” for its support.
iv
Abstract
Sewer networks are integral infrastructures in a well-planned city. Their vital role lies in efficiently
transporting both wastewater to treatment facilities and rainwater from residential areas. The
emission of hydrogen sulphide (H2S) combined with the oxygen (O2) present in the system can pose a
significant threat to the integrity of concrete channels which is amplified for older sewer systems. Not
only can its release lead to the erosion of sewer walls due to concrete corrosion, but it also presents a
safety hazard for those working in the sewer environment. Not to mention the accompanying high
costs for maintenance to mitigate these problems. The generation of hydrogen sulphide and the
concentration of oxygen in sewers are influenced by various factors, including turbulent flow
conditions, hydraulic retention time, flow velocities, and pH value. Numerical modeling with
Computational Fluid Dynamics (CFD) software provides a valuable tool for studying multiphase flows
and understanding the complex interactions between fluid dynamics and chemical processes. This
doctoral thesis focuses firstly on validating the air phase flow in the sewer headspace. The solver for
simulating mass transfer of H2S developed by Teuber (2020) in the OpenFOAM framework is further
validated and then extended and validated to account for O2. Simulations of the high-resolution
models were carried out on a high-performance computing cluster.
Chapter 1 of this thesis deal with the general introduction to the problems of odour and corrosion
in sewer systems, while chapter 2 provides a concise summary of the model's principles and tools used,
along with the developed solver extensions. In Chapter 3 the updated and extended solvers,
interH2SFoam and interO2Foam respectively, are validated using a quasi-steady state tank. These
solvers accurately reproduced concentration profiles and equilibrium concentrations based on Henry's
law, including the temperature-dependent behaviour of the Henry coefficient.
In Chapter 4, the volume-of-fluid (VOF) approach implemented in OpenFOAM was applied to
analyze two-phase flow hydraulics in a lab-scale rectangular duct. The interH2SFoam solver was further
validated for turbulent conditions later in the chapter, with results compared to the results of Teuber
et al. (2019b) showing good agreement. To validate the capability of the interO2Foam solver for gas
transport in sewer headspace, experimental data from Bentzen et al. (2016) was used. Simulated
results were compared to experimental data and a 1D analytical solution for transport, yielding
acceptable agreement.
In Chapter 5, the interO2Foam solver was validated using the field study of Madsen et al. (2006).
The interFoam solver achieved a hydraulically steady state and was validated against analytical data.
After which the setup was then investigated for grid convergence using different mesh resolutions.
Mesh convergence was investigated using different tools and observing residuals for each parameter,
providing a better understanding of flow behaviour versus simulation time required. The chosen mesh
was based on its accuracy and simulation time. The simulated data for point injection of O2 were
compared to the field results of Madsen et al. (2006), showing good agreement. The same setup was
then used for the study to investigate the effects of suction on O2 removal. It not only provided insights
into system dynamics, but also is of practical benefit for identifying potential hotspots for H2S and
designing strategies for H2S removal.
Chapter 6 aimed to establish the relationship between mass transfer and turbulence level by
varying the stirring rates in a rotating system. Dynamic meshing was employed for the setup, designed
to scale with the experiments conducted by Pacheco Fernández et al. (2020). Multiple mesh tests were
performed to achieve grid convergence, and the chosen mesh exhibited good results with optimal
computation time. Both solvers showed an increase in mass transfer with higher stirring rates which is
consistent with previous research. The time series for concentration of simulated data for H2S and O2
aligned well with measured data, providing valuable information on mass transfer operations in highly
turbulent systems.
The extended CFD model offers a comprehensive approach to better understand and predict the
distribution of H2S and O2 in sewer systems and can serve as a decision support tool for odour control
in sewers.
vi
Zusammenfassung
Kanalisationssysteme sind ein wichtiger Bestandteil der städtischen Infrastruktur. Sie spielen eine
elementare Rolle bei der Ableitung von Abwässern zu Kläranlagen sowie bei der Entwässerung von
Wohngebieten. Die Freisetzung von Schwefelwasserstoff (H2S) in Verbindung mit dem in den Systemen
vorhandenen Sauerstoff (O2) stellt eine erhebliche Gefährdung von Abwasserkanälen dar,
insbesondere in alten Systemen, da die Freisetzung von H2S nicht nur zur Schädigung von Kanalwänden
aufgrund von Betonkorrosion führt, sondern sie stellt auch ein Sicherheitsrisiko für die in der
Kanalisation arbeitenden Personen dar. Die damit einhergehenden hohen Instandhaltungskosten sind
waren und sind beträchtlich.
Die Bildung von Schwefelwasserstoff und die Konzentration von Sauerstoff in Abwasserkanälen
werden von verschiedenen Faktoren beeinflusst, darunter das Abflussregime, hydraulische
Verweilzeiten, Fließgeschwindigkeiten und der pH-Wert. Die numerische Modellierung mit
Computational Fluid Dynamics (CFD)-Software ist ein wertvolles Instrument zur Untersuchung von
Mehrphasenströmungen und um die komplexen Wechselwirkungen zwischen der Fluiddynamik und
chemischen Prozessen besser zu verstehen.
Zu Beginn der Dissertation wird die Validierung der Luftphasenströmung behandelt. In einem
ersten Schritt wird der von Teuber (2020) innerhalb des OpenFOAM Frameworks entwickelte Löser zur
Simulation von H2S-Stofftransport weiter validiert. Anschlie?end wird das System um die O2-
Komponente erweitert und ebenfalls validiert. Aufgrund der hohen Rechenanforderungen der
hochauflösenden Modelle wurden für alle Simulationen Hochleistungsrechner verwendet.
Kapitel 1 dieser Arbeit befasst sich mit einer allgemeinen Einführung in das Thema Geruch und
Korrosion in Abwassersystemen. Kapitel 2 bietet eine kurze Übersicht über die Modellkonzepte und -
werkzeuge, die verwendet wurden, sowie über die vorgenommenen Modifikationen am Solver. In
Kapitel 3 wurden die aktualisierten und erweiterten Solver, interH2SFoam und interO2Foam, in einem
quasistationären Tank validiert. Konzentrationsprofile und Gleichgewichtskonzentrationen basierend
auf dem Henry-Gestz wurden präzise reproduziert, einschließlich des temperaturabhängigen
Verhaltens des Henry-Koeffizienten.
In Kapitel 4 wurde der in OpenFOAM implementierte Volume-of-Fluid (VoF) Ansatz verwendet, um
die Hydraulik der Zweiphasenströmung in einem rechteckigen Kanal im Labormaßstab zu analysieren.
Der interH2SFoam Löser wurde erfolgreich für ein turbulentes Abflussregime validiert, wobei die
Ergebnisse eine gute Übereinstimmung mit den Ergebnissen von Teuber et al. (2019b) zeigten. Zur
Validierung der Fähigkeit des interO2Foam-Lösers für den Gastransport in der Luft im Abwasserkanal
wurden die experimentellen Daten von Bentzen et al. (2016) herangezogen, mit welchen die
Simulationsergebnisse eine akzeptable Übereinstimmung zeigten.
In Kapitel 5 erfolgte die Validierung des interO2Foam-Solvers anhand der Feldstudie von Madsen
et al. (2006). Es wurde ein hydraulisch stationärer Zustand simuliert, welcher zunächst anhand
analytischer Daten validiert wurde. Anschließend wurde die Gitterkonvergenz anhand verschiedener
Strömungsvariablen untersucht, um ein besseres Verständnis des Strömungsverhaltens in Bezug auf
die erforderliche Simulationszeit zu erlangen. Die Wahl des Gitters erfolgte auf der Grundlage von
Genauigkeit und Simulationszeit. Die simulierten Daten für die punktuelle Injektion von O2 wurden mit
den physikalischen Ergebnissen von Madsen et al. (2006) verglichen und zeigten eine gute
Übereinstimmung. Anschließend wurde eine Studie zur Absaugung von O2 durchgeführt, wodurch zum
einen weitere Einblicke in die Systemdynamik und zum anderen praktische Erkenntnisse zur Reduktion
der Geruchs- und Korrosionsproblematik gewonnen wurden.
Kapitel 6 zielte darauf ab, die Beziehung zwischen Massentransfer und Turbulenzgrad durch
Variation der Rührgeschwindigkeiten in einem rotierenden System zu ermitteln. Für den Aufbau wurde
ein dynamisches Gitternetz verwendet undes wurden Experimente von Pacheco Fernández et al.
(2020) simuliert. Mehrere Gittertests wurden durchgeführt, um die Gitterkonvergenz zu erreichen,
wobei das ausgewählte Gitter gute Ergebnisse bei angemessener Berechnungszeit lieferte. Beide Löser
berechneten eine Zunahme des Massentransfers bei höheren Rührgeschwindigkeiten, was mit
vorherigen Untersuchungen übereinstimmte. Die Zeitreihen der simulierten Konzentrationen von H2S
und O2 stimmten gut mit den gemessenen Daten überein und lieferten wertvolle Informationen über
den Massentransfer in hochturbulenten Systemen.
Das erweiterte CFD Modell bietet einen umfassenden Ansatz zum verbesserten Verständnis und
zur Untersuchung von H2S und O2 in Abwassersystemen und kann somitals Entscheidungshilfe für die
Geruchskontrolle in Abwasserkanälen herangezogen werden.
viii
Contents
Chapter 1 ..................................................................................................................................... 1
Introduction ............................................................................................................................. 1
1.1 Odour and corrosion in sewers ..................................................................................................1
1.2 Impact of H2S and O2 in causing odour and corrosion ................................................................3
1.3 Scientific background .................................................................................................................6
1.3.1 Preliminary model developments for odour and corrosion ................................................6
1.3.2 Three-dimensional two-phase flow modelling using OpenFOAM ................................... 10
1.3.3 Transport and mass transfer modelling ........................................................................... 15
1.4 Research Training Group: Urban Water Interfaces ................................................................. 18
1.5 Aim and outline of the work .................................................................................................... 18
1.5.1 Aim and innovation .......................................................................................................... 18
1.5.2 Outline of the thesis ......................................................................................................... 19
Chapter 2 .................................................................................................................................... 23
Model concepts and tools ........................................................................................................ 23
2.1 Numerical Methods ................................................................................................................. 23
2.1.1 Hydrodynamic simulations and turbulence models ......................................................... 23
2.1.2 Transport and mass transfer simulation .......................................................................... 28
2.2 Tools ........................................................................................................................................ 31
2.2.1 Pre-processing tools ......................................................................................................... 31
2.2.2 Processing tools ................................................................................................................ 33
2.2.3 Post-processing ................................................................................................................ 36
2.3 Conclusion ............................................................................................................................... 36
Chapter 3 .................................................................................................................................... 38
Update and validation of the solver ......................................................................................... 38
3.1 Methods .................................................................................................................................. 38
3.1.1 Equations .......................................................................................................................... 38
3.1.2 Case description ............................................................................................................... 39
3.2 H2S in a tank ............................................................................................................................. 40
3.3 O2 in a tank .............................................................................................................................. 42
3.4 Conclusion ............................................................................................................................... 45
Chapter 4 .................................................................................................................................... 47
Further validation of the mass transfer of H2S and first validation case for transport of O2 ........ 47
4.1 Introduction ............................................................................................................................. 47
4.2 Method .................................................................................................................................... 48
4.2.1 Experimental setup ........................................................................................................... 48
4.2.2 Numerical model and analytical solution ......................................................................... 49
4.3 Case setup and mesh ............................................................................................................... 51
4.3.1 Hydraulic simulations ....................................................................................................... 51
4.3.2 H2S mass transfer simulations .......................................................................................... 51
4.3.3 O2 transport in the sewer headspace ............................................................................... 51
4.4 Results and discussion ............................................................................................................. 52
4.4.1 Hydraulic simulations ....................................................................................................... 52
4.4.2 H2S mass transfer.............................................................................................................. 53
4.4.3 O2 mass transport ............................................................................................................. 55
4.5 Conclusion ............................................................................................................................... 57
Chapter 5 .................................................................................................................................... 58
Application of the solver for mitigation measures ..................................................................... 58
5.1 Mitigation measures: importance of ventilation .................................................................... 58
5.2 Description of experimental site ............................................................................................. 60
5.3 Section of the field study, geometry and mesh generation .................................................... 62
5.4 Case setup for the simulations ................................................................................................ 65
5.4.1 Hydraulic simulation study ............................................................................................... 65
5.4.2 Oxygen injection study ..................................................................................................... 65
5.4.3 Ventilation study .............................................................................................................. 66
5.5 Results and discussions ........................................................................................................... 66
5.5.1 Hydraulic simulations ....................................................................................................... 66
5.5.2 Solution and grid convergence study ............................................................................... 69
5.5.3 Oxygen injection study ..................................................................................................... 74
5.5.4 Ventilation study .............................................................................................................. 78
5.6 Conclusion ............................................................................................................................... 80
Chapter 6 .................................................................................................................................... 81
Mass transfer in rotating turbulent reactor .............................................................................. 81
6.1 Introduction ............................................................................................................................. 81
6.2 Case study: Turbulent reactor (Project S1: Urban Water Interfaces) ..................................... 82
6.2.1 Reactor setup and stirring rate selection ......................................................................... 82
6.2.2 Hydrogen sulphide experiments ...................................................................................... 83
6.2.3 Oxygen experiments ......................................................................................................... 83
6.3 Computational setup ............................................................................................................... 85
6.4 Results and discussion ............................................................................................................. 89
6.5 Conclusion ............................................................................................................................... 95
Chapter 7 .................................................................................................................................... 97
Synthesis ................................................................................................................................. 97
7.1 Conclusions .............................................................................................................................. 97
7.1.1 Update and extension of the solver ................................................................................. 97
7.1.2 Validation of the air phase behaviour .............................................................................. 98
7.1.3 Gas phase transport of oxygen ......................................................................................... 99
7.1.4 Validation of the mass transfer in a rotating turbulent reactor ..................................... 100
7.2 Limitations ............................................................................................................................. 101
7.3 Future outlook ....................................................................................................................... 102
Appendix A ............................................................................................................................ 104
Appendix B ............................................................................................................................ 111
Appendix C ............................................................................................................................ 121
Appendix D ............................................................................................................................ 140
Bibliography .......................................................................................................................... 142
List of Figures
1.1
Odour emission in the sewage system (H2: hydrogen gas, CO2: carbon di oxide, CH4:
methane, Cl2: chlorine gas, H2S: hydrogen sulphide, NH3: ammonia, VFAs: volatile fatty
acid, CH2SH: methanethiol, C6H5SH: thiophenol and HCHO: formaldehyde) (also
abbreviations are listed in Appendix D) (inspired by Pochwat et al.,
2019)…………………………………………………………………………….……………………………..………………
2
1.2
Sewer process (inspired by Hvitved-Jacobsen et al., 2013)……………………………………………
5
1.3
Connection between rising and gravity main (CH4: methane, H2S: hydrogen sulphide,
MT: methanethiol, SO42-: sulphate ion, VOSC: volatile organic sulpher compounds, H2O:
water, H2SO4: sulphuric acid, Fe2+: iron(II) or ferrous ion and Fe2O4: iron(II) oxide or
ferrous oxide) (also abbreviations are listed in Appendix D) (inspired by Jiang et al.,
2015)…………………………..……………………………………………………………..………………………………
6
1.4
Outline of WATS model (inspired by Hvitved-Jacobsen et al., 2005)……………………..………
8
1.5
Bridge between projects T3 (first cohort) and S2 (second cohort) of the Urban Water
Interfaces……………….…………………………………………………………………………………………………….
19
1.6
Urban Water Interfaces (inspired by Gessner et al., 2014)……………………………………………
21
1.7
Graphical overview of the thesis……………………………………………………………………………………
22
2.1
Classical CFD approaches for turbulent flow simulation: classification according to
levels of turbulence modelling and relative computational cost (inspired by Greco,
2018) ………..………..………..………..………..………..………..………..………..………..………..………..……
26
3.1
Diagrammatic representation of the quasi-steady state tank showing different
boundary conditions for different validation cases………………………………………………………
39
3.2
H2S in a quasi-steady state tank (left: phase fraction value, right: concentration profiles
along the vertical axis over time)……………………………………………………….…………………………
41
3.3
Comparison of the results of the two versions of the solver (left: phase fraction value,
right: concentration profiles along the vertical axis over time)………………………………………
41
3.4
H2S in a tank demonstrating the temperature dependency of Henry’s coefficient
(298.15 K (see also Figure 3.2, right) and 288.1 5K) (left: phase fraction value, right:
concentration profiles along the vertical axis)……………………………………………………………….
42
3.5
O2 in a tank with a boundary condition at the bottom wall (left: phase fraction value,
right: concentration profiles along the vertical axis over time)……………………………………….
44
3.6
O2 in a tank with a boundary condition at the top wall (top left: phase fraction value,
top right: concentration profiles along the vertical axis over time and bottom:
magnified concentration profile)…………………………………………………………………………………
44
3.7
O2 in a tank for different temperatures with boundary condition at the bottom wall
(298.15 K (see also Figure 3.5, right) and 288.15 K) (left: phase fraction value, right:
concentration profiles along the vertical axis over time)………………………………………………..
46
3.8
O2 in a tank for different temperatures with boundary condition at the top wall (298.15
K (see also Figure 3.6, top right and bottom) and 288.15 K) (top left: phase fraction
value, top right: concentration profiles along the vertical axis over time (zoom for the
concentration profile in the water phase on the right) and bottom: magnified
concentration profile)……………………………………………………………………………………………….…
46
4.1
Principal outline of the experimental setup, showing the flows involved and the duct
slope (the drawing is not to scale) (inspired by Bentzen et al., 2016)………………………………
50
4.2
Phase fraction and velocity profile along the height for case 7 at the center of the duct
(measurements as published in Bentzen et al., 2016)……………………………………………………
52
4.3
Phase fraction and velocity profile along the height for case 21 at the center of the duct
(measurements as published in Bentzen et al., 2016)……………………………………………………
53
4.4
Phase fraction (see also Figure 4.2), left and concentration profile of H2S along the
height for case 7 at the center of the duct, right……………………………………………………………
54
4.5
Phase fraction (see also Figure 4.3), left and concentration profile of H2S along the
height for case 21 at the center of the duct, right………………………………………………………..
54
4.6
Measurements (Bentzen et al., 2016), 1D analytical solution and simulated
concentration of oxygen at 5 m downstream from the oxygen injection point in case
21………………………………………………………………………………………………………………………………...
56
4.7
Measurements (Bentzen et al., 2016), 1D analytical solution and simulated
concentration of oxygen at 12 m downstream from the oxygen injection point in case
21…………………………..………..………..………..………..………..…..…..………..………..………..……………
56
5.1
Gas transport in sewer systems……………………………………………………………..……………………..
59
5.2
Overall principle of injections (inspired, Hvitved-Jacobsen et al., 2013)…………………………
60
5.3
Map of the field site (inspired by Madsen et al., 2006)……………………………………………………
61
5.4
(a) Section of the field experiment used for the case setup (see also Figure 5.3); (b)
simulation case set up with important patches………………………………………………………………
63
5.5
Unstructured (a) and structured mesh (b)………………………………………………………………..……
64
5.6
Hydraulic elements for circular sewer pipes (Eddy and Tchobanoglous, 1981)………………
68
5.7
Phase fraction and velocity profile along the height at the center of the duct…………………
69
5.8
From left to right: coarse, medium, medium refined at the walls, fine and very fine
mesh…………..………..………..………..………..………..………..………..………..………..………..…………….
70
5.9
Residual plots: coarse, medium, medium refined at the walls, fine and very fine mesh
for parameters (a) phase fraction (alpha.water) and (b) velocity magnitude U. ………..……
71
5.10
Residual plots: coarse, medium, medium refined at the walls, fine and very fine mesh
for parameters (a) pressure (p_rgh) and (b) turbulent kinetic energy (k)………………………
72
5.11
Comparison of simulated indicator values z (flow velocities) for different grid sizes in
five points within the domain ((a) set 1: coarse, medium and fine mesh, (b) set 2:
course, medium refined and very fine mesh)…………………………………………………………………
74
5.12
Simulated versus experimental (Madsen et al., 2006) oxygen concentration profile at
manhole 3 (Point E, Figure 5.5 (b)) for step 1: 0 – 1800 s (a) and step 2: 1800 - 3660 s
(b) ………..………..………..………..………..………..………..………..………..………..………..………..………..
76
5.13
Simulated versus experimental (Madsen et al., 2006) oxygen concentration profile at
manhole 3 (Point E, Figure 5.5 (b)) for step 3: 3600 - 5400 s (c) and step 4: 5400 - 7200
s (d) ………..………..………..………..………..………..………..………..………..………..……..………..……….
77
5.14
Cumulative mass of oxygen removed with time for different suction rates……………………
79
6.1
System sketch of stirring tank including relevant variables from the experimental works
of Wu (1995, modified) (left), experimental set up used for simulation (not to scale)
(right) ………..………..………..………..………..………..………..………..………..………..………..………..……
82
6.2
Experimental setup for the hydrogen sulphide experiments………………………………………….
84
6.3
Experimental setup for the oxygen experiments………………………………………………..…………
84
6.4
Geometry and mesh used for mass transfer simulations………………………………………………
86
6.5
Initial residuals for different parameters for the turbulent reactor………………………………
87
6.6
Geometry used for the simulations including boundaries (dark grey: blade; blue: outer
cylinder; green: reactor walls / inner cylinder; red: AMI /upper plane on top)………………
88
6.7
Vortex shapes for different stirring rates (left: 300 rpm, middle: 400 rpm and right: 500
rpm)…………………………………………………………..…………………………………………………………………
89
6.8
Comparison of the measured data to the results obtained from simulations for H2S for
different stirring rates ((a): N = 300rpm, (b): N = 400rpm, (c): N = 500rpm)……………………
91
6.9
Comparison of the measured data to the results obtained from simulations for O2 for
different stirring rates ((a): N= 300rpm, (b): N = 500rpm))……………………………………………
92
6.10
Resulting mass transfer coefficients and volumetric mass transfer coefficients for H2S
and O2 for different stirring rates………………………………………………………………………………….
94
6.11
Influence of stirring rate on mass transfer as published by Carrera et al. (2017) and
results of CFD simulation…………………………………………………………………………………………..…
95
6.12
Influence of stirring rate on 𝐾𝐿,𝐻2𝑆𝐾𝐿,𝑂2
⁄ as published by Carrera et al. (2017) and with
results of CFD simulation…………………………………………………………………………………………….
95
xv
List of Tables
1.1
Model development over the years……………………………………………………………………………
7
1.2
Classification of two-phase flows (inspired by Ishii and Hibiki, 2011)……………………………
12
3.1
Important parameters for quasi-one-dimensional cubic tank…………………………………….
40
4.1
Flow properties of analysed test cases……………………………………………………………………….
48
4.2
Different evaluation criteria to assess model performance calculated at the two
measurement points in the pipe…………………………………………………………………………………
57
5.1
Number of total injections in each pipe section and the designated monitoring stations
(location A – E, see Figure 5.3) (Madsen et al., 2006)……………………………………………………
61
5.2
Overall outline of field study (Madsen et al., 2006)………………………………………………………
61
5.3
Different time, volume, and flow rate for each step…………………………………………………….
66
5.4
K’ values in terms of diameter for circular channels (Eddy and Tchobanoglous, 1981)…..
68
5.5
Number of cells and time required for simulation according to different grid sizes……….
70
5.6
Calculations for the representative grid size and refinement factors……………………………
73
5.7
Peak concentration of O2 observed and simulated with the respective NSE for each
step………..………..………..………..………..………..………..………..………..………..………..………….……
75
5.8
Mass balance for oxygen in ventilation scenarios………………………………………………………..
78
6.1
Experimental set up data…………………………………………………….………………………………………
82
6.2
Details for different meshes generated and their respective simulation times………….…
86
6.3
Fluid properties as defined in the CFD simulations………………………………………………………
89
xvi
6.4
Different model efficiency criteria for the H2S and O2 solver with respect to the average
measurements…………………………………………………………………………………………………………..
93
6.5
Compilation of measured and simulated data for mass transfer coefficient
calculations.………..………..………..………..………..……………..………..………..……….………..………..
93
xvii
Appendix
List of Figures:
B1
Flow chart of the solver (following Devolder et al., 2015; Lopes et al., 2017; Teuber et
al., 2019b), solver extensions in blue………………………………………………………….………………..
B2
File structure for interFoam solver with the files modified highlighted in green…………..
List of Tables:
C1
Model setup of quasi one-dimensional cubic tank for H2S………………………………………………
C2
Boundary conditions for quasi one-dimensional cubic tank simulation for H2S mass
transfer from liquid to gas phase……………………………………………………………………………..……..
C3
Model setup of quasi one-dimensional cubic tank for O2…………………………………………………
C4
Boundary conditions for simulations of quasi one-dimensional cubic tank for O2 mass
transfer from liquid to gas phase……………………………………………………………………………………..
C5
Boundary conditions for simulations of quasi one-dimensional cubic tank for O2 mass
transfer from gas to liquid phase……………………………………………………………………………………..
C6
Model setup of lab scale setup of a rectangular duct for H2S……………………………………………
C7
Boundary conditions for simulations of the rectangular duct for H2S mass transfer………….
C8
Model setup of lab scale setup of a rectangular duct for oxygen transport………………………
C9
Boundary conditions for simulations of the rectangular duct for O2 transport…………………..
C10
Model setup of sewer geometry with closed utility manholes………………………………………….
C11
Boundary conditions for simulations of the sewer with closed utility holes………………………
C12
Model setup of sewer geometry with open utility manholes for ventilation……………………..
C13
Boundary conditions for simulations of the sewer with open utility holes for ventilation…
C14
Model setup of the turbulent reactor for H2S transfer from liquid to gas phase………………..
C15
Boundary conditions for simulations for mass transfer of H2S in a turbulent reactor………..
C16
Model setup of the turbulent reactor for O2 from gas to liquid phase……………………………….
C17
Boundary conditions for simulations for mass transfer of O2 in a turbulent reactor……………
D1
Abbreviations for the chemical names used in the text or figures used……………………………..
1
Chapter 1
Introduction
1.1 Odour and corrosion in sewers
The emission of hydrogen sulphide (H2S) in sewer systems significantly contributes to the biogenic
corrosion of sewers and the emanation of toxic odours to the urban environment and sewer workers
involved in the maintenance of sewers. Due to biogenic corrosion caused by H2S emission, sewer
maintenance costs pose a significant economic burden to authorities managing public sewer systems.
The restoration costs of damaged sewers in Germany were estimated to be about 100 billion US dollar,
as per a study conducted in 1998, from which 40 % of the damage was attributed to corrosion by
biogenic sulphuric acid (Kaempfer and Berndt, 1998). In fact, a recent survey on the status of sewer
systems in Germany indicated that 10 % of the sewer systems are estimated to show surface damages
including corrosion (Berger et al., 2016). H2S causes corrosion when it is exposed to damp concrete or
steel in the presence of oxygen. However, several studies have pointed out that H2S removal in sewers
can abate this process with an adequate oxygen supply (Gutierrez et al., 2008). An adequate supply of
oxygen can be ensured and improved by oxygen injection and air pressurisation, considering the
efficiency of the oxygen transfer (García et al., 2017; N. Tanaka and K. Takenaka, 1995; Zhang et al.,
2022).
The emission of odours in sewers originates from volatile sulphur compounds or volatile organic
compounds in sewer systems. Volatile sulphur compounds are often generated inside sewage
networks in gravity and pressure systems (Shammay et al., 2016). Sulphuric acid, formed from the
oxidation of hydrogen sulphide in the presence of moisture, is the leading cause of biogenic corrosion.
It has been found that H2S is responsible for 20 % of all damages to concrete surfaces in wastewater
plants, which documents the highest relevance of the damages. Sydney et al. (1996) investigated the
corrosion of sewage pipes in Los Angeles, USA. The study concluded that 10 % of the pipelines had
been attacked by hydrogen sulphide, causing 500 million US dollars in damage to the sewage network
that year. Kaempfer and Berndt (1998) conducted a similar study in Germany in 1998, which indicated
that 40 billion US dollar were spent on the restoration of damages caused by biogenic sulphuric acid-
induced corrosion. In a 2002 study, Vincke (2009) found that the damages caused by the corrosion of
sewage pipes by hydrogen sulphide in Belgium was about 6.2 million US dollar per year, equal to 10 %
of the total cost of wastewater collection and treatment. Biogenic corrosion thus represents one of
the most critical challenges for sewage systems today. In a recent study published by the Deutsche
Vereinigung für Wasserwirtschaft, Abwasser und Abfall (DWA) in Germany, the maintenance costs for
Chapter 1: Introduction
2
the sewer network including renovation and renewal for the period 2019 - 2023 are expected to be
around 2 billion Euro (Berger et al., 2020).
Several factors play a crucial role in H2S formation, such as total sulphur concentration, toxic
substances, biochemical oxygen demand, temperature, and pH of the wastewater. A higher amount
of H2S formation is associated with increased total sulphur concentration, the presence of less toxic
substances, low redox potential, more elevated BOD (biochemical oxygen demand), higher
temperature, and low pH (Chen and Szostak, 2012).
Figure 1.1: Odour emission in the sewage system (H2: hydrogen gas, CO2: carbon di oxide, CH4:
methane, Cl2: chlorine gas, H2S: hydrogen sulphide, NH3: ammonia, VFAs: volatile fatty acid, CH2SH:
methanethiol, C6H5SH: thiophenol and HCHO: formaldehyde) (also abbreviations are listed in Appendix
D) (inspired by Pochwat et al., 2019).
Understanding the sewer processes is pertinent in controlling and regulating sewer emissions. In
recent years, there has been extensive research on odour and corrosion in sewer systems due to H2S.
Studies on the same will continue to stay relevant in future years owing to the current developments,
such as the declining population in many regions, improved water usage efficiency, and reduced
wastewater generation. These factors resulted in an extended retention time of wastewater within
the aging sewer systems characterized by larger pipe dimensions, originally designed to accommodate
higher loads or combined systems incorporating stormwater. As water consumption decreases, the
ample pipe capacity enables the wastewater to accumulate and flow more slowly, consequently
leading to elevated hydrogen sulphide generation within sewage plants. The increasing trend to
connect more remote drainage areas to the central wastewater treatment plants via long pressure
lines also makes phenomena more of a concern in the future. It can cause the following effects
(Barjenbruch, 2007):
• Odour disturbance, particularly at transfer points from pressurised systems to gravity lines
Chapter 1: Introduction
3
• Negative effects on wastewater treatment such as deterioration brought on by biodegradation
and thickening sludge formation
• Sulphuric acid corrosion on pipelines, utility holes and other structures
• Occupational health and safety problems due to hazards to the facility personnel
Additionally, it is essential to account for the impacts of climate on the conveyance system. A study
from Hughes et al. (2021) pointed out that low flows due to low rainfall led to more extensive
anaerobic decomposition, eventually leading to increased H2S production. In addition, warmer
climates have a similar impact on H2S production, as there is an escalated reduction in the level of
oxygen (O2) in sewers, resulting in a reduced concentration of dissolved oxygen and expediting the
generation of H2S by the sulphate-reducing bacteria (Rootsey and Yuan, 2010). Thus, an in-depth
understanding of sewer processes is germane to regulating and controlling H2S generation in sewers.
1.2 Impact of H2S and O2 in causing odour and corrosion
In the following section, a general introduction concerning the processes inside the sewers with a
focus on the site with high H2S emission and mitigation strategies is given. For the current work and
other projects related to interfaces in the sewer, three primary interfaces are considered, namely:
• The biofilm – (waste) water interface
• The (waste)water – (sewer)air interface
• The (sewer) air – biofilm interface
Biofilms are biostructures built mainly through bacteria and archaea, with very complex and
heterogeneous structures and compositions. As a result, they may swiftly adjust to environmental
changes, such as the availability of organic nutrients or electron acceptors (oxygen, nitrate, and
sulphate). These conditions can vary based on the amount of organic matter, aeration, temperature,
and sewer design (Augustyniak et al., 2021). Sulphate-reducing bacteria (SRB) present in the biofilm
can decrease sulphate in the wastewater at the biofilm-(waste)water interface. The wastewater can
promote this activity under anaerobic environments. H2S and the bisulphide ion (HS-), which together
make up the total dissolved sulphide, are in equilibrium in the aqueous phase. This balance is
influenced by the temperature and pH level. Depending on various factors, including the pH level,
temperature, oxygen and nitrate content at the (waste)water – (sewer)air interface, H2S can be
released from the water phase into the air phase. H2S is categorised as a volatile chemical, defined as
a substance that, at normal temperatures, has a high vapour pressure that causes molecules to change
phases, in this instance, considered as emission. The Henry coefficient, a significant variable in this
thesis, can be used to characterise the water-air equilibrium for these compounds. It explains the state
where there is no net transfer between the phases because the transfer rates between the two phases
are equal (Hvitved-Jacobsen et al., 2013).
However, Henry’s coefficient depends on the solute, solvent, and temperature of the domain under
consideration. Moreover, the temperature dependency of Henry’s coefficient can be considered by
integrating the van Hoff equation (Hvitved-Jacobsen et al., 2013).
Chapter 1: Introduction
4
Various factors, such as the concentration of H2S in the water, influence the mass transfer between
the phases. The H2S concentration in the liquid phase is related to the pH value, sulphide content of
the sewage, and hydrodynamic parameters. The correlation can be derived as follows (Tian et al.,
2020):
𝐶𝐻2𝑆=𝑆𝑇 ∙ 34
32(1+ 𝐾𝑆1
10−𝑝𝐻+𝐾𝑆2𝐾𝑆1
10−𝑝𝐻)
Eq. 1.1
Where 𝐶𝐻2𝑆 is the H2S concentration in the liquid phase, ST is the concentration of total dissolved
sulphide in the wastewater (mg/m3) and KS1 and KS2 are the primary and secondary ionisation
equilibrium constants of H2S, respectively. Here pH quantifies the level of acidity or alkalinity exhibited
by a solution, serving as a unit of measurement, ranging from 0 to 14, this scale allows for the
characterisation of the solution's acidity (values lower than 7) or alkalinity (values higher than 7).
Besides, the transport is determined by the turbulence of the phases. The sewer system’s
turbulence and eventually turbulent diffusion, mass transfer, and equilibrium conditions develop more
rapidly as turbulence increases. It is crucial to adequately account for these impacts because
turbulence significantly affects local mass transfer.
Another critical process in the sewer system is the mass exchange between wastewater and the
sewer atmosphere ((waste) water – (sewer) air interface). The transfer of oxygen in-between this
interface, called reaeration, should also be considered while modelling. The potential of aerobic and
anaerobic processes in wastewater depends on the degree of reaeration during transport; Yongsiri et
al. (2005) and Hvitved-Jacobsen et al. (2013) state that it is the only way to aerate the liquid phase.
The third interface, the (sewer) air-biofilm - (concrete) wall interface, involves a complex sulphur
cycle uniquely present in unfilled gravity sewers (Wang et al., 2022). There is almost no corrosion below
the water level, but the most severe corrosion often occurs in the pipe’s crown and the vicinity of the
effluent level. This is caused by the effluent level’s division of the sewer’s ecosystem into an anaerobic
and an aerobic one. Sulphate in the effluent is converted by the sulphate-reducing bacteria (SRB) that
grew in the submerged biofilm to aqueous sulphide, which overflows and is adsorbed on the concrete
surface above the effluent level. Sulphur-oxidising bacteria (SOB) also convert sulphide into sulphuric
acid (biogenic H2SO4), which dissolves in the concrete’s pore water to create a highly concentrated acid
solution with a pH of under 2 (Hvitved-Jacobsen et al., 2013; Wang et al., 2022).
Along with the above-mentioned sewer processes, the design of sewers also influences the
formation of H2S and its emission. Water infrastructures are interconnected with spatial characteristics
since they are connected to the urban form. For instance, the location, size, and shape of sewage
infrastructures are impacted by the density and geographical distribution of water consumers and the
terrain and street layout (Duque et al., 2022). Sewers are generally classified in three different ways
(Hvitved-Jacobsen et al., 2013; Teuber, 2020):
• Based on the type of sewage collected (sanitary sewers, storm sewers and combined sewers)
Chapter 1: Introduction
5
• Based on the transport mechanisms (gravity sewers and pressure pipes)
• Based on the size and function
Figure 1.2: Sewer process (inspired by Hvitved-Jacobsen et al., 2013).
While the flow in a pressure sewer is primarily driven by a pump and only water is present in the
pipe, the flow in a gravity sewer is driven by the slope of the line and has a free water surface. Pressure
sewers are primarily anaerobic, and gravity sewers are aerobic. Reaeration occurs in the latter. The
oxygen content of the sewage is the primary distinction between gravity and pressure sewers. Pumping
stations collect wastewater in rising main sewers and then transport it along the pressure sewer, which
is often full of wastewater. When wastewater is pumped into the wet well, an intense gas-liquid
transfer may occur in the intersection between pressure and gravity sewers. When wastewater
reaches the wet well’s overflow level, it will flow to gravity sewers. Gravity drives the wastewater flow
in gravity sewers, which function in semi filled conditions. Due to oxygen transport across the air-water
interface, aerobic conditions may predominate in the wastewater phase. In pressure pipes, oxygen can
be depleted, resulting in anaerobic conditions allowing sulphate reduction. The two main
characteristics to be considered here in the design of sewers are the occurrence of anaerobic
conditions and the degree of turbulence downstream, which promotes H2S generation.
Similarly, different design aspects can significantly influence the sewer processes and,
consequently, lead the H2S emission to cause odour and corrosion in the system. Barjenbruch (2003),
in his study, pointed out that problematic sites are connection shafts between rising main and gravity
sewers, which have longer detention times (Figure 1.3). Such structures facilitate direct contact with
wastewater and the surrounding air and usually occur in locations of higher turbulence.
Chapter 1: Introduction
6
Figure 1.3: Connection between rising and gravity main (CH4: methane, H2S: hydrogen sulphide, MT:
methanethiol, SO42-: sulphate ion, VOSC: volatile organic sulpher compounds, H2O: water, H2SO4:
sulphuric acid, Fe2+: iron(II) or ferrous ion and Fe2O4: iron(II) oxide or ferrous oxide) (also abbreviations
are listed in Appendix D) (inspired by Jiang et al., 2015).
Different methods and technologies exist to mitigate and control odour and corrosion in sewers.
There exist manuals as well as chemical solutions. The chemical solution includes the reduction of
sulphide by oxidants, chemical oxidation of sulphide, pH controlling measures, enrichment of oxidants,
and precipitation of sulphides. At the same time, physical solutions include adsorption by activated
charcoal, biofilters, bio-trickling filters, and activated carbon, usage of bio-scrubbers, ionisation
systems for treatment of eradicated impure air, catalytic iron filters, and also constructive solutions
such as corrosion protection by using corrosion-proof concrete for sewer systems and taking into
account various hydraulic design parameters. A purely physical model may account for physical
solutions like covering systems, but chemical countermeasures require reactive transport modelling.
The long-term objective of the current model built as part of this thesis is to enable it to model
countermeasures, including ventilation, doses and flushing for better management of sewer networks.
1.3 Scientific background
1.3.1 Preliminary model developments for odour and corrosion
This section gives a short overview of existing model approaches. In addition, the advantages and
shortcomings of the previous models are discussed in an attempt to delineate the need for a new
model since 2015. The main model developments for odour and corrosion caused by H2S done by
various researchers are given in Table 1.1.
Chapter 1: Introduction
7
Table 1.1: Model development over the years.
Empirical models
1970s
Thisthlethwayte (1972) and Pomeroy and Parkhurst
(1997)
Conceptual
understanding
1990s - 2000s
WATS model (Hvitved-Jacobsen, 2013)
1D
model
Transient conditions
2008 - 2013
SCORe project (Sewer & Corrosion & Odour
Research)
Small-scale effects
Since 2015
RTG Urban Water Interfaces (UWI) Project T3, S2 &
S4
3D
model
Local turbulence
In 1970 some extensive studies were conducted in the US and Australia to develop empirical models
for evaluating H2S generation in sewers (Boon and Lister, 1975; Pomeroy and Parkhurst, 1978;
Thistlethwayte, 1972). These models disregarded numerous details of in-sewer biotransformation,
notably those related to the carbon cycles, and combined several variables impacting H2S generation
into a single rate expression. Since the late 1980s studies on sulphate-reducing bacteria (SRB) have
shown that SRB activity is significantly influenced by the type of carbon sources used. In this context,
it has been well shown that volatile fatty acids (VFAs) are a suitable carbon source for sulphate
reduction (Nielsen and Hvitved-Jacobsen, 1988). Research in the 1990s concentrated on developing a
conceptual understanding of how organic matter transformed sewers. The Danish research team led
by Thorkhild Hvitved-Jacobsen made significant contributions to conceptualising key processes during
H2S transformations from the early 1990s to the late 2000s.
To take into account the effects of carbon source on sulphate reduction, the team led by Hvitved-
Jacobsen developed Wastewater Aerobic/Anaerobic Transformations in Sewers (WATS) model (Bjerre
et al., 1998; Nielsen and Hvitved-Jacobsen, 1988; Hvitved-Jacobsen, 2001) which is in agreement with
the activated sludge model (ASM, Henze et al., 1987). Figure 1.4 shows an outline of the WATS model.
ASM is a one-dimensional model that describes the mechanisms of nitrification and denitrification, as
well as the nitrogen and chemical oxygen demand during suspended-growth treatment processes. The
model has been found to provide a good description of the activated sludge processes in wastewater
treatment plants. Still, the model’s applicability is limited as sewer water treatment plants differ quite
from wastewater treatment plants (Barjenbruch et al., 2008). In the early 2000s, research was carried
out to evaluate the oxidation of hydrogen sulphide produced by biofilms, the discharge of H2S from
bulk water into the sewage gas phase, and the injection of bulk water and air into pressure pipes. Later,
in the 2000s, studies were conducted to implement the dynamic modelling of H2S production,
especially in pressure mains and gravity sewers (Sharma et al., 2008).
Chapter 1: Introduction
8
Figure 1.4: Outline of WATS model (inspired by Hvitved-Jacobsen et al., 2005).
The current WATS model takes into account hydrodynamics describing the flow of gas and water
along the sewer, including the ventilation of sewer gas to the atmosphere, the water-air interface, air
phase, and water phase and focuses on dry weather conditions and not wet weather conditions
(Teuber, 2020). Despite the developments in the WATS model, the model considers uniform flow
under steady-state conditions limiting its application to sewer systems under a steady-state. The
model also assumes gas phase velocity as a proportion of the water phase velocity. However, sewer
systems are dynamic flows that vary significantly over time. Furthermore, the model does not consider
the dispersion of substances transported through water. When addressing the interaction between
sewage networks and treatment plants or receiving waters, the WATS model is suitable for engineering
applications in dry weather (Hvitved-Jacobsen et al., 2013).
In their review, Carrera et al. (2016) give an overview of sulphide and hydrogen sulphide emission
models in sewer networks with their limitations and perspectives to improve the current modelling
approaches. They indicate that sulphide formation and uptake models need refinements, especially in
phenomena like liquid-gas mass transfer. Matias et al. (2017), in their study investigated the
characteristics of drop structures on reaeration and established an empirical relationship between the
mass transfer of oxygen and the physical parameters of drop structures. In 2008, a research project
was launched by the Australian government and many other water utilities in Australia named Sewer
Corrosion and Odour Research (SCORe) Project. The project focussed mainly on four areas (Wells,
2014):
• Understanding and predicting corrosion processes
• Gas phase measurement with a focus on odour measurement and evaluation of odour
treatment technologies; ventilation technologies
Chapter 1: Introduction
9
• Liquid phase technologies for optimised use of chemicals, testing of emerging chemicals and
implementation of electrochemical methods for sulphide control
• Decision support and knowledge management to develop a model-based decision support
system and web-based knowledge management
Later an advanced mathematical modelling tool called SeweX was developed, capable of describing
the physical, chemical, and biological processes in sewers. In SeweX, the mathematical model of
Hvitved-Jacobsen et al. (2013) for predicting sulphide generation was improved to provide spatial and
temporal liquid sulphide profiles for any given sewer or network of sewers. The model has also been
connected to hydraulic sewer models to predict dynamic changes in sulphur compounds within the
sewage system owing to altering sewer characteristics such as diurnal fluctuations (Rootsey et al.,
2012). Despite improving the model based on ASM, the SeweX model employed the Anaerobic
Digestion Model No. 1 (ADM1) to account for anaerobic fermentation processes (Sharma et al., 2008).
SeweX models can also be used downstream of a sewer pipe to evaluate prospective odour and
corrosion control additives for sewers to investigate optimal dosing rates and their appropriate dozing
location (Rootsey et al., 2012; Sharma et al., 2008).
Ventilation systems play a crucial role in minimizing the build-up of H2S in the sewers. In addition
to that, ventilation systems aid in maintaining zero relative velocity between wastewater and
ventilating air to minimize the rate of H2S emission and evaporation from the wastewater surface and
to change the air sufficiently to maintain dry sewer structures at all times. A new ventilation algorithm
was implemented as an additional component of the SeweX model to provide a virtual dynamic
prediction of air movements and gas phase H2S concentrations within a sewer network (Rootsey et al.,
2012). The factors affecting ventilation are described in terms of force balance (Ward et al., 2011).
Influences are considered, including pressure variations, gravitational forces, drag at the air/water
interface, and friction at the air-water interface.
From the literature review, various shortcomings can be found after analysing the two primary
models established previously. The WATS model’s primary disadvantage of only considering steady-
state flow conditions has been eliminated in the SeweX model. However, neither model can simulate
the fluctuations in biofilm compositions and the potential for sulphide production in sewers under
dynamic conditions. Furthermore, both models are one-dimensional. Another limitation is the inability
to describe turbulent and non-uniform flows and the simplifications used to characterise very
turbulent regions (such as drops), gas flow velocities, and transport processes (Barjenbruch et al.,
2008). The models’ availability is another drawback. The SeweX model is neither in the public domain
nor the WATS model. These advantages and disadvantages demonstrate that, when using the steady-
flow assumption, the existing models are appropriate for analysing long sewer networks. From these
observations, a three-dimensional model could also be used to analyse the impacts of chemical or
physical countermeasures thoroughly. Physical countermeasures could initially be evaluated using a
non-reactive transport. Later the model can be extended to examine the impact of chemical reactions
by including reactive transport. In addition to the WATS model, scientific contributions from research
groups in Australia (Jiang et al., 2009; Sharma et al., 2008) and China (Liang et al., 2019a, 2019b have
Chapter 1: Introduction
10
been significant in the study of sulphide generation in sewers and the production of other sewer gases,
such as methane. It is worth noting that these process models can effectively simulate the impact of
mitigation measures, including the introduction of nitrate. However, one limitation of these process
models is the extensive requirement of input parameters and the need for expertise in hydraulics,
wastewater processes, and water chemistry to ensure accurate configuration. Consequently, they may
prove impractical for everyday practitioners.
When considering the flow within these systems, turbulence plays an important role. Various
turbulence models are accessible for calculating turbulent viscosity in computational fluid dynamics
(CFD) simulations. These models aim to simulate the complex behaviour of turbulence by predicting
the distribution of turbulent eddies and their effects on the flow. Some commonly used turbulence
models include the Reynolds-Averaged Navier-Stokes (RANS) models, such as the k-𝜖, k-𝜔, and Spalart-
Allmaras models, as well as the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS)
approaches, which provide more accurate representations of turbulence but are computationally
more expensive. The choice of turbulence model depends on the specific flow characteristics,
computational resources, and accuracy requirements of the simulation.
It should be noted that the state-of-the-art models are one-dimensional, not considering the three-
dimensional effects of flow velocities, non-uniform flow, and highly turbulent effects. A significant step
towards filling this gap is to develop a high-resolution three-dimensional model to understand and
simulate the processes involved. This contribution advances the doctoral thesis of (Teuber, 2020). It
concentrates on validating water-air flow in a sewer, focusing on the air phase, mass transport and
mass transfer occurring between the phases to study the local effects of H2S and O2 emissions. The
study aims to suggest suitable treatment of H2S hotspots and provide better configuration to enhance
the existing model approaches. The basis of this work is a three-dimensional water-air flow model
developed by Teuber (2020) within the framework of the open-source CFD platform OpenFOAM.
1.3.2 Three-dimensional two-phase flow modelling using OpenFOAM
H2S generation and the impact of O2 concentration in sewers are influenced by factors such as
turbulent conditions resulting in more air-water mass transfer, hydraulic retention time (HRT), and
flow velocities to biochemical factors such as pH. Several numerical methods and algorithms allow us
to make flow predictions by numerically solving the governing equations of fluid flows. Different
classifications of two-phase flow are mentioned in Table 1.2. Numerical modelling and CFD applications
range from biomechanics, aerospace, and chemical industry to natural sciences. In this regard, CFD
software is widely used to investigate multiphase flows. In the study of multiphase flows, CFD can
provide information that is hardly possible by physical experiments, which can help enhance the
characterisation of multiphase flows. Notably, 3D CFD simulations can offer comprehensive local and
global information on the interaction of fluid dynamics and underlying chemical processes for various
systems. Therefore, it can help identify the potential hotspots for H2S and O2 generation and help make
appropriate recommendations for preventing the consequences (Dixit et al., 2020). Numerical
modelling can help understand how sulphide generation and oxygeb concentration respond to
Chapter 1: Introduction
11
dynamic changes in sewer systems. A study in the late 1990s (Mark et al., 1998) showed the prospects
of simulating the flow and water depths in sewer systems. Additionally, the study of the capability of
a modelling system to describe the transport and dispersion of dissolved pollutants, inferring these
modelling systems, can be used for finding optimal dosing strategies.
The current approach is based on the fundamental equation of fluid dynamics known as Navier-
Stokes equations. They are nonlinear partial differential equations, which govern the motion of natural
viscous fluids and can be seen as Newton’s second law of motion for fluids. The Navier-Stokes
equations (NSE) are fundamentally the most basic equations that may be used to model fluid motion
from a continuum mechanics perspective. They are derived from a basic physical assumption that a
linear local relationship exists between stresses and strain rates (Bistafa, 2017; Temam, 1995). The
conservation of mass is expressed using the continuity equation using the fundamental principles in
fluid dynamics. When combined with the Navier-Stokes equations, both together ensure that the flow
remains consistent and in equilibrium throughout the system. This set of equations describes the
processes occurring in water bodies (Hinkelmann, 2005).
The fundamental idea behind an approximative numerical method is that a solution is pursued for
the discretised computational domain (in space and time), which consists of a finite number of
computational nodes in space and time. A good representation of the solution for the continuous
physical domain is what is generally intended. Various models exist for numerical simulations. The
choice of model for an application depends on the hydrodynamic process, spatial and temporal scale
under consideration, the water quality concerns, the proper scaling (time, space), and the most
suitable simulation scenario (Matta, 2018). The two primary choices in modelling sewer systems are
between one-dimensional and three-dimensional approaches.
Chapter 1: Introduction
12
Table 1.2: Classification of two-phase flows (inspired by Ishii and Hibiki, 2011).
Class
Typical regimes
Geometry
Configuration
Separated flows
Film flow
Liquid film in gas
Gas film in liquid
Annular flow
Liquid core in gas film
Gas jet in liquid film
Jet flow
Liquid jet in gas
Gas jet in liquid
Mixed or
transitional
flows
Cap, slug or churn
turbulent flow
Gas pocket in liquid
Bubbly annular flow
Gas bubbles in liquid
film with gas core
Droplet annular flow
Gas core with droplets
and liquid film
Bubbly droplet
annular flow
Gas core with droplet
and liquid film with gas
bubbles
Dispersed flow
Bubbly flow
Gas bubbles in liquid
Droplet flow
Liquid droplets in gas
Particulate flow
Solid particles in gas or
liquid
Chapter 1: Introduction
13
When the impacts in two of the three dimensions can be disregarded, a 1D approach is commonly
used. This is typical for sewer network modelling, where pipe-filling ratios and main flow rates are
crucial. In this thesis, the use of 3D modeling is advocated due to its ability to capture intricate features
and phenomena in the built environment, particularly when studying localized details and turbulent
phenomena like drops and hydraulic jumps. The work from Edwini-Bonsu and Steffler (2006) shows
that there are secondary flows in the air phase that do not move in the main flow direction. While it is
conceivable that water flow may exhibit predominant 1D characteristics, it was observed that air flow
possesses a 3D nature. This indicates that air flow operates in a more complex and multi-directional
manner compared to the predominantly unidirectional nature of water flow. This emphasises one key
benefit of the model built in this thesis: Within large sewage networks, a three-dimensional method
can be used locally, for example to improve designs for H2S hotspots (Teuber, 2020).
OpenFOAM has been one of the most popular open-source software programmes for numerical
simulations of fluid flows (CFD) in engineering applications for the past ten years. This flexible C++
library can be used to solve many continuum problems. With a collocated cell-centered variable
arrangement and unstructured boundary-fitted meshes (including topological mesh modifications) for
arbitrarily complicated geometries, OpenFOAM is based on an unstructured mesh formulation. In
addition to having second-order precision in its spatial and temporal discretization, OpenFOAM makes
it possible to analyse continuum issues broadly and flexibly (Marschall, 2011). The application also
allows one to create new solvers and utilities with some pre-requisite knowledge of the underlying
method, physics, and programming techniques. OpenFOAM also includes pre-and post-processing
environments. The interfaces to the pre-and post-processing are themselves OpenFOAM utilities,
ensuring consistent data handling across all environments (Weller et al., 1998). The partial differential
equations are spatially discretized based on Finite-Volume-Method (FVM) and temporally discretized
with a Finite-Differences-Scheme (Schulze and Thorenz, 2014).
A two-phase flow model is essential to account for both water and air movement, because of the
complexity of the problem this thesis proposes to solve. An introduction of the model setup in
OpenFOAM is provided in the following. There are three main phases to generating a model in
OpenFOAM:
• Pre-processing
• Solving
• Post-processing
The pre-processing stage comprises the definition of the geometry, generation of the
computational mesh and assignment of boundary and initial conditions. Since the solver is based on
the FVM for spatial discretisation, the computational domain is divided into a finite volume of control
volume where the governing equations are solved. The calculation time and effort depends on the
number of control volumes (Schulze and Thorenz, 2014). Structured meshes can be generated using
OpenFOAM’s built-in utility called blockMesh. Apart from the blockMesh, several other mesh
generators can also be used, such as snappyHexMesh, an in-built utility of OpenFOAM, and other open-
source mesh generators, such as Salomé (Aubry et al., 2020) and Gmsh (Geuzaine and Remacle, 2009).
Chapter 1: Introduction
14
Both mesh generators offer the possibility to choose from different meshing algorithms based on the
requirements. Both platforms use two languages, python and C++, and can be used as a post-
processor, too. Creating a high-quality three-dimensional mesh is laborious and time-consuming, but
the influence of mesh quality on simulated results is significant and should not be overlooked.
Furthermore, the assignment of boundaries and initial conditions significantly affects the solution.
Poorly defined boundary conditions may result in a low rate of convergence. There exist three types
of boundary conditions for PDEs. A Dirichlet boundary condition sets a fixed value at the boundary,
Neumann boundary condition defines the flow rate or flux across the boundary, and Cauchy boundary
condition combines fixed values and flux. These conditions play a crucial role in accurately representing
flow behaviour and boundary interactions in numerical simulations using OpenFOAM.
Multiphase flows can exist in many different forms. Around 22 solvers exist for multiphase flow in
OpenFOAM (Greenshields, 2022). Depending on the phases, two-phase flows can be classified based
on the state of different phases gas-fluid, gas-solid, fluid-solid and fluid-fluid phases. Gas-liquid flows
in themselves can have several different configurations, examples of which are bubbles in liquid flow
or the motion of liquid droplets in a gas; these both come under the category of dispersed flows (Yeoh
and Tu, 2019). In addition, the gaseous phases can further be categorised into compressible and
incompressible based on the velocity of flow and speed of sound in the medium. Depending on the
properties of the interface, multiphase flows can further be classified into separated and dispersed
flows (mentioned above). Dispersed flows are characterised by the flow where one phase is dispersed
in the other continuous phase (Serzawa, 2006). In contrast, a separated flow consists of separate,
parallel streams of two (or more) phases. Ishii and Hibiki (2011) give an overview of different categories
of two-phase flows. There are several subtypes within the dispersed flow class. One can consider
spherical, elliptical, granular particles, etc., depending on the geometry of the interface. However, it is
more practical to divide the category of dispersed flows according to the dispersion phase. As a result,
three regimes may be distinguished: bubbly, droplet or mist, and particle movement (Ishii and Hibiki,
2011).
Incompressible water-air flows are important for the free-surface flows that this thesis is
considering (Schulze and Thorenz, 2014). Only at extremely high velocities or pressure variations the
compressibility of air can become significant. The free-surface flow considered for this thesis is quite
similar to that in the field of hydraulics and river engineering, where free surface tracking and volume-
of-fluid (VOF) are widely used in CFD applications (Nguyen and Nestmann, 2004). This thesis will use
the VOF method as it best describes incompressible, separated two-phase flows. Hirt and Nichols
(1981) introduced the volume-of -fluid (VOF) method in the early 1980s. With this method, free
surfaces can be generated utilising parallel lines concerning one of the system’s primary coordinates.
The free surface is regarded as either a horizontal or a vertical line in the cell, depending on the
respective normal vector components. Moreover, to define the normal vector in a chosen cell and
account for flux variations, nine adjacent cells are considered.
In OpenFOAM, the interFoam solver algorithm is based on the VOF method. In the literature,
interFoam has been successfully used to model several air/water interaction problems. To mention a
Chapter 1: Introduction
15
few, Lobosco et al. (2011) in their study tested the interFoam solver in self-aeration areas of tiered
spillways. Deshpande et al. (2012) deployed the interFoam solver to horizontal jets dropping into a
pool and compared their findings with those from experiments. Satisfactory findings were shown, and
the solver exhibited good mass conservation, acceptable advection errors, and sufficient accuracy
concerning surface curvature, even at low grid resolution (Lopes, 2013). Also, Trujillo et al. (2007)
focused on experimental and computational investigations of horizontal jets below a free
surface. Further details on equations and the treatment of variables will be discussed in Chapter 2.
1.3.3 Transport and mass transfer modelling
Transport
To account for the movement of H2S and O2 in the sewer, the model must incorporate transport
processes. Although the two-phase hydrodynamics may be described using the previously described
interFoam solver in OpenFOAM, which employs the VOF approach, additional consideration must be
given to the transport of substances. This section gives some basics of transport processes.
Conservative and reactive transport are two different types of transport processes; reactive transport
considers substance formation due to chemical reactions. Only conservative transport is considered in
this work. The three driving processes that comprise conservative transportation are (Hinkelmann,
2005):
• Advection / convection
• Molecular diffusion
• Turbulent diffusion and dispersion
Advection describes the particle’s movement with the flow field in a vertical or horizontal direction
without spreading (Hinkelmann, 2005). Diffusion can be divided into molecular and turbulent diffusion.
Molecular diffusion results from Brown’s molecular movement and is induced by thermal motion. This
results in the random movement of water and molecules of dissolved substances. Consequently, the
dissolved substances gradually move from an area of high concentration to that of low concentration.
This process can be described using Fick’s law of diffusion which states that the rate of mass movement
due to molecular diffusion is proportional to the negative gradient of mass concentration (Hinkelmann,
2005).
In most practical cases, the molecular diffusion process has little bearing on the movement of
pollutants in water bodies. However, the movement of mass by random water movement in turbulent
flow provides an appealing parallel for the movement of mass by random molecular motion in
molecular diffusion. The idea of turbulent diffusion or dispersion is in line with Fick’s law, according to
which mass is transported by turbulence in a way similar to molecular diffusion from high-
concentration areas to low-concentration areas at a rate proportionate to the negative gradient of
concentration. Although turbulent diffusion is often associated with somewhat higher rates of
movement, it is nonetheless defined by the same rule as molecular diffusion (Lehr and Lehr, 2000).
Chapter 1: Introduction
16
In a gist, dispersion often described using Fick’s law of diffusion, is the apparent mixing that arises
from spatial variations in advective velocity. Dispersion is theoretically derived from spatial averaging
of the flow field and concentration distribution. The Schmidt number (Sc) relates the impact of
turbulence in momentum and mass transport in fluid mechanics, calculated as the ratio of kinematic
viscosity to turbulent diffusivity (see Chapter 2.1.1). In turbulent flows, the Schmidt number varies
based on fluid properties and flow conditions, dependent on turbulent viscosity estimated by
turbulence models.
The basis of this work was the equations that were incorporated into the interFoam solver of
OpenFOAM, which did not have previously a built-in solution for transport equations by Teuber et al.
(2019b). This extended model accounted for the mass transfer and transport of H2S. In this study the
solver was further extended to account for the mass transfer and transport of O2. More details about
this will be explained in the following chapter about the methods and tools used.
Mass transfer
The behaviour of mass transfer in multiphase systems and the main approaches to describe mass
transfer in the context of sewers is delineated in this section as the mass transfer between H2S and O2
from water to the air is significant for the current work. Mass transfer across the liquid-gas interface
in sewers is influenced by various factors. The conditions of equilibrium and mass transfer rates
determine mass transfer in a multiphase system. The mass transfer coefficient generally describes the
mass flow between the phases. The Henry coefficient is used to characterise the equilibrium between
the two phases.
Several theories address mass transfer across phases, including the two-film theory, the
penetration theory, and the surface renewal theory. In the current work, the focus is given to the air-
water interface.
Two-film theory (TFT) was first propounded by Lewis and Whitman (1924); it proposes the existence
of an interface-separated film of a certain thickness in both the liquid and gas phases and is predicated
on the assumption that mass transfer through the film occurs by molecular diffusion under steady-
state conditions. Beyond which the concentration is homogeneous, and the flux is small, and the mass
transfer occurs at low concentration (Morsi and Basha, 2015). Two-film theory was employed in the
WATS model to account for mass transfer in drop structure which was later also developed by Matias
et al. (2017). Hvitved-Jacobsen et al. (2013) stated that applying two-film theory results in simple
expressions for gas-liquid mass transfer, which are helpful for practical applications.
However, the assumption entailed with the adoption of two-film theory makes the model too
simple such as neglecting the spatial variations of the DO (dissolved oxygen) concentrations (Amaral
et al., 2019), making the model obsolete. Here are certain assumptions on which two-film theory is
based that forsake the intricacies of the oxygen mass transfer phenomenon in sewer systems:
• The species concentrations in any location is constant over time.
• The films at the interface of both phases are laminar.
• Equilibrium conditions at the interface are achieved immediately.
Chapter 1: Introduction
17
Wang et al. (2018) in their study pointed out that variations of gas and liquid velocity and fluid
characteristics frequently vary with location depending on the local flow regime, such as laminar,
transitional, or turbulent flows. This local variation in flow behaviour and fluid characteristics cannot
be adequately represented by a simple TFT. Moreover, in the event of flow instabilities induced by
oscillating solvent injection may cause waves to form along a falling film. In these situations, the mass
transfer coefficient may be significantly impacted by variations in the film thickness, which is not
adequately captured by TFT. In addition, TFT is one dimension based, as a result, it is unable to describe
the complex behaviour in real applications accurately. In comparison to the two-film theory, other
methods, including the penetration theory and the surface renewal theory, offer certain
advantages. However, the local changes in fluid velocities, physical attributes, and different flow
regimes are still not taken into account (Teuber, 2020; Wang et al., 2018).
In recent years, the use of CFD modelling to better analyse and understand mass transfer in
multiphase systems has become popular. CFD modelling techniques essentially help to understand
underlying crucial elements that may occur in the process of mass transfer in these systems. One of
the most typical approaches in this field of study is the VOF method with a continuum surface model.
Moreover, the approach defines the flow and chemical kinetics using the one-fluid formulation, which
considers diffusion, advection, and chemical reactions instead of values obtained from standard
correlations (Wang et al., 2018).
OpenFOAM offers several in-built solvers to simulate the mass transfer phenomena. From the
literature review, it can be inferred that even in simple case structures, H2S and O2 mass transfer
processes involved in significant turbulence effects and three-dimensionalities can affect the mass
transfer of H2S in sewers. For this reason, a three-dimensional, two-phase model that can take into
consideration mass transfer to the environment of a sewer system must be used. Considering the
advantages offered by the VOF approach, the current work employs one-fluid formulation for the VOF
method developed by Haroun et al. (2010a, 2010b) for modelling the mass transfer across immiscible
phases. The approach was implemented into JADIM (Joint Application Development for Interface
Modeling) code developed by IMFT (Institute of Fluid Mechanics of Toulouse, France), a multiphase
software (Legendre and Magnaudet, 1998). Nieves-Remacha et al. (2015), Marschall et al. (2012) and
Severin, (2017) implemented this approach in OpenFOAM. The two formulations of Haroun et al.
(2010a) and Marschall et al. (2012) were compared and were giving the same steady state results for
a variety of test cases (Prasad Thummala et al., 2019). The methodology employs the interFoam solver
and considers an additional transport equation for both phases. In the VOF approach, using the
additional mass flux term, the effect of the concentration jump at the interface is taken into account
(Dixit et al., 2019; Teuber, 2020). Henry’s law can be used to compute this additional mass flux, which
is caused by the solubility of gaseous species in the liquid. A detailed explanation and the
implementation of Henry coefficient is given in Chapter 2.1.2.
Chapter 1: Introduction
18
1.4 Research Training Group: Urban Water Interfaces
The current study was conducted within the framework of the DFG Research Training Group named
Urban Water Interfaces (UWI). UWI is an interdisciplinary research training group of engineers and
natural scientists of the Technische Universität Berlin (TUB, coordinator) and the Leibniz Institute of
Freshwater Ecology and Inland Fisheries (IGB) and is funded by the Deutsche Forschungsgemeinschaft
(DFG). To promote sustainable water resources management in urban environments, UWI aspires to
better understand and model processes and fluxes at urban water interfaces at different spatial and
temporal scales. An essential pre-requisite to achieving this objective is realising that natural and
technical system components of the urban water cycle need to be considered in an integrated way.
UWI’s foundation is predicated on the understanding that its objective can be realised only through
close collaboration of engineers and natural scientists with a common conceptual basis. This study
group also aims to explore the knowledge gleaned from the research as a tool to facilitate evidence-
based management decisions (Gessner et al., 2014).
Gessner et al. (2014) identified five key interfaces to be investigated (represented in Figure 1.6):
• Surface water – atmosphere
• Soil surface – atmosphere
• Surface water – sediment–groundwater
• Wastewater – gas space in sewer pipes
• Surface water – treated wastewater
The current study constitutes an integral part of research conducted by UWI as water-gas space in
sewers was identified as one of the key interfaces in urban water interfaces as indicated by the study
of Gessner et al. (2014). The current doctoral thesis is thus associated with the Common topic group
on “Interfaces in sewer systems” within UWI, focusing on two-phase simulation and odour control in
sewers (project S2). The study also emphasises the need to address the critical issues associated with
sewer networks, especially the problems concerning transport rates and kinetics of sulphuric acids in
sewers.
1.5 Aim and outline of the work
1.5.1 Aim and innovation
This thesis expands and further validates a model that accurately describes processes taking place
at the interface between water and air. This model is given by the three-dimensional two-phase solver
interH2Sfoam, which was initially developed and incorporated into OpenFOAM by Teuber et al.
(2019b). The aim is to employ this extended solver to effectively depict water-air flow and the release
of H2S at the air-water interface within enclosed conduits.
This research aimed to build upon the work of Teuber et al. (2020) by further investigating the
hydraulics of pipe flow and extending the focus to the sewer headspace (air phase). The study involved
simulating and verifying the single-phase transport of gases in the sewer headspace, with a specific
Chapter 1: Introduction
19
emphasis on oxygen (O2). This extension considered the mass transport and transfer of O2 within the
sewer system.
An important aspect of this research was the implementation of numerical simulations to identify
hotspots for the removal of harmful gases from the system. Notably, previous studies had not
undertaken such simulations. As an innovative contribution of the thesis, the research not only focused
on identifying these hotspots but also explored ventilation as a viable measure for effectively removing
gases from the system. Unlike past practices that focused on experimental studies or utilized idealized
geometries to examine the impact of turbulence on mass transfer, this study took a more
comprehensive approach. Collaborating with Project S1 of UWI, an experimental setup was designed,
and the data for H2S and O2 mass transfer was collected for validating the model. A to-scale geometry
was produced and simulated, and the results were compared with the data collected. The thesis also
stands out for its utilization of intricate meshing techniques for complicated cases such as the use of
dynamic/movable mesh.
Figure 1.5: Bridge between projects T3 (first cohort) and S2 (second cohort) of the Urban Water
Interfaces.
1.5.2 Outline of the thesis
This thesis is organized into eight comprehensive chapters, offering a detailed exploration of the
subject matter. The current chapter, Chapter 1, serves as an introduction, setting the stage for the
subsequent chapters. A brief overview of all the chapters is pictorially represented in Figure 1.7.
Chapter 2 introduces the mathematical modelling concepts and tools utilized in the present study,
which focus on understanding the mechanisms behind odour in sewer systems and extending and
further validating a CFD simulation model. The research begins with a comprehensive investigation of
H2S and O2 formation in sewers, building upon previous conceptual models that estimate odour risks
Chapter 1: Introduction
20
and propose mitigation strategies for H2S production. The current study expands upon these models
to include O2 mass transfer in gravity sewers.
Chapter 3 focuses on the extension and validation of the interH2SFoam solver, which is extended
to interO2Foam by accounting for the transfer and transport of O2. This chapter delves into the
technical details and rigorous testing of the solver, ensuring its accuracy and reliability.
Chapter 4 and Chapter 5 describe the validation process of the solver, examining its performance
in various setups at different scales. These chapters provide a thorough analysis of the solver's
capabilities and its ability to accurately capture the intricacies of the systems under investigation. In
Chapter 4, the focus is on the practical application of the H2S and O2 mass transfer solvers in a
laboratory-scale setup, as previously explored by Bentzen et al. (2016). They conducted a series of
experiments aimed at enhancing the understanding of wastewater drag and the wall frictional force
affecting the air in the headspace of gravity sewers. The data obtained from these experiments played
a crucial role in validating the hydraulics of the air phase. Additionally, measurements of oxygen
concentration were utilized to verify the accuracy of the solver in representing the transport of oxygen
in the air phase.
Chapter 5 delves into two aspects: the flow of a tracer, focusing on O2, and the ventilation of this
tracer within the system. To investigate these aspects, the capabilities of the solver are examined
through a complex three-dimensional test case. This test case is developed based on the field
experiments conducted by Madsen et al. (2006), providing a realistic and challenging scenario for
validation purposes. Through this test case, the solver's performance is assessed, and its ability to
identify hotspots where the tracer accumulates is evaluated. Additionally, it showcases the solver's
capabilities through a comprehensive and complex test case, enabling further validation and
investigation of tracer behaviour and ventilation strategies.
In Chapter 6, the attention shifts to the study of turbulence and its impact on the mass transfer of
H2S and O2. This chapter presents an in-depth analysis of the influence of turbulence on the behaviour
of a rotating system, shedding light on important factors that contribute to the overall understanding
of the mass transfer process in highly turbulent sewer systems.
Chapter 1: Introduction
21
Figure 1.6: Urban Water Interfaces (inspired by Gessner et al., 2014).
Chapter 1: Introduction
22
Chapter 7 serves as a pivotal section, presenting the conclusions drawn from the extensive research
conducted throughout the thesis. Additionally, it outlines steps for further exploration and
development of the model, paving the way for future research endeavors.
Appendix A provides a succinct overview of the contributions made to conferences, summarizing
the findings and insights shared with the scientific community. Appendix B and Appendix C give an
overview of the solver modifications and all the case setups used in this study. These chapters ensure
a comprehensive and systematic approach towards investigating the cause and mitigation of odour in
sewer systems, covering various aspects of the topic while providing a solid foundation for further
research.
Figure 1.7: Graphical overview of the thesis.
23
Chapter 2
Model concepts and tools
This chapter presents the concepts associated with mathematical modelling and tools used in the
current study. The current work focuses on two key elements: a better understanding of the
mechanisms causing odour in sewer systems and further development of a CFD simulation model. To
achieve this, a comprehensive study on the formation of H2S and O2 in sewers was carried out. In the
seminal works in the field of study, conceptual model approaches were developed to estimate odour
and to make appropriate suggestions for the abatement of H2S production. Current research extends
them to O2 mass transfer in gravity sewers. In light of the inferences from the literature study, a 3D
CFD model was deemed essential to take into account the three-dimensional effects, to carefully
analyse the physical and chemical countermeasures against odour. In this regard, using the interFOAM
solver, a 3D CFD model was extended to describe the formation of H2S and O2 in OpenFOAM. The
solver interFOAM is a “solver for two incompressible, isothermal immiscible fluids using a VOF
(volume-of-fluids) phase fraction-based interface capturing approach with optional mesh motion and
mesh topology changes including adaptive re-meshing” (Greenshields, 2022). The interFOAM is an
inbuilt solver provided by the CFD-toolbox OpenFOAM, a multiphase solver used in simulations with a
sharp and well-defined interface between the fluid phases (Schulze and Thorenz, 2014). Further details
about the solver will be explained in the following sections of this chapter.
2.1 Numerical Methods
2.1.1 Hydrodynamic simulations and turbulence models
InterFoam is a solver based on the volume-of-fluid (VOF) method. In the VOF method originally
developed by Hirt and Nichols (1981), a scalar function representing the volume fraction of phases in
the computational cells is advected. To avoid the interface thickness being excessively smeared, the
advection of the volume fraction equation is done using specific discretisation schemes such as
interface compression (Vachaparambil and Einarsrud, 2019).
Hydrodynamic simulations
The VOF approach solves a single set of equations, including continuity and momentum equations
for the whole domain. The continuity equation for incompressible flow, the momentum equations, a
Chapter 2: Model concepts and tools
24
specific transport equation, and the constitutive relations for density and dynamic viscosity are the
governing equations that must be solved simultaneously (Ubbinik, 1997).
The continuity equation can be represented by:
∇ ∙ U = 0
Eq. 2.1
Where U is the fluid velocity field (m/s).
The momentum equation can be written as follows:
𝜕𝜌𝑈
𝜕𝑡 + 𝛻∙ (𝜌𝑈𝑈)= −𝛻𝑝+ 𝛻 ∙ 𝑇+ 𝜌𝑓U
Eq. 2.2
Where 𝜌 is the density of the fluid (kg/m3), t is time in seconds (s), 𝑝 is the pressure (Pa), 𝑇 is the
deviatoric stress tensor which is the symmetric component of strain rate tensor (N/m2), and 𝑓 are
body forces per unit mass (m/s2).
As both fluids under consideration in the study are incompressible and Newtonian, the deviatoric
stress tensor can be reformulated to the following form for application in the computational domain
as follows:
𝛻∙ 𝑇= 𝜇[∇U+(∇U)T]= 𝛻∙ (𝜇𝛻𝑈)+(𝛻𝑈)∙𝛻𝜇
Eq. 2.3
Where 𝜇 is the dynamic viscosity (Ns/m2).
The interFOAM solver's VOF approach only takes into account one pressure system. In order to
avoid the formation of steep pressure gradients brought on by hydrostatic effects and to simplify the
boundary conditions, a modified pressure prgh is adopted, which defines the static pressure component
reduced by the hydrostatic pressure component (Rusche, 2003; Teuber et al., 2019a). 𝜌∙𝑔∙𝑥
represents the hydrostatic component of the pressure:
𝑝𝑟𝑔ℎ=𝑝 − 𝜌∙ 𝑔∙ 𝑥
Eq. 2.4
Where g is the acceleration vector due to gravity in m/s2 and x is a spatial position vector in meter
(m).
The density and viscosity of the fluids in the domain are characterized by a scalar function called
volume fraction 𝛼 as the VOF approach treats the two immiscible fluids, liquid and gas, as one fluid.
The following equations give the relation between volume 𝛼, density and viscosity respectively.
𝜌=𝛼𝜌L+𝜌G(1−𝛼)
Eq. 2.5
𝜇= 𝛼 𝜇𝐿+𝜇𝐺(1−𝛼)
Eq. 2.6
Chapter 2: Model concepts and tools
25
In the above two equations (Eq. 2.5 and Eq. 2.6), 𝛼 is the volume of fraction or indicator function. The
subscript L denotes water (L- liquid) and G denoted air (G- gas). The viscosity has two components the
physical viscosity 𝜇𝑝ℎ𝑦𝑠 and turbulent viscosity 𝜇𝑡𝑢𝑟𝑏. Turbulent viscosity has to be determined by a
turbulence model:
𝜇𝑖=𝜇𝑖,𝑝ℎ𝑦𝑠+𝜇𝑖,𝑡𝑢𝑟𝑏
Eq. 2.7
Here 𝑖 stand for the respective phase L or G.
VOF equation is a transport equation and is utilized with an advanced formulation. It is
implemented as an additional transport equation that serves as a marker to explain the distribution of
the phases across the domain and, consequently, the position of the free surface (Morgan, 2013). The
above-mentioned volume fraction 𝛼 is strictly bounded 0≤𝛼≤1. Also, it is assumed that at the
interface both the phases have same velocity (Schulze and Thorenz, 2014; Teuber et al., 2019a). For
two-phase flow, the model utilizes a two-fluid Eulerian model, in which the phase fraction equations
are individually solved for each phase (Berberović et al., 2009). The transport equation for phase
fraction is modified in this model to incorporate an added convective term that results from
modelling the velocity as a weighted average of the respective liquid and gas velocities, giving a better
interface resolution:
𝜕𝛼
𝜕𝑡 +𝛻(𝛼𝑈𝐿)=0
Eq. 2.8
𝜕(1−𝛼)
𝜕𝑡 +𝛻((1−𝛼)𝑈𝐺)=0
Eq. 2.9
Now the velocity of the effective fluid in a VOF model is defined as a weighted average and it is
assumed that the contributions of the liquid and gas velocities to the evolution of the free surface are
proportional to the respective phase fraction, according to Berberović et al. (2009):
𝑈=𝛼𝑈𝐿+(1−𝛼)𝑈𝐺
Eq. 2.10
Therefore, on rearranging Eq. 2.8, we get the implemented Eq. 2.11 for volume fraction in interFoam:
𝜕𝛼
𝜕𝑡+𝛻∙(𝛼𝑈)+𝛻∙((1−𝛼)𝑈𝑟 𝛼)=0
Eq. 2.11
Where 𝑈𝑟 is relative velocity:
𝑈𝑟= 𝑈𝐺 – 𝑈𝐿
Eq. 2.12
known as compression velocity. The artificial compression term was introduced to make the interface
sharp (Rusche, 2003). The function 𝛼 can take the following values for a water-air flow as given below:
Chapter 2: Model concepts and tools
26
𝛼= {1 𝑓𝑙𝑢𝑖𝑑 𝐿− 𝑤𝑎𝑡𝑒𝑟
0<𝛼<1 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑟𝑒𝑔𝑖𝑜𝑛
0 𝑓𝑙𝑢𝑖𝑑 𝐺− 𝑎𝑖𝑟
Eq. 2.13
In the transitional region, the water surface is assumed to be the region where 𝛼=0.5. The volume
fraction 𝛼 for single-phase simulations is 1 and constant across the whole domain and the simulation
period.
Turbulence models
Since the current study involves fluid flows characterized by high Reynolds numbers, deployment
of appropriate turbulence models is pertinent to solve the CFD problems at hand. Several turbulence
models including some hybrid ones, from Reynolds averaging to Direct Numerical Simulation, are
available in OpenFOAM (see Figure 2.1).
Figure 2.1: Classical CFD approaches for turbulent flow simulation: classification according to levels of
turbulence modelling and relative computational cost (inspired by Greco, 2018).
An approach to solving the governing equations of motion for fluid-solid and fluid-fluid systems
without any coarse graining, filtering, or averaging of the governing equations is known as direct
numerical simulation (DNS) of multiphase flows, also known as particle-resolved DNS (Joshi et al.,
2019). DNS has been proven to have highest accuracy of simulation but requires highest computation
effort as the turbulence is discretized by very small cell sizes and time steps to display all the vortices
(Marić et al., 2014). The advent of massively parallel computing platforms, however, provides a means
for performing a direct numerical simulation (DNS) of the Navier-Stokes equations for canonical flows
with simple geometries and increasing Reynolds numbers (Kim et al., 2023).
In terms of complexity, Large Eddy Simulation (LES) falls between DNS and RANS models. By
adopting small enough cell sizes, large eddies could be spatially resolved, and small eddies can be
modelled using a subgrid-scale model, such as the Smagorinsky model (subgrid-scale turbulence
model) used in Large Eddy Simulation (LES), where the turbulent stresses are modeled based on the
local strain rate and a user-defined constant called the Smagorinsky coefficient resulting in reduced
required cell sizes than RANS models (Marić et al., 2014).
Chapter 2: Model concepts and tools
27
In the Navier-Stokes equations, the mean velocity is separated into an average velocity component
and a fluctuating velocity component using Reynolds temporal averaging, yielding a Reynolds stress
tensor (RANS). The equations then have new unknowns as a result of this tensor's characterization of
an additional eddy viscosity. A two-equation model, which includes two coupled transport equations
to explain convection and diffusion of turbulent kinetic energy, may be utilized to solve these
unknowns. These variables are predicated on the model chosen. In different two-equation models that
exists, k (m²/s²) stands for turbulent kinetic energy, 𝜖 (m³/s³) stands for the turbulent dissipation, and
𝜔 (s⁻¹) stands for the specific dissipation. For k-𝜖 in which turbulence is assumed to be isotropic, three
different formulations exist: the Standard (STD) k-𝜖 model, the Realizable (Shih et al., 1995) and the
RNG k-𝜖 model using Re-Normalisation Group (RNG) methods (Yakhot et al., 1992). RANS models used
in the current study are standard k-𝜖, RNG k-𝜖, and Shear Stress transport SST.
In the standard k- 𝜖 model, the turbulent kinetic energy (k) and the turbulence eddy dissipation (𝜖),
which measure the rate at which the turbulent kinetic energy dissipates, are solved as two partial
differential equations (transport equations). One issue with several two-equation turbulence models,
such as the k-𝜖 model, is their inability to capture the finer relationships between the turbulent energy
output and the turbulent stresses produced by anisotropy of the normal stresses (Shaheed et al.,
2019). In order to re-normalise the Navier-Stokes equations and take into consideration the effects of
lower scales of motion, Yakhot et al. (1992) created the RNG model using Re-Normalisation Group.
Also, the SST k-omega model, created by Menter, (1994) may be utilized as a low-Reynolds number
turbulence model without the need for additional damping functions due to the use of a k-formulation
in the inner parts of the boundary layer that offer direct usage of the model to the wall through the
viscous sub-layer. By transitioning to a k-𝜖 behaviour in the free-stream, the SST formulation also
avoids the usual k-behaviour issue where the model is overly susceptible to the inlet free-stream
turbulence features.
In the region near the wall, turbulence models like the k-𝜖 are redundant since they are only
effective when the turbulence is fully developed. There are typically two approaches suggested to
handle the near wall region. Assigning turbulence to the wall is one method. In order to resolve the
viscosity-affected region with the whole mesh all the way to the wall, including the viscous sublayer,
turbulence models are modified. The first cell centre must be placed in the viscous sublayer when
utilizing the modified low Reynolds number turbulence model to solve the near wall area (Liu, 2017).
This method necessitates higher mesh resolution.
Care must be taken that the first cell centre must be positioned in the log-law area to ensure the
accuracy of the outcome. Another approach is to make advantage of wall functions, which can model
the area near the wall. Wall functions are empirical equations used to fulfil the physics of the flow in
the near wall region. Instead of defining the boundary conditions for the momentum and turbulence
transport equations at the wall itself, wall functions are utilized to connect the inner area between the
wall and the turbulence fully formed region (Liu, 2017).
Chapter 2: Model concepts and tools
28
The velocity profile normal to the wall follows the log-law, a logarithmic profile, which is explained
by these wall functions. The dimensionless wall distance 𝑦+ can be used to define the applicability of
certain wall functions:
𝑦+=𝑦
𝑣𝑣𝜏
Eq. 2.14
Where 𝑦 (m) stands for the absolute distance from the wall, 𝑣 stands for the friction velocity (m/s)
and 𝑣𝜏 stands for the kinematic viscosity (m²/s). Different values of 𝑦+ and thus various cell sizes in the
nearfield of the wall are required depending on the chosen RANS turbulence model and the relevant
wall function (Marić et al., 2014). This must be considered while deciding the cell size for meshing near
the wall. Because of the log-law, RANS turbulence models have lower requirements for cell size and
time step than LES and DNS, and are thus more likely to result in the least computing effort (Teuber et
al., 2019a).
2.1.2 Transport and mass transfer simulation
Transport
The interFoam solver in OpenFOAM did not include built-in equations for transport; therefore, the
appropriate equations had to be implemented. An equation for the advection-diffusion of passive
tracer with concentration “C” as shown in Eq. 2.15 was included and implemented by Teuber et al.
(2019b). As it can be inferred from the equation, the diffusivity is separated into two components:
physical diffusivity 𝐷𝑝ℎ𝑦𝑠 and turbulent diffusivity 𝐷𝑡𝑢𝑟𝑏, which are computed using Eq. 2.15 and the
user must define the turbulent Schmidt number 𝑆𝑐𝑡𝑢𝑟𝑏 and the physical diffusivity 𝐷𝑝ℎ𝑦𝑠.
Advection-diffusion equation:
𝜕𝐶
𝜕𝑡+𝛻∙(𝑈𝐶)=𝛻∙((𝐷𝑝ℎ𝑦𝑠+ 𝐷𝑡𝑢𝑟𝑏)𝛻𝐶)+𝑊
Eq. 2.15
Where 𝐷𝑡𝑢𝑟𝑏 using the equation for 𝑆𝑐𝑡𝑢𝑟𝑏 can be written as:
𝑆𝑐𝑡𝑢𝑟𝑏 =𝜐𝑡𝑢𝑟𝑏
𝐷𝑡𝑢𝑟𝑏= 𝜇𝑡𝑢𝑟𝑏
𝜌
𝐷𝑡𝑢𝑟𝑏 ⇒𝐷𝑡𝑢𝑟𝑏= 𝜇𝑡𝑢𝑟𝑏
𝜌
𝑆𝑐𝑡𝑢𝑟𝑏
Eq. 2.16
And W is a sink or source term, or the production term related to chemical reaction which has not
been considered here.
Mass transfer
A review of the literature revealed that the 3D model for the current study should include H2S and
O2 mass transfer and transport to accurately study odour in sewer systems. As explained in Chapter 1,
Chapter 2: Model concepts and tools
29
even in simple structures, significant turbulence effects and three-dimensionalities can affect the mass
transfer of H2S and O2 in sewers. As a result, a three-dimensional two-phase model that can account
for mass transfer to the environment of a sewer system is required. The ability to account for three-
dimensional effects is one of the benefits of using a CFD technique to characterize transport and mass
transfer processes across the interfaces and interaction with sewer walls and its atmosphere (Teuber,
2020). There are several solvers available in OpenFOAM to simulate transport and mass transfer in
multiphase systems. The VOF approach with a continuum surface model, however, offers a number of
advantages to characterize the systems taken into account in this thesis.
As mentioned above, the VOF method as it has been defined by Haroun et al. (2010a, 2010b) and
was implemented in OpenFOAM by Nieves-Remacha et al. (2015) for mass transfer is applied.
Henry's coefficient was used in the one fluid formulation for transport and mass transfer developed by
Haroun et al. (2010a). It should be noted that the formulation by Haroun et al. (2010b) only accounts
for the physical diffusivity and ignores the turbulent diffusivity Dturb.
Using Henry's law with a constant coefficient, the thermodynamic equilibrium of chemical species
at the interface is resolved. A good agreement has been found between this method, which has been
included into the JADIM code, and the penetration theory. The interface between phases cannot be
accounted for by a standard advection-diffusion equation since one set of Navier-Stokes equations is
solved. Non-physical spreading may happen, if a tracer is modelled in the vicinity of an interface
between two phases. One can perhaps prevent the unphysical spreading by adopting the method
proposed by Haroun et al. (2010a), with a low value for the Henry coefficient, allowing the user to
simulate single-phase transport.
The quations including turbulent diffusivity 𝐷𝑡𝑢𝑟𝑏 and mass transfer is as follows:
𝜕𝐶
𝜕𝑡+𝛻∙(𝑈𝐶)=𝛻∙((𝐷𝑝ℎ𝑦𝑠+𝐷𝑡𝑢𝑟𝑏)𝛻𝐶+𝜙)+𝑊
Eq. 2.17
Where 𝜙 is the concentration flux at the interface given by the following expression:
𝜙= −(𝐷𝑝ℎ𝑦𝑠+ 𝐷𝑡𝑢𝑟𝑏)( 𝐶 (1−𝐻𝑒)
𝛼+𝐻𝑒(1−𝛼))𝛻𝛼
Eq. 2.18
Sink or source term W is not taken into consideration in the current study. According to Yongsiri
(2004), the mass transfer is dependent on the Reynold number and pH value. In addition, the Henry
coefficient is highly influenced by the temperature (Hvitved-Jacobsen et al., 2013). The diffusive
transport described by Fick's law is expected to be the same in both phases at the interface, where
Henry's law must be satisfied:
𝐻𝑒=𝐶𝐿
𝐶𝐺
Eq. 2.19
Chapter 2: Model concepts and tools
30
(𝐷𝑝ℎ𝑦𝑠,𝐿+ 𝐷𝑡𝑢𝑟𝑏,𝐿)𝛻𝐶𝐿=(𝐷𝑝ℎ𝑦𝑠,𝐺+ 𝐷𝑡𝑢𝑟𝑏,𝐺)𝛻𝐶𝐺
Eq. 2.20
Depending on the phase fraction value 𝛼, the concentrations and diffusion coefficients are treated
as single-phase characteristics. The diffusion coefficient is determined using a harmonic average,
whereas the concentrations are derived using linear averaging:
𝐶=𝛼𝐶𝐿 + 𝐶𝐺(1−𝛼)
Eq. 2.21
𝐷𝑝ℎ𝑦𝑠,𝐿= (𝐷𝑝ℎ𝑦𝑠,𝐿∙𝐷𝑝ℎ𝑦𝑠,𝐺
𝛼𝐷𝑝ℎ𝑦𝑠,𝐿+(1−𝛼)𝐷𝑝ℎ𝑦𝑠,𝐺)
Eq. 2.22
The diffusion coefficients 𝐷𝑝ℎ𝑦𝑠,𝐿 and 𝐷𝑝ℎ𝑦𝑠,𝐺 are defined by the user. However, these coefficients
are also temperature dependent, which must be taken account by the user when assigning the values.
The local mass transfer can be calculated as follows in order to validate mass transfer rates:
𝐾𝐿,𝑙𝑜𝑐𝑎𝑙= − ((𝐷𝑝ℎ𝑦𝑠,𝐿+ 𝐷𝑝ℎ𝑦𝑠,𝐺)𝛻𝐶+ 𝜙) ∙ 𝑛𝐿
∆𝐶𝐿,𝑙𝑜𝑐𝑎𝑙
Eq. 2.23
Where 𝑛𝐿= 𝛻𝛼
|𝛻𝛼| is normal to the interface pointing to the liquid.
Here ∆𝐶𝐿,𝑙𝑜𝑐𝑎𝑙 is the difference between the concentration in the free surface region and the bulk
liquid concentration (mol/m3).
The overall mass transfer across the interface is obtained by integrating over the interface:
𝐾𝐿= 1𝜆∫𝐾𝐿,𝑙𝑜𝑐𝑎𝑙
𝜆
0𝑑𝜉
Eq. 2.24
Where 𝜆 is the interface length (m) and 𝜉 (dimensionless) is the curvilinear coordinate associated
to the interface. According to Carrera et al. (2017), to calculate the mass transfer, the following
function may be fitted to the drop in concentration in the liquid phase:
𝐶𝐿,𝐻2𝑆=𝐶𝐿,0𝑒−𝐾𝐿,𝐻2𝑆𝑎(𝑡−𝑡0)
Eq. 2.25
Where 𝐶𝐿,0 (mg/L) is the initial concentration at t = t0, 𝐾𝐿,𝐻2𝑆 is the overall mass transfer coefficient
(m/h), 𝑎 is the specific interfacial area (m2/m3) and 𝑡 is the time (h).
Chapter 2: Model concepts and tools
31
2.2 Tools
2.2.1 Pre-processing tools
OpenFOAM utilities (Block Mesh and SnappyHexMesh)
This section gives an overview of the pre-processing tools used in the current work. OpenFOAM
framework offers two inbuilt utilities for mesh namely BlockMesh and SnappyHexMesh. BlockMesh is
a tool that generates graded and curved edged parametric meshes. The underlying idea of blockMesh
is to divide the domain geometry into a number of three-dimensional, hexahedral blocks. Block edges
can be straight lines, arcs, or splines. The mesh is apparently defined by a certain number of cells in
each direction of the block, providing blockMesh with enough information to produce the mesh data
(Greenshields, 2022; Schulze and Thorenz, 2014). The blockMesh utility has been used in Chapter 3
and Chapter 4 due to the simplicity of the mesh that is used for the simulation. On the other hand, this
utility can also be used to mesh complicated geometries, but there are several other tools that provide
more freedom and a better GUI (graphical user interface).
The snappyHexMesh utility simply generates three-dimensional meshes from triangulated surface
geometries in stereolithography (STL) format that comprises hexahedra (hex) and split-hexahedra
(split-hex). Iteratively refining a starting mesh and morphing the resulting split-hex mesh to the surface
causes the mesh to substantially conform to the surface. The generated mesh will be shrunk back and
have cell layers added as an optional phase. The surface handling is robust with a pre-specified final
mesh quality, and the setting of the mesh refinement level is quite flexible. In every iteration, it
operates parallel with a load balancing step (Greenshields, 2022). The snappyHexMesh utility has been
used intensively in Chapter 5 for the mesh used for the simulated case and in Chapter 6 for comparing
different meshes and the corresponding time taken by them. The stereolithography files utilized for
snapping have been generated using an external tool “SALOME-MECA”.
Salome-Meca
Salome-Meca (acronym in French, Simulation numérique par Architecture Logicielle en Open
source et à Méthodologie d'Évolution, which means Numerical Simulation by Computing Architecture
in Open Source and with Evolving Methodology) is an open-source software from Code_Aster
Professional Network which has a shaper module, geometry module, and mesh module (Electricité de
France, 1989). The geometry module supports geometry construction, optimization of geometrical
objects, defining fields and designing shapes from pictures. Shaper is a comparatively new module in
SALOME-MECA which supports parametric modelling and transformation of geometrical objects. Mesh
module in SALOME-MECA aids automatic generation of meshes and contains the following set of
algorithms:
NETGEN 1D-2D-3D algorithm was largely used for mesh generation throughout the current thesis.
This was facilitated in Salome-Meca using NETGENPLUGIN which allows for meshing of 1D, 2D, and 3D
entities. Input can be Constructive Solid Geometry, Triangulated Surfaces or Boundary Representation.
Chapter 2: Model concepts and tools
32
It should be noted that Netgen requires the input mesh to be a manifold shell, when working without
geometrical objects (Electricité de France, 1989). Further details can be found in Schöberl (1997).
Few other meshing algorithms available on the platform Salome-Meca are:
For meshing of 1D entities:
• Wire Discretization meshing algorithm
• Composite Side discretization algorithm
For meshing of 2D entities:
• Triangle: Mefisto meshing algorithm - splits faces into triangular elements
• Quadrangle: Mapping meshing algorithm - splits faces into quadrangular elements
For meshing 3D entities:
• Hexahedron (i,j,k) meshing algorithm
• Body Fitting meshing algorithm
Further details can be found in Electricité de France (1989-2017).
In the current work, SALOME-MECA was considerably used for mesh generation. As it provides a
better user interface to construct complicated geometries, its “geometry module” was used in
constructing stereolithography files for the cases in Chapter 5 and Chapter 6. The “mesh module” was
used for creating a non-uniform mesh for the case simulated in Chapter 6. Chapter 6 also includes
dynamic meshing techniques using SlomeMeca and the cyclic Arbitrary Mesh Interface (AMI) boundary
in OpenFOAM.
Gmsh
Gmsh (Geuzen mesh generator for structured and unstructured meshes) in the current work was
mainly used for comparing dynamic meshes generated for studying the effect of turbulence on mass
transfer through the liquid-gas interface. Gmsh is a three-dimensional finite element mesh generator
with a built-in CAD (Computer-Aided Design) engine and post-processor with four modules: geometry,
mesh, solver, and post-processing. In Gmsh, a model is described by its Boundary Representation
(BRep). The mesh module comprises a number of algorithms to generate meshes automatically. Even
though Gmsh meshes were built in a structured manner, they are by default considered as
unstructured. Gmsh offers the following algorithms for mesh generation for 3D entities:
• Delaunay algorithm
• Frontal algorithm
• HXT algorithm etc.
Gmsh is quite good at creating simple extruded geometries and meshes and allows to automatically
couple such structured meshes with unstructured ones (Geuzaine and Remacle, 2009). Although the
dynamic mesh developed was not utilised for the simulation of the case in Chapter 6 (highly time
intensive), it provided the basis for further developing a time efficient mesh using SALOME-MECA.
Chapter 2: Model concepts and tools
33
2.2.2 Processing tools
In-built solver: interFOAM
InterFOAM is one of the in-built multiphase flow solvers available in OpenFOAM which is based on
VOF approach. The solver considers an interfacial compression flux term to alleviate the effects of
numerical smearing at the interface (Eq. 2.3). For the solution of two-phase equations of flow, the
solver uses finite volume discretization on collocated grids. The solution process additionally takes into
account the face interpolated values of the flow variables, which are cell-centered (Deshpande et al.,
2012). In order to keep the volume fraction confined, the volume fraction equation as shown in Eq.
2.11 is solved using Multidimensional Universal Limiter with Explicit Solution (MULES) algorithm in the
interFOAM solver (Cifani et al., 2016). The Pressure Implicit with Splitting of Operator (PISO) approach
is then used to solve the continuity equation (Eq. 2.1) and momentum equation (Eq. 2.2), once the
volume fraction equation (Eq. 2.11) has been solved. To advance velocity and pressure fields in time in
the PISO algorithm, a predicted velocity is updated using a pressure correction method (Deshpande et
al., 2012; Rusche, 2003). The number the equations are solved by the PISO algorithm in each step can
be chosen by setting the Parameter “nCorrector” in the solver (Larsen et al., 2019). Additionally, the
solver also gives choices between PISO (Pressure Implicit with Splitting of Operators), PIMPLE
(PISO/SIMPLE), and SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) solvers. More details
about the interFOAM solver can be found in Deshpande et al. (2012).
Solver modifications
Temperature dependency of Henry coefficient
Overall temperature of the domain influences the Henry’s coefficient. This temperature
dependency of the Henry’s coefficient was integrated into the solver in such a way that the solver
allows for one global temperature value as the input parameter.
The Henry coefficient which is dependent on the temperature is calculated using the Van’t Hoff
equation (Sander, 2015):
𝐻𝑐𝑝(𝑇)= 𝐻𝑐𝑝𝑒𝑥𝑝 (𝐶(1𝑇−1
𝑇𝛷))
Eq. 2.26
Here, 𝐻𝑐𝑝 is the Henry coefficient (mol/m3Pa), C is the temperature coefficient dependent on the
enthalpy of dissolution and assigned as 2100 K for the H2S solver and 1700 K for the O2 solver (Sander,
2015), and 𝑇𝛷is the standard temperature 298.15 K corresponding to 25°𝐶.
Equilibrium conditions for H2S
In accordance with Hvitved-Jacobsen et al. (2013), the equilibrium conditions are taken into
account. Since those values are typically measured in field investigations, the objective is to determine
the water-phase concentration of H2S dependent on the amount of total dissolved sulphide and the
pH value.
Chapter 2: Model concepts and tools
34
The Henry coefficient is used to characterize the equilibrium between H2S in the aqueous phase
(H2Saq) and H2S in the gas phase (H2Sg). In the aqueous phase, hydrogen sulphide H2Saq and bisulphide
ion (HS-) are in equilibrium, and the sum of their concentrations is referred to as total dissolved
sulphide.
The dissociation of H2S is generally expressed by the following equilibrium:
𝐻2𝑆𝑔 ↔ 𝐻2𝑆𝑎𝑞 ↔ 𝐻𝑆−+ 𝐻+ ↔ 𝑆2−+ 2𝐻+
Eq. 2.27
Only H2Saq, not the ionized form HS-, may penetrate the air-water contact, however pH and total
dissolved sulphide concentrations are often measured. Therefore, deriving a method to determine the
concentration of 𝑐𝐻2𝑆𝑎𝑞, when given cS and pH would be really useful.
The equilibrium depends on the equilibrium constant known as acid dissociation constant 𝐾𝑎1,
which is given by:
𝐾𝑎1= 𝑐𝐻+𝑐𝐻𝑆−
𝑐𝐻2𝑆𝑎𝑞
Eq. 2.28
Where 𝑐𝐻+, 𝑐𝐻𝑆− and 𝑐𝐻2𝑆𝑎𝑞 are the concentration of H+ ions, HS- ions and H2S in the aqueous phase
(mol/m3). It can also be described in terms of negative algorithm, which give rise to the Henderson-
Hasselbalch equation as shown below:
𝑙𝑜𝑔10𝑐𝐻2𝑆𝑎𝑞
𝑐𝐻𝑆−=𝑝𝐾𝑎1−𝑝𝐻
Eq. 2.29
The equilibrium constant for a temperature of 20°𝐶 is 𝑝𝐾𝑎1 = 7.0 and pH is the dimensionless
constant defining acidity (value between 0 - 14). Another equilibrium exists in the water phase
between the ionized form HS- and the S2- :
𝐻𝑆−↔ 𝑆2−+ 2𝐻+
Eq. 2.30
𝐾𝑎2= 𝑐𝐻+𝑐𝑆−2
𝑐𝐻𝑆−
Eq. 2.31
Given the 𝑝𝐾𝑎1 value of 14.0, significant measurable amounts of sulphide ion S2- can only be
found at pH levels greater than or equal to 12. Consequently, only the equilibrium value of 𝐾𝑎1 is
important for wastewater. The interHarounFoam solver in OpenFOAM has been implemented using
the utilities funkySetFields (for initial conditions) and funkySetBoundaryFields (as boundary conditions)
from swak4Foam utility (Gschaider, 2011).
Chapter 2: Model concepts and tools
35
In Eq. 2.2, solving for the log function and substituting for 𝑐𝐻𝑆− as 𝑐𝑆− 𝑐𝐻2𝑆𝑎𝑞 for the total dissolved
sulphide, the equation becomes:
10𝑝𝐾𝑎1−𝑝𝐻= 𝑐𝐻2𝑆𝑎𝑞
𝑐𝐻𝑆−=𝑐𝐻2𝑆𝑎𝑞
𝑐𝑆− 𝑐𝐻2𝑆𝑎𝑞
Eq. 2.32
On reformulation, the following equation for the mass concentration 𝛾𝐻2𝑆𝑎𝑞 (kg/m3) is obtained:
𝛾𝐻2𝑆𝑎𝑞= 𝑐𝑆 ∙ 10𝑝𝐾𝑎1−𝑝𝐻
1 + 10𝑝𝐾𝑎1−𝑝𝐻
Eq. 2.33
The above equation can further be converted into (mol/m3) by dividing through the atomic weight
of sulphur:
𝑐𝐻2𝑆𝑎𝑞= 𝛾𝐻2𝑆𝑎𝑞
𝑀𝑆 = 𝛾𝐻2𝑆𝑎𝑞
0.032 𝑘𝑔/𝑚𝑜𝑙
Eq. 2.34
Substituting for 𝛾𝐻2𝑆𝑎𝑞 as per equation 2.31 in the above equation results in:
𝑐𝐻2𝑆𝑎𝑞= 𝑐𝑆 ∙ 10𝑝𝐾𝑎1−𝑝𝐻
1+ 10𝑝𝐾𝑎1−𝑝𝐻
32
Eq. 2.35
The above equation 2.33 is implemented in OpenFOAM. It should be noted that 𝐾𝑎1 and 𝐾𝑎2 are
influenced by temperature (Yongsiri, 2004), which has not been taken into account in the current
implementation of the code. The solver enables 𝐾𝑎1 to be defined by the user and the influence of
temperature on the equilibrium constant must be considered while defining it.
Calculation of partial pressure in ppm
The partial pressure of 𝐻2𝑆𝑔 is calculated using a function object in swak4Foam. The input value
of the tracer 𝑐𝐻2𝑆𝑎𝑞 in (mol/m3), for which conversion is necessary is shown in Eq 2.34:
𝑐[𝑚𝑜𝑙
𝐿]=1𝑚𝑜𝑙
𝐿=𝑐𝐻2𝑆𝑎𝑞
1000 =1000𝑚𝑜𝑙
𝑚3
1000
Eq. 2.36
The conversion from ppm to atm is:
10−6𝑎𝑡𝑚=1 𝑝𝑝𝑚
Eq. 2.37
Where atm is the atmospheric pressure (Pa) and ppm is parts per million (ppm).
Hvitved-Jacobsen et al. (2013) state that it is possible calculate the partial pressure of a tracer
amount in the air phase by multiplying the molar concentration by the molar volume:
𝑝𝐻2𝑆𝑔[𝑎𝑡𝑚]= 𝑐𝐻2𝑆𝑎𝑞[𝑚𝑜𝑙
𝐿]∙22.4𝐿
𝑚𝑜𝑙
Eq. 2.38
Chapter 2: Model concepts and tools
36
Where 𝑝𝐻2𝑆𝑔 (atm) is the partial pressure of H2S gas. OpenFOAM takes tracer 𝑐𝐻2𝑆𝑎𝑞 in (mol/m3) as
input, which has to be converted to (mol/L). This results in the following equation:
𝑝𝐻2𝑆𝑔[𝑝𝑝𝑚]=106∙ 𝑐𝐻2𝑆𝑎𝑞
1000 [𝑚𝑜𝑙
𝐿]∙22.4𝐿
𝑚𝑜𝑙
Eq. 2.39
It should be noted that as this conversion is only valid for gas phase concentration, the equation is
multiplied by (1−𝛼) to keep the values to the air phase.
Similarly, the partial pressure of oxygen in air phase can be expressed as follows:
𝑝𝑂2 [𝑎𝑡𝑚]= 𝑐𝑂2[𝑚𝑜𝑙
𝐿]∙22.4𝐿
𝑚𝑜𝑙
Eq. 2.40
Where 𝑝𝑂2 (atm ) is the partial pressure of O2 gas and 𝑐𝑂2 is the concentration of oxygen in (mol/m3)
and needs to be converted to (mol/L). With conversion, the above equation results in the following:
𝑝𝑂2[𝑝𝑝𝑚]=106∙ 𝑐𝑂2𝑎𝑞
1000[𝑚𝑜𝑙
𝐿]∙22.4𝐿
𝑚𝑜𝑙
Eq. 2.41
2.2.3 Post-processing
ParaView, an open-source data analysis and scientific visualization platform, was mainly used for
post-processing of models and results in the current work. To allow interactive display of extremely
big datasets, ParaView uses parallel data processing and rendering. In order to modify the data,
ParaView also allows users to construct and use filters, and display the data in a view to generate
renderings or photographs (Henderson Squillacote and Squillacote, 2007). Python scripting and batch
processing are also supported by ParaView. VTK, the Visualization Toolkit, serves as the foundation for
visualization and data processing in ParaView. All the data analysed and presented in the following
chapters is through ParaView interface.
Labplot (Version 15.3) and Gnuplot (Version 5.4) were used to plot graphs after post processing.
LabPlot is a free software and cross-platform computer programme for interactive scientific graphing
and data analysis, written for the KDE (K desktop environment) desktop. It is similar to Origin and is
able to import Origin's data files (LabPlot Team, 2022). LabPlot was primarily employed for visualizing
simulation data through graphical representation. Gnuplot is a portable command-line driven graphing
utility for Linux, OS/2, MS Windows, OSX, VMS, and many other platforms. The source code is
copyrighted but freely distributed (Williams and Kelley, 2007). Gnuplot was utilized for visualizing the
initial residuals from the simulations.
2.3 Conclusion
In this chapter, a brief overview of the model concepts and tools utilized, and the modifications
made to the solver in order to accomplish the objectives of the thesis was given. Additionally, a
comprehensive list of the equations employed for modelling, which have been implemented in
OpenFOAM by Teuber (2020), are also provided. It should also be mentioned that almost for all the
Chapter 2: Model concepts and tools
37
simulation done as a part of this research, a high-performance computer was used. High performance
computation systems provide the computational resources necessary to handle large CFD models in
OpenFOAM enabling efficient simulations by harnessing the power of parallel processing and
distributed computing. Furthermore, we discuss the enhancements made to incorporate the transfer
of H2S and O2. In which H2S solver was already implemented as per Teuber et al. (2019b) for OpenFOAM
V2.4 and was updated to version V6 and then further extended to include O2 mass transfer. Validation
of both solvers was done, and the results are listed in the forthcoming chapters.
38
Chapter 3
Update and validation of the solver
In the following, two cases will be used to validate the updated solver for H2S in OpenFOAM V6,
and to extend the solver for O2. A simple quasi-one-dimensional cubic tank will be used to see the
applicability of the two solvers to quantify the mass transfer through the liquid-gas film. The following
sections will delineate the methods which include the equations implemented in the OpenFOAM
solver, case description, and the results for the same.
3.1 Methods
All the necessary tools have been already discussed in detail in Chapter 2. This section just highlights
the important equations that have been already mentioned earlier.
3.1.1 Equations
Henry coefficient
The temperature dependency of Henry coefficient is defined as (also Eq. 2.26):
𝐻𝑐𝑝(𝑇)= 𝐻𝑐𝑝 𝑒𝑥𝑝(𝐶(1𝑇−1
𝑇Φ))
Eq. 3.1
For H2S
The corresponding values in the gas phase is defined by the equation (also Eq. 2.19):
𝑐𝐻2𝑆𝑔=𝑐𝐻2𝑆𝑎𝑞
𝐻𝐻2𝑆
𝑐𝑐
Eq. 3.2
Partial pressure is given by the equation (also Eq. 2.39):
𝑝𝐻2𝑆𝑔[𝑝𝑝𝑚]=106∙ 𝑐𝐻2𝑆𝑎𝑞
1000[𝑚𝑜𝑙
𝑙]∙22.4𝑙
𝑚𝑜𝑙
Eq. 3.3
For O2
Similarly, for oxygen the gas phase concentration can be given by the equation:
Chapter 3: Update and validation of the solver
39
𝑐𝑂2𝑔=𝑐𝑂2𝑎𝑞
𝐻𝑂2
𝑐𝑐
Eq. 3.4
Partial pressure is given by the equation (also Eq. 2.41):
𝑝𝑂2[𝑝𝑝𝑚]=106∙𝑐𝑂2
1000[𝑚𝑜𝑙
𝑙]∙22.4𝑙
𝑚𝑜𝑙
Eq. 3.5
3.1.2 Case description
The case setup is similar to what was used by Teuber et al. (2019b). It is a quasi-one-dimensional
cubic tank with the dimensions 1m x 1m x 1m bounded by upper, lower and sidewalls with no-slip
conditions Figure 3.1. The domain is discretised with 100 cells in the z-direction, which is the vertical
dimension of the domain, and 10 cells in the x- and y-direction. The tank has a water depth of 0.5 m,
and both fluids are at rest for both cases of H2S and O2. The case for H2S uses the same methodology
as used by Teuber et al. (2019). As an initial condition, an H2S concentration of 1 mol/m3 is given
wherever phase fraction alpha (α) is greater than 0.5 (water phase) and 0 mol/m3 otherwise. At the
bottom wall, a concentration is assumed, using a fixed value boundary condition of 1 mol/m3 (Teuber
et al., 2019b). All the other confining walls are defined with zeroGradient conditions. This setup
illustrates the solver's capabilities in a simple setup. In the first example, mass transfer, as it can be
described with the existing interHarounFoam solver, is shown in a vertical one-dimensional case. Then,
the extensions leading to the interH2SFoam solver are demonstrated in different examples using this
first setup. The details of the case setup are given in Appendix C.1.
Figure 3.1: Diagrammatic representation of the quasi-steady state tank showing different boundary
conditions for different validation cases.
In the second case, for the validation of the extended O2 solver, a similar approach is taken. But the
investigation is done in two parts. In the first part, a concentration is assumed at the bottom wall, using
a fixed value boundary condition of 1 mol/m3; meanwhile, the other boundaries remain zeroGradient.
In the second part, the top wall is assumed to provide the input of oxygen gas with a fixed value
boundary condition of 1 mol/m3. For all cases, a higher value of physical diffusivities was chosen for
Chapter 3: Update and validation of the solver
40
both air and water phase to expedite the process of reaching the equilibrium state. Table 3.1 gives a
list of important parameters used in this simulation. Appendix C.2 gives the details of all the boundary
conditions and initial conditions for this case.
Table 3.1: Important parameters for quasi-one-dimensional cubic tank.
for H2S
for O2
Physical diffusivity in water [m2/s]
1·10-3
1·10-3
Physical diffusivity in air [m2/s]
1·10-3
1·10-3
Temperature [K]
298.15, 288.15
298.15, 288.15
Water depth [m]
0.5
0.5
3.2 H2S in a tank
The first test case illustrates the advantage of the new model in describing vertical concentration
profiles in contrast to the existing horizontal one-dimensional approaches (Teuber et al., 2019b). The
concentration profile illustrated in Figure 3.2 has the resulting air phase concentration which is 𝑐𝐻2𝑆𝑔
= 0.4034 mol/m3 which is the expected concentration for the Henry coefficient at 298.15 K for H2S:
𝑐𝐻2𝑆𝑔=𝑐𝐻2𝑆𝑎𝑞
𝐻𝐻2𝑆
𝑐𝑐 = 1𝑚𝑜𝑙
𝑚3
2.479=0.4034 𝑚𝑜𝑙
𝑚3
Eq. 3.6
The graph on the left in Figure 3.2 shows the phase fraction in the domain (α = 1: water, α = 0: air)
and the one on the right shows the development of the concentration profile with time. There is a
concentration jump at the first computational time step due to a direct flux of concentration across
the interface. This decrease is still visible at t = 50 s. Following this, the system starts to stabilize, and
the concentration in the water phase is re-established by the boundary condition at the bottom. The
system reaches equilibrium at t = 1000 s where the concentration in the water phase (𝑐𝐻2𝑆𝑎𝑞) is equal
to 1 mol/m3 and the concentration in the gas phase (𝑐𝐻2𝑆𝑔) is equal to 0.4034 mol/m3 (Teuber et al.,
2019b).
Figure 3.3 compares the results between the solver from Teuber et al. (2019b), developed in
OpenFOAM V2.4 and the updated solver in OpenFOAM V6. As both the solvers have the same profile,
it would be feasible to say that the updated interH2SFoam solvers have the same functionality as the
previous version.
Chapter 3: Update and validation of the solver
41
Figure 3.2: H2S in a quasi-steady state tank (left: phase fraction value, right: concentration profiles
along the vertical axis over time).
Figure 3.3: Comparison of the results of the two versions of the solver (left: phase fraction value, right:
concentration profiles along the vertical axis over time).
The temperature dependency of the solver is tested using the conditions based on example 4.3 in
Hvitved-Jacobsen et al. (2013) (Teuber et al., 2019b). For a temperature of 15 °C, the Henry coefficient
and the corresponding gas phase concentration of H2S are calculated. The resulting Henry coefficient
can be determined as follows (following Eq. 3.1):
𝐻𝑐𝑐= 𝐻𝑐𝑝𝑒𝑥𝑝(𝐶(1𝑇− 1
𝑇𝜃))𝑅
Eq. 3.7
Chapter 3: Update and validation of the solver
42
Where all the other variables have been explained earlier, the new variable R (J/(mol∙K)) or
kg·m²/(mol·s⁻²∙K) is the universal gas constant.
𝐻𝑐𝑐(288.15)=0.0010∙ exp (2200(1
288.15− 1
298.15))∙8.1345
∙288.15
Eq. 3.8
𝐻288.15=3.0836
Eq. 3.9
Resulting in the following expected gas phase concentration:
𝑐𝐻2𝑆𝑔(288.15)= 1
3.0836=0.3243 𝑚𝑜𝑙/𝑚3
Eq. 3.10
Figure 3.4 shows that the simulation results match with the expected concentration. Hence, the
implemented temperature dependency in the updated solver can therefore be considered as accurate.
Figure 3.4: H2S in a tank demonstrating the temperature dependency of Henry’s coefficient (298.15 K
(see also Figure 3.2, right) and 288.1 5K) (left: phase fraction value, right: concentration profiles along
the vertical axis).
3.3 O2 in a tank
Boundary condition at the bottom
This case validates the solver extension for O2 (interO2Foam). A boundary condition of O2 of
1mol/m3 is assumed at the bottom wall of the quasi-one-dimensional cubic tank. This means that there
will be a constant introduction of oxygen from the bottom wall until the saturation conditions are
achieved in the air phase. Figure 3.5 shows the phase fraction in the domain (𝛼 = 1: water, 𝛼 = 0: air)
in the left and the one on the right shows the development of the concentration profile with time.
After an initial concentration jump at the interface causing the decrease in the concentration in the
Chapter 3: Update and validation of the solver
43
water phase (𝑐𝑂2𝑎𝑞), the system starts to stabilize. The time taken to stabilize is higher than that in the
case for H2S.
At t = 35000s the system reaches equilibrium with the water phase concentration (𝑐𝑂2𝑎𝑞) re-
establishing to 1mol/m3 and the gas phase concentration (𝑐𝑂2𝑔) equal to 31.0559mol/m3.
This is the expected concentration in the air phase when applying Henry’s law for O2 at 298.15 K:
𝑐𝑂2𝑔=𝑐𝑂2𝑎𝑞
𝐻𝑂2
𝑐𝑐 = 1𝑚𝑜𝑙
𝑚3
0.03220=31.0559 𝑚𝑜𝑙
𝑚3
Eq. 3.11
Boundary condition at the top
In this case, a boundary condition of O2 of 1mol/m3 is assumed at the top wall of the quasi-one-
dimensional cubic tank.
Figure 3.6 depicts the phase fraction in the domain (𝛼 = 1: water, 𝛼 = 0: air) in the graph on the left.
The one on the right shows the development of the concentration profile with time. As it is difficult to
see the concentration profile development, the graph at the bottom depicts the concentration profile
in the water phase. Similar to the previous cases there is an initial concentration jump at the interface
causing the decrease in the concentration in the air phase (𝑐𝑂2𝑔), after which the system starts to
stabilize. At t = 1000 s the system reaches equilibrium with the water phase concentration (𝑐𝑂2𝑔), re-
establishing to 1mol/m3 and the gas phase concentration (𝑐𝑂2𝑎𝑞) equal to 0.0322mol/m3:
𝑐𝑂2𝑎𝑞=𝑐𝑂2𝑔∙𝐻𝑂2
𝑐𝑐=1𝑚𝑜𝑙
𝑚3∙0.03220= 0.0322 𝑚𝑜𝑙
𝑚3
Eq. 3.12
Temperature dependency of the interO2Foam solver was also investigated for a temperature of 15
°C, the Henry coeffiecient and the corresponding gas phase concentration of O2 is calculated. Using the
values available for 𝐻𝑐𝑝 (mol/m3Pa) from Sander, (2015b) and the value of R, 8.3145 J/(mol·K), the
resulting Henry coefficient can be determined as follows:
Chapter 3: Update and validation of the solver
44
Figure 3.5: O2 in a tank with a boundary condition at the bottom wall (left: phase fraction value, right: concentration profiles along the vertical axis over time).
Figure 3.6: O2 in a tank with a boundary condition at the top wall (top left: phase fraction value, top right: concentration profiles along the vertical axis over
time and bottom: magnified concentration profile).
Chapter 3: Update and validation of the solver
45
𝐻𝑐𝑐= 𝐻𝑐𝑝𝑒𝑥𝑝(𝐶(1𝑇− 1
𝑇𝜃))𝑅𝑇
Eq. 3.13
𝐻𝑐𝑐(288.15)=1.3∙10−5∙ exp (1700(1
288.15− 1
298.15))∙8.1345
∙288.15
Eq. 3.14
𝐻288.15=0.0371
Eq. 3.15
Therefore, the resulting gas phase concentration when the boundary condition is at the bottom is:
𝑐𝑂2𝑔(288.15)= 1
0.03714=26.9276 𝑚𝑜𝑙/𝑚3
Eq. 3.16
The resulting liquid phase concentration when the boundary condition is at the top is:
𝑐𝑂2𝑎𝑞(288.15)= 1 ∙ 0.03714=0.0371 𝑚𝑜𝑙/𝑚3
Eq. 3.17
Figure 3.7 and Figure 3.8 show the concentration profiles for different temperatures. As the
simulated data agrees with the analytical solution, the implemented approach for the O2 mass transfer
is correct.
3.4 Conclusion
This chapter presented the validation of the updated solver for H2S and the extended solver for O2
in OpenFOAM V6. For the case for H2S, the concentration profile in the tank was examined over time.
The results demonstrated that the updated solver accurately reproduced the concentration profiles
obtained using the previous version of the solver. The equilibrium concentrations in both, the water
phase and the gas phase were consistent with expectations based on Henry's law.
O2 in the tank was analysed using two different approaches: a boundary condition at the bottom
wall and one at the top wall. The concentration profiles and equilibrium concentrations were analysed
for both scenarios. The results showed that the solvers accurately captured the concentration profiles
and achieved equilibrium concentrations consistent with the predictions based on Henry's law. The
temperature dependency of the solver was also validated, and the simulated data aligned with the
analytical solution. Overall, the validation of the solvers for H2S and O2 in OpenFOAM V6 demonstrated
their applicability and accuracy in simulating mass transfer through liquid-gas interfaces.
Chapter 3: Update and validation of the solver
46
Figure 3.7: O2 in a tank for different temperatures with boundary condition at the bottom wall (298.15 K (see also Figure 3.5, right) and 288.15 K) (left: phase
fraction value, right: concentration profiles along the vertical axis over time).
Figure 3.8: O2 in a tank for different temperatures with boundary condition at the top wall (298.15 K (see also Figure 3.6, top right and bottom) and 288.15 K)
(top left: phase fraction value, top right: concentration profiles along the vertical axis over time (zoom for the concentration profile in the water phase on the
right) and bottom: magnified concentration profile).
47
Chapter 4
Further validation of the mass transfer of H2S
and first validation case for transport of O2
The following chapter discusses the application of the H2S and O2 mass transfer solvers in a
laboratory scale setup. The cases are developed using the works of Bentzen et al. (2016). Several
experiments were conducted to improve the understanding of the wastewater drag and the wall
frictional force acting on the headspace air in gravity sewers (Bentzen et al., 2016). The aim of these
experiments was to improve the numerical models for ventilation in natural sewer systems. The data
available from these experiments was used to validate the hydraulics in the air phase. Oxygen
concentration measurements, on the other hand, were used for the validation of the applicability of
the solver to accurately depict the air phase transport of oxygen.
4.1 Introduction
The wastewater collection system infrastructure is an industry worth billions of dollars, with
significant capital investment and ongoing maintenance required to keep it running. The bulk of this
infrastructure was designed and constructed exclusively for wastewater conveyance, with little
thought given to headspace air or the consequences of collection system ventilation (Ward et al.,
2011). Inadequate ventilation of headspaces within wastewater collection systems is a major
contributor to corrosion, particularly from hydrogen sulphide, which can cause damage to concrete
and steel. Thus, proper ventilation is crucial to prevent such corrosion. A ventilated system in cases
where H2S is being produced may enhances mass transfer from wastewater to air resulting in odour
and toxic gas emissions (Corsi and Schroeder, 1989; Melcer et al., 1997; Ward et al., 2011). The expense
associated with odour and corrosion in wastewater collection systems could be avoided if ventilation
was included as a parameter while designing the systems. Thus, there are two strategies that can be
employed to tackle this issue. The first is to consider the effects of ventilation in the sewer head space
during the design of future wastewater collection systems. The second is to use more sophisticated
field measurement techniques to deal with gas emissions and corrosion issues in existing
infrastructure. Despite its importance to wastewater odour and corrosion control, collection system
ventilation typically is understood at only a basic level among wastewater professionals (Ward et al.,
2011). Hence increased knowledge on the air flow characteristics may contribute to the better
understanding of the hydrogen sulphide adsorption process (Bentzen et al., 2016).
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
48
4.2 Method
4.2.1 Experimental setup
The experimental setup used by Bentzen et al. (2016) was a rectangular duct with an adjustable
slope and water flow rate at the inlet (Dixit et al., 2020). The duct's side walls were made of glass, while
the top wall was made of painted wood. Figure 4.1 depicts the outline and the flows involved in the
experiment. The 15 m long pipe has a height of 0.26 m and a width of 0.3 m. To collect data for the
drag and friction models, mean air velocities were measured at steady flow at 26 different
configurations (Bentzen et al., 2016). From these configurations, case 7 and case 21 were selected to
analyze the air flow behaviour. Both cases have different slopes and water depths hence providing a
good range of increasing turbulence in the system and how it impacts the mass transfer in the system.
The air phase is only accelerated by the movement of the water surface.
The mean air-flow velocity was measured using pulse injection of oxygen as described by Madsen
et al. (2006), in which the oxygen concentration is measured in each distance from the injection point
to yield a mean velocity based on the mean travel time (Bentzen et al., 2016; Madsen et al., 2006). The
injection of oxygen was done perpendicularly to the water flow at the inlet. The duration of injection
ranged from 3 to 8 seconds, depending on the head space volume, while maintaining a flow rate of
0.125 L/s. The data from the streamwise velocity profile measurements will be utilized to validate the
air phase flow in the simulated cases. Replicating the results from Teuber et al. (2019b) was essential
to ensure the applicability of the updated solver in turbulent cases. Therefore, both cases are also used
to simulate the mass transfer of H2S from liquid to gas phase using a similar case setup as defined in
Teuber et al. (2019b). The oxygen trace gas experiments to determine the mean air velocity also
yielded results for oxygen concentration over time at two locations in the system (5 m and 12 m
respectively). These results were valuable for validating the transport of oxygen through the
rectangular channel. Case 21 was chosen for testing the mass transport of oxygen in the air phase as
it had higher turbulence than case 7. Table 4.1 shows the values for different parameters for the
investigated cases.
Table 4.1: Flow properties of analysed test cases.
Test no.
Duct slope
Water
Uaq
Ug
Reynolds no.
Reynolds no.
[%]
depth [cm]
[m/s]
[m/s]
Reaq
Reg
7
0.57
3.15
0.77
0.226
72300
5400
21
1.34
4
1.37
0.336
175300
7900
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
49
4.2.2 Numerical model and analytical solution
The simulations modelled within the domain of this chapter follow the solver implementations as
mentioned in Chapter 2. All the important equations have already been mentioned previously except
the 1D analytical solution utilized for comparison of the dispersion of oxygen in the duct head space.
The mean air velocity at both sensors was determined visually by fitting curves to the 1D
transport/dispersion model (Eq. 4.1). This process allowed the estimation of the mean air velocity from
which tmean was found as the ratio between the distance travelled and the mean air velocity at the
oxygen sensor (Bentzen et al., 2016). It is important to note that the 1D analytical solution provides a
reasonable representation of what occurs in the air phase, it may not capture the full complexity of
real-world scenarios. Nonetheless, the 1D model remains a valuable tool for validating the data
accumulated from the simulation.
𝐶(𝑥,𝑡)= 𝑚𝑖𝑛𝑗 𝐴𝑎
⁄
√4𝜋𝐷𝑥∙(𝑡−𝑡0)exp(−[(𝑥−𝑥0)−𝒰𝑎(𝑡−𝑡0)]2
4𝐷𝑥∙(𝑡−𝑡0))
Eq. 4.1
Here, 𝐶(𝑥,𝑡) (mg/L) is the oxygen concentration at a distance (𝑥−𝑥0) where 𝑥0 (m) is the point
of injection and 𝑥 (m) is the point of measurement. The initial time is defined by 𝑡0 (s) and 𝑡 (s) is the
time of measurement. The term 𝑚𝑖𝑛𝑗 is the mass of pulse injection (gm) and 𝐴𝑎 (m2) represents the
air flow cross sectional area. The term 𝐷𝑥 (m2/s) is the longitudinal coefficient of dispersion, an𝑑 𝒰𝑎
(m/s) is the mean air velocity (Kinzelbach, 1992).
The resultant values are plotted along with the measured results as well as the results from the
simulation later in this chapter.
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
50
Figure 4.1: Principal outline of the experimental setup, showing the flows involved and the duct slope (the drawing is not to scale) (inspired by Bentzen et al.,
2016).
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
51
4.3 Case setup and mesh
4.3.1 Hydraulic simulations
A simple three-dimensional mesh is generated with the same dimensions as described in the
experimental setup. The geometry has approximately 31,000 cells with uniform distribution in all
directions. The details about the geometry and the mesh can be found in Appendix C.3. The cases
consist of top, bottom and side walls, with an inlet and an outlet. Initially, the pipe is considered to be
completely empty and the standard fluid properties are defined for the case. The inlet is divided into
two parts, one for air and the other for water. Phase fraction was set to 1 for water inlet and 0 for the
inlet for air. A fixed discharge value was given at the water inlet and null Neumann condition was used
to define the pressure boundary. As mentioned earlier, the flow in the air phase was developed due
to the movement of water, null Neumann condition was used for the velocity boundary with a fixed
pressure boundary. Outlet patch was defined with a fixed pressure and a free outflow condition. No-
slip conditions were applied at the walls. The simulation run time was 200 s for the system to reach a
quasi-steady state condition. These cases were simulated in order to replicate the results of Teuber et
al. (2019b), which were helpful in order to validate the updated solver for H2S mass transfer in non-
stationary conditions (case 7 and 21) as well as for the transport of O2 in the duct headspace (case 21).
4.3.2 H2S mass transfer simulations
For the mass-transfer simulations, H2S was introduced at the water inlet. This is analogues to
conditions where the sewer system is contaminated with H2S in the water phase and transfer mainly
occurs from the aqueous to the air phase. The hydraulically stabilized cases from the previous
investigation were taken. A concentration of 1mol/m3 was chosen for water inlet (cH2Saq) and 0mol/m3
at the air inlet (cH2Sg). All remaining boundaries were defined with null Neumann conditions. Simulation
time was set to 50 s and the results are presented later in the chapter.
4.3.3 O2 transport in the sewer headspace
Case 21 was chosen for investigating the O2 transport in the air phase. Experimentally, Bentzen et
al. (2016) used a pulse injection of oxygen with a concentration higher than that of the initial
atmospheric concentration. The injection was so violent that it could be seen on the water surface,
and complete mixing of the oxygen at the injection point was assumed (Bentzen et al., 2016). The
oxygen concentration was then measured downstream at two points (5m and 12m from the point of
injection, see Figure 4.1). The concentration data was then plotted against time for both points. This
data was used to validate the oxygen mass transfer solver (interO2Foam). The case setup and boundary
conditions can be found in detail in Appendix C.4.
To simulate the experimental conditions, the simulation case began by introducing an oxygen
concentration of 1mol/m3 at the inlet for air (cO2g) and 0mol/m3 at the water inlet (cO2aq) with all
remaining boundaries set to null Neumann conditions. The case was then simulated for 200 s to reach
a steady state. Similar to the experiment, a pulse injection of oxygen with a higher concentration (7 %
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
52
higher than the initial concentration, Bentzen et al., 2016) was introduced at the air inlet for 8 s. After
this, the concentration was again set to 1mol/m3 and the simulation ran for another 165s.
4.4 Results and discussion
4.4.1 Hydraulic simulations
Figure 4.2 and Figure 4.3 represent the phase fraction and the velocity profile against the height of
the pipe in a fully developed flow close to the duct center. The results achieved are similar to those
found by Teuber et. al (2019b) and are in good agreement with the experimental data published by
Bentzen et al. (2016). This provides an essential basis for investigating the transport operations
occurring in sewer headspace as a positive correlation between the air flow velocity and hydrogen
sulphide kinetics has been found (Nielsen et al., 2012). In the water phase, the velocity profile across
the pipe's cross-section is almost parabolic. The highest velocity occurs near the air-water interface,
while the velocity gradually decreases towards the pipe walls. In the air phase, an S-shaped profile
develops which is quite similar to that from the three velocity measurements by Laser Doppler
Anemometry (LDA) in the experiment. Three sets of measurements were conducted, and the results
align relatively close together. This profile plays an important role in the transport of oxygen as in the
case of the 1D analytical solution, a constant flow is assumed. The assumption of constant flow is often
made in analytical solutions for the ease of calculation and can be a reasonable approximation,
specially in certain steady-state systems where the flow conditions are relatively stable and the effects
of changes in velocity or flow rate are negligible.
Figure 4.2: Phase fraction and velocity profile along the height for case 7 at the center of the duct
(measurements as published in Bentzen et al., 2016).
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
53
Figure 4.3: Phase fraction and velocity profile along the height for case 21 at the center of the duct
(measurements as published in Bentzen et al., 2016).
4.4.2 H2S mass transfer
In the aforementioned scenarios, H2S is introduced into the system through the water inlet
boundary once a stable flow has been established. However, the concentration profiles in Figure 4.4
and Figure 4.5 suggest that there is minimal transfer of mass from the water surface to the air phase
for the flow velocities analyzed in the 15m pipe. The reason for this is that velocities in directions other
than the main flow direction (i.e., in the yz-plane) are small, leading to advective transport occurring
mostly in the main flow direction (x-direction). In addition, the small diffusion coefficients primarily
result in advective transport (Teuber et al., 2019b). Mass transfer is influenced by both the flow
velocity and diffusion. As a rule of thumb, in cases with stronger flows and slower diffusion (small
diffusivity coefficient), tracer has lesser time to spread (Socolofsky and Jirka, 2002). Therefore, to study
the impact of increasing turbulence rates on mass transfer, a lab scale reactor will be simulated,
analyzed and the results will be presented in Chapter 6. Therefore, for the same reason, the study for
O2 also focuses on the transport of the gas in this chapter.
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
54
Figure 4.4: Phase fraction (see also Figure 4.2), left and concentration profile of H2S along the height
for case 7 at the center of the duct, right.
Figure 4.5: Phase fraction (see also Figure 4.3), left and concentration profile of H2S along the height
for case 21 at the center of the duct, right.
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
55
4.4.3 O2 mass transport
In case 21, after the simulation is hydraulically in a steady state, a continuous injection of oxygen
for 200 s was done. After reaching equilibrium conditions, another 8 s pulse injection of oxygen with a
concentration 107 % greater than the average concentration in the air phase was done to replicate
conditions in the experiment. Then, the simulation proceeded for 165 s, and the resulting
concentrations are presented as the percentages of the initial concentration. Figure 4.6 and Figure 4.7
present the results for the measuring points at 5 m and 12 m, respectively. The figure shows the CFD
data plotted against the 1D analytical solution (see eq. 4.1) and the measurements of oxygen
concentration using fiber optic oxygen sensors (PSt3-NOP sensor spots and Fibox 3 transmitter from
PreSens) (Bentzen et al., 2016). Fiber active sensors are very sensitive. Variations in the sample
conditions, such as turbulence, mixing, or flow rates, and optical interference from external sources
can introduce noise or variations in the sensor's measurement. This can be seen in the measurements
in Figure 4.6 and Figure 4.7. Bentzen et al. (2016) already found that there is a good agreement
between the experimental results and the 1D analytical solution. Simulating the case using
interO2Foam, the results are within the range of plausibility. The measurements at point 5m
downstream of the point of injection shows a much better agreement with the 1D analytical solution
than that at the 12m point. This can be attributed to the fact that the 1D analytical model for
transport/dispersion considers only one dimension (along the x-axis) and assumes that dispersion
process is homogeneous. On the other hand, the 3D simulation considers all three dimensions of space
and provides a more detailed representation of the flow profiles (for flow profiles see Figure 4.2 and
Figure 4.3). Another point to consider is that the 3D simulations give an S shape velocity profile in the
air phase which aligns with the measured data. But the 1D analytical solutions assumes a constant
profile, hence a perfect alignment between the two cannot be expected. The impact of dispersion in
the yz plane is less evident at the measurement point at 5 m but the effect is more visible at the 12m
point. The numerical simulations are within the range of the measurements although they show high
fluctuations.
The Nash-Sutcliffe model efficiency coefficient (NSE between 1D analytical solution and the CFD
data) of 0.9 and 0.8 for the 5m and 12m measurement points, respectively, is very reasonable. NSE
between the CFD data and the measured data would not be a good representation of the performance
of the solver due to high noise in the measured data (reason mentioned above). Other model
evaluation criteria have also been calculated and are presented in Table 4.2. The RMSE (Root Mean
Square error) for 5m and 12m measuring point is 0.103 (0.06 normalized RMSE) and 0.106 (0.09
normalized RMSE) respectively. Respective correlation coefficients were also calculated for the results
at each point with a value of 0.97 at the 5m point and 0.96 at the 12m point. Considering the strong
correspondence between the simulated results and the experimental measurements, it can be
concluded that the interO2foam solver is a reliable tool for predicting oxygen concentration in sewer
channels.
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
56
Figure 4.6: Measurements (Bentzen et al., 2016), 1D analytical solution and simulated concentration
of oxygen at 5 m downstream from the oxygen injection point in case 21.
Figure 4.7: Measurements (Bentzen et al., 2016), 1D analytical solution and simulated concentration
of oxygen at 12 m downstream from the oxygen injection point in case 21.
Chapter 4: Validation of the transport and mass transfer solver for H2S and O2
57
Table 4.2: Different evaluation criteria to assess model performance calculated at the two
measurement points in the pipe.
Measuring
point
NSE
RMSE
Normalized
RMSE
Correlation
coefficient
5 m
0.900
0.103
0.055
0.970
12 m
0.800
0.106
0.094
0.960
4.5 Conclusion
The findings from the conducted research indicate that the VOF approach implemented in
OpenFOAM is highly proficient in describing the behaviour of two-phase flows within enclosed ducts.
Furthermore, the updated solver for H2S (upgraded from OpenFOAM V2.4 to V6.0), has facilitated the
analysis of mass transfer in three-dimensional test cases that were previously only feasible through
significant simplifications. The accuracy of the local mass transfer rates has been validated through
comparison with the results published by Teuber et al. (2019b), demonstrating good agreement.
Additionally, the interO2Foam solver for oxygen has also exhibited favourable consistency with the
experimental works of Bentzen et al. (2016) in predicting the transport of oxygen in the headspace of
a square duct. However, it is crucial to note that the solver's accuracy needs to be evaluated in
scenarios with higher turbulence levels, preferably in real-world environments. As a result, the
subsequent chapters will aim to explore the solver's overall applicability and performance, taking into
account different variables and parameters to ensure its reliability and effectiveness. Overall, the
findings suggest that the updated solver is a valuable tool for predicting mass transfer and two-phase
flows in ducts, but further testing and refinement are needed to ensure its suitability for a wider range
of real-world applications.
58
Chapter 5
Application of the solver for mitigation
measures
This chapter outlines an overview of methods and techniques used to solve flow and tracer
transport for ventilation simulation in a real-world environment. This is followed by the description of
the geometry design and the mesh creation which is imperative for achieving an efficient flow
simulation. Capabilities of the solver are being explored in a highly complex three-dimensional test
case developed on the field experiments of Madsen et al. (2006). This step helps in further validation
of the solver as well as examine hotspots for extraction of tracers such as hydrogen sulphide using
ventilation with different suction rates.
5.1 Mitigation measures: importance of ventilation
All previous examinations were done on a lab scale experiment (Bentzen et al., 2016), which was
developed on the studies of Madsen et al. (2006). As the study was conducted on a large scale, the
field data published could be used to further validate the applicability of the solver for oxygen
(interO2Foam).
Ventilation, in general, is the exchange between the sewer system and the atmosphere. Ventilation
can either be natural or forced, where natural ventilation is dependent on factors such as climate, the
ambient water level in the sewers and the drag effects caused by the wastewater interface in contact
with the air (Madsen et al., 2006; Olson et al., 1997). On the other hand, forced ventilation in sewer
systems is usually achieved through external mechanisms such as blowers (Pomeroy, 1945) or
ventilation fans (Corsi and Schroeder, 1989), as opposed to the natural air flow that occurs with the
latter mechanisms. The implementation of forced ventilation is often necessary for scenarios where
there is a high concentration of odorous compounds in the sewer system, which can lead to unpleasant
and potentially harmful conditions for both workers and the public. Overall, while forced ventilation is
commonly used in situations with gravity sewers with low slopes (Corsi and Schroeder, 1989), it can
also act as a valuable tool in the management of sewer networks for a variety of scenarios to improve
the overall functionality and safety of the system.
For ventilation to function properly, it needs an opening to allow gas to flow in and out of the
system. In the headspace of sewers, gases can travel either horizontally above the water-air interface
or vertically through manholes (as shown in Figure 5.1). The movement of sewer gas and its
Chapter 5: Application of the solver for mitigation measures
59
components in the horizontal direction is determined by factors such as gas velocity and dispersion, as
described by Madsen et al., (2006). If these are quantifiable, the transport of hydrogen sulphide and
oxygen in the sewer atmosphere can be predicted. In addition, it should be noted that ventilation of
the system cannot be accomplished by horizontal gas transport alone; therefore, vertical gas transport
(or ventilation) is the only way to achieve proper ventilation in the system (Pescod and Price, 1982).
Effective ventilation is crucial in managing odour and corrosion in sewer systems. This is germane
to areas of sewer systems used for maintenance, where it is essential to maintain optimal conditions
for workers entering through manholes. Also, in wet sewers, corrosion caused by H2S and O2 can be
mitigated by proper ventilation, which can help to dry out the sewer and reduce the associated risks.
A high ventilation rate may dry out the sewer, whereby corrosion is reduced (Madsen et al., 2006).
The process of flow visualisation typically entails introducing an inert flue gas into the sewer
atmosphere, which is then observed to determine the flow pattern downstream (Madsen et al., 2006).
By measuring the differences in velocities and concentrations of the tracer, it is possible to obtain a
comprehensive understanding of the level of ventilation (Rebideau et al., 1996). Madsen et al. (2006)
investigated the potential of molecular oxygen to quantify horizontal gas transport and the loss of
oxygen between two monitoring stations to determine natural ventilation in sewer systems. The field
results from these experiments are helpful for validating the accuracy of the CFD model to represent
tracer transport and dispersion horizontally through the system.
Figure 5.1: Gas transport in sewer systems.
The plausibility of the hydraulics in the simulated sewer system geometry was verified using
"interfoam", and the accuracy of the results was confirmed by comparing them to the flow patterns
presented in previous chapters. This chapter focuses on further validation of the solver and using
different simulation parameters for effectively ventilating the system of gases causing odour and
corrosion (focus on O2).
Chapter 5: Application of the solver for mitigation measures
60
5.2 Description of experimental site
Madsen et al. (2006) developed a methodology for determining horizontal gas transport and
ventilation in gravity sewers. This was achieved by injecting 40 oxygen gas pulses as a tracer and
subsequent measuring the oxygen concentration in a maintenance hole downstream. Figure 5.2
illustrates the general principle of these injections.
Figure 5.2: Overall principle of injections (inspired, Hvitved-Jacobsen et al., 2013).
The combined gravity sewer network in this study is located between Dronninglund and the
wastewater treatment plant in Asaa, Denmark. The location of each injection and monitoring station
along the gravity sewer is shown in Figure 5.3. The oxygen flow volume was kept constant at 5.4 L/s
during the time of injection. Subsequently, the oxygen concentration in the sewer atmosphere was
measured at two downstream monitoring stations. The duration of each injection varied from 2.5 to
10 minutes, which corresponds to 0.8 and 3.2 m3 injected oxygen volume. The oxygen concentration
at the monitoring stations was measured by Evita Oxy dissolved oxygen meter, located between 10 to
20 cm above the water surface. Table 5.1 provides detailed information on the number of injections
conducted and the monitoring stations designated for each pipe section.
Chapter 5: Application of the solver for mitigation measures
61
Figure 5.3: Map of the field site (inspired by Madsen et al., 2006).
Table 5.1: Number of total injections in each pipe section and the designated monitoring stations
(location A – E, see Figure 5.3) (Madsen et al., 2006).
Injection
station
First
monitoring
station
Second
monitoring
station
Number of
total
injections
Number of injections
with increased
ventilation
Pipe Section 1
D
E
–
2
–
Pipe Section 2
C
D
E
13
–
Pipe Section 3
A
B
E
15
10
The crucial parameters measured or calculated which are pertinent to the case development for
the computational model are mentioned in Table 5.2.
Table 5.2: Overall outline of field study (Madsen et al., 2006).
Parameter
Values
Gas velocity
0.05 - 0.22 m/s
Dispersion coefficients
0.05 - 1.1 m2/s
Daytime dry weather flow rate
0.013 - 0.016 m3/s
Sewer diameter
0.5 m
Average slope
0.0027 m/m
Manhole locations
Generally, every 70 m
Number of injections
40
Oxygen injection flow
5.4 L/s
Injection time
2.5 - 10 minutes
Injection volume
0.8 - 3.2 m3
Oxygen meter's accuracy
5% concentration
Placement of oxygen meters
10 - 20 cm above water surface
Gas velocity was calculated from the distance and detention time between an injection station and
a monitoring station (Madsen et al., 2006). According to Levenspiel (1991), based on a general
Chapter 5: Application of the solver for mitigation measures
62
dispersion model applicable for large dispersions, D = (L∙𝑢𝑔) > 0.01m2/s, the simulation of measured
response curves was accomplished by Eq. (5.1) and the coefficient of dispersion is then calculated
subsequently:
𝐶𝑖= 𝐶𝑎𝑡𝑚+ 𝐶0∙1
2∙√𝜋∙𝜃∙ 𝐷
𝐿∙𝑢𝑔∙ 𝑒𝑥𝑝 (−(1−𝜃)2
4∙𝜃∙ 𝐷
𝐿∙𝑢𝑔)
Eq. 5.1
Here, 𝐶𝑖 (mg/L) is the oxygen concentration at time ti, 𝐶𝑎𝑡𝑚 (mg/L) is the oxygen concentration
before injection, 𝐶0 (mg/L) is the oxygen concentration at time 0 at injection station. 𝐷 (m2/s) is the
coefficient of dispersion in the air phase. The symbol 𝑡 (s) represents the time. 𝜃 is the normalized time
t/ 𝜏 , where 𝜏 (s) is the theoretical detention time, 𝑢𝑔 (m/s) represents the gas velocity and 𝐿 (m) is
the sewer length.
The theoretical detention time,𝜏 can be obtained from the following equation:
𝜏= ∑(𝐶𝑖− 𝐶𝑎𝑡𝑚)
𝑖=∞
𝑖=0 ∙𝑡𝑖∙∆𝑡
∑(𝐶𝑖− 𝐶𝑎𝑡𝑚)
𝑖=∞
𝑖=0 ∙∆𝑡
Eq. 5.2
Here ∆𝑡 (s) is the difference between the initial and final time. The gas velocity, 𝑢𝑔 can be written as:
𝑢𝑔=𝐿/𝜏
Eq. 5.3
The oxygen concentration after injection (𝐶0) and the coefficient of dispersion (𝐷) are the unknown
variables of Eq. 5.1, which can be found by fitting the simulated response curve to the measured
response curve. Madsen et al. (2006) used Eq. 5.1 to verify their experimental procedure by comparing
the measured and modelled values for coefficients of dispersion D (m2/s) and Co (mg/L). But for the
validation of the CFD simulations in this chapter, the published field data was chosen.
5.3 Section of the field study, geometry and mesh generation
As described in Table 5.1 and pictorially represented in Figure 5.3, ‘Pipe Section 2’ was selected for
the simulation case. In this section of the system, there is an injection station located at point ‘C’ and
two monitoring stations positioned at pipe sections ‘D’ and ‘E’, respectively. Over the course of the
study, a total of 13 oxygen injections were carried out from the injection station at point ‘C’. The
findings from these injections were collected and analysed, and the average results were subsequently
published by Madsen et al. (2006).
Chapter 5: Application of the solver for mitigation measures
63
(a)
(b)
Figure 5.4: (a) Section of the field experiment used for the case setup (see also Figure 5.3); (b) simulation case set up with important patches
64
This data serves as a valuable resource for understanding the behaviour and characteristics of the air
flow and transport of the tracer in the air duct of the system. Figure 5.4 highlights the section of the
field experiment used for simulation at the top and the constructed geometry at the bottom.
The geometry structure being studied consists of three utility holes that are connected to a 110-
meter-long sewer pipe. The pipe has a slope of 0.0027 m/m and a diameter of 0.5 meters. The first
two utility holes, labeled as ‘C’ and ‘D’, are located 70 meters apart, while the second and third utility
holes, labeled as ‘E’, are separated by a distance of 30 meters. To ensure a stable hydraulic state at the
locations of the utility holes, the pipe was extended by 5 meters in both directions. The geometry
design was conducted using Salome-Meca software (for details check Chapter 2.2.1).
Two types of grids, namely unstructured and structured grids, were created and compared before
starting the study. The unstructured grid was generated using the ‘NETGEN 1D-2D-3D’ algorithm in
Salome-Meca, which does not require the definition of lower-level hypotheses and algorithms. The
structured grid was generated using the geometry generated in Salome-Meca as a ‘.stl’ file and the
snappyHexMesh utility in OpenFoam (for details check Chapter 2.2.1). Figure 5.5 illustrates the
structured and unstructured meshes that were constructed. In this case, the main advantage of the
structured mesh is its smaller size, which results in significantly lower computational times during the
simulations. Hence, the structured mesh was utilized for hydraulic and transport simulations. The mesh
was run on HLRN (Norddeutscher Verbund für Hoch- und Höchstleistungsrechnen), with 2 nodes of 96
cores each and took approximately 30 s of simulation for 1 s of real time.
Figure 5.5: Unstructured (a) and structured mesh (b).
Chapter 5: Application of the solver for mitigation measures
65
5.4 Case setup for the simulations
5.4.1 Hydraulic simulation study
The hydraulic simulations were carried out using interFoam, a computational fluid dynamics
software, with the k-ϵ model selected to account for turbulence for all the cases simulated for this
study (Chapter 2.1.1). Initially, it was considered that there was no water in the pipe geometry, and
the corresponding standard viscosities were defined for both the fluids. Top and bottom walls bound
this three-dimensional setup; the utility manholes were considered completely closed and treated as
walls with no-slip conditions. The inlet was divided into two parts, with one part for the water phase
and the other for the air phase. In order to get an approximation of the water height in order to define
the patch for water inlet, theoretical water depth in the sewer was calculated which was around
0.09m. The volumetric flow rate in the field experiments was between 0.013 and 0.016m3/s, and
therefore a mean fixed discharge value of 0.0145m3/s was given at the water inlet and the null
Neumann condition was used to define the pressure boundary. The air phase velocity was dependent
on the water velocity and the pressure difference in the pipe, and it was assumed that no external
conditions affected the velocity. Therefore, the null Neumann condition was used for the velocity
boundary with a fixed pressure boundary. The boundary conditions in alpha.water for inlet water was
set to a phase fraction value (𝛼) of 1, and for inlet air it was set to 0. The rest of the boundary conditions
in alpha.water were set to null Neumann condition, which means that the gradient of the variable is
set to zero. The outlet patch was defined with fixed pressure and a free outflow condition.
The values for k and ϵ were uniform and calculated based on the turbulence intensity and water
velocity, and they were set as boundaries. The boundary condition zeroGradient was selected for the
air phase as the air velocity was unknown at the start of the simulation. To account for roughness
effects, wall functions were included, and the parameters were calculated and incorporated in the nut
file. The nutkRoughWallFunction boundary condition was utilized to limit the turbulent viscosity at the
walls. The ks parameter represented the roughness, as depicted in the Moody diagramme. Given the
considerable length and complexity of the geometry, to achieve quasi-steady-state conditions, the
case was simulated for the 1500 s. More details about the case setup can be found in Appendix C.5.
5.4.2 Oxygen injection study
After reaching a steady state, oxygen was injected into the system. In the field experiments of
Madsen et al. (2006), the injection study was conducted in a set of four steps, each consisting of a
different time and volume of injection. The injection was done at pipe section ‘C’, 10 cm above the
water surface. Each injection step was 30 minutes, and the system was allowed to stabilize before the
next injection. The concentration was then measured at the second monitoring station, ‘E’.
In order to replicate the field conditions, an initial concentration of oxygen was introduced in the
air phase wherever the phase fraction value (𝛼) was less than 0.5 using the utilities funkySetFields (for
initial conditions) from swak4Foam. Then a baffle was introduced after the system reached a quasi-
steady state.
Chapter 5: Application of the solver for mitigation measures
66
The location of the baffle was 10 cm above the water surface with a radius of 1 cm at point ‘C’
(see Figure 5.4 b). This baffle had a fixed discharge value as the velocity boundary condition, which was
calculated from the data published in the field study (see Table 5.3). Oxygen concentration was kept
constant in all four steps. Standard values for diffusion coefficient for oxygen in water and air were
defined in the transport properties, with Schmidt’s number (Sc) set to 1. All other boundary conditions
were set to null Neumann for the baffle. The mass transfer solver with a modified Henry coefficient
(HinterO2Foam) was then used for the simulations (for details check Chapter 2.1.2). The dimensionless
Henry coefficient was set to a high value (103) to prevent the tracer from spreading across the surface
and entering the water phase. The concentration was then measured at point ‘E’, and the profile was
plotted against time. The results were then compared to the published results by Madsen et al. (2006).
NSE (Nash-Sutcliffe efficiency) was then determined between the measured values and the CFD results
to observe how well the solver predicts the transport of O2.
Table 5.3: Different time, volume, and flow rate for each step.
Injection time (s)
Injection volume (m3)
Volumetric flow rate (m3/s)
Case
(measured)
(measured)
(calculated)
Step 1
540
2.7
0.0050
Step 2
360
1.86
0.0052
Step 3
300
1.48
0.0049
Step 4
160
0.47
0.0029
5.4.3 Ventilation study
For this study, the case setup remains the same, except that the manhole at point ‘D’ was opened
and ambient air and oxygen was allowed to flow out. This required the patch name Manhole 2 to be
an open boundary. In order to understand the effect of suction on the ventilation, different pressure
values were taken. A fixed pressure for prgh ranging from 0 to -2.5 Pa was used in 5 cases with null
Neumann condition of velocity at the open manhole. All the remaining boundary conditions for all the
other patches were the same as in the previous case. For each pressure value, the geometry was
hydraulically stabilized by running the simulation for 1500 s. After reaching a steady state, a pulse
injection of the 50 s with an oxygen concentration of 1mol/m³ was introduced at the inlet for air (𝑐𝑂2𝑔)
with 0 mol/m3 at the water inlet (𝑐𝑂2𝑎𝑞). After which, the concentration was again set to 0 mol/m3, and
the simulation was run until 600 s. The mass of oxygen removed from the system through Manhole 2
was then calculated and plotted against time to understand the effect of suction on ventilation. Further
details about the case setup are presented in Appendix C.6.
5.5 Results and discussions
5.5.1 Hydraulic simulations
For hydraulic simulations, the case runtime was 1500 s considering the pipe’s length. No
measurements were available for the flow profile except the flow rate range, which was between 0.013
Chapter 5: Application of the solver for mitigation measures
67
and 0.016 m3/s. Therefore, to validate the results after the steady state was achieved, the simulated
average velocity in the water phase was compared to the velocity calculated using Manning’s equation
for the volumetric flow:
𝑄= 1𝑛∙𝐴∙𝑅ℎ23∙𝐼𝑜12
Eq. 5.4
In which n (s/m1/3) is Manning’s roughness coefficient, A (m2) is the cross-section of the wetted area,
Rh (m) is the hydraulic radius, and S (m/m) is the channel’s bottom slope. According to Madsen et al.
(2006), the volumetric flow of water in the pipe is Qwater = 0.0145m3/s, Manning’s coefficient is n =
0.012s/m1/3, the pipe diameter is D = 0.5m, and the pipe slope is S = 0.0027(m/m). In order to calculate
the water velocity and the depth of water, the modified Manning’s equation for partly full sewer pipes
was utilised:
𝑄= 𝐾′
𝑛∙𝐷83∙𝐼𝑜12
Eq. 5.5
Solving for unknown K’:
𝐾′=0.02126≈ 0.0213
Eq. 5.6
In Table 5.4 first, the values closest to the calculated K’ (highlighted in bold) are located. The ratio
of the depth of flow to the pipe diameter (𝑑𝑏𝐷
⁄) is calculated by taking the values from the
corresponding row (0.08) and column (0.1), which sums up to 0.18. Using this value the depth of flow
becomes:
𝑑𝑏
𝐷= 0.18
Eq. 5.7
𝑑𝑏=0.09 𝑚
Eq. 5.8
To validate the calculations, an EXCEL solver was employed, utilizing the flow variables described
earlier. The Manning's coefficient was estimated by approximating the depth of flow. By setting the
solver to converge on a value of n near 0.012 s/m1/3, the resulting water depth was determined to be
approximately 0.085m. This value closely aligns with the previous calculations (Eq. 5.8).
Using the Manning’s partial flow diagramme (Figure 5.6), for db / D = 0.18, the wetted area to the
pipe is ratio A / Afull = 0.12, where Afull if the total cross-sectional are of the pipe (D = 0.5 m) .Therefore,
the wetted area is equal to:
𝐴=0.0236 𝑚2
Eq. 5.9
Chapter 5: Application of the solver for mitigation measures
68
Following the continuity equation:
𝑄=𝑣∙ 𝐴
Eq. 5.10
Where 𝑄 is the flow rate (m3/s), 𝐴 is the area (m2) and 𝑣 is the velocity (m/s). On substituting the
values:
𝑣 ≈0.6 𝑚/𝑠
Eq. 5.11
Table 5.4: K’ values in terms of diameter for circular channels (Eddy and Tchobanoglous, 1981).
Figure 5.6: Hydraulic elements for circular sewer pipes (Eddy and Tchobanoglous, 1981).
𝒅𝒃
𝑫
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.000047
0.00021
0.00050
0.00093
0.0015
0.00221
0.00306
0.00407
0.00521
0.1
0.00651
0.00795
0.00953
0.0113
0.0131
0.0152
0.0173
0.0196
0.0220
0.0246
0.2
0.0273
0.0301
0.0331
0.0362
0.0394
0.0427
0.0461
0.0497
0.0534
0.0572
0.3
0.0610
0.0650
0.0691
0.0733
0.0776
0.0820
0.0864
0.0910
0.0956
0.1003
0.4
0.1050
0.1099
0.1148
0.1197
0.1248
0.1298
0.1349
0.1401
0.1453
0.1506
0.5
0.156
0.161
0.166
0.172
0.177
0.183
0.188
0.193
0.199
0.204
0.6
0.209
0.215
0.220
0.225
0.231
0.236
0.241
0.246
0.251
0.256
0.7
0.261
0.266
0.271
0.275
0.280
0.284
0.289
0.293
0.297
0.301
0.8
0.305
0.308
0.312
0.315
0.318
0.321
0.324
0.326
0.329
0.331
0.9
0.332
0.334
0.335
0.335
0.335
0.335
0.334
0.332
0.329
0.325
1.0
0.312
Chapter 5: Application of the solver for mitigation measures
69
Figure 5.7 shows the results obtained after the 1500 s of simulation. The vertical flow profile after
the steady state was achieved and resembles the one presented in the case of Bentzen et al. (2016)
(Figure 4.2 and Figure 4.3). The velocity profile at the cross section resembles a parabolic shape in the
water phase and an S-shape profile in the air phase. The profile for alpha.water representing the phase
fraction shows the value 1 for the water phase, 0 for the air phase, and the inclined line connecting
the values represents the transition zones at the interface. The average water depth from the
simulation was 0.088 m, taken to the point where the value of phase fraction (𝛼) is higher than 0.5.
The average water velocity for the flow was approximately 0.58 m/s. These values are in good
agreement with the values calculated using Manning’s equation for the flow velocity of 0.60 m/s. The
simulation demonstrated that the solver successfully reproduced the flow pattern observed in the field
study, with an approximate error rate of 3 %.
Figure 5.7: Phase fraction and velocity profile along the height at the center of the duct.
5.5.2 Solution and grid convergence study
Various grid resolutions were evaluated to investigate the simulation’s independence on the
numerical grid. Five different meshes were created, beginning with 298,683 hexahedral grid cells in
the first mesh, and the number of cells was increased up to 5,994,366 in subsequent meshes. Figure
5.8 shows the distribution of cells and sections of the three grid gradations from the pipe’s inlet. The
complete mesh statistics for all five meshes are presented in Table 5.5. The next step for checking the
convergence of the simulation is done by plotting the residuals for each parameter for each iteration.
The residual is one of the most fundamental measures of an iterative solution’s convergence, as it
directly quantifies the error in the solution of the system of equations. In a CFD analysis, the residual
measures the local imbalance of a conserved variable in each control volume (Kuron, 2015). In
OpenFOAM, residuals are computed at each iteration for every equation being solved by comparing
the current and previous solutions, quantifying imbalances in each cell/control volume. The residuals
are then typically normalized by dividing them by a reference value or the characteristic value of the
Chapter 5: Application of the solver for mitigation measures
70
parameter that is solved, therefore they are dimensionless. The values of the residuals are plotted
logarithmically. The abscissa shows the simulation time in seconds.
Figure 5.8: From left to right: coarse, medium, medium refined at the walls, fine and very fine mesh.
Table 5.5: Number of cells and time required for simulation according to different grid sizes.
Figure 5.9 and Figure 5.10 present the residual errors for different meshes and for different
parameters over a period of 500 seconds. At the start of the simulations, all cases exhibit very high
residuals, which gradually decrease and reach their minimum value after 500 s.
By analysing the graphs, two noticeable characteristics can be observed. Firstly, as the number of
cells in the grid increases, the length of the jumps in the residuals decreases, indicating that finer
meshes have a faster stabilisation rate than coarser ones. Secondly, the initial residual varies among
the cases. The coarse mesh has a residual of approximately 10-2 to 10-3, while the medium mesh has
residuals ranging from 10-3 to 10-4, and the finer meshes have residuals predominantly around 10-4 and
10-5.
In CFD simulations, residual levels of 10-4 are considered loosely converged, 10-5 is regarded as well
converged, and 10-6 is seen as tightly converged. However, for complex problems, achieving such low
residual levels may not always be feasible (Kuron, 2015). To ensure convergence, residual errors should
be under 10-4, and the best results are attained in cases where the residual errors are below this
threshold.
Number of cells
Time required per
second of simulation
Coarse
298,683
10 seconds
Medium
1,425,117
25 seconds
Medium refined
1,469,159
32 seconds
Fine
3,554,131
66 seconds
Very fine
4,334,065
300 seconds
Chapter 5: Application of the solver for mitigation measures
71
(a)
(b)
Figure 5.9: Residual plots: coarse, medium, medium refined at the walls, fine and very fine mesh for
parameters (a) phase fraction (alpha.water) and (b) velocity magnitude U.
Chapter 5: Application of the solver for mitigation measures
72
(a)
(b)
Figure 5.10: Residual plots: coarse, medium, medium refined at the walls, fine and very fine mesh for
parameters (a) pressure (p_rgh) and (b) turbulent kinetic energy (k).
Chapter 5: Application of the solver for mitigation measures
73
Figure 5.9 and Figure 5.10 demonstrate that the medium mesh refined at the walls and the very
fine mesh meet these criteria, and the simulations converge effectively.
Another aspect of the study was to verify the independence of the simulation from the grid
resolution and the estimation of discretization errors. For this purpose, the methodology suggested by
Celik et al. (2008) was chosen. Firstly, one has to define a representative cell, mesh, or grid size h given
as:
ℎ= [1
𝑁∑(∆𝑉𝑖)
𝑁
𝑖=1 ]13
⁄
Eq. 5.12
where ∆𝑉𝑖 is the volume, and N is the total number of cells used for the computations. For good grid
convergence, it is desirable that the grid refinement factor r = hcoarse / hfine should be greater than 1.3
(Celik et al., 2008). Therefore, Table 5.6 shows the refinement factor calculated for the generated
meshes. The five grids were divided into two sets, set 1 consisting of coarse, medium and fine mesh
where all the cells where divided uniformly when increasing the number of cells (using geometrically
similar cells), and set 2 consisting of course, medium refined and very fine mesh, where
snappyhexmesh was used to refine the mesh at the walls. The refinement factor for both sets has
values far bigger than 1.3 what should be shown.
Table 5.6: Calculations for the representative grid size and refinement factors.
In the current study the velocity magnitude 𝑈𝑚𝑎𝑔 at the center of the pipe was chosen as an
indicator at 15 locations along the height of the pipe (z1 = 0.01, z2= 0.015, …, z15 = 0.08m). Figure 5.11
shows the results at five locations for both sets (z1, z3, z5, z7 and z9). On calculating the RMSE values
for each refinement step (two in each set of meshes), it was found that in set 1 refining from medium
to fine mesh, RMSE of 6 x 10-2 m/s was achieved. Meanwhile in set 2 when refining from medium to
very fine mesh, RMSE of 4 x 10-2 m/s was achieved.
Although there is still scope for further refinement, considering the amount of time needed for
each simulation with HLRN (Norddeutscher Verbund für Hoch- und Höchstleistungsrechnen, 2 nodes
with 96 cores each), medium refined mesh was chosen for further investigations. There were other
factors facilitating this decision, for example the medium refined mesh showed good agreement with
the analytical solution as observable in the hydraulic simulations done in the previous section (Chapter
5.5.1). The mesh also showed a good level of simulation convergence when plotting the residuals.
Set 1
Set 2
Avg. volume
of cells
h
r
Avg. volume
of cells
h
r
(m3)
(m)
(m3)
(m)
Coarse
7.32·10-5
2.44·10-5
Coarse
7.32·10-5
2.44·10-5
Medium
1.55·10-5
5.15·10-6
4.7
Medium
refined
1.50·10-5
5.00·10-6
4.9
Fine
6.21·10-6
2.07·10-6
2.5
Very fine
5.17·10-6
1.72·10-6
2.9
Chapter 5: Application of the solver for mitigation measures
74
The results are close to grid convergence at several locations but at not (for example z1). However
further grid refinement was not feasible due to time constraint. Complimentarily the time required for
the simulation by the medium refined mesh made it ideal when considering the number and the length
scale of the simulations that were done in the oxygen injection (Chapter 5.4.2) and ventilation study
(Chapter 5.5.4).
(a) (b)
Figure 5.11: Comparison of simulated indicator values z (flow velocities) for different grid sizes in five
points within the domain ((a) set 1: coarse, medium and fine mesh, (b) set 2: course, medium refined
and very fine mesh).
5.5.3 Oxygen injection study
After conducting the simulation and analysing the results above, an initial concentration is injected
at the first manhole (Point C, Figure 5.4 (b)), approximately 10 cm above the water surface. The
injection simulation is demonstrated by applying the modified interO2Foam solver to the geometry.
The simulation results, including an overview of the computational domain and the air phase
behaviour, are illustrated in Figure 5.12 and Figure 5.13, with a concentration range between 213000
ppm and 322000 ppm.
The comparison between the simulation and the experimental response curves shows the same
trend for all four injection steps. As initial conditions were established and a minimum oxygen
concentration was maintained in the system, the pulse injection can be seen as the rise and fall of the
Chapter 5: Application of the solver for mitigation measures
75
concentration values above the baseline. Initially, the manhole near monitoring station ‘E’ was opened
in order to fix the sensors, and after that, all the manholes were sealed in order to stabilize the
conditions inside the system. Therefore, this concentration profile is only visible in Figure 5.12
(a) before the injection starts. After which, all the other steps have stable conditions before and after
the simulation. Figure 5.11 (a) exhibits a comparable initial response curve to that observed in the
experiments. The overall response duration, or peak width, also demonstrates substantial agreement
with the presented data. The response curve's maximum concentration (peak concentration) closely
approximates the peak observed in the field study. The difference in the concentration profile shape
between the CFD model and the field data is evident. This dissimilarity arises from various additional
factors influencing flow in the natural system such as external forces occurring due improper closure
of the manhole for the experiment, fluctuating temporal conditions, obstruction in flow among other
factors.
Figures 5.11 (b) and 5.12 (a) and (b), illustrating the following time steps of the simulation, also
exhibit similar behaviour. The peak concentrations of oxygen and the five evaluation criteria used to
assess model performance for the simulation steps are presented in Table 5.7. Considering that the
solver was modified to keep the maximum concentration of O2 reactive tracer in the air phase, the
result’s agreement with the experimental data is quite acceptable.
Table 5.7: Peak concentration of O2 observed and simulated with the respective model evaluation
criterion for each step.
Case
Max. Conc. of O2
recorded (ppm·105)
Nash–Sutcliffe
efficiency
RMSE
Normalized
RMSE
Correlation
coefficient
R2
Field
Simulation
Step 1
3.195
3.187
0.87
0.179
0.166
0.951
0.905
Step 2
3.184
3.177
0.9
0.107
0.095
0.972
0.945
Step 3
2.894
2.89
0.7
0.170
0.201
0.878
0.77
Step 4
2.328
2.329
0.82
0.038
0.132
0.931
0.867
Chapter 5: Application of the solver for mitigation measures
76
(a)
(b)
Figure 5.12: Simulated versus experimental (Madsen et al., 2006) oxygen concentration profile at
manhole 3 (Point E, Figure 5.4 (b)) for step 1: 0 – 1800 s (a) and step 2: 1800 - 3600 s (b).
Chapter 5: Application of the solver for mitigation measures
77
(c)
(d)
Figure 5.13: Simulated versus experimental (Madsen et al., 2006) oxygen concentration profile at
manhole 3 (Point E, Figure 5.4 (b)) for step 3: 3600 - 5400 s (c) and step 4: 5400 - 7200 s (d).
Chapter 5: Application of the solver for mitigation measures
78
5.5.4 Ventilation study
This study considered five cases with different suction pressures at manhole 2 (pipe section ‘D’).
These simulations aim to investigate the ventilation in sewer systems by utilizing oxygen as a tracer.
This approach will be valuable, particularly in scenarios where the removal of hydrogen sulphide (H2S)
is required. In this study, the selection of suction pressure values (prgh) was based on the value ranges
observed for ventilation/exhaust fans. The performance of these fans is measured in terms of the
amount of air that the fan can move or exhaust from a space within a given period (m3/h). As the
diameter of the utility manholes in this study is 0.5m, ventilation fans with these dimensions typically
perform within the ranges of 100 m3/h to 500 m3/h. These values are contingent upon specific
requirements and design factors and may change. For the purpose of this study, the suction pressure
values were chosen to produce flow rates from ~150 m3/h (for prgh – 1 Pa) to ~300 m3/h (for prgh -
2.5 Pa). The prgh values were increased until reaching a point where further increment was no longer
feasible. All the cases were hydraulically stabilised and were allowed to reach a steady state. The
volumetric flow rate in the air phase was then calculated using the formula:
𝑄𝑎=𝐴𝑎∙ 𝑈𝑎𝑣𝑔
Eq. 5.13
Where Aa is the area of the air inlet in (m2) and Uavg is the average air flow velocity in (m/s). Using this
flow rate the mass flow rate was calculated:
𝑀𝑂2=𝑄𝑎∙𝐶𝑂2𝑔
Eq. 5.14
Where MO2 (mol/s) is the molar flow rate of oxygen and CO2g (mol/m3) is the average concentration
of O2. The total mass of oxygen was calculated by multiplying the molar flow rate with the injection
time and the molecular mass of oxygen. Similarly, the mass of oxygen removed at manhole 2 and the
outlet was calculated. Table 5.8 shows all the values calculated from the simulation data and the
percentage removal rate for oxygen in different cases.
Table 5.8: Mass balance for oxygen in ventilation scenarios.
Suction pressure
Mass at inlet
(air phase)
Manhole 2
(Point D)
Mass at outlet
(air phase)
Residual
oxygen
Mass
removed
prgh (Pa*)
(g)
(g)
(g)
(g)
(%)
Without Ventilation
133.3
0.0
96.0
37.3
0.0
0
132.8
0.0
95.6
37.2
0.0
-1
147.2
67.0
76.5
3.7
45.5
-1.5
174.4
95.4
69.1
9.8
54.7
-2
186.2
119.6
65.1
1.5
64.2
-2.5
196.5
139.9
52.5
4.1
71.2
* prgh is a modified pressure which is used to avoid the occurrence of steep pressure gradients
caused by hydrostatic effects and in order to simplify the definition of boundary conditions (Rusche,
2003).
Chapter 5: Application of the solver for mitigation measures
79
The first case is inspected without ventilation, where manhole 2 was considered as closed (wall). A
pulse injection of 50 s with an oxygen concentration of 1 mol/m3 was introduced for the simulation.
As expected, there was no oxygen removed at the manhole 2. The second case included the same
setup with the manhole 2 open, and no negative pressure was provided. Even with an open boundary,
still, no oxygen was removed from the system. This is because the horizontal flow is significantly higher
than the one in the vertical direction induced by the open manhole. On increasing the suction to 1 Pa,
the first signs of oxygen removal were noticed. At the initial time point of 0 s on the graph in Figure
5.14, oxygen particles required a certain duration to traverse the distance between the inlet and the
open manhole. Subsequently, the process of oxygen removal initiated and continued until reaching a
state where no further removal was achievable. It is noteworthy that this consistent behaviour was
observed across all the suction pressure lines, indicating a common pattern. It was also found that
increasing the suction rate not only increases the mass of oxygen removed but also reduced the time
taken for removal. This can be clearly observed in the graph shown in Figure 5.14; the maximum
removal of oxygen is achieved faster when the suction pressure is higher. For example, if we just isolate
the 150 s mark (marked in yellow in Figure 5.14), it is clearly visible that the mass of oxygen removed
is higher for a higher suction rate. Contemporarily if one looks at the time required by each case to
remove 50 g of oxygen (marked in red in Figure 5.14), the time required is lesser when the suction
force is higher.
Figure 5.14: Cumulative mass of oxygen removed with time for different suction rates.
Chapter 5: Application of the solver for mitigation measures
80
However, it is also important to highlight a potential limitation associated with increasing suction
pressure beyond a certain point. The simulation study shows that increasing the suction pressure
beyond a certain threshold causes the simulation to stop abruptly after a certain number of time steps.
This occurs due to the vertical flow at the manhole becoming significantly higher than the horizontal
flow, resulting in air being drawn from both directions below the manhole. This contradicts the
boundary conditions at the outlet of the pipe, which can lead to simulation errors.
5.6 Conclusion
The research conducted in this chapter verifies the applicability of the VOF approach implemented
in OpenFOAM for a real-world case. This approach investigated the two-phase flow hydraulics in a
turbulent three-dimensional complex sewer geometry. A structured hexahedral mesh was created,
and a mesh convergence test was conducted to assess solution accuracy. The mesh quality was
acceptable, and residual errors ranged from 10-3 to 10-4. The interFoam solver was used to simulate for
1500 seconds, achieving a hydraulically steady state with no significant changes in velocity, water
depth, and pressure. The solver’s performance was acceptable, and the desired experimental water
velocity was achieved with a minor error of approximately 3 %.
For the oxygen injection study, the interO2Foam solver with modified Henry’s coefficient was
suitable in predicting the transport of oxygen through the circular sewer channel. The oxygen
concentration was measured at the third utility manhole (Point ’E’, Figure 5.4), and the simulated
response curve matched the measured response curve of Madsen et al.’s (2006) experiments. The
transport profiles for different injection parameters, including volumetric flow rate and time of
injection, were predicted with adequate accuracy (average Nash–Sutcliffe efficiency of approximately
0.83). This verifies the applicability of the solver in long channels. The ventilation study conducted
simulations to investigate the effects of ventilation on oxygen removal in a system with utility
manholes. It provided valuable insights into the role of suction pressure in removing oxygen. The
analysed results show the highest oxygen concentration at the second utility manhole, indicating an
ideal location for testing different ventilation scenarios. It was observed that the increase in the suction
rate indeed increased the mass of oxygen removed. But another important outcome was that the
increase in suction pressure also decreased the amount of time required for the removal of a certain
mass of O2. This model provides valuable insights into system dynamics for ventilation. It also offers
practical benefits by facilitating the development of strategies for H2S removal and improving the
overall environmental conditions within the sewer network. These models can become helpful in
identifying locations of the utility manhole that can be selected for ventilation scenarios when there
are a series of utility holes introducing turbulence in the system.
81
Chapter 6
Mass transfer in rotating turbulent reactor
The focus of this chapter is on examining the release of H2S and absorption of O2 in a stirring tank
under turbulent conditions. Two-phase solvers have been created and linked to a dynamic meshing
feature, allowing for the calculation of the mass-transfer taking place. The impact of turbulence on the
mass transfer coefficient has been explored using a three-dimensional model that simulates the direct
exchange of H2S and O2 between the water and air phases using the modified solvers.
6.1 Introduction
Previously, there has been considerable advancement in comprehending the emission of hydrogen
sulphide (H2S) in sewage systems. On the one hand, conceptual model approaches have been
developed to describe the occurrence of odour and corrosion (Hvitved-Jacobsen et al., 2013; Teuber,
2020). On the other hand, numerous experiments have been conducted to better understand driving
factors such as the influence of turbulence on H2S mass transfer across the water surface (Carrera et
al., 2017; Matias et al., 2017; Teuber, 2020; Wu, 1995). Yongsiri (2004) conducted a study indicating
that the accurate depiction of turbulence is crucial since it offers a similar framework to the usual
conditions encountered during the reaeration process in sewer networks. Turbulent flow occurrences
are widespread in sewer systems. These can be due to the flow velocities involved in the system.
However, even larger levels of turbulence can also be observed in drop structures because of the links
between pipes and manholes or due to various obstructions in the flow. A correct quantification of the
effects of turbulence, which is highly three-dimensional, on the H2S mass transfer is therefore crucial
for the development of reliable models (Teuber, 2020).
According to Lucie Carrera (2017), the mass transfer coefficient of oxygen between liquid-gas
interface is strongly connected to the flow conditions. Stirring tanks have been often used in the
experimental setup for studying mass transfer due to turbulence. The studies of Wu (1995) (for O2
mass transfer) and Carrera et al. (2017) (for H2S mass transfer) analysed the influence of different
factors such as stirring rate. Describing these emissions in a stirring tank with a CFD model cannot only
enable us to investigate more complex phenomena on a larger scale but could also help avoiding lab
experiments that come with a health risk and decrease the number of experiments necessary (Teuber,
2020). The cases simulated in the current chapter were developed using the same methodology from
Carrera et al.(2017) and the cases developed by Teuber (2020). The experiments were conducted
under the project S1 (On the application of online monitoring for hydrogen sulphide in sewer systems)
Chapter 6: Mass transfer in rotating turbulent reactor
82
of the DFG Research Training Group Urban Water Interfaces and were published as the bachelor works
of Tang (2019) and as a part of conference contribution of Pacheco Fernández et al. (2020). Figure 6.1
shows the experimental set up used in the study of Wu (1995) as well as the experimental setup used
for the CFD study here.
Figure 6.1: System sketch of stirring tank including relevant variables from the experimental works of
Wu (1995, modified) (left), experimental set up used for simulation(not to scale) (right).
6.2 Case study: Turbulent reactor (Project S1: Urban Water Interfaces)
The experiments were divided into two methodologies, namely, absorption method for measuring
the mass transfer coefficient of oxygen and a desorption method for measuring the mass transfer
coefficient of hydrogen sulphide. The principle of the absorption method was to get the relationship
between the time and the concentration of dissolved oxygen in the water phase after an initial
concentration was set to zero. The desorption method determines the mass transfer by the decrease
of the previously dissolved hydrogen sulphide concentration in the water phase with time.
6.2.1 Reactor setup and stirring rate selection
The equipment consists of an 80 cm high tempered glass tank, with outside diameter of 30 cm and
an inside diameter of 29 cm, and a stirrer (PHOENIX RSO 20A, see Figure 6.2). The tank had a maximum
volume of 52.8 L. Different probes were installed at the depth of 8 cm below the water surface. The
stirrer had a range from 50 rpm (revolutions per minute) to 2200 rpm. 300 rpm, 400 rpm and 500 rpm
were chosen for the experiments of oxygen and hydrogen sulphide mass transfer. Table 6.1 gives the
details of the dimensions of the experimental setup.
Table 6.1: Experimental set up data.
Shape
Height
Maximu
m volume
Dout
Din
Dstirrer
Water height H2S
experiments
Water height
O2 experiments
Cylinder
80 cm
52.8 L
30 cm
29 cm
10 cm
16 cm
15 cm
Chapter 6: Mass transfer in rotating turbulent reactor
83
6.2.2 Hydrogen sulphide experiments
The initial experimental setup consisted of a stirrer and oxygen probe which were installed in the
reactor at the height of 8 cm. Figure 6.2 gives the general setup used for the H2S experiment. The
reactor was filled with 10.6 L pure water and the filling height reached 16 cm. The volume required for
the H2S experiment was more than the one in the O2 experiment (0.7 L more, see section 6.2.3),
because the concentration of H2S in the liquid phase was not measured online. The samples were taken
manually after a certain time interval, which in turn lowered the volume a bit. So, to have similar
volumes of water in both the experiments a higher volume was chosen. Nitrogen was used to
deoxygenate the pure water until the dissolved oxygen concentration was approximately 0.1 mg/L.
The air phase was also flushed continuously with nitrogen in order to avoid the oxygen in the
atmosphere being transferred to the liquid phase. Na2S·9H2O (Sodium sulphide nonahydrate) was used
to introduce H2S in the water phase in the presence of HCl (Hydrochloric acid, 8% concentration) and
a pH of 7. After the chemicals were introduced in the tank, the stirrer was switched on with different
stirring rates depending on the experiment (5 1/s, 6.66 1/s, 8.33 1/s). The H2S measurements were
carried out by manually taking samples from the reactor and using an H2S-analyzer (DIN 38405-
27:2017-10). The results were than plotted against time to get a concentration profile, which was then
used to validate the results from the simulation to validate the solver (interH2SFoam). Experimental
results for respective rpms are shown in Figure 6.8.
6.2.3 Oxygen experiments
The basic experimental set up remained similar to that of H2S experiments (see Figure 6.3). The
reactor was filled with 9.9 L pure water and the water height reached 15 cm. Nitrogen was used to
deoxygenate the dissolved oxygen in the liquid phase. DO (dissolve oxygen) value was lowered to
approximately 0.1 mg/L, before all the inlets were open for the absorption process for different stirring
rates (5 1/s, 6.66 1/s and 8.33 1/s). The results available from the 6.66 1/s stirring rate experiment
showed some anomalies and therefore they were utilized for the validation process. The oxygen
concentration was measured using an on-line electrode (LDO HQ40d), and the concentration of
dissolved oxygen was logged automatically using the sensor. Similar to the H2S experiments the results
were plotted against time to get a concentration profile, which was then utilized for the validation of
the oxygen solver (interO2Foam) shown in Figure 6.9.
Chapter 6: Mass transfer in rotating turbulent reactor
84
Figure 6.2: Experimental setup for the hydrogen sulphide experiments.
Figure 6.3: Experimental setup for the oxygen experiments.
Chapter 6: Mass transfer in rotating turbulent reactor
85
6.3 Computational setup
Solver and model
The current setup utilizes the interFOAM solver for the hydrodynamic simulations. The dynamic
mesh utility is activated by introducing a cyclic AMIs (cyclic Arbitrary Mesh Interface) as a boundary
condition. The cyclic AMI boundary condition facilitates a smooth and continuous connection between
two patches in a cyclic fashion. This is particularly useful in simulations in this study with a rotating
equipment. The k-𝜖 turbulence model was chosen for all the simulations. The extended solvers for H2S
(interH2SFoam) and O2 (interO2Foam) were used for the simulation of mass transfer. The details of
the turbulence models and solvers used are mentioned in Chapter 2.1.
Geometry and mesh
For the construction of the geometry, all the dimensions were manually measured from the lab-
scale set up. The dimensions were than utilized to make the geometry for meshing using the open
source software Salome-Meca. The blade and the reactor tank were drawn to scale and can be seen in
the Figure 6.4. The figure consists of the main reactor tank which is a cylinder and contains a rotating
blade within its domain. The blade is enclosed within a cyclic AMI boundary, which can be seen in
Figure 6.6 marked in green. The unstructured grid was then meshed using the meshing utility in
Salome-Meca. Several other meshes were also constructed using GMSH and snappyHexMesh utility in
OpenFOAM. All the meshing tools are discussed at length in Chapter 2.2. These meshes were initially
compared according to the time required for simulation. The details for the meshes generated are
presented in Table 6.2. The table lists the number of cells and the respective time taken for 1 s of
simulation. All the simulations were conducted using the same number of compute nodes and cores
on HLRN (Norddeutscher Verbund für Hoch- und Höchstleistungsrechnen). One compute node with 96
cores was utilized in all the simulations as it was found that increasing the computation power further
increased the computation time. For a structured grid to be constructed, the minimum length of the
cell was equal to the width of the blade (1 mm or 0.001 m) which drastically increased the number of
cells. Varying the cell size distribution with smaller cells around the blade and increasing the cell size
for the surrounding reactor, caused a huge gradient in cell size, which either took more time to
simulate or caused the mesh to crash after few seconds of simulation.
86
Figure 6.4: Geometry and mesh used for mass transfer simulations.
Table 6.2: Details for different meshes generated and their respective simulation times.
Tool
Mesh
Number of
cells
Approx. time required
per second simulation
Salome-Meca
Unstructured
Fine
179,213
7200 seconds
Unstructured
Moderate
63,237
300 seconds
GMESH
Structured
Fine
243,612
3600 seconds
snappyHexMesh
Structured
Coarse
421,725
2400 seconds
Structured
Moderate
3,370,568
10,800 seconds
Chapter 6: Mass transfer in rotating turbulent reactor
87
Therefore, considering the huge amount of computational time required for simulating 300 s of real
time and with 1 node and 96 cores (with no further increase in compute nodes possible due to negative
impact on the computation time), a uniform unstructured grid was considered for the mass transfer
simulations. The initial and final residuals for the different parameters also showed a good level of
convergence. Initial residuals for phase fraction (𝛼), pressure (prgh) and turbulent kinetic energy (k)
were in the range of 10-5. While for velocity magnitude, concentration of O2 (O) and concentration of
H2S (H), the initial residuals were in the range of 10-6 (Figure 6.5). Although the values of these residuals
are subjective and depend on the case itself, but from the general rule of thumb, residual levels of 10-
4 are considered loosely converged, 10-5 is regarded as well converged, and 10-6 is seen as tightly
converged (Kuron, 2015). Considering the complexity of the mesh and the residuals being in expectable
range, the uniform unstructured grid was utilised for the simulations.
Figure 6.5: Initial residuals for different parameters for the turbulent reactor.
Boundary and initial conditions
The boundary conditions applied to model the turbulent reactor (stirring tank) consists of a
cylindrical shape including cylinder walls forming the sides, a circular bottom, and top wall, and internal
walls represented the stirring blade. The usage of a dynamic meshing algorithm also requires the
definition of an internal boundary surface between rotating and static mesh (Teuber, 2020). The
moving boundaries between these regions were defined using a cyclic Arbitrary Mesh Interface (AMI).
These boundaries use a coupling condition between a pair of patches that share the same outer
Chapter 6: Mass transfer in rotating turbulent reactor
88
bounds, but whose inner construction may be dissimilar (OpenFOAM Foundation, documentation
v2112). The boundary regions are displayed in Figure 6.6. At the walls, a no-slip condition is imposed.
Figure 6.6: Geometry used for the simulations including boundaries (dark grey: blade; blue: outer
cylinder; green: rotor walls / inner cylinder; red: AMI /upper plane on top).
For the H2S simulations, in order to replicate the conditions in the experiment, the top wall was
closed using a no slip condition. So, the H2S released from the water phase into the gas phase still
remains in the system. For the O2 simulations oxygen gas was allowed into the system by opening the
valves at the top (see Figure 6.2). Therefore, to replicate the conditions at the top, an atmospheric
boundary condition is defined to allow fluids to enter and leave the domain by imposing a zero gradient
(Neumann) condition to all variables except the pressure (prgh) boundary condition, which is set to a
fixed value of zero (Dirichlet, atmospheric pressure) (Teuber, 2020). Arbitrary low values were set for
variables of the turbulence model in the beginning of the simulations and these values are corrected
by the solver using calculated values during the simulation. The fluid properties and the transport
properties are given in Table 6.3. Further details about the case setup and boundary conditions can be
found in Appendix C.7 (H2S) and C.8 (O2)
For H2S simulations a constant concentration was set as intial condition in the water phase (𝑐𝐻2𝑆𝑎𝑞),
the values of which were taken from the experimental data available. Similarly, for the O2 simulations,
initial concentration in the water phase (𝑐𝑂2𝑎𝑞) was set to the vaules recorded before the beginning of
the experiment using the utilities funkySetFields (for initial conditions) from the swak4Foam utility.
NSE was then applied to check the efficiency of the two solvers as well as to give a justification for the
applicability of the two solvers.
Chapter 6: Mass transfer in rotating turbulent reactor
89
Table 6.3: Fluid properties as defined in the CFD simulations.
Water phase
Air phase
Density 𝝆 [kg/m3]
1,000
1.2
Kinematic viscosity 𝝊 [m2/s]
1.0 · 10-6
1.48 · 10-5
Diffusion coefficient Dphys (H2S) [m2/s]
1.8 · 10-9
1.74 · 10-5
Diffusion coefficient Dphys (O2) [m2/s]
2.42 · 10-9
1.98 · 10-5
6.4 Results and discussion
After an initial visual examination of the three different stirring rates, it can be concluded that the
fluids in the turbulent reactor exhibit a plausible surface profile at the interface. This is visible in the
vortex profiles depicted in Figure 6.7.
Figure 6.7: Vortex shapes for different stirring rates (left: 300 rpm, middle: 400 rpm and right: 500
rpm).
Furthermore, on plotting the concentration profile against the data available from the
measurements, the preliminary examination confirms that the simulated data has quite a good
agreement with the experimental data. Figure 6.8 illustrates the graphs for the interH2SFoam solver
for different rotation speeds (300, 400 and 500 rpm). Samples for measurements were taken manually
every 60 s, hence only five data points were available for the plots. The graph depicts the experimental
and computational fluid dynamics (CFD) results, with the red line representing the experiments and
the black line representing the CFD simulations. The experiments were conducted in triplicate, and
ideally all three measurements were meant to be used for validation. But in a few experiments, the
Chapter 6: Mass transfer in rotating turbulent reactor
90
initial concentration of H2S at time 0 s differed (e.g., for cases represented in Figure 6.8 (a) and (b)). To
ensure a fair comparison between the measured and CFD data, for the experiments approximately the
same initial concentrations were selected, and these concentration values were used as the initial
condition for all numerical cases. Therefore, in Figure 6.8 (a) and (b) only one measurement was usable
and in Figure 6.8 (c), two of them were considered. The simulated results are plotted accordingly in
the graphs and the units were converted to mg/L to match the units of the measured data. It was
observed that mass transfer increases with an increase in the stirring rate. This can also be written as
the mass transfer coefficient increases with an increase in stirring rate. This behaviour agrees with
results and observations by Carrera et al. (2017) as well as Wu (1995). It becomes clear that a significant
increase of the mass transfer coefficient with increasing stirring rate is to be expected (Teuber, 2020).
The tendency of the solver to predict the mass transfer is better at higher stirring rates.
Similarly, for O2, the plots show a good agreement with measured data. The data was measured
using an online sensor and recorded every 10 s, therefore giving a better data density for plotting the
graph. Figure 6.9 illustrates the concentration time series for different stirring rates. Similar to the
preceding investigation on hydrogen sulphide (H2S), the black lines in the figures represent CFD data,
while the red lines correspond to three experimental data sets. As mentioned earlier in this section,
the system was thoroughly purged of O2 using nitrogen gas. However, trace amounts of residual
oxygen were still present in the system. Hence, these residual O2 concentrations were considered as
the initial conditions for the system, resulting in a slightly higher concentration than zero at time 0 s as
observed in the CFD data series. Throughout the course of the experiment, O2 enters from the top
inlet, initiating the mass transfer process of oxygen from the air phase to the water phase. There is a
good agreement observed between the numerical and the experimental data. This validates the
applicability of the interO2Foam solver for highly turbulent cases.
Table 6.4 lists the calculated model efficiency criteria for the simulated results to the measured
data. The resultant NSE for H2S (approx. 0.8) and O2 (approx. 0.9) show that the solvers can produce
acceptable representation of mass transfer processes under turbulent conditions. The calculated RMSE
and normalized RMSE also indicate reasonable acceptance between the modeled and the
experimental results. The correlation factors also represent a good fit between the two results. In
general, all the calculations show that the solvers can be a useful tool for quantitatively predicting the
mass transfer of H2S and O2 in highly turbulent cases.
Chapter 6: Mass transfer in rotating turbulent reactor
91
(a)
(b)
(c)
Figure 6.8: Comparison of the measured data to the results obtained from simulations for H2S for
different stirring rates ((a): N = 300rpm, (b): N = 400rpm, (c): N = 500rpm).
Chapter 6: Mass transfer in rotating turbulent reactor
92
(a)
(b)
Figure 6.9: Comparison of the measured data to the results obtained from simulations for O2 for
different stirring rates ((a): N= 300rpm, (b): N = 500rpm)).
Chapter 6: Mass transfer in rotating turbulent reactor
93
Table 6.4: Different model efficiency criteria for the H2S and O2 solver with respect to the average
measurements.
NSE
RMSE
Correlation
Coefficient
R2
Averaged
results
Averaged results
[RPM]
H2S
O2
H2S
Normalized
O2
Normalized
H2S
O2
H2S
O2
300
0.66
0.91
0.002
0.274
0.004
0.128
0.932
0.995
0.87
0.99
400
0.85
0.0012
0.118
-
-
0.949
0.90
500
0.83
0.93
0.002
0.161
0.012
0.102
0.876
0.994
0.77
0.98
The mass transfer coefficient KL and the volumetric mass transfer coefficient KLa, which is the
product of multiplying KLa with a [m-1], the ratio between interfacial area and water volume, were also
calculated using the formulas:
𝐶𝐿,𝑂2= 𝐶𝑆,𝑂2(1−𝑒−𝐾𝐿,𝑂2𝑎(𝑡−𝑡0))
Eq. 6.2
for O2 and
𝐶𝐿,𝐻2𝑆= 𝐶𝐿,𝐻2𝑆0𝑒−𝐾𝐿,𝐻2𝑆𝑎(𝑡−𝑡0)
Eq. 6.3
For H2S.
Here all the terms except KLa, are known either from the simulation or from the measured data.
Usually, the model is fitted to the experimental data with a curve fitting tool (e.g. Python) to get the
values for the mass transfer coefficient. However, as the simulation run time was 300 s, the plotted
data shows, for both H2S and O2 simulation, the system is nowhere near equilibrium conditions. Hence,
the mass transfer coefficient KL and second the volumetric mass transfer coefficient KLa, were
calculated for the time steps available. 𝐶𝐿,𝐻2𝑆0 is the initial concentration of H2S in the liquid phase
taken from the simulation results. But in the case of O2, saturation concentration of oxygen is required
and therefore,𝐶𝑆,𝑂2 is taken from the measured data. Inundation ratio (h/R) and specific interfacial
area (the ratio between interfacial area and water volume) were calculated using the results from the
simulation.
Table 6.5: Compilation of measured and simulated data for mass transfer coefficient calculations.
Stirring
rate
Total
volume
(water)
Immersion
depth
(stirrer)
Stirrer
Dia
Ratio
Surface
area
(vortex)
Specific
interfacia
l area
rpm
V [m3]
h [m]
R [m]
h/R
[m2]
[m2m-3]
H2S
300
0.0105
0.08
0.1
0.8
0.0665
6.33
400
0.0105
0.08
0.1
0.8
0.0688
6.55
500
0.0105
0.08
0.1
0.8
0.0724
6.90
O2
300
0.0099
0.07
0.1
0.7
0.0665
6.72
500
0.0099
0.07
0.1
0.7
0.0724
7.31
Chapter 6: Mass transfer in rotating turbulent reactor
94
Using the data shown in Table 6.5, corresponding mass transfer and volumetric mass transfer
coefficients were calculated and are illustrated in the graphs in Figure 6.10 (a and b).
(a) (b)
Figure 6.10: Resulting mass transfer coefficients and volumetric mass transfer coefficients for H2S and
O2 for different stirring rates.
Furthermore, the mass transfer coefficients for H2S and O2 were compared to get an average ratio
𝐾𝐿,𝐻2𝑆/𝐾𝐿,𝑂2 which equals to 0.70. This agrees with the observations of Carrera et al. (2017) who
determined:
𝐾𝐿,𝐻2𝑆
𝐾𝐿,𝑂2=0.64 ± 0.24
Eq. 6.4
US EPA (1974) suggested that the 𝐾𝐿,𝐻2𝑆𝑎/𝐾𝐿,𝑂2𝑎 ratio was 0.72, which is consistent with the
average results from the simulations. The results for the mass transfer coefficient and the ratio of the
two coefficients as published by Carrera et al. (2017) were also plotted with the results obtained by
the CFD model. It is observed that the plot for the influence of the stirring rate on the mass transfer in
Figure 6.11 shows the same tendency as was observed by Carrera et al. (2017). Similarly, the individual
values for the ratio 𝐾𝐿,𝐻2𝑆/𝐾𝐿,𝑂2 for each stirring rate, when plotted with the observation of Carrera et
al. (2017), lie in the same range (represented as a band in Figure 6.12)
Chapter 6: Mass transfer in rotating turbulent reactor
95
Figure 6.11: Influence of stirring rate on mass transfer as published by Carrera et al. (2017) and results
of CFD simulation.
Figure 6.12: Influence of stirring rate on 𝐾𝐿,𝐻2𝑆
𝐾𝐿,𝑂2 as published by Carrera et al. (2017) and with results
of CFD simulation.
6.5 Conclusion
The influence of turbulence on H2S mass transfer has been subject to intensive research in the past
years. So far, a general understanding has been gained from experimental investigations, but the
influence has not been simulated using a numerical three-dimensional model (Teuber 2020). Teuber
(2020) in her research work laid the groundwork for establishing the relation between turbulence and
the mass transfer rate. Her simulations and cases closely resembled to the experimental works of
Carrera et al. (2017). This chapter presents the extension application of a computational fluid dynamics
(CFD) model that qualitatively characterizes the mass transfer of H2S and O2 in a stirring tank. To predict
the mass transfer coefficient KL and the volumetric mass transfer coefficient KLa, the model
Chapter 6: Mass transfer in rotating turbulent reactor
96
incorporates a dynamic meshing functionality, specifically designed to manage turbulent conditions.
Being able to describe H2S emissions in a stirring tank with a CFD model cannot only enable us to
investigate more complex phenomena on a larger scale but could also help avoiding lab experiments
that come with a health risk and decrease the number of experiments necessary (Carrera et al., 2017).
The utilization of the two solvers (interH2SFoam and interO2Foam) in this study enables the
quantification of mass transfer for both species within a complex turbulent system. Moreover, a
comprehensive assessment of the influence of turbulence on the mass transfer phenomenon was
successfully conducted. In comparison to the findings presented in previous publications, as well as
Tang’s (2019) bachelor work conducted within the framework of project S1 (Urban Water Interfaces),
a remarkable level of agreement is observed. This convergence of results not only enhances the
reliability of the current study but also reinforces the potential of these solvers as suitable tools for
investigating mass transfer phenomena in turbulent systems.
To enhance the robustness of the model and facilitate comprehensive comparisons with
experimental findings, further validation is required for a wider range of stirring rates and inundation
ratios in future research endeavors. This would enable better assessments against the works of Wu
(1995), Carrera et al. (2017) and other pertinent publications available in the same research domain.
Additionally, it is recommended to investigate the development of a structured uniform mesh, as the
current study utilized an unstructured grid due to time constraints (1 s of real time required
approximately 300 s of simulation time with 96 cores on HLRN). The incorporation of such a mesh
would contribute to a more systematic and refined analysis.
By utilizing the simulation results, a deeper understanding of the influence of hydraulic design on
the measured concentrations of H2S and O2 can be gained. These findings offer valuable insights into
the related mass transfer processes. Although limited by the current time constraints, the present
study successfully demonstrates the accuracy of the new model for three-dimensional simulation of
mass transfer in dynamic meshing environments, particularly in describing H2S and O2 mass transfer
phenomena. Nonetheless, further research and validation are necessary to explore the full potential
of the model and its applicability in practical scenarios.
97
Chapter 7
Synthesis
This chapter summarizes the main conclusions and implications derived from this study and serves
as the culmination of this research work. The goal of this chapter is to give a thorough overview of the
solvers’ tendency to quantify the mass transport and transfer of H2S and O2, emphasising their
importance and possible applications in the field of odour control in sewer systems.
7.1 Conclusions
Sewer networks are one of the most critical infrastructure assets of modern urban societies. Odour
and corrosion problems associated with sewer systems are primarily due to hydrogen sulphide and
other organic odorous compounds generated in sewage (Jiang et al., 2015). Currently employed
modelling approaches typically depict these processes using one-dimensional models, which result in
simplified estimations of overall emissions (Teuber, 2020). Previous works from Teuber (2020) was
able to include small-scale influencers such as geometric features and she incorporated mass transfer
in the model for H2S (interH2SFoam). Based on these findings the solver was updated as well as
extended to include O2 mass transfer (interO2Foam) because in the sewer headspace it is an important
factor leading to odour and corrosion. A low oxygen concentration in sewers results in anaerobic
conditions, in which volatile fatty acids and hydrogen sulphide are produced, resulting in unpleasant
odours (e.g. Huisman et al., 2004). Many studies such as Ganigué and Yuan (2014), Gutierrez et al.
(2008), Jiang et al. (2015) and Pikaar et al. (2014) have shown the importance of injection of O2 as a
control measure to curb H2S emission (Park et al., 2022). Therefore, inclusion of O2 mass transport and
transfer in the model becomes important in understanding the processes causing odour and corrosion
in sewers.
7.1.1 Update and extension of the solver
Chapter 1 of this study gives a general overview of the odour and corrosion problem in sewer
systems, primarily caused by the emission of hydrogen sulfide (H2S). The existing models are discussed
mentioning their limitations and reason for the need of a three-dimensional computational fluid
dynamics (CFD) model to better understand and simulate the processes in sewer systems. Chapter 2
details the methods and tools used in this study. A detailed description of all the equations used by
the solvers including the extensions implemented in the existing solver (interFOAM) to include
Chapter 7: Synthesis
98
transport and mass transfer. All the pre- and post-processing tools which facilitated the study are also
reviewed.
Chapter 3 focused on the update and validation of the solver for H2S (Teuber et al., 2019b) and the
extension of the solver for O2 in OpenFOAM V6. A quasi-one-dimensional cubic tank was simulated to
quantify mass transfer through the liquid-gas film. Following conclusion can be derived from this study:
• For H2S, the solver accurately reproduces the concentration profiles obtained with the
previous version of the solver. The equilibrium concentrations in the water and gas phases
align with analytical solution based on Henry's law. The temperature dependency of the solver
is also tested and validated. The outcome shows that the solver accounts for the temperature
dependency of Henry’s coefficient for mass transfer of H2S.
• Replication of the H2S mass transfer in a rectangular duct as done by Teuber et al. (2019b) was
done to further validate the updated solver. Simulation results agreed with the results from
the publication but showed minimal mass transfer from water to air phase due to small
velocities in directions other than the main flow direction.
• For O2, two scenarios were considered: a boundary condition at the bottom wall for
quantifying the transfer of oxygen from liquid to gas phase and a boundary condition at the
top wall of the tank for the mass transfer occurring from the gas to liquid phase. In both cases,
the solver accurately depicts the concentration profiles and achieves equilibrium
concentrations which are consistent with predictions based on Henry's law. The temperature
dependency of Henry’s coefficient for mass transfer of O2 is validated, showing agreement
with analytical solutions.
• Overall, the validation of the solvers for H2S (interH2SFoam) and O2 (interO2Foam) in
OpenFOAM V6 demonstrates their applicability and accuracy in simulating mass transfer
through liquid-gas interfaces.
7.1.2 Validation of the air phase behaviour
The sewer system infrastructure, worth billions of dollars, requires proper ventilation to prevent
odour and corrosion caused by hydrogen sulphide. The lack of ventilation leads to odour and toxic gas
emissions. Increased knowledge on air flow characteristics can contribute to understanding the
hydrogen sulphide adsorption process. The first step towards understanding these processes is to have
a reliable model that quantifies the transport of gas in the air phase or the sewer headspace. Chapter
4 uses the experimental works of Bentzen et al. (2016) aimed to improve numerical models and
validate the hydraulics and oxygen transport in a laboratory-scale setup. The experimental setup
involved a rectangular duct with adjustable slope and water flow rate. Key findings from this study
were:
• The interFOAM solver was used for simulating the two-phase flow hydraulics. The phase
fraction (water depth) and velocity profiles for different cases with different inclinations had a
good agreement with experimental data.
Chapter 7: Synthesis
99
• Further validation was done using the complicated sewer geometry in Chapter 5. The hydraulic
simulations were performed using the interFoam software with the k-ϵ turbulence model. A
grid convergence study was done before application of the extended solver (interO2FOAM). A
combination of the field data published by Madsen et al. (2006) and an analytical solution were
used to validate the results obtained from the simulations. Average water velocities and water
depths were calculated for open channel flow and were compared to the results obtained from
the simulations. A good agreement was found.
• The need for implementing a three-dimensional model was also corroborated. VOF approach
for describing two-phase flows in ducts implemented in interFOAM is applicable in predicting
the flow in sewers.
7.1.3 Gas phase transport of oxygen
Ventilation in sewer systems can be natural or forced. Latter is commonly used to mitigate odour
and create a safer environment. Proper ventilation requires openings for gas flow, and both horizontal
and vertical gas transport are essential. Horizontal gas transport depends on the velocity of flow and
the dispersion of the gas and understanding this helps to predict the behaviour of compounds such as
H2S. Vertical gas transport helps in ventilation which in turn maintains optimal conditions for workers
and reduces corrosion caused by hydrogen sulphide and oxygen. Tracer injection method has been
used in many studies such as Parker and Ryan (2001) who used carbon monoxide as tracer and Melcer
et al. (1997) who used sulphur hexafluoride. These gases are toxic or deemed as greenhouse gases.
For a tracer to be useful for a long-term application, it should be non-toxic, non-flammable,
inexpensive and readily available (Sherma, 1990). Therefore, oxygen was chosen as tracer in the works
of Madsen et al. (2006) and Bentzen et al. (2016). Mean air velocities were measured at different
configurations to analyze the air flow behaviour. Oxygen concentration measurements were used to
validate the transport of oxygen. Following things can be postulated from the findings:
• The CFD model for transport of oxygen in a rectangular pipe (Chapter 4) followed the lab scale
experiments of Bentzen et al. (2016) solver implementations and utilized a 1D analytical
solution for comparing oxygen dispersion in the system by measuring the concentration profile
at two different points from the point of injection. The case setup designed to scale was used
for the CFD simulations using the interO2Foam solver. The simulation results showed a good
agreement with experimental measurements, validating the reliability of the solver for
predicting oxygen transport in the sewer headspace.
• The simulated results in the duct were in the range of the measured data. When compared to
the analytical solution the results were in good agreement when measured near the injection
point but at the end of the duct slight differences in the results can be attributed to the fact
that the analytical solution was 1D and the dispersion in the simulation was occurring in three
dimensions.
• The field experiments of Madsen et al. (2006) involved injecting oxygen gas pulses as a tracer
and measuring oxygen concentrations at monitoring stations downstream. Various
parameters, such as the sewer dimensions, gas velocity, dispersion coefficients and flow rates,
Chapter 7: Synthesis
100
were measured or calculated to develop the computational model. The boundary conditions
and properties of the sewer system were defined, and the simulations were run to achieve
quasi-steady-state conditions. After reaching steady state, oxygen injections were conducted
at specific locations, and the concentration was measured at the same points as the
monitoring stations in the field.
• The simulation results of the pulse injection study had a good agreement with the field results
of Madsen et al. (2006).
• Ventilation study with different suction pressures at the open manhole also provided valuable
insights including the maximum removal that can be achieved and the subsequent
entrainment of O2 in the system.
• The solver was able to validate the accuracy of the computational model in representing tracer
transport and dispersion in sewer systems as well as its application to find hotspots for
ventilation of the system for optimal removal of O2. These cases offered significant information
towards understanding ventilation system dynamics. The results of the ventilation study gave
insights about the relations between the suction forces and the removal of the oxygen. These
suction forces are equivalent to using ventilation fans (forced ventilation) at manholes with
hotspots for the removal of hazardous gases. Therefore, it holds practical implications by
enabling the formulation of effective strategies for the removal of hydrogen sulphide (H2S).
7.1.4 Validation of the mass transfer in a rotating turbulent reactor
Chapter 6 focused on studying the release of hydrogen sulphide (H2S) and the absorption of oxygen
(O2) in a rotating reactor or stirring tank under turbulent conditions. Previous research has made
significant progress in understanding H2S emissions in sewage systems and exploring factors such as
turbulence's influence on H2S mass transfer. Turbulent flow occurs frequently in sewer systems due to
flow velocities and various obstructions, making it essential to accurately quantify the effects of
turbulence on mass transfer using reliable modelling techniques.
The stirring tank experiment was designed on the basis of the published work of Carrera et al.
(2017). The reactor setup included a glass tank and a stirrer, with different stirring rates selected for
the experiments. The experiments used absorption and desorption methods to measure the
concentration of dissolved oxygen and hydrogen sulphide over time. Due to the dynamic nature of the
mesh, the simulations in this study required a lot of computational power. The following points can be
postulated from the study:
• Dynamic meshes were developed for replicating the conditions of the experiment. It was
observed that the time taken for simulation was heavily dependent on the type of mesh and
the number of cells. Considering the time limitations (approx. 300 s simulation for 1 s of real
time with 96 cores on HLRN), a mesh was selected that could sufficiently represent the visual
hydraulics, closely resembling the results obtained from physical experiments, while still
maintaining a reasonable simulation time.
• Two-phase solvers were linked to a dynamic meshing feature, enabling the calculation of mass
transfer. The impact of turbulence on the mass transfer coefficient was explored using a three-
Chapter 7: Synthesis
101
dimensional model that simulated the direct exchange of H2S and O2 between the water and
air phases. The experimental setup provided validation data for the simulation results
obtained using the interH2SFoam and interO2Foam solvers.
• The simulated results depicted the same trend as the measured values. The dependency of
the stirring rate on the mass transfer of the two species was established using the model. The
correlation between the mass transfer coefficient for H2S and O2 from the modeled results was
also in the ranges as published in the works of Carrera et al. (2017).
• These results are useful in understanding the mass transfer processes in sewers. The increasing
velocities in the gravity pipes attribute to higher turbulence levels and therefore increase the
mass transfer through the liquid-gas film. Hence understanding the relation between
turbulence and mass transfer can help to optimize sewer system designs without the need for
costly and potentially hazardous lab experiments.
7.2 Limitations
Although providing a reliable means to quantify processes in sewer systems, CFD modelling also has
its limitations. It is important to be aware of these limitations and uncertainties when using the solvers
and interpreting the results. Several limitations that were found during this research work are listed
below:
• Grid resolution: The discretization of the fluid domain into a grid or mesh is an important
factor defining the accuracy of the results. Achieving mesh independence typically involves a
laborious process of initially creating multiple meshes and subsequently simulating them to
determine the optimal mesh configuration. Insufficient grid resolution can lead to inaccurate
predictions and loss of important details. In Chapter 5 and Chapter 6, evaluation of multiple
meshes was conducted to identify the most suitable one for simulation. However, the time
required for the simulation remained a key factor for considering the mesh for simulations.
• Validation and experimental data: Validating CFD results against experimental data is crucial
to assess the accuracy and reliability of the simulations. However, obtaining comprehensive
and high-quality experimental data for validation can be challenging. Many of the results used
for validation in this study are either graphically extracted from the publications or
numerical/analytical solutions. While the obtained results demonstrate a certain degree of
accuracy and can serve as a foundation for validating the solvers, the inclusion of a
comprehensive data set would significantly enhance confidence in utilizing these models.
• Simulation time: Time can be a limiting factor in the applicability of the two solvers due to the
computational resources required for running simulations. The simulations in this study are
computationally expensive and time consuming, especially for large and detailed models.
Especially the simulations mentioned in Chapter 6, which include sophisticated meshes that
are dynamic, require almost 300 s of simulation for 1 s of real time on 1 node with 96 cores on
HLRN (further increasing the number of cores negatively affected the time required). Similarly,
in Chapter 5, it was observed that each second of real-time simulation corresponded to
approximately 32 seconds of simulation time. While this may not appear to be a significant
Chapter 7: Synthesis
102
factor at first glance, it becomes noteworthy when considering the extensive time series
spanning nearly two hours that is necessary to obtain computational fluid dynamics (CFD)
results comparable to the field data. Consequently, the cumulative simulation time becomes
considerably substantial. Hence, the computational cost associated with grid convergence,
sensitivity analysis, and calibration becomes significant.
• Model spatial size: It is important to note that the 3D models discussed in this study are
primarily applicable for recognizing hotspots or establishing relations between mass transfer
and other parameters, within a range of a few hundred meters. However, it is not suitable for
extensive networks spanning tens or hundreds of kilometers. It is crucial to highlight this
limitation in order to maintain a realistic understanding of the model's capabilities and
limitations with the respect to the spatial dimensions of each case setup.
7.3 Future outlook
Considering the limitations mentioned above and the future scope of the topic following points can
be considered:
• Turbulent reactor project: The ongoing development of the turbulent reactor project should
include expanding the scope of the stirring rate and exploring various types of grids (meshes).
The ranges for these variables should be chosen based on those employed in the study
conducted by (Wu, 1995). Since the experimental setup is already in place, it is feasible to
conduct experiments within these ranges. The data obtained from these experiments can then
be utilized to validate the solver.
• Validation and extension: Further exploration of validation scenarios is recommended,
including the investigation of drop structures, weirs, and other factors known to induce
turbulence. The solvers developed for H2S by Teuber et al.( 2019b) and O2 within this work
have been validated in different scales (lab and field) and different turbulence levels. The
solvers are able to quantify the mass transport and transfer of the two species with good
accuracy. The solver modification done to account for O2 confirms that the solver can also be
extended to include other organic species in the sewer system such as methane (CH4).
• Reactive transport: Inclusion of reactive transport may facilitate to explore other
countermeasures such as chemical stripping of H2S. The interHarounFoam solver implemented
by Nieves-Remacha et al. (2015) offers the possibility of adding reactive transport by including
the production term into the mass transport equation (Teuber, 2020). In addition,
incorporating reactive transport will be beneficial for developing a solver that can handle
multiple chemical species.
• Bacterial growth / potential corrosion: Biofilm modelling plays a crucial role in understanding
the behaviour and dynamics of microbial communities in sewer systems. Biofilm modelling
using OpenFOAM has gained significant attention in recent years. For example, a study by
Huynh et al. (2014) demonstrated the application of OpenFOAM for simulating biofilm growth
and mass transport in porous media. Additionally, OpenFOAM has been employed to
investigate the effects of hydrodynamics on biofilm development, as shown in the work by
Chapter 7: Synthesis
103
Chambon et al. (2016). These studies proved a good basis for developing a solver that could
include a biofilm as an interface in the system.
• Large-scale applications and scalability: Conducting three dimensional simulations in sewer
systems with extensive pipe networks and long-term corrosion processes becomes
computationally impractical. To overcome this challenge, extracting key parameters from the
computational fluid dynamics (CFD) model to form a parametric data set, which can then be
integrated into 1D models such as WATS or 2D models such as SWIMM models, can enhance
the applicability of the solvers.
104
Appendix A
Conference contributions
Appendix A
105
Extension of a 3D two-phase flow model to multicomponent reactive transport
for odour and corrosion control in sewer systems.
This study was published as:
Dixit, A., Teuber, K., Barjenbruch, M., Stephan, D. & Hinkelmann, R. (2019): Extension of a 3D two-
phase flow model to multicomponent reactive transport for odour and corrosion control in sewer
systems, Workshop on Applications of Multi-scale Approaches in Environmental Chemistry (AMARE
2019) 22-28 April 2019 Rennes, France.
Submitted as a poster.
Biological corrosion of sewers and sewage treatment plants constitutes a serious problem and its
effects result in the loss of billions of dollars every year (Stanaszek-Tomala and Fiertaka, 2016).
Changing demography and more efficient use of water resources will lead to the reduction of the
average volume of wastewater and leads to higher residence times in the sewer canals. Due to climate
change, i.e. warmer temperatures, the waste water in the canal will become more anaerobic.
Therefore, sewer networks with a concrete construction are subjected to various mechanisms that
subject it to rapid degradation. Due to the anaerobic conditions in sewage, sulphate present in the
waste water can be reduced to sulfide by sulphate-reducing bacteria residing in the biofilms on the
walls of the pipelines (Sharma et al., 2008).
For more than 70 years, researchers have been committed not only to study the processes for odour
and corrosion but also to creating empirical and conceptual models for explanations. However, within
the last 20 years a deeper understanding has been gained thanks to the efforts of research groups in
Denmark and Australia (Rootsey et al., 2012; Teuber et al., 2017). Nearly all current models are
confined to a one-dimensional approach which is very suitable but is unable to sufficiently capture the
turbulent effects. However, for processes which are affected by the concentration profiles (e.g. H2S
formation, mass transfer) and the air flow as well as for the surroundings of drops, steps and hydraulic
jumps, a three- dimensional approach should be preferred accounting for water and gas phase. For
this purpose, a high-resolution three-dimensional model in OpenFOAM for water and air flow, multi-
component reactive transport and mass transfer between the water and air phase must be developed.
Teuber et al. (2019a) have developed a 3D two-phase (water, air) flow and transport model that can
account for temperature and pH dependency of the mass transfer of H2S. This poster concentrates on
the conceptual and computational extension of the model of Teuber et al. (2019a) for reactive
transport using and probably extending OpenFOAM libraries and the model validation.
Appendix A
106
Determining the turbulent H2S mass transfer coefficient across the liquid-gas
interface in sewer systems.
This study was published as:
Dixit, A., Teuber, K., Pacheco Fernández, M., Barjenbruch, M., & Hinkelmann, R. (2020): Validation
of air phase flow, mass transport and mass transfer in a sewer pipe, First International Conference on
Urban Water Interfaces (UWI) (p. 59). [Technische Universität Berlin, Urban Water Interfaces].
https://doi.org/10.24407/KXP:174470919X
Submitted as an abstract and digitally presented.
Hydrogen sulphide (H2S) gas is formed by the bacterial decomposition of organic matter in the
sewer under anaerobic conditions. H2S gas is the major contributor to the odour and corrosion
occurring in the sewer networks. These emissions not only increase the cost of maintenance but also
pose a threat to the human health of sewer workers. Optimal odour and corrosion management has
been hindered by limited understanding of several of the key sewerage processes contributing to the
problems, and the lack of tools and reliable technologies to support strategic decisions and cost-
effective sewer operations (Rootsey et al., 2012). A significant step towards filling this gap is to develop
a high-resolution three-dimensional model to understand and simulate the processes involved. This
contribution advances the doctoral thesis of Teuber (2020) and concentrates on the validation of
water-air flow in a sewer with a focus on air phase flow, mass transport and mass transfer occurring
between the phases. The basis of this work is a three-dimensional water-air flow model developed
within the framework of the open-source CFD platform OpenFOAM. First, simple plausibility tests with
regard to water-air flow in a sewer pipe are investigated. Second, the modeling of water-air flow in a
sewer will be validated using experimental studies of Bentzen et al. (2016) which aimed to improve
the data basis for numerical modeling of sewer ventilation. Third, the mass transfer of H2S and O2 from
the water to the air phase will be considered in stagnant water and air. Fourth, transport will be
analyzed by first injecting O2 into the air phase and then also including H2S. The transport and mass
transfer of both tracers will be tested in a closed pipe (verification: functionality of the solver) as well
as in a pipe with manholes (validation: experimental data).
Appendix A
107
CFD model development and sensitivity analysis for water-air flow in a close
conduit sewer pipe
This study was published as:
Dixit, A., Teuber, K., Barjenbruch, M., Stephan, D. & Hinkelmann, R. (2020): CFD model
development and sensitivity analysis for water-air flow in a close conduit sewer pipe, Proceedings of
the 1st IAHR Young Professionals Congress, Online. 17-18 November 2020. ISBN: 978-90-82484-6-63
Submitted as a conference paper and digitally presented.
Biological corrosion of sewers networks and treatment plants constitutes a problem for asset
management, and its effects result in the loss of billions of dollars per year. Hydrogen sulphide (H2S)
gas is the major contributor to the odour and corrosion occurring in the sewer networks. H2S gas is
formed by the breakdown of organic matter in the sewer under anaerobic conditions. These emissions
not only increase the cost of maintenance but also pose a threat to the human health of sewer workers.
To understand and to be able to estimate transformation processes at the air-water interface, it is
important to study the hydraulics and flow patterns in sewers. For this purpose, a model has been set
up in the open-source platform OpenFOAM, which is aimed to improve the data basis for a numerical
model of natural sewer ventilation.
Appendix A
108
A three-dimensional model for H2S mass transfer in sewers and its use cases.
This study was published as:
Teuber, K., Gnirß, R., Dixit, A., & Hinkelmann, R. (2020): A three-dimensional model for H2S mass
transfer in sewers and its use cases, First International Conference on Urban Water Interfaces (UWI)
(p. 63). [Technische Universität Berlin, Urban Water Interfaces].
https://doi.org/10.24407/KXP:1744776784
Submitted as an abstract.
The talk gives an overview over a new three-dimensional mass transfer solver and its application
field. Use cases apart from the solver’s direct applications are being presented and necessary
modifications are being outlined. Within the open source software OpenFOAM, users can customize
solvers to fit their own needs. In the dissertation of Teuber (2020), as part of the DFG Research Training
Group “Urban Water Interfaces”, a mass transfer solver has been extended to describe hydrogen
sulphide (H2S) mass transfer across the interface between wastewater and air in sewers. The aim of
the developed model was to predict H2S emissions in sewer systems.
The solver uses a volume of fluid formulation to account for two-phase flow. Haroun et al. (2010)
defined a mass transfer formulation to account for species transport within the two phases and mass
transfer between them. Following this formulation, mass transfer is limited by the Henry coefficient.
The solver extensions made in Teuber (2020) include the description of the temperature dependency
of the Henry coefficient, the equilibrium between H2S and bisulphide ion (HS-) in the water phase and
the influence of the pH value on this equilibrium.
From the viewpoint of a water company, this solver shows the potential of being applied to a
number of other use cases apart from sewers, which will be presented in this contribution. The first
use case addresses H2S emissions at the inlet of wastewater treatment plants (WWTPs) as well as
mitigation strategies. At WWTP Schönerlinde in Berlin, exhaust air from ventilated grid chambers is
being co-treated in the aerobic stage. The H2S is then oxidized to sulphate. Modelling the H2S uptake
in the basin could give insights regarding requirements on air volumes and bubble structure. Further
use cases address the quantification of greenhouse gases, for example emissions of nitrous oxide from
WWTPs or methane emissions in pumping stations.
Appendix A
109
Determining the turbulent H2S mass transfer coefficient across the liquid-gas
interface in sewer systems.
This study was published as:
Pacheco Fernández, M., Despot, D., Dixit, A., Hinkelmann, R., Stephan, D., & Barjenbruch, M.
(2020). Determining the turbulent H2S mass transfer coefficient across the liquid-gas interface in sewer
systems. In First International Conference on Urban Water Interfaces (UWI) (p. 66). [Technische
Universität Berlin, Urban Water Interfaces]. https://doi.org/10.24407/KXP:1744779899
Submitted as an abstract.
Development of hydrogen sulphide (H2S) in sewer systems poses a high risk to human health and
sewer structures. H2S is formed in the liquid phase, however, its effects are severe when released into
the air. Therefore, studying the mass transport of H2S from the liquid phase into the air phase is of
great importance. In the presentation the turbulent transport of hydrogen sulphide from the liquid
into the gas phase will be discussed. Turbulence can be used as a method to enhance H2S-stripping in
sewage systems before being locally treated with an exhaust air method. For this aim, a two-step setup
has been planned, which investigates the mass transfer coefficient under laboratory and real
conditions.
Laboratory experiments were carried out in a 52 L cylindrical reactor equipped with a four-blade
stirrer, a pH and temperature sensor, and an OdaLog for the gas phase. Three stirring velocities were
investigated: 300, 400 and 500 rpm. Oversaturated conditions in the liquid phase were created by
adding sodium sulphide (Na2S 3H2O, CAS 27610-45-3). The pH was stabilised at 7 by addition of
hydrochloric acid (HCl).
To avoid chemical interactions between oxygen and hydrogen sulphide, the reactor was purged
continuously with nitrogen gas (N2). The H2S decrease in the liquid phase was measured manually at
regular time intervals (1, 2 and 10 min) using the H2S-Analyser from ECH Halle. The Reynolds number
was computed to quantify the turbulence level of the stirring rates as well as to provide comparability
with other geometries. A general outcome is that the higher the turbulence level, the higher the KLa
coefficient. In this work, the KLa values range between 1.5 and 4.9 h-1. As a comparison oxygen values
for this experiment range between 2.67 and 7.59 h-1. To validate the laboratory results, experiments
under real conditions will be performed at a sewer pilot plant located in Berlin which is fed with
wastewater from the Neukölln district. Turbulence will be enhanced in this case through a weir and
through the addition of obstacles (e.g. stones) in the flow regime. The pumping flow rate can be
adjusted between 1.5 and 10 m3/h.
Appendix A
110
Bacteria from sewers and their potential to improve the sustainability of
construction materials.
This study was published as:
Augustyniak, A., Jabło´nska, J., Pacheco Fernández, M., Dixit, A., Braun, B., Szewzyk, U.,
Hinkelmann, R., Stephan, D., & Barjenbruch, M. (2020): Bacteria from sewers and their potential to
improve the sustainability of construction materials, First International Conference on Urban Water
Interfaces (UWI) (p.68). [Technische Universität Berlin, Urban Water Interfaces].
//doi.org/10.24407/KXP:1744780668
Submitted as an abstract.
Sewer systems are rich in microorganisms. Bacteria, fungi, and protozoans can play an important
role in pre-treatment of sewage before it is transported to the wastewater treatment plant (WWTP).
They are transferred via sewer pipes together with water and particulate matter that forms sediment.
While sediment is being transported in the pipe, some microorganisms can form a biofilm that may
firmly stick to the surface of the pipe. The composition and quantity of biofilms in sewer systems
depend on the flow rate, contaminations, dispersed nutrients and gases, and even material from which
the pipe is created. Cementitious materials that are often used for the construction of sewage
transport systems are susceptible to biodeterioration due to the biological production of sulphates.
On the other hand, some microorganisms can produce urease, an enzyme that can break urea into
carbon dioxide and ammonium that increases pH and protects the composite.
The aim of this study was to isolate urease-producing bacteria in environmental samples, including
soil, activated sludge, and sewer biofilm, and describe their ability to withstand conditions associated
with the surfaces on cementitious materials. The material consisted of environmental samples (sewer
biofilm, activated sludge, soil). The samples were diluted and propagated on growth media.
Sporulating, Gram-positive bacteria were sought and isolated in monocultures. Afterwards, the
isolates were subjected to various environmental conditions including low or high pH (from 4 to 10)
and high salinity. Urease production and biofilm formation abilities were also examined. The
taxonomic affiliation was determined by the analysis of 16S rDNA analysis. Furthermore, the
microbiomes of the studied environmental samples were studied via nanopore sequencing. In total,
28 bacterial strains were isolated. Seven were urease positive. Relatively high resistance to harsh
environmental conditions was detected among strains. On the other hand, isolates expressed a low
ability to form biofilms. The group was diversified and consisted of strains from genera Bacillus,
Solibacillus, Lysinibacillus, Sporosarcina, and Brevibacterium. Apart from the relatively low biofilm
formation abilities in the isolates, high resistance to high pH and salinity suggests that isolates have
the potential to be used on cementitious materials. Further tests are necessary to validate this
hypothesis.
111
Appendix B
Solver update and modification
Appendix B
112
B.1 Integration of the tracer in the solution procedure
B.1.1 Solving mechanism
In Figure B 1, the solution procedure of the inter(Tracer)Foam solver is shown. The extensions made
to the interFoam solver initially were made as a part of the doctoral work of Teuber (2020), and was
published in Teuber et al. (2019b). interDyMFoam in the previous versions provided the option for
mesh motion and mesh topology changes including adaptive re-meshing. The majority of dynamic
solvers, denoted by the prefix "Dy(namic)", have been merged or integrated into their corresponding
non-dynamic counterparts in OpenFOAM V6. The inclusion of the motion solver dictionary within the
simulation setup enables the utilization of these solvers seamlessly.
Figure B 1: Flow chart of the solver (following Devolder et al., 2015; Lopes et al., 2017; Teuber et al.,
2019b), solver extensions in blue.
Appendix B
113
B.1.2 Solver file structure in OpenFOAM V6
Figure B 2: File structure for interFoam solver with the files modified highlighted in green.
Appendix B
114
B.2 Changes in code to include the solver extensions
B.2.1 Make/files
In order to achieve accurate initialization of the solver, it is crucial to make modifications to the files
within the Make directory. The contents of the files in the subfolder Make, as presented in Figure B 2,
provide a specific illustration for the interH2SFoam and interO2Foam solver according to Nilsson
(2019). For the interDyMH2SFoam and passiveScalarInterFoam solvers, similar adjustments need to
be implemented accordingly.
For the solver for H2S:
interH2SFoam.C
EXE = $(FOAM_APPBIN)/interH2SFoam
For the solver for O2:
interO2Foam.C
EXE = $(FOAM_APPBIN)/interO2Foam
Appendix B
115
B.2.1 createFields.H
The necessary field variables and additional variables for extending the interFoam solver are
defined in the file createFields.H, as shown below. Within this file, the tracer is specifically defined as
a volScalarField labeled as C. Moreover, the temperature dependent Henry coefficient is computed by
retrieving the user-defined temperature information from the case directory. Additionally, the
diffusivity is read from the case directory as well.
Info << " Reading field C" << endl ;
volScalarField C
(
IOobject
(
"C",
runTime . timeName () ,
mesh ,
IOobject :: MUST_READ ,
IOobject :: AUTO_WRITE
),
mesh
);
Info << " Reading transportProperties \n" << endl ;
IOdictionary transportProperties
(
IOobject
(
" transportProperties ",
runTime . constant () ,
mesh ,
IOobject :: MUST_READ_IF_MODIFIED ,
IOobject :: NO_WRITE
)
);
//water phase (phase 1)
dimensionedScalar Dwater
(
transportProperties.lookup("Dwater")
);
//air phase
dimensionedScalar Dair
(
transportProperties.lookup("Dair")
);
dimensionedScalar Schmidtnumber
Appendix B
116
(
transportProperties.lookup("Schmidtnumber")
);
volScalarField DT
(
"DT",
Dwater * Dair / (alpha1 * Dair + (1 - alpha1) * Dwater)
);
//Constant temperature in domain
dimensionedScalar Temp
(
transportProperties.lookup("Temp")
);
//Temperature dependent Henry coefficient for H2S, normal temperature of
25.15 degree
dimensionedScalar He
(
"He",
1/(0.001 * Foam::exp(2200.0*(1/Temp-1/298.15)) * 8.314 * Temp) //
formula for H2S
);
//Temperature dependent Henry coefficient for O2, normal temperature of 25.15
degree
dimensionedScalar He
(
"He",
1/(1.3e-5 * Foam::exp(1500.0*(1/Temp-1/298.15)) * 8.314 * Temp) //
formula for O2
);
Appendix B
117
B.2.2 inter(Tracer)Foam.C
In order to solve the mass transfer equation, it must be incorporated into the file
inter(Tracer)Foam.C where (Tracer) represents either H2S or O2. This is accomplished by using the
include command. Additionally, the turbulent viscosity is stored in a volScalarField to enable its
utilization during the solution of the mass transfer equation. Several modifications have been
implemented in the code. Notably, the equation was directly written into the solver without including
cEqn.H, driven by personal preference. Additionally, newer API (Application Programming Interface)
functions were utilized, enabling relaxation and constraint enforcement for the cEqn.H equation.
These changes were introduced to enhance the solver's functionality and performance. The contents
of inter(Tracer)Foam.C, including the highlighted changes in green, are presented below.
/*--------------------------------------------------------------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2011-2018 OpenFOAM Foundation
\\/ M anipulation |
--------------------------------------------------------------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM is free software: you can redistribute it and/or modify it under the terms of the GNU General Public
License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later
version.
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
License for more details.
You should have received a copy of the GNU General Public License along with OpenFOAM. If not, see
<http://www.gnu.org/licenses/>.
Application
interFoam
Description
Solver for 2 incompressible, isothermal immiscible fluids using a VOF (volume-of-fluid) phase-fraction based
interface capturing approach, with optional mesh motion and mesh topology changes including adaptive re-
meshing.
\*--------------------------------------------------------------------------------------------------------------------------------*/
#include "fvCFD.H"
#include "dynamicFvMesh.H"
#include "CMULES.H"
#include "EulerDdtScheme.H"
#include "localEulerDdtScheme.H"
#include "CrankNicolsonDdtScheme.H"
#include "subCycle.H"
#include "immiscibleIncompressibleTwoPhaseMixture.H"
#include "turbulentTransportModel.H"
#include "pimpleControl.H"
Appendix B
118
#include "fvOptions.H"
#include "CorrectPhi.H"
#include "fvcSmooth.H"
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
int main(int argc, char *argv[])
{
#include "postProcess.H"
#include "setRootCaseLists.H"
#include "createTime.H"
#include "createDynamicFvMesh.H"
#include "initContinuityErrs.H"
#include "createDyMControls.H"
#include "createFields.H"
#include "createAlphaFluxes.H"
#include "initCorrectPhi.H"
#include "createUfIfPresent.H"
turbulence->validate();
if (!LTS)
{
#include "CourantNo.H"
#include "setInitialDeltaT.H"
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Info<< "\nStarting time loop\n" << endl;
while (runTime.run())
{
#include "readDyMControls.H"
if (LTS)
{
#include "setRDeltaT.H"
}
else
{
#include "CourantNo.H"
#include "alphaCourantNo.H"
#include "setDeltaT.H"
}
runTime++;
Info<< "Time = " << runTime.timeName() << nl << endl;
// --- Pressure-velocity PIMPLE corrector loop
while (pimple.loop())
{
if (pimple.firstIter() || moveMeshOuterCorrectors)
{
mesh.update();
if (mesh.changing())
{
// Do not apply previous time-step mesh compression
flux
// if the mesh topology changed
Appendix B
119
if (mesh.topoChanging())
{
talphaPhi1Corr0.clear();
}
gh = (g & mesh.C()) - ghRef;
ghf = (g & mesh.Cf()) - ghRef;
MRF.update();
if (correctPhi)
{
// Calculate absolute flux
// from the mapped surface velocity
phi = mesh.Sf() & Uf();
#include "correctPhi.H"
// Make the flux relative to the mesh motion
fvc::makeRelative(phi, U);
mixture.correct();
}
if (checkMeshCourantNo)
{
#include "meshCourantNo.H"
}
}
}
#include "alphaControls.H"
#include "alphaEqnSubCycle.H"
mixture.correct();
#include "UEqn.H"
// --- Pressure corrector loop
while (pimple.correct())
{
#include "pEqn.H"
}
if (pimple.turbCorr())
{
turbulence->correct();
}
}
// Modification made for tracer “C” where C is replace by O for oxygen and
H // for hydrogen sulphide
volScalarField nut("nut", turbulence->nut());
volVectorField phiCiTemp = ((DT+(nut/Schmidtnumber)) * C *(1-He)/(alpha1 +
(1-alpha1)*He) * fvc::grad(alpha1));
// volScalarField nut("nut", turbulence->nut());
surfaceScalarField phiCi =
(
(
Appendix B
120
fvc::interpolate((DT+(nut/Schmidtnumber))) *
(1-He)
/ (fvc::interpolate(alpha1)+(1-fvc::interpolate(alpha1))*He)
)
* fvc::snGrad(alpha1)
) * mesh.magSf();
solve
(
fvm::ddt(C)
+ fvm::div(phi, C, "div(phi,C)")
- fvm::laplacian(fvc::interpolate(DT), C, "laplacian(C)")
- fvm::laplacian((nut/Schmidtnumber), C, "laplacian(C)")
+ fvm::div(phiCi, C, "div(phi,C)")
,
mesh.solver("C")
);
runTime.write();
Info<< "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
<< " ClockTime = " << runTime.elapsedClockTime() << " s"
<< nl << endl;
}
Info<< "End\n" << endl;
return 0;
}
// ********************************************************************* //
121
Appendix C
Case setups
Appendix C
122
C.1 Quasi one-dimensional cubic tank (H2S)
Table C.1: Model setup of quasi one-dimensional cubic tank for H2S.
Title: Quasi one-dimensional cubic tank for H2S mass transfer from liquid to gas.
General
Case description
validation of mass transfer solver extensions using a cubic tank setup
and analysing the equilibrium conditions at steady state
case 1: analysis of concentration profile at normal temperature (298.15
K)
case 2: analysis of concentration profile at different temperature
(288.15 K)
Referred to in chapters
3.2
References
(Hvitved-Jacobsen et al., 2013)
Domain discretization
Dimensions
quasi one-dimensional (height: 1 m, width: 1 m, depth: 1 m)
Mesh generator
blockMesh
Number of cells
10,000
Turbulence models
laminar
Hydrodynamic
simulations
none performed (no fluid flow in domain)
Single-phase transport
simulations
None performed
Mass transfer
simulations
Solver
interH2SFoam
Simulation time
1000s
Time step
0.1 s
Tracer diffusivity
water: 10-2 m2/s air: 10-2 m2/s (a high diffusivity was chosen because only
the equilibrium conditions established were of interest)
Temperature
298.15 K, 288.15 K
Appendix C
123
Table C.2: Boundary conditions for quasi one-dimensional cubic tank simulation for H2S mass transfer from liquid to gas phase.
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
C [𝒎𝒐𝒍
𝒎𝟑]
Bottom
zeroGradient
zeroGradient
fixedValue
value: uniform (0 0 0)
cases 1 and 2:
fixedValue value:
uniform 1
Top wall and side
walls
zeroGradient
zeroGradient
fixedValue
value: uniform (0 0 0)
zeroGradient
Initial conditions
use setFields to define
a water level of 0.5 m
(alpha.water = 1 for h < 0.5m,
alpha.water = 0 elsewhere)
uniform 0
uniform (0 0 0)
use setFields to define
initial concentration
in water phase (C = 1
for h < 0.5m, C = 0
elsewhere)
Appendix C
124
C.2 Quasi one-dimensional cubic tank (O2)
Table C.3: Model setup of quasi one-dimensional cubic tank for O2.
Title: Quasi one-dimensional cubic tank for O2 mass transfer
General
Case description
validation of mass transfer solver extensions using a cubic tank setup and
analysing the equilibrium conditions at steady state
case 1: analysis of concentration profile for mass transfer from liquid to
gas (298.15 K)
case 2: analysis of concentration profile for mass transfer from gas to liquid
(298.15 K)
case 3: analysis of concentration profile at different temperature from
liquid to gas (288.15 K)
case 4: analysis of concentration profile at different temperature from gas
to liquid (288.15 K)
Referred to in chapters
3.3
References
(-)
Domain discretization
Dimensions
quasi one-dimensional (height: 1m, width: 1m, depth: 1m)
Mesh generator
blockMesh
Number of cells
10,000
Turbulence models
laminar
Hydrodynamic
simulations
none performed (no fluid flow in domain)
Single-phase transport
simulations
none performed
Mass transfer
simulations
Solver
interO2Foam
Simulation time
1500 s (gas to liquid), 35000 s (liquid to gas)
Time step
0.1 s
Tracer diffusivity
water: 10-2 m2/s air: 10-2 m2/s (a high diffusivity was chosen because only
the equilibrium conditions established were of interest)
Temperature
298.15 K, 288.15 K
Appendix C
125
Table C.4: Boundary conditions for simulations of quasi one-dimensional cubic tank for O2 mass transfer from liquid to gas phase.
Table C.5: Boundary conditions for simulations of quasi one-dimensional cubic tank for O2 mass transfer from gas to liquid phase.
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
C [𝒎𝒐𝒍
𝒎𝟑]
Bottom
zeroGradient
zeroGradient
fixedValue
value: uniform (0 0 0)
cases 1 and 3: fixedValue
value: uniform 1
Top wall and side walls
zeroGradient
zeroGradient
fixedValue
value: uniform (0 0 0)
zeroGradient
Initial conditions
use setFields to define
a water level of 0.5 m
(alpha.water = 1 for h < 0.5m,
alpha.water = 0 elsewhere)
uniform 0
uniform (0 0 0)
use setFields to define
initial concentration
in water phase (C = 1
for h < 0.5m, C = 0
elsewhere)
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
C [𝒎𝒐𝒍
𝒎𝟑]
Top
zeroGradient
zeroGradient
fixedValue
value: uniform (0 0 0)
cases 2 and 4: fixedValue
value: uniform 1
Bottom wall and side
walls
zeroGradient
zeroGradient
fixedValue
value: uniform (0 0 0)
zeroGradient
Initial conditions
use setFields to define
a water level of 0.5 m
(alpha.water = 1 for h < 0.5m,
alpha.water = 0 elsewhere)
uniform 0
uniform (0 0 0)
use setFields to define
initial concentration
in water phase (C = 1
for h < 0.5m, C = 0
elsewhere)
Appendix C
126
C.3 Mass transfer in rectangular duct (H2S)
Table C.6: Model setup of lab scale setup of a rectangular duct for H2S.
Title: Mass transfer of H2S in a lab scale experiment (rectangular duct)
General
Case description
mass transfer simulations according to test cases 7 and 21 as carried out
by Bentzen et al. (2016)
hydrodynamic simulations: quasi steady-state
mass transfer: constant injection of H2S in water phase
Referred to in chapters
4.3.2
References
Bentzen et al. (2016) and Teuber et al. (2019b)
Domain discretization
Dimensions
three-dimensional (length: 15 m, height: 0.26 m, width: 0.3 m)
Mesh generator
GMSH
Number of cells
307,970
Turbulence models
laminar
Hydrodynamic
simulations
Solver
interFoam
Time step
variable, converged against 0.007 s (case 7), 0.019 s (case 21)
Simulation time
200 s
Single-phase transport
simulations
none performed
Mass transfer
simulations
Solver
interH2SFoam
Simulation time
50s after hydraulic stability
Time step
0.001 s
Tracer diffusivity
water: 2.2 10-9 m2/s, air: 1.74 10-5 m2/s
Schmidt number
1
Temperature
298.15 K
Appendix C
127
Table C.7:Boundary conditions for simulations of the rectangular duct for H2S mass transfer.
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer case)
Inlet_air
inletOutlet
inletValue: uniform 0
value: uniform 0
totalPressure
p0: uniform 0
U: U
phi: phi
rho: rho
psi: none
gamma: 1
value: uniform 0
pressureInletOutlet-
Velocity
phi: phi
tangentialVelocity:
uniform (0 0 0)
value: uniform (0 0 0)
zeroGradient
Inlet_water
inletOutlet
inletValue: uniform 1
value: uniform 1
fixedFluxPressure
flowRateInletVelocity
volumetricFlowRate:
Case 7: 0.0072
Case 21: 0.0164
fixedValue
value: uniform 1
Outlet
zeroGradient
fixedValue
value: uniform -0.025
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
Bottom
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
zeroGradient
Top wall and side walls
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
zeroGradient
Initial conditions
uniform 0
uniform 0
uniform (0 0 0)
uniform 0, use expression
in funkySetFields to define
C = 1 where
alpha.water > 0.5
Appendix C
128
C.4 Mass transport in rectangular duct (O2)
Table C.8:Model setup of lab scale setup of a rectangular duct for oxygen transport.
Title: Mass transport of O2 in the air phase in a lab scale experiment (rectangular duct)
General
Case description
mass transport simulations according to test case 21 as carried out by
Bentzen et al. (2016)
hydrodynamic simulations: quasi steady-state
mass transfer: 8 s pulse injection in the air phase
Referred to in chapters
4.3.3
References
Bentzen et al. (2016)
Domain discretization
Dimensions
three-dimensional (length: 15 m, height: 0.26 m, width: 0.3 m)
Mesh generator
GMSH
Number of cells
307,970
Turbulence models
laminar
Hydrodynamic
simulations
Solver
interFoam
Time step
variable, converged against 0.019 s (case 21)
Simulation time
200 s
Single-phase transport
simulations
none performed
Mass transfer
simulations
Solver
interO2Foam
Simulation time
200 s continuous injection of oxygen conc. 1 mol/m3
8 s pulse injection with increased conc. of oxygen
157 s continuous injection of oxygen conc. 1 mol/m3
Time step
0.001 s
Tracer diffusivity
water: 2.42 10-9 m2/s, air: 1.98 10-5 m2/s
Schmidt number
1
Temperature
298.15 K
Appendix C
129
Table C.9: Boundary conditions for simulations of the rectangular duct for O2 transport.
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer case)
Inlet_air
inletOutlet
inletValue: uniform 0
value: uniform 0
totalPressure
p0: uniform 0
U: U
phi: phi
rho: rho
psi: none
gamma: 1
value: uniform 0
pressureInletOutlet-
Velocity
phi: phi
tangentialVelocity:
uniform (0 0 0)
value: uniform (0 0 0)
fixedValue
value (200 s): uniform 1
value (8 s): uniform 1.02
value (157 s): uniform 1
Inlet_water
inletOutlet
inletValue: uniform 1
value: uniform 1
fixedFluxPressure
flowRateInletVelocity
volumetricFlowRate:
Case 21: 0.0164
zeroGradient
Outlet
zeroGradient
fixedValue
value: uniform -0.025
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
Bottom
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
zeroGradient
Top wall and side walls
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
zeroGradient
Initial conditions
uniform 0
uniform 0
uniform (0 0 0)
uniform 0, use expression
in funkySetFields to define
C = 1 where
alpha.water < 0.5
Appendix C
130
C.5 Mass transport of oxygen in sewer headspace
Table C.10: Model setup of sewer geometry with closed utility manholes.
Title: Mass transport of O2 in the air phase in a lab scale experiment (rectangular duct)
General
Case description
mass transport simulations according to the field experiments of Madsen
et al. (2006)
hydrodynamic simulations: quasi steady-state
mass transfer: pulse injection in the air phase
case 1: 1800 s with 540 s injection of oxygen
case 2: 1800 s with 360 s injection of oxygen
case 3: 1800 s with 300 s injection of oxygen
case 4: 1800 s with 160 s injection of oxygen
Referred to in chapters
5.4.1, 5.4.2
References
(Madsen et al., 2006)
Domain discretization
Dimensions
three-dimensional (length: 110 m, dia. (main sewer): 0.5 m, height
(manholes): 2 m, dia. (manholes): 0.5 m)
Mesh generator
Salome Meca
Number of cells
1,469,159
Turbulence models
standard k-𝜖
Hydrodynamic
simulations
Solver
interFoam
Time step
0.001 s
Simulation time
1500 s
Single-phase transport
simulations
Solver
interO2Foam with modified Henry’s coefficient
Simulation time
7200 s in 4 steps of 1800 s with variable injection time for oxygen
Time step
0.001 s
Tracer diffusivity
water: 2.42 10-9 m2/s, air: 1.98 10-5 m2/s
Schmidt number
1
Temperature
298.15 K
Mass transfer
simulations
None performed
Appendix C
131
Table C.11: Boundary conditions for simulations of the sewer with closed utility holes.
alpha.water
[-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
k [𝒎𝟐
𝒔𝟐]
𝝐 [𝒎𝟐
𝒔𝟑]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer
case)
Inlet_air
inletOutlet
inletValue:
uniform 0
value:
uniform 0
totalPressure
p0: uniform 0
U: U
phi: phi
rho: rho
psi: none
gamma: 1
value: uniform 0
pressureInletOutlet-
Velocity
phi: phi
tangentialVelocity:
uniform (0 0 0)
value: uniform (0 0 0)
zeroGradient
zeroGradient
fixedValue
value: uniform 0
Inlet_water
inletOutlet
inletValue:
uniform 1
value:
uniform 1
fixedFluxPressure
flowRateInletVelocity
volumetricFlowRate:
value: 0.0145
fixedValue
value: uniform
0.001
turbulentMixing-
LengthDissipation-
RateInletmixingLength:
0.04
value: uniform 6∙10-5
fixedValue
value: uniform 0
Outlet
zeroGradient
fixedValue
value: uniform -0
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
zeroGradient
inletOutlet
inletValue:$internalField
value: $internalField
zeroGradient
Bottom_wall
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Top_wall
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Appendix C
132
Table continued
*: values were calculated for each case according to the measured values from the field.
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
k [𝒎𝟐
𝒔𝟐]
𝝐 [𝒎𝟐
𝒔𝟑]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer case)
Manhole_1
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Manhole_2
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Manhole_3
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Baffle
inletOutlet
inletValue:
uniform 0
value: uniform 0
zeroGradient
flowRateInletVelocity
volumetricFlowRate:
value*
zeroGradient
zeroGradient
fixedValue
value: uniform*
Initial
conditions
uniform 0
use setFields to
define water
phase
(alpha.water = 1)
within a bounding
uniform 0
uniform (0 0 0)
uniform 0.001
uniform 6∙10-5
uniform 0, use
expression in
funkySetFields to define
C* where
alpha.water < 0.5
Appendix C
133
C.6 Mass transfer and ventilation of oxygen in sewer headspace
Table C.12: Model setup of sewer geometry with open utility manholes for ventilation.
Title: Mass transport of O2 in the air phase in a lab scale experiment (rectangular duct)
General
Case description
mass transport and ventilation simulations
hydrodynamic simulations: quasi steady-state with open manhole_2 for
different suction pressure
mass transfer: pulse injection in the air phase
Referred to in chapters
5.4.3
References
Madsen et al. (2006)
Domain discretization
Dimensions
three-dimensional (length: 110 m, dia. (main sewer): 0.5 m, height
(manholes): 2 m, dia. (manholes): 0.5 m)
Mesh generator
Salome Meca
Number of cells
1,469,159
Turbulence models
standard k-𝜖
Hydrodynamic
simulations
Solver
interFoam
Time step
0.001 s
Simulation time
1500 s for each suction pressure value
Single-phase transport
simulations
none performed
Mass transfer
simulations
Solver
interO2Foam
Simulation time
50 s of pulse injection of oxygen, 540 s without oxygen injection
Time step
0.001 s
Tracer diffusivity
water: 2.42 10-9 m2/s, air: 1.98 10-5 m2/s
Schmidt number
1
Temperature
298.15 K
Appendix C
134
Table C.13: Boundary conditions for simulations of the sewer with open utility holes for ventilation.
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
k [𝒎𝟐
𝒔𝟐]
𝝐 [𝒎𝟐
𝒔𝟑]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer
case)
Inlet_air
inletOutlet
inletValue:
uniform 0
value: uniform 0
totalPressure
p0: uniform 0
U: U
phi: phi
rho: rho
psi: none
gamma: 1
value: uniform 0
pressureInletOutlet-
Velocity
phi: phi
tangentialVelocity:
uniform (0 0 0)
value: uniform (0 0 0)
zeroGradient
zeroGradient
fixedValue
value: uniform 1
Inlet_water
inletOutlet
inletValue:
uniform 1
value: uniform 1
fixedFluxPressure
flowRateInletVelocity
volumetricFlowRate:
value: 0.0145
fixedValue
value: uniform
0.001
turbulentMixing-
LengthDissipation-
RateInletmixingLength:
0.04
value: uniform 6∙10-5
fixedValue
value: uniform 0
Outlet
zeroGradient
fixedValue
value: uniform -0
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
zeroGradient
inletOutlet
inletValue:$internalField
value: $internalField
zeroGradient
Bottom_wall
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform 0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Top_wall
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform 0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Appendix C
135
Table continued
*: values different for each case from just open to -2.5 (p_rgh)
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
k [𝒎𝟐
𝒔𝟐]
𝝐 [𝒎𝟐
𝒔𝟑]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer case)
Manhole_1
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
Manhole_2
zeroGradient
fixedValue
value: uniform*
inletOutlet
inletValue:
uniform (0 0 0)
value: uniform (0 0 0)
zeroGradient
inletOutlet
inletValue:$internalField
value: $internalField
inletOutlet
inletValue: uniform 0
value: uniform 0
Manhole_3
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform
0.001
epsilonWallFunction
value: uniform 6∙10-5
fixedValue
value: uniform 0
initial
conditions
uniform 0
use setFields to
define water
phase
(alpha.water =
1) within a
bounding
uniform 0
uniform (0 0 0)
uniform 0.001
uniform 6∙10-5
uniform 0
Appendix C
136
C.7 Mass transfer in a turbulent reactor (H2S)
Table C.14: Model setup of the turbulent reactor for H2S transfer from liquid to gas phase.
Title: Mass transport of O2 in the air phase in a lab scale experiment (rectangular duct)
General
Case description
mass transfer of H2S under turbulent conditions
mass transfer: done for different stirring rates (case 1: 300 rpm, case 2:
400 rpm and case 3: 500 rpm)
Referred to in chapters
5.4.3
References
Tang (2019)
Domain discretization
Dimensions
three-dimensional (tank dia.: 0.29 m, tank height: 0.8m, stirrer depth:
0.08 m (below the water surface), stirrer dia.: 0.1 m, stirrer thickness:
0.001m)
Mesh generator
Salome Meca
Number of cells
63,237
Turbulence models
standard k-𝜖
Hydrodynamic
simulations
none performed
Single-phase transport
simulations
none performed
Mass transfer
simulations
Solver
interH2SFoam (modified)
Simulation time
300 s
Time step
1e-5 s
Tracer diffusivity
water:1.4 10-9 m2/s, air: 1.5 10-5 m2/s
Schmidt number
1
Temperature
298.15 K
Appendix C
137
Table C. 15: Boundary conditions for simulations for mass transfer of H2S in a turbulent reactor
*: values taken from the experiment
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
k [𝒎𝟐
𝒔𝟐]
𝝐 [𝒎𝟐
𝒔𝟑]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass transfer
case)
Reactor_wall
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform 1∙10-5
epsilonWallFunction
value: uniform 1∙10-5
zeroGradient
Blade
zeroGradient
fixedFluxPressure
movingWallVelocity
value: $internalField
kqRWallFunction
value: uniform 1∙10-5
epsilonWallFunction
value: uniform 1∙10-5
zeroGradient
AMI1
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
AMI2
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
Outlet
zeroGradient
fixedFluxPressure
fixedValue
value: uniform
(0 0 0)
kqRWallFunction
value: uniform 1∙10-5
epsilonWallFunction
value: uniform 1∙10-5
zeroGradient
Initial
conditions
uniform 0
use setFields to
define water
phase of
height:0.16 m
(alpha.water = 1)
uniform 0
uniform (0 0 0)
uniform 1∙10-5
uniform 1∙10-5
use setFields to define
conc.* where
alpha.water > 0.5
Appendix C
138
C.8 Mass transfer in a turbulent reactor (O2)
Table C.16: Model setup of the turbulent reactor for O2 from gas to liquid phase.
Title: Mass transport of O2 in the air phase in a lab scale experiment (rectangular duct)
General
Case description
mass transfer of O2 under turbulent conditions
mass transfer: done for different stirring rates (case 1: 300 rpm, case 2: 500
rpm)
Referred to in chapters
6.2.3
References
Tang (2019)
Domain discretization
Dimensions
three-dimensional (tank dia.: 0.29 m, tank height: 0.8 m, stirrer depth: 0.08
m (below the water surface), stirrer dia.: 0.1 m, stirrer thickness: 0.001 m)
Mesh generator
Salome Meca
Number of cells
63,237
Turbulence models
standard k-𝜖
Hydrodynamic
simulations
none performed
Single-phase transport
simulations
none performed
Mass transfer
simulations
Solver
interO2Foam
Simulation time
300 s
Time step
1e-5 s
Tracer diffusivity
water: 2.42 10-9 m2/s, air: 1.98 10-5 m2/s
Schmidt number
1
Temperature
298.15 K
Appendix C
139
Table C.17: Boundary conditions for simulations for mass transfer of O2 in a turbulent reactor.
*: values taken from the experiment
alpha.water [-]
prgh [𝒌𝒈
𝒎𝒔𝟐]
U [𝒎
𝒔]
k[𝒎𝟐
𝒔𝟐]
𝝐[𝒎𝟐
𝒔𝟑]
C [𝒎𝒐𝒍
𝒎𝟑]
(for mass
transfer case)
Reactor_wall
zeroGradient
fixedFluxPressure
fixedValue
value: uniform (0 0 0)
kqRWallFunction
value: uniform 1∙10-5
epsilonWallFunction
value: uniform 1∙10-5
zeroGradient
Blade
zeroGradient
fixedFluxPressure
movingWallVelocity
value: $internalField
kqRWallFunction
value: uniform 1∙10-5
epsilonWallFunction
value: uniform 1∙10-5
zeroGradient
AMI1
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
AMI2
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
cyclicAMI
Outlet
zeroGradient
fixedFluxPressure
fixedValue
value: uniform
(0 0 0)
inletOutlet
inletValue:$internalField
value: $internalField
epsilonWallFunction
value: uniform 1∙10-5
fixedValue
value*
Initial
conditions
uniform 0
use setFields to
define water
phase of height:
0.15 m
(alpha.water =
1)
uniform 0
uniform (0 0 0)
uniform 1∙10-5
uniform 1∙10-5
use setFields to
define conc.*
where
alpha.water > 0.5
140
Appendix D
Chemical abbreviations
Appendix D
141
D.1 Chemical name abbreviations
Table D.1: Abbreviations for the chemical names used in the text or figures used.
(Referred in: Figure 1.1, Figure 1.3)
Symbols
Abbreviation
C6H5SH
thiophenol
CH2SH
methanethiol
CH4
methane
Cl2
chlorine
CO2
carbon di oxide
Fe2+
iron(II) or ferrous ion
Fe2O4
iron(II) oxide or ferrous oxide
H2
hydrogen gas
H2O
water
H2S
hydrogen sulphide
H2SO4
sulphuric acid
HCHO
formaldehyde
MT
methanothiol
N
nitrogen
NH3
ammonia
O2
oxygen
SO42-
sulphate ion
VFAs
volatile fatty acids
VOSC
volatile organic sulphur compounds
Bibliography
142
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