Elkalsh, Ahmed (2017) Coupled electro-thermal transmission line modelling

138 Pages·2017·16.8 MB·English

by  Christine Middleton

Coupled Electro-Thermal Transmission Line
Modelling (TLM) Method
Ahmed Elkalsh, BEng(Hons)
Thesis submitted to The University of Nottingham
for the degree of Doctor of Philosophy, September 2016
Abstract
The theme of this thesis is concerned with the modelling of the multi-physics inter-
actions that occur in lightning and arc discharge. The main contributions of this
research are presented as combining different physical studies namely, electromag-
netic (EM) propagation, thermal diffusion and non-linear materials using a numer-
ical algorithm. The algorithm was developed based on the two dimensional (2D)
numerical transmission line method (TLM). The algorithm was applied to several
practical examples namely, to model the electro-thermal analysis and the temper-
ature development in a plasmonic nano-heat sources for terahertz applications; to
predict the shape and the location of an arc discharge channel caused by a lightning
strike using electro-thermal analysis, and to model diverter strips for lightning pro-
tection on aeroplanes. Different electro-thermal coupling approaches, such as fully
and partially coupled methods were used to investigate the efficiency and accuracy
of the model. In the fully coupled method the thermal model was allowed to change
the electrical properties of materials in the electromagnetic model. On the other
hand partial coupling did not consider the temperature dependency of the electrical
properties in the electromagnetics model. Both of the models used the dissipated
powerfromtheelectromagneticmodelasasourcesignaltoevaluatethetemperature
profile in the thermal model. Also different coupling interval timesteps were inves-
tigated to minimize the computational power needed without affecting the model
accuracy.
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Acknowledgements
During my PhD journey, I have received immeasurable support from many individ-
uals who have made this thesis possible. First and foremost, I would like to express
my deepest gratitude to my main supervisor, Dr Ana Vukovic for her unwavering
support during my studies. I would like to thank Ana for being so approachable
and understanding during the times of hardship. Thank you for the countless times
where you were so patient reading my work and suggesting improvements. I would
like to thank Prof Philip Sewell for the fruitful discussions, enlightening suggestions
and questions. Without these inputs, it would not have been possible to complete
this work. I would like to thank Prof Trevor Benson for the support and help during
the preparation of the publications, where he provided immense patience and advice
during my learning process for writing journals.
I would like to thank the GGIEMR group members for the fun times and the in-
teresting discussions during my academic work and outside. Thank you all DR
Xuesong Meng(Vicky), Dr Sendy Phang, Dr Daniel Simmons, Dr Brian Teo, Dr
Hayan Nasser, Zhang Zhewen(Edward), Latifa Abdul Aziz, Dr Afonos almeida, Na-
jla Najeeb, Lu Zhengyu and Andrew Morley.
I would like to thank my second family who have shared the experiences with me
as a welfare tutor at the university. You have been supportive and patient with me
during my writing up period, and covering my duties when extra work was needed
for my PhD. Thank you Prof Glenn McDowell, Dr Lina Bader, Minh Hoang(Harry),
Connor Jones, Dr Spandan karla, Yousuf Mansoor, Dr Tiziana Marrocco, Georgina
Marsh, Nirav Nagda, Mina Tahsiri and Long Van.
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None of this would have been possible without the support of my family and my
mother Magda who brought me up and put me up on the right track early in life.
Thank you mother, I am in your debt for as long I live. I would like to thank my
father Ibrahim, who has shaped the core of who I am today as a person, and who
would be very proud if he had lived to witness my achievements.
Last but not least I would like to thank my wife Kamr. Her unwavering love,
patience, encouragement and tremendous support during all stages of my PhD has
made it a much easier and better experience.
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Publications related to this thesis
Peer reviewed journal articles:
[J1] A. Elkalsh, A. Vukovic, P. Sewell, and T. M. Benson, “Electro-thermal mod-
elling for plasmonic structures in the TLM method,” Optical and Quantum
Electronics 48: 263 (2016).
Publications in conference proceedings:
[C1] A. Elkalsh, A. Vukovic, P. Sewell, and, T. Benson, “Coupled electromag-
netic - thermal model for arc discharge in plasma,” in 9th IET International
Conference on Computation in Electromagnetics (CEM 2014), London, UK.
[C2] A. Elkalsh, A. Vukovic, P. Sewell, and, T. Benson, “Coupled arc discharge
models in the TLM method,” in 2015 IEEE International Symposium on Elec-
tromagnetic Compatibility (EMC), Dresden, Germany pp. 987 - 990.
Conferences with abstract:
[A1] A. Elkalsh, A.Vukovic, P.Sewell, and, T. Benson, “CoupledElectromagnetic
Thermal Model for Plasmonic Waveguides,” in Optical Wave and Waveguide
Theory and Numerical Modelling Workshop (2015), London, UK.
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Contents
Abstract i
Acknowledgements ii
List of Publications iv
List of Symbols viii
List of Abbreviations x
1 Introduction 1
1.1 Introduction and overview . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Electromagnetism and TLM 17
2.1 Electromagnetic field analogy . . . . . . . . . . . . . . . . . . . . . . 17
2.2 One-dimensional TLM method . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Two-dimensional TLM method . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 TLM Series node . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Modelling different materials using a stub technique . . . . . . . . . . 28
2.5 TLM Condensed Node . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3 Thermal diffusion in TLM 43
3.1 Heat diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Formulation of thermal 2D-TLM . . . . . . . . . . . . . . . . . . . . 49
3.3 Modelling different materials in thermal TLM . . . . . . . . . . . . . 53
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3.4 Heat source modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Plasma modelling and coupled model 60
4.1 Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.1.1 Plasma modelling in TLM . . . . . . . . . . . . . . . . . . . . 61
4.2 Thermal TLM model convergence . . . . . . . . . . . . . . . . . . . . 64
4.2.1 Scaling of the thermal source . . . . . . . . . . . . . . . . . . 65
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5 Plasmonic nano heat sources 71
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 The Electromagnetic (EM) model . . . . . . . . . . . . . . . . . . . . 75
5.3 EM-thermal results and convergence of the model . . . . . . . . . . . 78
5.3.1 Excitation signal setup . . . . . . . . . . . . . . . . . . . . . . 79
5.3.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 81
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 Arc discharge modelling 92
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.1 The plasma model . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.2 Electro-thermal coupling . . . . . . . . . . . . . . . . . . . . . 98
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7 Conclusions and future work 121
7.1 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
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List of Symbols
This list includes all symbols that are frequently used in this thesis.
Symbol Description Unit First used
E Electric field vector (TD∗) V/m (2.1a)
H Magnetic field vector (TD) A/m (2.1a)
B Magnetic flux density vector (TD) Wb/m2 (2.1a)
J Magnetic voltage density vector (TD) V/m2 (2.1a)
m
D Electric flux density vector (TD) C/m2 (2.1b)
J Electric current density vector (TD) A/m2 (2.1b)
e
ε Electric permittivity F/m (2.1c)
µ Magnetic permeability H/m (2.1d)
R Resistance Ohm (2.9)
L Inductance Henry (2.9)
C Capacitance Farad (2.10)
G Admittance S (2.10)
t Time s (2.16)
Z Characteristic impedance of transmission line Ohm (2.17)
TL
c Speed of light in free space m/s (2.31)
ε Electric permittivity of free Space F/m (2.31)
o
µ Magnetic permeability of free space H/m (2.31)
o
Z Impedance of free space Ohm (2.32)
o
ε Electric relative permittivity − (2.33)
r
χ Electric susceptibility − (2.33)
e
∗Time-Domain
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E Electric field vector (FD†) V/m (2.41)
H Magnetic field vector (FD) A/m (2.41)
B Magnetic flux density vector (FD) Wb/m2 (2.41)
J Magnetic voltage density vector (FD) V/m2 (2.41)
m
D Electric flux density vector (FD) C/m2 (2.41)
J Electric current density vector (FD) A/m2 (2.41)
e
ω Angular frequency rad/s (2.42)
χ Magnetic susceptibility − (2.43)
m
σ Electrical conductivity S/m (2.44)
e
σ Magnetic resistivity Ω/m (2.45)
m
s Laplace complex frequency variable 1/s (2.54)
s Normalised Laplace variable − (2.54)
z Time shift operator (Z-transform) − (2.54)
q Heat flux W/m2 (3.1)
th
k Thermal conductivity W/m.K (3.1)
th
T Temperature K (3.1)
c Specific heat capacities at constant volume J/kg K (3.5)
v
c Specific heat capacities at constant pressure J/kg K (3.5)
p
ρ Volumetric mass density kg/m3 (3.9)
ω Plasma frequency rad/s (4.1)
p
ν Collision frequency 1/s (4.1)
c
√
j Imaginary number −1 − (4.1)
P Dissipated power W/m2 (4.13)
d
†Frequency-Domain
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