Studies on Current Distribution in Water Circumference under Air

Transcription

東海大学大学院平成 26 年度博士論文
Studies on Current Distribution in Water Circumference
under Air-Phase Spark Discharge
指導
大山龍一郎
教授
東海大学大学院総合理工学研究科
総合理工学専攻
Nur Shahida Binti Midi
Table of Contents
List of symbols
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i
Chapter 1
Foreword
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1.1 Introduction
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1.1.1 Background and Problem Statement
1.1.2 Research Objective
1.2 Research Methodology
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1.3 Other Works on Electrical Discharge in Dielectric Two-Phase Gas-Liquid System
1.4 Organization of Dissertation
References
Chapter 2
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Electrical Discharge on Water Surface of a
1D Experimental Model ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・19
2.1 Introduction
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2.2 Experimental Methods
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2.2.1 Electrode System
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2.2.2 Probe for Electric Potential Measurement
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2.2.3 Experimental Setup and Procedures
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2.3 Results and Discussion
2.3.1 Breakdown Properties of Spark Discharge on Water Surface
2.3.2 Discharge Current Distribution to Underwater
2.3.3 Electric Potential Distribution
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2.4 Summary
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References
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Chapter 3
Effect of Water Conductivity to the Electrical Discharge
on Water Surface using a 2D Experimental Model
3.1 Introduction
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3.4 Summary
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References
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Chapter 4
Evaluation of Water-Phase Current Distribution
by the means of Numerical Calculation
4.1 Introduction
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4.2 General Approach of the Numerical Calculation
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4.2.2 Equations Employed
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4.2.3 Calculation Parameters
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4.2.1 COMSOL Multiphysics, AC/DC Module
4.3 Numerical calculation of 1D Model
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4.3.1 Calculation Model and Boundary Condition
4.3.2 Calculation Results
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4.4 Numerical Calculation of 2D Model
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4.4.3 Remarks on the Prediction of Current due to Natural Lightning
based on the Calculation Results
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4.5 Summary
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References
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Chapter 5 Conclusion and Future Prospect
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5.1 Conclusion
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5.2 Future Prospect
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Acknowledgment
List of symbols
i
: number of grounding electrodes
σ
: conductivity of water
[S/m]
Vd
: Voltage at discharge electrode
[kV]
Vd-peak
: Spark voltage / Peak value of Vd
[kV peak]
Id
: Current at discharge electrode
[A]
Id-peak
: Discharge current / Peak value of Id
[A peak]
Igi
: Current at grounding electrode numbered i
[A]
igi
: Current density at grounding electrode numbered i
[A/m2]
qgi
: Charge density at grounding electrode numbered i
[μC/m2]
Igi-N
: Current at grounding electrode normalized to Id-peak
[%]
igi-N
: Current at grounding electrode normalized to Id-peak divided by the electrode’s area
Vw (x, y)
: Electric potential of water for 1D model
[kV]
Vw (r, z)
: Electric potential of water for 2D model
[kV]
Vw (x, 0)
: Electric potential on water surface, y = 0 mm (1D model)
[kV]
Vw (0, y)
: Electric potential on y-axis, x = 0 mm (1D model)
[kV]
Vw (r, 0)
: Electric potential on water surface, z = 0 mm (2D model)
[kV]
Vw (0, 0)
: Electric potential at x = y = 0 mm (1D model) or r = z = 0 mm (2D model)
Vdrop
: Voltage drop at the air gap ( = Vd-peak – Vw (0, 0) )
tV-max
: Time for maximum electric potential
l
: Filamentary discharge length or luminous area diameter
[mm]
lcalc
: Boundary condition length
[mm]
∅
: Electric potential (boundary condition)
[kV]
E
: Electric field
[kV/m]
D
: Electric displacement field
[kV/m]
n
: Normal vector
i
[kV]
[μs]
[kV]
σ＊
: Complex conductivity
[S/m]
σ
: Real part of complex conductivity
[S/m]
σ′′
: Imaginary part of complex conductivity
[S/m]
′
ε
＊
ε′
′′
ε
: Complex permittivity
: Real part of complex permittivity (Permittivity)
: Imaginary part of complex permittivity (Losses)
ii
Chapter 1
Foreword
1.1 Introduction
1.1.1 Background and Problem Statement
Lightning is a type of electric discharge that can be observed in nature. Due to its character that is
capable of causing injuries to human [1-1], and bringing damages to other objects such as buildings
[1-2] and power transmission lines [1-3]; lightning protection had become a subject of interest. The
first lightning protection system had been introduced by Benjamin Franklin, initiated from his
famous kite experiment, where he proposed a sharp pointed metal rode to channel the lightning
current to ground in order to protect houses or buildings from damages.
Recent researches on lightning and lightning protection can be summarized into five general
categories [1-4], (i) observation on lightning discharge; (ii) modeling of lightning discharge; (iii)
lightning occurrence characteristics and lightning locating systems; (iv) lightning electromagnetic
pulse (LEMP) and induced effects; and (v) protection against lightning-induced effects.
Investigations of lightning and lightning protection are usually being done hand in hand. The
observation of the lightning parameters and characteristics are indispensable in lightning protection
development as can be seen in the case of Benjamin Franklin and his lightning rod. For example, in
designing lightning protection such as surge protecting devices (SPDs), it is first important to grasp
the lightning parameters such as the voltage, current and the wave shape [1-5, 1-6]. For the detection
and prediction of lightning, knowledge on the electromagnetic field distribution of lightning is
needed. The generated electric fields due to lightning are sensed using antennas or sensors [1-7, 1-8],
and later are used along with other input such as wind, temperature and moisture to predict the
lightning [1-9].
However, observations on lightning discharge are mainly focusing on lightning that occurred on
land area or high population areas, where observation on sea is still a minority. The increase in
human activities at sea area had raised the demand of lightning protection in sea area [1-10]. This
include recreation activities such as swimming and diving, where human are in direct contact with
water. Indirect contact with water includes the usage of boats and ships for private activities and
economic activities such as fisheries and transportation. Other than that, in considering the lack of
space in ground areas and to protect human comfort; some industrial activities such as wind [1-11,
1-12] and photovoltaic [1-13, 1-14] power generating farm, began to be developed at the sea areas.
This is especially in insular countries such as Japan and South East Asia region. In this situation, a
critical role of lightning protection is needed where the maintenance and repairing are sought to be
minimized due to difficulties in access and also for reduction of cost and man power.
Compared to lightning on ground, lightning on sea in Indonesia for example was reported to have
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higher current, where the median of negative first strokes current amplitudes on sea are higher
compared to those on land [1-15]. The median current amplitudes were reported to be 23.1 kA for
those on land and 32.0 kA for those on sea. The minimum and maximum current amplitudes also
showed the same trend. Although lightning in sea area is generally fewer compared to lightning in
land area, winter lightning had been known to be concentrated in sea area. A work done by Saito et
al [1-16] shows that winter lightning in Japan including high current discharge (higher than 150 kA)
is mostly distributed in coastal area, which is a zone between about 20 km inland and 10 km seaward
from the shoreline.
Researches regarding lightning on sea are mostly focusing on the detection and prediction, where
the distribution of lightning is obtained. Other than that, investigations regarding the characteristics
of lightning on water surface, which needs actual measurements of the lightning parameters are also
important for the consideration of a lightning protection system. However, as actual outdoor
measurement is not practical considering the cost and time needed, a laboratory-experimental
observation would be a good alternative. Observation considering lightning on water environment
includes study by Okano [1-17] where the discharge impedance in a short composite gap consisting
of atmospheric air and tap water, for development of SPDs against lightning surges invading via
water media was investigated. In this work, impulse voltage applied to air and water gap is an
interpretation of lightning on water surface.
Currently, investigation of lightning on water surface for development of lightning protection is still
insufficient compared to the increase of risk and damages due to those activities mentioned before.
Prediction of discharge current within a seawater circumference is important for the consideration in
safety procedures. A discharge model on the lightning phenomenon on water surface would be a
guideline for development of a lightning protection system at those areas. To achieve that, a
thorough understanding of the characteristics is important. In this work, investigation on the
characteristics of lightning on water surface was done by the means of laboratory experimental
observations, and was evaluated using numerical calculation. This phenomenon was imitated using
impulse voltage applied to water surface in a reservoir, and from there the electrical characteristics
were observed. The observations include spatial and temporal evaluation of the electrical quantities
under the effect of water properties.
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1.1.2 Research Objective
The objective of this work is to investigate the characteristics of lightning on water surface for the
development of a discharge model of the phenomenon, focusing on the current distribution; as an
evaluation of the lightning phenomenon on water surface. To accomplish this objective, two
methodologies were employed; which are experimental laboratory observation done by reproducing
the phenomenon using a laboratory-scale electrical discharge in dielectric two-phase gas-liquid
system, and followed by numerical calculations.
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1.2 Research Methodology
Lightning is the breakdown process of the atmospheric insulation, where the turbulence in the
cloud causing the charges to separate and negative charges clustered at the base of the clouds. As a
result, positive charges are induced to the ground surface, creating a strong electric field between the
cloud and earth. Then, a streamer propagates down towards the earth in a stepped manner due to the
electric field, known as stepped leader. As the leader tip approaches ground, upward moving positive
charges are initiated from the ground and the attachment process begin, allowing for the
neutralization of the cloud charges. This upward moving propagation is known as return stroke. In
the case of incomplete neutralization of the cloud charges, dart leader (leader with no stepped
manner) occurred, following almost the same path of the previous stepped leader. In the same
manner, attachment with the return stroke then occurred, completing the neutralization process. This
process with more than one leader propagate in a same path is known as multiple lightning flash
[1-18, 1-19].
During a lightning strike, disturbance in electric circuit and communication signal due to lightning,
or known as lightning surge [1-20] is one of the critical problems occurred. The lightning surges
exist in wide variety with various amplitudes and sustaining period. Accordance to that, lightning
impulse voltage which imitates the lightning surge is widely being used in the investigations of
lightning protection for electrical instrument. In high voltage field, the lightning impulse voltage is
expressed as :
duration of wave front / duration of wave tail [μs]
The duration of wave front indicates the time taken for the impulse to reach its peak value (±30%);
and the duration of wave tail indicates the time taken to decay from the peak to its 50% value
(±20%). Among this variety, the standard lightning impulse voltage is fixed to be as 1.2/50 μs
(duration of wave front = 1.2 μs; duration of wave tail = 50 μs). Both the times are being accordance
with established standards of impulse testing techniques. The waveform of this impulse voltage is
shown in Fig. 1-1 [1-18 ~ 1-20].
For the first methodology of this work, the characteristics of lightning on water surface were
investigated by the means of experimental laboratory experiments, where the standard lightning
impulse voltage was employed to simulate the lightning on water surface in a laboratory-scale
dielectric two-phase gas-liquid system.
The dielectric two-phase gas-liquid system is a stratified electrode system consisted of a discharge
electrode applied with the standard lightning impulse voltage, an air gap, and underwater grounding
electrodes. The layout of the multiple underwater grounding electrodes was configured so that both
water surface and underwater are covered. This is to obtain a thorough observation of the discharge
current spatial distribution.
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The equivalent circuit of the system is shown in Fig. 1-2. This equivalent circuit is consisted from
three sections; namely the impulse voltage generator, air-phase breakdown and water-phase
conduction. These are representing the charged clouds, lightning at atmosphere and underwater
current distribution. In the equivalent circuit, the impulse voltage generator is represented by a
capacitance, while the air-phase breakdown is represented by a resistance and an inductance. For
underwater conduction, the circuit is consisted of parallel resistance and capacitance. This
composition is the common composition of equivalent circuits for conduction in water [1-21~ 1-24].
As the water properties differ according to the environment (e.g. : rivers, lakes, seas), it is
important to investigate the effect of water properties on the discharge phenomenon. Furthermore, it
is known that the electrical properties of water will determine the interaction of water with the
electric field. In this work, the effect of water properties is investigated by varying the conductivity
of water using NaCl. This is represented by the variable R and C of the equivalent circuit in Fig. 1-2.
Another important parameter that should be considered is the polarity of the discharge. According
to Uman, about 90% of worldwide cloud-to-ground (CG) lightning are negatively-charged leaders,
and less than 10% are positively-charged leaders, i.e. natural lightning is mainly consist of negative
polarity compared to positive polarity [1-25]. However, the observations in this work are mainly
consisted of positive polarity discharge. This is because, as the streamers in gas discharge
phenomenon [1-26], it is expected that positive polarity will give a wider propagation under the
same voltage. Therefore, a broader data of the discharge is expected to be obtained.
A numerical calculation of the electrical quantities is necessary in order to evaluate the
experimental observations. Other than that, it is also important so that the results that could not be
obtained from the experiments procedures for example, the directions of vector quantities should be
able to be compensated. Therefore, numerical calculation using Comsol Multiphysics is also
included in this work. A two-dimension axial-symmetry model was employed; where the boundary
conditions are using the potential data obtained from the experiments and was determined by
considering other observations. Both calculations under stationary and time-dependent conditions
were considered in this work.
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V [%]
100
90
50
30
0
01
1.2
t [μs]
50
Fig. 1-1 Waveform of standard lightning impulse voltage (1.2/50μs)
Cg
impulse generator
switch
Ra
air-phase spark
discharge
La
water surface
water-phase
conduction
(R-C circuit)
Rwn
Rwn
Cwn
Rwn
Cwn
Rwn
Rwn
Cwn
Cwn
ground
n : 1, 2, …
Fig. 1-2 Equivalent circuit of the dielectric two-phase gas-liquid system
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Cwn
1.2 Other Works on Electrical Discharge in Dielectric Two-phase Gas-Liquid
System
Electrical discharge in dielectric two-phase gas-liquid system is widely being investigated using
various electrode configurations under high-voltage AC, DC or impulse discharge, covering
investigations of the fundamental characteristics and investigations for various applications. In this
subchapter, other investigations regarding electrical discharge in dielectric two-phase gas-liquid
system will be reviewed, where investigations regarding electrical discharge in dielectric two-phase
gas-liquid system seen from electrical viewpoint and electrochemical viewpoint are included.
Electrical discharge in dielectric two-phase gas-liquid system of liquid other than water will also be
discussed generally.
i)
Electrical viewpoint
From electrical viewpoint, electrical discharge in dielectric two-phase gas-liquid system is mainly
investigated for the fundamental understanding of the phenomenon itself.
Lightning had been a well-known electrical discharge that can be observed in nature, and is widely
investigated through the ages. As stated earlier, with the increase on human activities in water
environment especially sea area, lightning phenomena on water surface had become a subject of
interest in lightning research. A work by Selin et al [1-27] had observed the propagation of spark on
water surface in concern to the involvement of objects situated far from lightning hit on water
surface. Probe-technique was used to measure the potentials and voltage drops in a surface discharge
channel. Takahashi [1-28] had observed the surface discharge on electrolyte solution for the concern
of lightning on wet soil and water surface. The dependence of electric discharge voltage the
conductivity and solution depth were investigated. A voltage model of uniform current flow was
proposed to summarize the dependency of voltage. For lightning protection in water area, a work by
Okano [1-17] had determined the discharge impedance in a short composite gap consisting of
atmospheric air and tap water for the development of surge protecting devices (SPDs) against
lightning surges via multiple media which is water in this case.
Other than for understanding the lightning phenomenon on water surface, there are also works that
are focusing on understanding the physics of the discharge itself. The observations were expected to
be beneficial in understanding the lightning phenomenon and also in other applications of the
discharge. Belosheev [1-29] had investigated the dynamic of the evolution of leader over water
surface, where five aspects which are the initial stage of the appearance of the discharge, the
structure of the channel, the discharge as an element of an RC circuit, plasma formation in the head
and its motion, and the parameters of the plasma were distinguished. In works by Aleksandrov et al
[1-30], development stages of electric discharge gliding on water surface; by varying the distance
between electrodes, distance between electrode and water surface, ballast resistor value, supplied
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voltage and discharge pulse duration was investigated; where three stages of pulse electric discharge
were revealed.
Besides on gaining the fundamental knowledge of lightning phenomenon in water environment,
electrical discharge on water surface is investigated for industrial requirements regarding surface
flashover phenomena on wet and polluted insulator. Works by Nakao et al [1-31] had investigated
the propagation of surface discharge on water surface under impulse voltage with water of different
conductivities. In their works, the shapes, sizes, features and propagation mechanism of the
discharge were observed by considering the voltage crest value, polarity, and liquid conductivity. For
development of a propagation model of a local discharge on polluted insulators, Matsuo et al [1-32~
1-36] had investigated the contacting area at the interface between the discharge and the solution
surface; where the contacting area, potential distribution, discharge current and propagation of the
local discharge were observed. Impulse voltage was employed as the applied voltage in
consideration of insulators threatened by the lightning. The investigations include both experimental
measurement and calculation analysis.
Besides reports on laboratory experiments, numerical analysis is also one of the techniques used for
investigation. Hadi et al [1-24] had reported the mathematical expression of characteristic constants
of DC and AC flashover discharge of insulator covered by electrolyte, where the analytical
relationships of critical flashover voltage and current to the physical meaning of discharge
characteristics were elaborated. Other work [1-37] had presented experimental and mathematical
modeling of the influence of type of pollutants (non-soluble salt, low soluble salt, and mixtures of
salts) on discharge parameters and their implication on the value of DC critical flashover voltage,
under both positive and negative polarity. The pollutions tested consist of simple electrolyte
(AjBj+H2O), mixtures of salts (AjBj+CjDj+….+H2O) and chalk as non-soluble matter.
ii)
Electrochemistry viewpoint
From electrochemistry viewpoint, electrical discharge in air with water as one of the electrode
[1-38, 1-39] had been a promising method for environmental applications such as water treatment
[1-40, 1-41], ozone generator [1-42] and NOx treatment [1-43]. Researches considering this field of
application include investigations of the electrical characteristics and also the plasma spectral
characteristics, aiming for the optimum configuration and arrangement of the electrodes and
parameters.
In determining the optimum electrode configuration and the suitable parameters for the applications,
knowledge on the electrical characteristics is indispensable. Robinson et al [1-44 ~ 1-46] had
investigated the breakdown voltage of an air gap over water surface with various parameters to
understand the phenomena leading to air breakdown in water-electrode ozone generator. Meanwhile,
works by Fujii et al [1-47, 1-48] is focusing on obtaining the fundamental data of corona discharge
over the water surface; which is expected to induce good conditions for the proceeding of NO
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oxidation and the NO2 dissolution removal into water for NOx treatment technology. Two reactor
models, which are multi-needle type and saw-edge type under DC and pulsed high voltage were
employed in their works. Bozhko et al [1-49] had analyzed the effect of the water layer on a flat
metallic electrode on the parameters of impulse corona discharge to the water surface and its
transition to a spark. The water layer has been known to play a role of capacitive-resistive impedance
during the corona discharge. In the work by Gaisin et al [1-50], investigation of the structures and
electrical characteristics of vapor-air discharge between a metal (solid, hollow, pointed) anode and
electrolyte cathode under atmospheric pressure were done; where the inter-electrode spacing,
discharge current and electrolyte composition were found to significantly affecting the discharge.
Besides the electrical characteristics, the spectral characteristic of the plasma generated by the
electrical discharge in dielectric two-phase gas-liquid system is one of the needed knowledge for the
applications [1-51 ~ 1-54]. Works under this topic are mainly focusing on the observation of the
chemical species generated by the discharge, the species transport between atmospheric plasma and
liquid, the electron characteristics, and the gas (plasma) temperature. Approaches used in the
observation include optical emission spectroscopy, laser induced fluorescence (LIF), and CCD
camera.
There are also works that are focusing on both electrical characteristics and plasma spectral
characteristics. Works by Bruggeman et al [1-55 ~ 1-59] investigated DC electrical discharge in
metal pin-water electrode system, for application in water treatment where the electrical
characteristics of the breakdown, water surface deformation, and emission spectroscopy are
observed. On the other hand, Anpilov et al [1-60, 1-61] had investigated the electrical and spectral
characteristics of high voltage pulsed discharge on water surface. The dynamics and parameters of
an atmospheric spark discharge reaching the water surface with different conductivities, where the
difference between underwater and over-water discharge; and the effect of air gap existence was
discussed.
iii) Discharge involving liquids other than water
Besides on water, investigations of electrical discharge in dielectric two-phase gas-liquid system of
other liquids are also available. Besides discharge propagation on liquid surface, Nakao et al [1-62]
had also investigated the surface discharge propagation on surface of insulating liquid by the means
of optical observation. Aleksandrov et al [1-63] work had performed electrode pulsed discharge
experiments realization over a fluid (tap water, covered by a film of benzene) in low speed air flow.
The experiments include corona discharge over kerosene, and multiple electrodes corona discharge
over a surface of water and alcohol.
From the viewpoint of electrohydrodynamics, discharge in dielectric two-phase gas-liquid system is
investigated to observe the electrostatic effects on liquid concerned with the fluids mechanics, for
liquids such as insulating oil and cooling liquid of electrical apparatus. Investigations in this area
9
include the role of interfacial shear-stresses [1-64], the effect of applied electric field by the
flow-pattern transition [1-65], and instability and motion induced by injected space charge [1-66].
This discussion on electrical discharge in dielectric two-phase gas-liquid system and the
references are summarized in Fig. 1-3.
From the literature review, it can be seen that various
investigations on electrical discharge in dielectric two-phase gas liquid system are available.
However, there is only one part [1-17, 1-27, 1-28] of the works that are actually focusing on the
lightning phenomenon on water surface. Although most of the works on surface discharge were
employing impulse voltage power supply [1-29 ~ 1-36] as required in investigation of lightning,
only the discharge occurred on water surface was focused. This is inadequate for investigation of
lightning on sea water surface, where the other quantities such as underwater current distribution and
potential distribution were not observed.
10
Electrical discharge in dielectric twophase gas-liquid system
Discharge type
Electrical
viewpoint
1-17, 1-27, 1-28
Lightning on
water surface
Electrochemistry
viewpoint
1-29, 1-30
Surface discharge
on water surface
application
Lightning 1-17
protection
system
Electrode
configuration
1-38, 1-39
Plasma from the discharge on
water surface
1-44 ~ 1-50
1-31 ~ 1-37
Insulator
maintenance
Liquid other
than water
Electrical
investigation
~
Plasma 1-51
1-54
spectral
investigation
1-55 ~ 1-61
Electrical and plasma spectral
investigations
1-43, 1-49, 1-50
1-42, 1-46 ~ 1-48
Ozone generator
NOx treatment
1-40, 1-41
Water treatment
Fig. 1-3 Summary of literature review on electrical discharge in
dielectric two-phase gas-liquid system
11
~
Effects of 1-62
1-66
electrostatics on
liquid
1-62
Test for
insulating liquid
1.3 Organization of Dissertation
This dissertation consists of 5 chapters. Below is the brief summary of the chapters.
Chapter 1
In this chapter the introduction to this work is delivered. The motivation to this work is explained
as the background and problem statement. The objective and a brief explanation on the methods of
this work are clarified in Research Objective and Methodology section. An introduction to the
electrical discharge in dielectric two-phase gas-liquid system is also included. Lastly, the flow of this
dissertation is stated in this section.
Chapter 2
In this chapter, a 1D model of electrical discharge on water surface is introduced. Two conductivity
of water, representing tap water and seawater were employed. This model employs a square water
reservoir with the same horizontal and vertical length. The discharge electrode was placed at the
edge of the reservoir with minimal air gap from the water surface. The results showed different
electrical characteristics between tap water and seawater. The current distribution showed
dependency to the distance from the discharge point, and the discharge condition on the water
surface.
Chapter 3
In this chapter, a 2D model of electrical discharge on water surface is introduced as a continuation
and improvement of the discharge model in previous chapter. This is so that a detailed observation
on the spatial distribution of the electrical parameters can be obtained. This 2D model employs a
cylindrical water reservoir, and the discharge electrode was placed at the center of the reservoir. The
variety of water conductivity was also increased by using tap water and saline solutions. The results
showed a significant difference between tap water and saline solutions, even with a small difference
in conductivity. The electrical quantities showed dependency to the conductivity, and showed the
tendency to saturate at higher conductivity. Comparison with 1D model had shown different current
distribution where the influence of distance can be seen on the effects of discharge condition.
Chapter 4
In this chapter, numerical calculation of the discharge on water surface using COMSOL
Multiphysics is presented. Calculations for both 1D model and 2D model are included, where
stationary and time-dependent calculations were done. The boundary conditions are using the
experimental data obtained in the previous chapters. In this stage of study, the permittivity of water
and saline solution are also considered besides the conductivity. Comparable results to the
12
experimental observation were estimated, and it was confirmed that the boundary condition which
considered the discharge condition on water surface is the appropriate for the numerical calculation
of current distribution.
Chapter 5
In this chapter, the final concluding remarks of this work and the future prospects are stated.
13
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18
Chapter 2 Electrical Discharge on Water Surface of a 1D Experimental Model
2.1 Introduction
In order to understand the lightning phenomenon on water surface, it is necessary for an
experimental observation of the electrical characteristics. An on-site observation of water surface
lightning is unpractical considering the cost and required time, added to the high safety risk. To that
matter, an indoor experimental observation of this phenomenon in anticipated. To realize this, a
laboratory-scale discharge-model of lightning on water surface was developed. In the development
of this discharge model for the mean of lightning protection in water area, the discharge current
distribution to water is an important parameter. This is because, lightning current was reported to be
one of the sources of damages in facilities [2-1]; and human injury due to lightning, where tissues
are damaged as an effect the current flow [2-2].
As already discussed in previous chapter, there are several other works [2-3 ~ 2-7] that were
investigating the electrical characteristics of discharge on water surface with various configuration of
discharge model, generally consisted of pin electrode in the air phase, and a plate electrode installed
either at the side of the water reservoir or at the bottom of the water reservoir. Their works were
mainly focusing on the discharge occurred on water surface, where the dynamics of evolution and
propagation of the discharge were focused. Observation of discharge current was also done but
limited to the current at the discharge channel. A work by Takahashi had proposed a voltage model
[2-8] of impulse discharge on water surface. However, as this model is limited to a uniform current
flow, obtaining the current distribution from the model can be considered difficult.
For that reason, a model of electrical discharge on water surface considering the lightning
phenomenon on water area is necessary, where the electrical characteristics including the discharge
current should be able to be observed. In this chapter, a 1-dimensional (1D) two-phase gas-liquid
model was developed for a laboratory experiment in order to investigate the phenomenon [2-9]. This
1D model is an electrode system with a square-shaped water reservoir of the same horizontal and
vertical length, where the lightning was imitated by an impulse discharge. From there, the electrical
properties of the impulse discharge on water surface were observed, by focusing on the current
conduction property. The underwater grounding electrode of this model was divided into several
channels so that the spatial distribution of the discharge current can be observed.
The organization of this chapter is as in the following sequence. Firstly, the objective of this chapter
is stated in section 2.1 as above. The experimental setup and procedures are explained in section 2.2.
In this section, the specification of the 1D model will be explained in detail along with the
experimental procedures and parameters. In section 2.3, the results of the experiments are presented.
The results will be discussed by focusing on underwater current conduction. Finally, the concluding
remark of this work is stated in section 2.4.
19
In order for an observation of the current distribution to the water circumference, a discharge model
that is emphasizing on both the water surface and underwater area is needed. For that reason, a water
reservoir with adequate length and depth is necessary. Besides that, the grounding electrode
placement is also need to be considered so that the spatial distribution can be observed.
Fig. 2-1 shows the electrodes’ configuration for the 1D model. This 1D model is consisted of a
stainless steel discharge electrode with 12 mm diameter and 45° tip angle. This discharge electrode
was placed with an air gap of 2 mm from the water surface, and was connected to a power source to
generate the discharge on the water surface.
The water reservoir is an acrylic box with inner measurement of 200 × 200 × 30 mm (tall × wide ×
depth). Water was filled up to the upper edge of the reservoir. The underwater electrodes are 30 × 30
× 0.1mm (tall × wide × thick) copper tape with conductive adhesive (TERAOKA TAPE) attached to
the inner surface of the water reservoir. There were distances of 10 mm between each adjacent
electrode. These electrodes were numbered in an anti-clockwise order as i, where i = 1, 2, …, 10.
Electrodes 1 to 5 were placed at the bottom of the water reservoir horizontal to the water surface. On
the other hand, electrodes 6 to 10 were placed at the side of the reservoir perpendicular to the water
surface. This placement of the grounding electrodes was considered so that the whole underwater
area is covered for the observation of current distribution. All the grounding electrodes were attached
with conductive wires connected to the ground.
2.2.2 Probe for Electric Potential Measurement
Besides the current conduction, other electrical properties during the discharge such as the electric
potential also need to be considered.
Fig. 2-2 shows the probe used for the measurement of electric potential distribution in water. This
measurement probe was made of a 0.8 mm diameter, 1 mm length tungsten rod and covered by a
Teflon tube before connected to a glass tube in order to hold it in place during the experiments. The
tungsten rod was attached to conductive wire which is to be connected to measuring apparatus.
Epoxy resin was used to attach the three parts together, where the insulating and
water-penetration-prevention properties should be enhanced.
20
Discharge
electrode, Ø 12
Copper
grounding
electrode
y
2
x
0
Water level
10
9
Acrylic
water reservoir
200
8
7
6
30
2
1
30
3
4
5
10
200 mm
Fig. 2-1 Electrodes’ configuration of 1D model (not to scale)
Conductive wire
Tungsten Teflon
tube
Glass tube
Fig. 2-2 Measurement probe specification
21
Fig. 2-3 shows the experimental setup for the investigation of electrical properties of spark
discharge on the water surface.
The discharge electrode, installed with a 2 mm air gap from the water surface, was connected to a
400 kV impulse voltage generator (Tokyo Transformer) as the voltage source. Spark discharge on
water surface was generated by applying 20 kV of standard lightning impulse voltage (1.2/50μs) to
the discharge electrode. The spark voltage was observed using a resistance voltage divider with
dividing ration of 39881 : 1, connected to an oscilloscope (LeCroy WaveSurfer MXs-B). The
oscilloscope was triggered by the rise in the voltage at the discharge electrode. Current at the
discharge electrode was measured using a current probe (Pearson, 6585) connected to the same
oscilloscope. Current distribution to the 10 channel grounding electrodes was observed using the
same combination of current probe and oscilloscope.
The measurement of electric potential using the measurement probe in Fig. 2-2 was done in an x-y
plane which is parallel to the discharge electrode point, in a 30 mm interval starting from x = y = 0
mm. A total of 49 (x, y) points were measured. The measurement probe was connected to the
oscilloscope through a voltage divider with dividing ratio of 1000 : 1.
The discharge conditions on the water surface were recorded as still image using digital camera.
The experiments were done using two water samples; tap water and saline solution with conductivity,
σ of 0.07 S/m and 5 S/m respectively, measured by a conductivity meter (Horiba, ES-51). The saline
solution was prepared by dissolving table salt to tap water. The saline solution’s σ is the same to that
of seawater, thus will be refer as seawater onwards.
The experiments were done under atmospheric pressure in room temperature.
22
Oscilloscope
Vd
400 kV impulse
voltage generator
Id
Vw (x, y)
Voltage divider
1000 : 1
Measurement
probe
Igi
Current
probe
Digital
camera
Electrode
system
Fig. 2-3 Experimental setup
23
Fig. 2-4 (a) and (b) shows the typical waveforms of voltage and current at the discharge electrode,
Vd and Id for tap water and seawater, where Fig. 2-4-1 shows the full time scale (0 to 100 μs) and Fig.
2-4-1 gives a shorter time scale (0 to 20 μs). From the waveforms, it can be seen that the voltage and
current waveforms are different for tap water and seawater.
For tap water, Vd shows a similar waveform to the standard lightning impulse voltage, where the
voltage gradually decreased after reaching the peak value, Vd-peak (which is also the spark voltage
value) of 19.5 kV peak at 1.6 μs. Both of the waveforms take about 100 μs to decrease to their
minimum values. On the other hand, Vd waveform of seawater shows a sudden drop after reaching
the Vd-peak of 10.5 kV peak at 0.6 μs, and take about 50 μs to decrease to the minimum values. The
averaged values of Vd-peak and Id-peak are shown in Table 1. From the Vd-peak values, it can be
concluded that the voltage for breakdown of the air gap are different between the discharges on the
surface of tap water and seawater.
The Id waveforms show resemblance to the Vd waveforms for both tap water and seawater. A
gradual decrease in tap water with discharge current, Id-peak of 5.8 A peak; and a sudden drop in
seawater with Id-peak of 98.9 A peak can be seen. However, for seawater, a second peak of current was
observed after the sudden drop. This is expected to be due to the higher ion concentration during the
discharge of seawater which is affecting the current conduction [2-10, 2-11], and also as a result of
the transient characteristic of the discharge.
Fig. 2-5 shows the discharge profile on water surface where (a) is the tap water and (b) is the
seawater. A filamentary discharge sprouting on the water surface with 100 mm length was observed
during the discharge on tap water. For seawater, the discharge only localized at the local discharge
point (x = y = 0 mm) with luminous area radius of 7 mm. The difference in the discharge color is due
to the higher sodium concentration in seawater; and also suggests a difference in the temperature of
the discharge.
From these observations, a significant difference of the breakdown can be seen between tap water
and seawater. To discuss this, the impedance Z of the discharge system was calculated from the
voltage and current waveform, where Z = IR [Ω], as shown in Fig. 2-6 (a) and (b) for tap water and
seawater respectively with smaller time scale from 0 to 5 μs. The time resolution for the waveforms
in this figure is higher than that of Fig. 2-4 with slight difference in the peak values. However, the
same characteristics are shown. The spiked waveform around t < 0.8 μs is due to the noise during the
charging process of impulse generator. From the figures, it can be seen that Z drop to the lowest
value after the spark discharge (represented by the peak of Vd) at the air gap for both tap water and
seawater. However, one order of difference of the Z value can be seen between them suggesting
24
different values of the R and C components of the equivalent circuit shown in Fig. 1-2.
From the Z waveform of tap water, the relatively high impedance suggest high resistance,
explaining the propagation of filamentary discharge on the tap water surface, which is also known as
an effect of resistive barrier discharge [2-12] where the distributed resistance of water prevents the
localization of the discharge. This also suggests higher capacitance which provides longer time for
the dispersion of energy from the discharge, which is represented by the gradual decrease of current.
For seawater with relatively low Z, the lower resistance of water had provided a good conduction of
the discharge current which can be seen from the sudden decrease of current. A lower capacitance is
also expected, but still enough to provide some time for the energy dispersion although shorter than
that of tap water.
25
8
Vd
Id
15
6
10
4
5
2
0
Current at discharge electrode, Id
[A]
Voltage at discharge electrode, Vd
[kV]
20
0
0
20
40
60
Time [μs]
80
100
(a) Tap water
120
Vd
10
100
Id
8
80
6
60
4
40
2
20
0
Current at discharge electrode, Id
[A]
Voltage at discharge electrode, Vd
[kV]
12
0
0
20
40
60
Time [μs]
80
100
(b) Seawater
Fig. 2-4-1 Typical waveforms of voltage and current at the discharge electrode, Vd and Id
26
8
Vd
Id
15
6
10
4
5
2
0
Current at discharge electrode, Id [A]
Voltage at discharge electrode, Vd [kV]
20
0
0
5
10
Time [μs]
15
20
(a) Tap water
120
Vd
10
100
Id
8
80
6
60
4
40
2
20
0
Current at discharge electrode, Id [A]
Voltage at discharge electrode, Vd [kV]
12
0
0
5
10
Time [μs]
15
20
(b) Seawater
Fig. 2-4-2 Typical waveforms of voltage and current at the discharge electrode, Vd and Id
(shorter time scale)
27
Table 2-1 Averaged values of Vd-peak and Id-peak
Vd-peak [kV]
Id-peak [A]
tap water
19.5
5.8
seawater
10.5
98.9
Water surface
Water surface
7 mm
100 mm
(a) Tap water
(b) Seawater
Fig. 2-5 Discharge profile on water surface
28
Water
Water surface
Air
Discharge
electrode
Discharge
electrode
1000
100
Vd
Id
Z=Vd/Id
15
10
10
1
5
Z [kΩ]
Vd [kV], Id [A]
20
0.1
0
0.01
0
1
2
3
Time [μs]
4
5
(a) Tap water
1000
Vd
Id
Z=Vd/Id
80
100
60
10
40
1
20
0.1
0
0.01
0
1
2
3
Time [μs]
4
(b) Seawater
Fig. 2-6 Impedance Z (= Vd/Id) of the discharge system
29
5
Z [kΩ]
Vd×10 [kV], Id [A]
100
Fig. 2-7 shows the typical discharge current waveform at the grounding electrodes, Igi (i = 1,2,3, …,
10) for (a) tap water and (b) seawater. These grounding current waveforms show similar wave shape
to the discharge current waveform, Id.
The discharge current distribution to the grounding electrodes, in current density [A/m2] is shown
in Fig. 2-8, where the values of current [A] were obtained from the peak value of Igi. From the figure,
it can be seen that the current distribution was dependent to the electrode distance from the local
discharge point, d. The d for each electrode is shown at the top of the figure. As the water reservoir is
a square-shape with the same height and width, there are two electrodes that are sharing the each d.
As a result, almost the same current distribution pattern can be observed between electrodes 1 - 5
and electrodes 6 - 10. However, there are electrodes that show difference in the current density even
with the same d, where current density of electrode 4 and 5 are lower than that of 7 and 6.
The maximum current density was observed in electrode 10 for tap water, and electrode 1 for
seawater. To discuss this, the current distribution to the grounding electrode is normalized to the
Id-peak ( = the sum of the 9 grounding electrodes’ current), shown in Fig. 2-9 as Igi-N. Here, Igi-N = (Igi/
Id-peak)×100. From the figure, it can be seen that the normalized current of seawater are generally
higher than that of tap water. However, this pattern inverted as it is getting nearer to the water
surface as can be seen at electrode 9 and 10. This is thought to be as an effect of the filamentary
discharge as shown in Fig. 2-5, where half of the surface length was covered by the filamentary
discharge. Moreover, there might also be discharge propagation that is not visible with bare eyes and
could not be captured by the digital camera. On the other hand, as no filamentary discharge was
observed on seawater surface, the discharge current is less distributed to the water surface compared
to underwater especially to electrode 1.
From these observations, it can be concluded that the current distribution to underwater is
depending on the distance, but the existence of filamentary discharge on the water surface is
affecting the distribution.
Fig. 2-10 shows the charge density at each grounding electrodes, obtained from the same current
waveforms, where q = (∑ 𝑖i ) × ∆𝑡. The charge density at the grounding electrodes show almost the
same distribution pattern to the current density, except for electrodes that are situated at the corner of
the water reservoir (electrode 4 and 5) in the case of tap water. Unlike other electrodes that showed
almost one order of difference to seawater, the charge density of these two electrodes showed almost
the same density to seawater. This might be caused by the residual charge on the surface of
electrodes.
It is expected that residual charge are more likely to be accumulated at these electrodes due to the
location and the existence of nearby electrode. This was confirmed by the current waveforms of the
concerned electrodes. The current waveforms at these electrodes showed jagged (spiky) appearance
30
compared to other electrodes. In contrast to that, the current waveforms of electrode 1 and 10
showed clean appearance. The regularity of jagged appearance on waveforms increased as the
distance to the corner decrease. On the other hand, the current waveforms of seawater showed clean
appearance for all electrodes. The high σ of water had probably prevented the accumulation of
residual charge. The slight difference between the current distribution pattern of tap water and
seawater at these electrodes is expected to be related to this matter.
31
Current at grounding electrode, Igi [A]
1.0
Ig1
Ig2
0.8
Ig3
Ig4
0.6
Ig5
Ig6
0.4
Ig7
Ig8
0.2
Ig9
Ig10
0.0
0
5
10
Time [μs]
15
20
(a) Tap water
Current at grounding electrode, Igi [A]
16
Ig1
14
Ig2
12
Ig3
10
Ig4
Ig5
8
Ig6
6
Ig7
4
Ig8
Ig9
2
Ig10
0
0
5
10
Time [μs]
15
20
(b) Seawater
Fig. 2-7 Typical waveforms of current at the grounding electrodes, Igi
32
Electrode distance, d [m]
0.20 0.21 0.22 0.24 0.27 0.27 0.24 0.22 0.21 0.20
Current density, igi[A/m2]
100000
10000
1000
100
10
Tapwater
Seawater
1
1
2
3
4
5
6
7
8
Grounding electrode number
9
10
Fig. 2-8 Current distribution at the grounding electrodes
Normalized current, Igi-N [%]
20
15
10
5
Tapwater
Seawater
0
1
2
3
4
5
6
7
8
9
10
Fig. 2-9 Current distribution normalized to the Id-peak
Charge density, qi [μC/m2]
1000
100
10
Tapwater
Seawater
1
1
2
3
4
5
6
7
8
9
10
Fig. 2-10 Charge distribution at the grounding electrodes
33
Fig. 2-11 (a) and (b) show the typical waveforms of electric potential on water surface (y = 0 mm),
Vw (x, 0) for tap water and seawater. The typical waveforms for electric potential on y-axis (x = 0
mm), Vw (0, y) are shown in the next Fig. 2-12 (a) and (b). The Vw (x, 0) for tap water showed a
gradual transition from Vd-like waveform to Id-like waveform, where the waveform for x closer to
the local discharge point showed stronger similarity to the Vd waveform. On the other hand, Vw (0,
y) had shown less Vd-like waveform, where only waveform for y = 0 mm had shown Vd-like
waveform. This variety in waveform was considered as an effect of filamentary discharge on water
surface, from the observation that the Vd-like waveforms were only observed at where filamentary
discharge was observed. For seawater, most of both Vw (x, 0) and Vw (0, y) had shown similar
waveform to Id, coherent to the absence on filamentary discharge on seawater surface.
The time for the maximum potentials for tap water were different to the time of Vd-peak, and
increased as it is getting further from the local discharge point ( x = y = 0 mm). The time for the
maximum potentials are shown in Fig. 2-13. The propagation velocity of the potential for tap water
obtained from this maximum time is approximately in the order of 104 m/s for both water surface
potential and y-axis potential. This is similar to the propagation velocity of local discharge on the
electrolyte surface [2-13, 2-14]. For seawater, the propagation velocity of the discharge is high due
to the high σ, as there was no significant delay in the maximum potential as the distance from the
local discharge point increase.
From the electric potential at the local discharge point V0mm, the voltage drop at the air gap Vdrop
was obtained, where Vdrop = Vd-peak-Vw (0, 0).The Vdrop values are 0.6 kV for tap water and 5.6 kV for
seawater. This is equivalent to less than 10 % and more than 50 % of the Vd-peak for tap water and
seawater respectively. For tap water, this suggests that most of the voltage drop occurred at the water
phase. For seawater, most of the voltage drop at the air phase, suggesting a low voltage drop at the
water phase.
Fig. 2-14 shows the electric potential distribution, Vw (x, y) in tap water; where (a) is the potential
as a function of x and (b) is the potential as a function of y. From these two figures, two patterns on
potential distribution can be seen. This different distribution pattern is explained by the presence of
the filamentary discharge on the water surface, as shown in Fig. 2-5. The potential as a function of x
(Fig. 2-14(a)) with y = 0 mm is the potential distribution on water surface. The potential decreased as
the depth, y increase; with a large decrease can be seen between y = 0 mm and y = -30 mm. This is
especially prominent in the area between x = 0 mm to x = 100 mm, which is coherent to the
filamentary discharge length observed. However, this effect of filamentary discharge on the potential
seems to decrease as it is getting deeper (i.e. as y increase). Therefore, the filamentary discharge
effect on the electrodes at its’ bottom was not observed. This is confirmed from the prominent
decrease of current density from electrode 1 to electrode 3 as in Fig. 2-8. In the area where x > 100
34
mm, the surface potential ( y = 0 mm ) showed a slight difference to other y. This difference should
explain the increase of current distribution at electrode 10.
The Vw (x, y) for seawater are shown in Fig. 2-15. From this figures, a sudden drop of the electric
potential can be seen at x = 30 mm in (a) and y = -30 mm in (b), before a constant electric potential.
This is coherent to the discharge on water surface where no filamentary discharge was observed. The
same pattern of potential distribution between (a) and (b) confirms the relation between the
filamentary discharge and the potential distribution.
From the results, the current density, i is governed by i = σE which is a variant of the Ohm’s law.
The current density observed in the experiment is proportional to the conductivity σ, with a little
inconsistency in the order of magnitude. From this, the significance of the electric field E to the
current density can be seen. From the electric potential distribution above, it can be seen that the
potential gradient (or the electric field E as in the equation) is did not show large difference between
tap water and seawater at the local discharge point (x = y = 0 mm). However, at other points which
are in the vicinity of it, the difference of potential gradient can be seen between tap water and
seawater. These translate to the difference in the current distribution between tap water and saline
seawater, as can be seen in section 2.3.2.
35
tV-max
20
x [mm]
Potential, Vw (x, 0) [kV]
0
15
30
60
10
90
120
5
150
180
0
0
5
10
Time [μs]
15
20
(a) Tap water
tV-max
6
x [mm]
0
Potential, Vw (x, 0) [kV]
5
30
4
60
3
90
120
2
150
1
180
0
0
5
10
Time [μs]
15
20
(b) Seawater
Fig. 2-11 Typical waveforms of electric potential on water surface, Vw (x, 0)
36
tV-max
20
-y [mm]
Potential, Vw (0, y) [kV]
0
15
30
60
10
90
120
5
150
180
0
0
5
10
Time [μs]
15
20
(a) Tap water
tV-max
6
-y [mm]
0
Potential, Vw (0, y) [kV]
5
30
4
60
3
90
120
2
150
1
180
0
0
5
10
Time [μs]
15
20
(b) Seawater
Fig. 2-12 Typical waveforms of electric potential on y-axis, Vw (0, y)
37
14
Time for maximum potential, tV-max [μs]
Tap water
12
Seawater
10
8
6
4
2
Tap water
12
Seawater
10
8
6
4
2
0
0
0
30
60
90
x [mm]
120
150
0
180
30
60
(a) Water surface
90
120
-y [mm]
150
180
(b) y-axis
Fig. 2-13 Time for maximum electric potential on water surface and y-axis
20
16
30
14
60
12
90
10
120
8
150
6
x [mm]
18
0
Potential, Vw (x, y) [kV]
20
-y [mm]
18
180
0
16
30
14
60
12
90
10
120
8
150
6
4
4
2
2
180
0
0
0
50
100
x [mm]
150
0
200
(a) Potential as a function of x
50
100
-y [mm]
150
200
(b) Potential as a function of y
Fig. 2-14 Electric potential distribution in tap water
6
6
-y [mm]
x [mm]
0
5
4
60
90
3
120
150
2
0
5
30
Time for maximum potential, tV-max [μs]
14
180
1
30
4
60
90
3
120
150
2
180
1
0
0
0
50
100
x [mm]
150
200
0
(a) Potential as a function of x
50
100
-y [mm]
150
(b) Potential as a function of y
Fig. 2-15 Electric potential distribution in seawater
38
200
2.4 Summary
In this chapter, the electrical characteristics during the spark discharge on water surface of a
1-dimensional two-phase gas-liquid system with a square-shaped water reservoir were observed. A
water reservoir with the same vertical and horizontal length was employed, where 10 underwater
grounding electrodes were installed. The experiments were done with tap water; and saline solution
with the same conductivity to seawater.
The breakdown process had showed different characteristics between tap water and seawater.
Higher spark voltage was observed for discharge on tap water compared to seawater. The voltage
waveforms were also different between the two conductivities. A gradual voltage decrease was
observed during discharge on tap water, while the discharge on seawater had shown a drastic
decrease of voltage. Voltage drop at the air gap also had shown a notable difference between tap
water and seawater. Significant difference also can be seen in the current waveform of seawater,
where two-peaks of current was observed, suggesting the difference velocity between electron
current and ion current during the discharge. This was not observed during discharge on tap water.
Filamentary discharge sprouting on water surface was observed during discharge on tap water.
During the discharge on seawater, the discharge only localized at the local discharge point. This
filamentary discharge was remarked to affect the discharge current distribution to the grounding
electrodes, besides the distance from the local discharge point. The current density was observed to
decrease with the increase in distance. The effect of filamentary discharge on the current was mostly
prominent at the water surface. In the case of seawater where no filamentary discharge was observed,
the current is less distributed to the water surface but more to underwater. The electric potential
distribution also had shown a dependency to the filamentary discharge.
The geometry and layout of the electrode system of this 1D model had promote the accumulation of
residual charge at the grounding electrodes located at the corner of the water reservoir, particularly
during discharge on tap water. This can be seen from the charge distribution of tap water which at
some electrodes had shown almost the same values to seawater, and was confirmed from the current
waveforms of the grounding electrodes.
39
References
[2-1]
M. Kinsler, “A Damage Mechanism : Lightning-Initiated Fault-Current Area to
Communication Cables Buried Beneath Overhead Electric Power Lines”, 1998 IEEE
Industrial and Commercial Power Systems Technical Conf., pp. 109-118, 1998.
[2-2]
G. Dzhokic, J. Jovchevska, A. Dika, “Electrical Injuries : Etiology, Pathophysiology and
Mechanism of Injury”, Macedonian Journal of Medical Sciences, vol. 1, no. 2, pp. 54-58,
2008.
[2-3]
V.P. Belosheev, “Study of the Leader of a Spark Discharge over a Water Surface”, Tech.
Phys., vol. 43, no. 7, pp. 783-789, 1998.
[2-4]
A.F. Aleksandrov, D.N. Vaulin, A.P. Ershow, V.A. Chernikov, “Stages of an Electric
Discharge Gliding on a Water Surface”, Moscow University Physics Bulletin, vol. 64, no. 1,
pp. 100-102, 2009.
[2-5]
Y. Nakao, H. Itoh, Y. Sakai, H. Tagashira, “Studies of the Creepage Discharge on the
Surface of Liquids”, IEEE Trans. Electr. Insul., vol. 23, no. 4, pp. 677-687, 1988.
[2-6]
H. Matsuo, T. Fujishima, T. Yamashita, “Propagation Velocity and Photoemission Intensity
of a Local Discharge on an Electrolytic Surface”, IEEE Trans. Dielectr. Electr. Insul., vol.
3, no. 3, pp. 444-449, 1996.
[2-7]
10, no. 4, pp. 634-640, 2003.
[2-8]
T. Takahashi, “Surface Discharge on Electrolyte Solution”, J. IEIE Jpn., vol. 24, no.1, pp.
67-72, 2004. (in Japanese)
[2-9]
N.S. Midi, R. Ohyama , “Discharge Current Distribution to Underwater due to Spark
Discharge on Water Surface of a 1D Model”, MJIIT-JUC Joint International Symposium
2014, 1E1-ESE-2, pp. 1-4, 2014.
[2-10]
M. Abdel-Salam : “Electrical Breakdown of Gases,” in High-Voltage Engineering : Theory
and Practice, M. Khalifa, Ed. , New York, United States of America, Marcel Dekker Inc,
1990, ch. 4, pp. 94-96.
[2-11]
M. Higashiyama, H. Suzuki, T. Hirose, T. Maeda, S. Nakamura, T. Umemura, M. Kozako,
M. Hikita, “Insulation Behavior of Small-air-gap for the Molded-Insulation System (2) –
Partial Discharge Behavior of MGM and MGI Systems,” IEEJ Trans. Power and Energy,
vol. 133, no. 2, pp. 203-209, 2013.
[2-12]
M. Laroussi, I. Alexeff, J.P. Richardson, and F.F. Dyer, “The Resistive Barrier Discharge,”
IEEE Trans. Plasma Sci., vol. 30, no. 1, pp. 158-159, 2002.
[2-13]
T. Yamashita, H. Matsuo, and H. Fujiyama, “Relationship between Photo-Emission and
Propagation Velocity of Local Discharge on Electrolytic Surfaces”, IEEE Trans. Electr.
40
Insul., EI-22, 6, 811–817, 1987.
[2-14]
H.M. Jones and E.E. Kunhardt, “The Influence of Pressure and Conductivity on the Pulsed
Breakdown of Water”, IEEE Trans. Dielectr. Electr. Insul., 1, 6, 1016–1025, 1994.
41
Chapter 3
Effect of Water Conductivity to the Electrical Discharge on Water
Surface using a 2D Experimental Model
3.1 Introduction
In previous chapter, the spark discharge on water surface of a 1-dimensional (1D) model was
investigated as a laboratory observation of lightning discharge on water surface. Two type of water
which are tap water and saline solution with conductivity, σ of 0.07 S/m and 5.0 S/m respectively
were investigated, where distinctive characteristics of discharge and conduction were observed
between the two σ. The 5.0 S/m value is the generally known σ of seawater, which is approximately
equivalent to 35g/kg of total dissolved solids (TDS) or 35 parts per million (ppm) in salinity, mainly
consisted of Na and Cl [3-1].
However, a map of ocean’s surface salinity released by National Aeronautics and Space
Administration (NASA) had reported that the salinity diverse between 30 ppt to 40 ppt, which means
a diversity of the σ. Besides seawater, difference in salinity and σ can also be seen in other surface
water such as rivers and lakes (fresh water and saline), with different type and quantity of dissolved
solids [3-1]. As the sea, these water areas are also expected to be exposed to the risk of lightning.
Thus, it is important to look into the effect of water properties on the discharge characteristics as
the lighting on various water environments should be considered. Besides that, it is also important to
consider discharge propagation in a wide area.
In this chapter, the effect of water conductivity, σ to the spark discharge on water surface was
investigated using a 2-dimensional (2D) two-phase gas-liquid model [3-2]. The σ was set as the
parameter instead of the salinity as the σ determines the electric field reaction with water. This 2D
model is an electrode system with a cylindrical water reservoir, where the discharge electrode was
installed at the center of the water surface, providing an unrestricted propagation area. As the 1D
model, the lightning was imitated by an impulse discharge, and the underwater grounding electrode
was divided into several channels covering the underwater area and water surface.
The organization of this chapter as in the following sequence. Firstly, the objective of this chapter is
stated in section 3.1 as above. The experimental setup and procedures are explained in section 3.2. In
this section, the specification of the 1D model will be explained in detail along with the experimental
procedures and parameters. In section 3.3, the results of the experiments are presented. The results
will be discussed by focusing on the effect of σ to the electrical characteristics. Finally, the
concluding remark of this work is stated in section 3.4.
42
Fig. 3-1 shows the electrode’s configuration of the 2D model, where (a) is the aerial view and (b) is
the cross sectional diagram. The discharge electrode was the same discharge electrode used in 1D
model, a stainless steel electrode with 12 mm diameter and 45° tip angle. It was placed 5 mm from
the water surface; connected to the power source to generate the spark discharge on water surface.
The water reservoir was a water tub made of vinyl chloride with largest diameter of 750 mm.
There were 9 grounding electrodes for this electrode system numbered in an anti-clockwise order as
i, where i = 1, 2, …, 9. Electrodes 1 to 6 were aligned parallel to the water surface at a depth of 130
mm on an acrylic sheet. Electrode 1 was a circular copper plate (thickness: 1 mm; diameter: 40 mm),
while electrodes 2 to 6 were ring-shaped copper plates of the same thickness to electrode 1, and their
outer radius was 40 mm greater than their inner radius. On the other hand, electrodes 7 to 9 were
copper tape (thickness: 0.1 mm; width: 40 mm) attached to the inner surface of the water tub,
perpendicular to the water surface. Electrode 9 was placed on the water surface with 20 mm of its
width submerged beneath underwater. There were distances of 15 mm between each adjacent
electrode. All the grounding electrodes were attached to conductive wires connected to the ground.
Fig. 3-2 shows the experimental setup for the investigation of spark discharge on water surface
using 2D model. The composition of this experimental setup is almost similar to the experimental
setup using the 1D model.
The discharge electrode was installed with 5 mm air gap from the water surface and was connected
to the 400 kV impulse voltage generator (Tokyo Transformer).The spark discharge on water surface
was generated by applying 25 kV of standard lightning impulse voltage (1.2/50μs) to the discharge
electrode, and was recorded using an oscilloscope (Tektronix, TDS5054B) though a resistance
divider with voltage dividing ratio of 39881 : 1. Current at the discharge electrode was observed
using a current probe (Pearson, 6585) connected to the oscilloscope. The same combination was
employed to observe the current distribution to the 9 channel grounding electrodes.
For the electric potential measurement, the same probe as in Fig. 2-2 was used, placed
perpendicular to the water surface. The measurement was done in a 20 mm interval starting from r =
0 mm to r = 320 mm, at z = 0 mm.The experiment was done with tap water and saline solutions of
different σ varied by dissolving table salt into tap water. The σ for tap water was 0.07 S/m. For saline
solutions, the σ were 0.2 S/m, 0.5 S/m, 1.0 S/m, 2.5 S/m, 5.0 S/m and 10.0 S/m. The σ were
measured using a conductivity meter (Horiba, ES-51).
43
Copper grounding
electrode
Water
surface
Discharge electrode
Plastic water reservoir
(a) Aerial view
Discharge
electrode, Ø 12
z
5
20
r
9
15
40
8
130 mm
40 15
1
2
3
4
5
6 7
Copper grounding
electrode
Acrylic
sheet
Plastic water reservoir
(b) Cross-sectional diagram
Fig. 3-1 Electrode’s configuration of 2D model (not to scale)
44
Oscilloscope
Vd
400 kV impulse
voltage generator
Voltage divider
1000 : 1
Id
Vw (r, z)
Igi
Measurement
probe
Digital
camera
Fig. 3-2 Experimental setup
45
Current
probe
Fig. 3-3 shows the typical discharge emission profiles during the discharge on water surface of
different σ. For low σ (Fig. 3-3 (a) ~ (d)), it can be seen that the spark discharge at the air gap
propagates into filamentary discharge sprouting radially on the water surface, originating from the
local discharge point (r = z = 0mm). This is considered to be due to the effect of resistive barrier
discharge [3-3], where the distributed resistance of water prevents the localization of discharge. The
lengths of these filamentary discharges were observed to decrease with the increase in σ. This
decrease in length shows the characteristics of an incomplete discharge on water surface [3-4, 3-5],
and can also be observed during pulsed corona discharge on water surface with an immersed ground
electrode [3-6]. However, this decrease in length had shown a drastic decrease between tap water
(Fig. 3-3 (a)) saline solution of 0.2 S/m (Fig. 3-3 (b)), which is only a small increase in σ. The
filamentary length on water surface was observed to be approximately 100 mm for tap water (0.07
S/m), and 35 mm for 0.2 S/m. During the discharge on water with high σ (Fig. 3-3 (e) ~ (g)), less or
almost no filamentary discharge was observed, where the discharge was observed to only localizing
at the local discharge point. Fig. 3-4 shows the maximum extend length (due to the long exposure) of
these discharges on water surface as a function of σ. This figure suggests an adequate inverse power
law correlation between the maximum extend length and σ.
Fig. 3-5 shows the typical waveforms of voltage and current at the discharge electrode, Vd and Id
for the spark discharge on water surface of water with σ in the range between 0.07 S/m and 10.0 S/m,
with the correspondence impedance Z (=Vd/Id). Similar waveforms to 1D model were observed
during the discharge on tap water (Fig. 3-5 (a)) and seawater (Fig. 3-5 (f)). The Vd for tap water is
similar to the standard lightning impulse voltage waveform, where a gradual decrease can be
observed which is also seen in the Id waveform. For seawater, a sudden drop in Vd after reaching the
Vd-peak (spark voltage) value; and second peak in Id due to velocity difference of electron and positive
ion can be seen. From these figures, it can be seen that the waveforms can be generally classified
into two categories which are tap water and saline solutions, where almost similar waveforms can be
observed in all saline solutions despite the difference in σ. This similarity can be seen in the sudden
drop of Vd after reaching the spark voltage and the second peak in Id observed in the waveforms of
all saline solutions. However, the decrease percentage of Vd after reaching Vd-peak is be seen to be
increased as the σ increase. In higher σ, the voltage decrease to almost 100 % of the peak value,
which were not observed in saline solutions with lower σ. The impedance Z (after the spark
discharge which is represented by the peak in Vd) showed one order of decrease from tap water to
0.02 S/m saline solution. This relatively large decrease explained the significant decrease of
filamentary discharge length on the water surface. As the σ increased, lower Z was observed
46
resulting to no filamentary discharge observed during the discharge of saline solution with σ of 5
S/m and above.
The values of Vd-peak and Id-peak as a function of σ are shown in Fig. 3-6. As the σ increase, the
Vd-peak decreases while the Id-peak increases. Both of Vd-peak and Id-peak showed a tendency to saturate at
high σ region. Besides that, a significant difference of these values can be seen with a small increase
in σ between tap water and seawater, as can be seen in the discharge emission profiles.
From these observations, it can be concluded that the discharge emission on water surface is
associated with the voltage and current waveforms. During spark discharge on water surface with
low σ, Vd waveform with a low voltage-drop was observed, and the Id was limited due to the high
impedance. This limitation of Id resulted to the filamentary discharge propagating on the water
surface. On the other hand, during discharge of high σ, a high voltage-drop was observed in Vd with
highly induced Id. The relatively high σ of water produced a small propagation of filamentary
discharge on the water surface. In addition, the equivalent impedance for 0.07 S/m is higher than
other σ used in this work, with notable difference between 0.07 S/m, and 0.2 S/m and above;
appropriate to the changes of voltage and current, and as can be seen from the impedance Z obtained
from the Vd and Id waveforms.
47
discharge
electrode
discharge
electrode
40mm
50mm
(a) 0.07 S/m
(b) 0.2 S/m
discharge
electrode
discharge
electrode
40mm
20mm
(c) 0.5 S/m
(d) 1.0 S/m
discharge
electrode
discharge
electrode
20mm
20mm
(e) 2.5 S/m
(f) 5.0 S/m
discharge
electrode
20mm
(g) 10.0 S/m
Fig. 3-3 Typical discharge emission profiles on water surface
48
Averaged length of filamentary discharge, l [mm]
1000
100
10
1
0.01
0.1
1
Conductivity,σ [S/m]
10
Fig. 3-4 Averaged filamentary discharge length, l as a function of σ
49
60
1000
Vd
50
Id
100
Vd×2 [kV], Id [A]
Z
40
Z [kΩ]
10
30
1
20
0.1
10
0
0.01
0
1
2
3
4
5
Time [μs]
(a) 0.07 S/m
200
200
1000
1000
Vd
Vd
Id
1
50
Z [kΩ]
10
100
0.1
0
3
4
1
50
0.1
0.01
0
5
1
2
3
4
Time [μs]
Time [μs]
(b) 0.2 S/m
(c) 0.5 S/m
200
1000
200
1000
Vd
Vd
Id
100
10
100
1
50
Z [kΩ]
Z
Vd×10 [kV], Id [A]
Vd×10 [kV], Id [A]
Id
150
0.1
0
0.01
0
1
2
3
4
150
10
100
1
50
0.1
0
5
0.01
0
1
2
3
4
(e) 2.5 S/m
200
1000
200
1000
Vd
Vd
Id
100
10
100
1
50
Z [kΩ]
Z
Vd×10 [kV], Id [A]
Vd×10 [kV], Id [A]
Id
150
0.1
0
0.01
2
5
Time [μs]
(d) 1.0 S/m
1
100
Z
Time [μs]
0
5
Z [kΩ]
2
10
100
3
4
150
100
Z
10
100
1
50
0.1
0
5
0.01
0
Time [μs]
Z [kΩ]
1
100
Z
0
0.01
0
150
Z [kΩ]
100
Z
Vd×10 [kV], Id [A]
Vd×10 [kV], Id [A]
Id
150
1
2
3
4
5
Time [μs]
(f) 5.0 S/m
(g) 10.0 S/m
Fig. 3-5 Typical waveforms of voltage and current at the discharge electrode, Vd and Id for water
with different σ; with the correspondent impedance Z
50
200
20
160
15
120
10
80
Vd-peak
Vd
5
40
IdId-peak
0
0.01
0
0.1
1
Conductivity [S/m]
Fig. 3-6 Vd-peak and Id-peak as a function of σ
51
10
Current at discharge electrode, Id-peak
[A peak]
Voltage at discharge electrode, Vd-peak [kV
peak]
25
Fig. 3-7 shows the typical discharge current waveforms at the grounding electrodes Igi (i = 1, 2, 3,
… 9) for water with different σ. As the Vd and Id, a significant difference can be seen between tap
water and saline solutions even with a small increase in σ. The current distribution to the grounding
electrodes in current density, igi [A/m2] is shown in Fig. 3-8, where the current [A] values were
obtained from the peak value of Igi. The unequal scale at the upper part of the figure is the
r-coordinate for each grounding electrodes. The significant difference between tap water and saline
solution with small σ increase can also be observed from this figure.
Generally, the current distribution in this 2D model is depending to the distance of grounding
electrode from the local discharge point, which was also observed in 1D model. The current density
decrease as it is getting further from the local discharge point (expressed as r in the figure), which
can be seen in electrode 1 to 5. However, the current density increased from electrode 6 to 9 despite
the increase in r. This is assumed to be as an effect of current at the water surface, considering that
the electrodes are nearing the water surface, compared to the other horizontal electrodes. As the σ
increased, different characteristics between horizontal electrodes and vertical electrodes can be seen.
The current density showed a small difference between all the σ at electrodes 2 to 5. This was not
observed in other electrodes (electrode 1, electrode 6 to 9), where the increase in current density can
be seen as σ increase. This is thought to be caused by the filamentary discharge on the surface of tap
water.
To discuss the effect of filamentary discharge, the current distribution is expressed as normalized
current divided by the electrodes’ area Ai as shown in Fig. 3-9, where iN = (Igi/Itotal)/Ai. From this
figure, it can be seen that iN for tap water (σ = 0.07 S/m) at electrodes 2 to 5 are highest compared to
other σ. This is seen as the effect of filamentary discharge on the water surface, considering the 100
mm of averaged filamentary discharge length observed (Fig. 3-3 (a)), which is approximately same
to the r of electrode 3. As the σ increase, iN at these electrode decreased which can be explained by
the decrease in the filamentary discharge length. This was also observed during local discharge on
the surface of electrolytic solution with low water depth; which the relative current was observed
high at where the local discharge is in contact with the surface, especially at the tip of the discharge
[3-7, 3-8]. On the other hand, the opposite characteristic was observed for electrode 1, where iN
increased with the increase in σ. From this, it can be assumed that the filamentary discharge did not
affect the current distribution to the direct underneath of the local discharge point. At electrodes
other than that (electrodes 6 to 9), the iN increased as σ increase; seen as the general effect of the σ
on current magnitude.
In this model, the effect of filamentary discharge can be observed in the grounding electrodes
situated at the bottom of it. This was not observed during the discharge on 1D model. This is
considered to be cause by the different water depth of the two models, where the water was deeper in
52
1D model compared to 2D model. Furthermore, the effect of filamentary discharge on the current
distribution to grounding electrode at water surface which was observed in 1D model was not seen in
this 2D model. This is considered to be caused by the longer r (of 2D model) compared to x (of 1D
model).
From these observations, it can be concluded that the current distribution to underwater is
depending on the distance from the local discharge point, where the existence of filamentary
discharge on water surface is also affecting the distribution. However, this effect of filamentary
discharge is also influenced by the distance from the discharge.
53
Current at discharge electrode, Igi [A]
15
Ig1
Ig2
10
Ig3
Ig4
5
Ig5
Ig6
Ig7
0
Ig8
Ig9
-5
0
5
10
Time [μs]
15
20
(a) 0.07 S/m
30
30
Ig1
25
Ig2
20
Ig3
15
Ig4
Ig5
10
Ig6
5
Ig7
0
Ig8
Ig9
-5
Ig1
25
Ig2
20
Ig3
15
Ig4
Ig5
10
Ig6
5
Ig7
0
Ig8
Ig9
-5
0
5
10
Time [μs]
15
20
0
5
(b) 0.2 S/m
20
30
15
(c) 0.5 S/m
30
Ig1
25
Ig2
20
Ig3
15
Ig4
Ig5
10
Ig6
5
Ig7
0
Ig8
Ig9
-5
Ig1
25
Ig2
20
Ig3
15
Ig4
Ig5
10
Ig6
5
Ig7
0
Ig8
Ig9
-5
0
5
10
Time [μs]
15
20
0
5
(d) 1.0 S/m
10
Time [μs]
15
20
(e) 2.5 S/m
30
30
10
Time [μs]
Ig1
25
Ig2
20
Ig3
15
Ig4
Ig5
10
Ig6
5
Ig7
0
Ig8
Ig9
-5
Ig1
25
Ig2
20
Ig3
15
Ig4
Ig5
10
Ig6
5
Ig7
0
Ig8
Ig9
-5
0
5
10
Time [μs]
15
20
0
(f) 5.0 S/m
5
10
Time [μs]
15
20
(g) 10.0 S/m
Fig. 3-7 Typical waveforms of current at the grounding electrodes, Igi for water with different σ
54
unequal scale
0
55
110
165
220
275
315
306
325
r [mm]
Current density, igi [A/m2]
100000
0.07 S/m
0.5 S/m
2.5 S/m
10.0 S/m
10000
0.2 S/m
1.0 S/m
5.0 S/m
1000
100
10
1
1
2
3
4
5
6
7
8
9
Fig. 3-8 Current distribution to the discharge electrodes
Normalized current density, igi-N
100
0.07 S/m
0.5 S/m
2.5 S/m
10.0 S/m
0.2 S/m
1.0 S/m
5.0 S/m
10
1
0
1
2
3
4
5
6
7
8
9
Fig. 3-9 Normalized current at the discharge electrodes divided by the electrodes’ area, igi-N
55
Fig. 3-10 shows the typical waveforms of electric potential on water surface, Vw (r, 0). As observed
in 1D model, the Vw (r, 0) for tap water showed a transition from Vd-like waveforms to Id-like
waveform. On the other hand, all of Vw (r, 0) for seawater showed Id-like waveforms, even with the
appearance filamentary discharge.
As already observed and discussed in the 1D model, there is time lag in the time for the maximum
potentials, tV-max of tap water as it is getting further from the local discharge point (r = z = 0 mm).
The tV-max of saline solutions did not show any lag even with the increase in σ. The tV-max for all σ is
shown in Fig. 3-11. From the figure, it can be seen that tV-max for tap water increased with the
increase of r to about r = 100 mm, which is consistent to the length of filamentary discharge
observed. From this, the propagation velocity of the surface discharge in this range of r is
approximately in the order of 104 m/s, which is similar to the order of propagation velocity of local
discharge on the surface of electrolyte [3-9, 3-10]. This is also as the same as the velocity observed
in 1D model. For saline solutions, the tV-max did not showed any significant delay with the increase in
r for all σ. It is considered that the propagation velocity of the discharge on the surface of saline
solutions is high due to the high σ.
Fig. 3-12 shows the electric potential distribution on water surface, which is the maximum of Vw (r,
0) immediately after the commencement of discharge as a function of r. Unlike the waveforms, the
significant difference between tap water and saline solutions can be observed unambiguously. This
measurement result of Vw (r, 0) is seen to qualitatively agree with the changes of filamentary
discharge on water surface. For 0.07 S/m, Vw (r, 0) decrease gradually as r increased to 100 mm,
consistent to the filamentary discharge length observed. For higher σ where almost no filamentary
discharge was observed, the Vw (r, 0) showed a sudden decrease between r = 0 mm and other r
positions. A prominent difference in the magnitude of Vw (r, 0) can be seen between 0.07 S/m and
0.2 S/m. However, for saline solutions which filamentary discharge was observed (lower σ), the
decrease of Vw (r, 0) had shown the similar pattern to 0.07 S/m, which is consistent with the
filamentary discharge length ranging from 15 to 35 mm.
Fig. 3-13 shows the potential at r = z = 0 mm, Vw (0, 0) and voltage drop at the air gap, Vdrop-air;
normalized to the Vd-peak. The Vdrop-air is given by Vdrop-air = Vd-peak–Vw (0, 0). From the figure, it can
be seen that Vw (0, 0) decrease with the increase in σ and showed a tendency to saturate at higher σ.
This is consistent with the Vd-peak as shown in Fig. 3-6. On the other hand, Vdrop-air increased as σ
increase; where the tendency of saturation can also be observed. For low σ, the low Vdrop-air suggest
that the voltage drop occur at both the air and water phase, leading to the filamentary discharge on
water surface. On the other hand, the high Vdrop-air of during higher σ suggests that most of voltage
drop occurred at the air phase, suggesting a good conductance of water preventing the filamentary
discharge from occurring.
56
tV-max
r [mm]
0
16
20
Potential, Vw(r, 0) [kV]
18
14
40
12
60
10
80
8
100
6
120
4
180
2
240
0
300
-2
0
5
10
Time [μs]
15
20
(a) 0.07 S/m
tV-max
20
5
40
4
60
3
80
100
2
120
1
180
0
240
300
-1
0
5
10
Time [μs]
15
r [mm]
0
6
tV-max
r [mm]
0
6
20
5
40
4
60
3
80
100
2
120
1
180
0
240
300
-1
20
0
5
(b) 0.2 S/m
15
20
(c) 0.5 S/m
tV-max
tV-max
r [mm]
0
6
r [mm]
0
2
20
20
5
10
Time [μs]
40
4
60
3
80
100
2
120
1
180
0
240
0
5
10
Time [μs]
15
60
80
100
120
0
180
240
300
-1
40
1
300
-1
0
20
5
(d) 1.0 S/m
10
Time [μs]
15
20
(e) 2.5 S/m
tV-max
tV-max
r [mm]
0
2
r [mm]
0
2
20
20
40
60
1
80
100
120
0
180
40
60
1
80
100
120
0
180
240
240
300
-1
0
5
10
Time [μs]
15
300
-1
0
20
(f) 5.0 S/m
5
10
Time [μs]
15
(g) 10.0 S/m
Fig. 3-10 Typical waveforms of electric potential on water surface ,Vw (r, 0)
57
20
Time for maximum electric potential,
tV-max [μs]
8
7
0.07 S/m
6
0.2 S/m
5
0.5 S/m
4
1.0 S/m
3
2.5 S/m
2
5.0 S/m
1
10.0 S/m
0
0
50
100
150
200
250
300
350
r [mm]
Fig. 3-11 Time for maximum potential on water surface, tV-max
Potential on water surface, Vw (r, 0) [kV]
18
0.07 S/m
16
0.2 S/m
14
0.5 S/m
12
1.0 S/m
10
2.5 S/m
8
5.0 S/m
6
10.0 S/m
4
2
0
0
50
100
150
200
250
300
r [mm]
Fig. 3-12 Electric potential distribution on water surface, Vw (r, 0)
58
350
100
Normalized voltage [%]
Vw (0, 0)
V0mm
80
Vdrop-air
Vdrop
60
40
20
0
0.01
0.1
1
Conductivity [S/m]
10
Fig. 3-13 Vw (0, 0) and Vdrop-air as a function of σ; normalized to Vd-peak
59
3.4 Summary
In this chapter, the effect of water conductivity, σ to the electrical characteristics of spark discharge
on water surface was investigated using a 2D model, which employed a cylindrical water reservoir.
The σ was varied using tap water and saline solutions, where the saline solutions were prepared by
dissolving table salt into tap water. The σ are 0.07 S/m for tap water; and 0.2 S/m, 0.5 S/m, 1.0 S/m,
2.5 S/m, 5.0 S/m and 10.0 S/m for saline solutions.
The lengths of filamentary discharges on water surface were observed to decrease with the increase
of σ, showing the characteristics of incomplete discharge on water surface. Although filamentary
discharge was also observed during discharge on saline solutions with lower σ, the length decreased
drastically with small increase of σ compared to that of tap water. This is consistent with the
waveforms of voltage and current at the discharge electrode.
The current distribution to the grounding electrodes was observed to increase with the increase in σ.
However, the opposite characteristic was exhibited at the electrodes that were situated at the bottom
of the filamentary discharge. As this was not observed in current distribution in 1D model, it is
assumed that the effect of filamentary discharge is determined by the distance between the discharge
itself and the grounding electrodes.
The water surface potential distributions were observed to qualitatively agree with the changes of
filamentary discharge on water surface, where it decreases gradually at where the filamentary
discharge was observed. During discharge with no filamentary discharge on water surface, the
potential distribution showed a sudden decrease with the increase of distance from the local
discharge point.
In general, the results showed a significant difference between tap water and saline solution even
with a small increase of σ, where two different characteristics between the two types of water had
been observed. This especially can be seen from the waveforms of the electrical quantities, which are
the voltage and current at discharge electrode; and current at grounding electrodes. However, the
increase in σ of the saline solutions had also shown effects on the measured quantities, which then
exhibit a tendency to saturate at higher σ.
In chapter 2 where the electrical characteristics during the discharge on water surface of tap water
and seawater, two different characteristics between the two type of water was observed. In this
chapter, it was observed that the electrical characteristics showed a significant difference between
tap water and saline solutions with different conductivity. This was observed even with a small
difference in σ of tap water and saline solution with the lowest σ used. It was also observed that the
changes of the electrical quantities showed the tendency to saturate at high σ.
Besides that, summarizing the observation obtained in both 1D and 2D model, it is concluded that
the current distribution was affected by the filamentary discharge. However, this effect was
determined by the distance from the filamentary discharge itself; where in 1D model the effect was
60
seen at the water surface, and in 2D model it was observed underwater.
61
References
[3-1]
K.E. Chave, “Chemical Reactions and the Compositions of Sea Water”, J. Chem. Educ.,
vol. 48, no. 3, pp. 148-151, 1971.
[3-2]
N.S. Midi, R. Ohyama, S. Yamaguchi, “Underwater Current Distribution Induced by Spark
Discharge on a Water Surface”, J. Electrostat., vol. 71, no. 4, pp. 823-828, 2013.
[3-3]
M. Laroussi, I. Alexeff, J.P. Richardson, and F.F. Dyer, “The Resistive Barrier Discharge,”
IEEE Trans. Plasma Sci., vol. 30, no. 1, pp. 158-159, 2002.
[3-4]
A.M. Anpilov, E.M. Barkhudarov, V.A. Kop’ev, and I. A. Kossyi, “High-voltage Pulsed
Discharge along the Water Surface. Electric and Spectral Characteristics”, 28th Int. Conf.
on Phenomena in Ionized Gases, vol. 10, pp. 1030–1033, 2007.
[3-5]
P. Bruggeman, J. Liu, J. Degroote, M.G. Kong, J. Vierendeels, and C. Leys, “DC Excited
Glow Discharges in Atmospheric Pressure Air in Pin-to-Water Electrode System”, J. Phys.
D: Appl. Phys., vol. 41, pp. 1–11, 2008.
[3-6]
P. Lukes, M. Clupek, and V. Babicky, “Discharge Filamentary Patterns Produced by Pulsed
Corona Discharge at the Interface between a Water Surface and Air”, IEEE Trans. Plasma
Sci., vol. 39, no. 11, 2644-2645, 2011.
[3-7]
10, no. 4, pp. 634-640, 2003.
[3-8]
T. Yasmashita, T. Fujishima, D. Tachibana, R. Kumagai, H. Matsuo, “Electric Potential
near the Tip of a Local Discharge on an Electrolytic Solution in the Low Pressure Air”,
IEEJ Trans. PE, vol. 127, no. 1, pp. 224-228, 2007.
[3-9]
T. Yamashita, H. Matsuo, and H. Fujiyama, “Relationship between Photo-Emission and
Propagation Velocity of Local Discharge on Electrolytic Surfaces”, IEEE Trans. Electr.
Insul., vol. EI-22, no. 6, pp. 811–817, 1987.
[3-10]
H.M. Jones and E.E. Kunhardt, “The Influence of Pressure and Conductivity on the Pulsed
Breakdown of Water”, IEEE Trans. Dielectr. Electr. Insul., vol. 1, no. 6, pp. 1016–1025,
1994.
62
Chapter 4 Evaluation of Water-Phase Current Distribution by the means of
Numerical Calculation
4.1 Introduction
In the previous two chapters, lightning phenomenon on water surface was investigated by imitating
the phenomenon using a laboratory scale spark discharge on water surface, as an effort for
developing lightning protection in water areas. Two discharge models (1D model and 2D model)
were introduced, where the electrical characteristics were observed.
However, considering the small scale of these experimental models, it is beyond comparison to the
lightning phenomenon in actual natural environment; where larger scale of voltage, current and
distance are involved. To that matter, a numerical calculation is considered so that a prediction of an
equivalent scale to the natural lightning phenomenon could be made into realization.
In this chapter, evaluation of current distribution to underwater due to spark discharge on water
surface by the mean of numerical calculation was done [4-1]. Here, the current distribution is
highlighted as the injury due to lightning are mostly caused by the current flow into human bodies
due to the potential rise in distant areas, rather than the direct strike itself [4-2]. Calculation models
similar to the experimental models were used, which the input boundary condition is the quantities
obtained from the experiments. A numerical calculation using minimal input of the boundary
condition with comparable results to the experimental observations was aimed.
With the anticipation of comparable results, a guideline for future calculation of current distribution
could be established. This should be a stepping stone for a larger scale of numerical calculation of
discharge on water surface, where the current conduction due to natural lighting on water surface
might be able to be predicted. Also from this numerical calculation, the electrical quantities that were
un-obtainable from the experiments will be compensated. This includes the electric field with its
components and also the vectors of the electrical quantities.
The calculation was done using both the 1D model and 2D models. Firstly, the numerical
calculation of 1D model under stationary condition was done in order to determine the optimum
minimal input of boundary condition for the calculation. The suitable boundary condition was
decided by evaluating the potential distribution obtained, which was compared to the experimental
results. 1D model was used for this preliminary calculation considering the fewer dimensions of the
model itself and the filamentary discharge, which propagated in one direction compared to radial
direction in 2D model. From there, the calculation was done with the 2D model by employing the
obtained suitable boundary condition. This calculation was done under both stationary and
time-dependent condition; where the existence of the air phase was also considered. The calculation
was done under both conditions as the discharge is a transient phenomenon, and a stationary
calculation could be utilized as a quick spatial evaluation of the electrical properties. As a significant
63
difference was observed between tap water and saline solution, the calculation was done for tap
water and seawater only.
The organization of this chapter as in the following sequence. Firstly, the objective of this chapter is
stated in section 4.1 as above. In section 4.2, the general approach of the numerical calculation will
be stated. The numerical calculation of 1D and 2D models are presented in section 4.3 and 4.4
respectively. Finally, the concluding remark of this work is stated in section 4.5.
64
4.2 General Approach of the Numerical Calculation
4.2.1 COMSOL Multiphysics, AC/DC Module
The numerical calculation of current distribution was done using COMSOL Multiphysics’ AC/DC
module. COMSOL Multiphysics provides a simulation environment that included the possibility to
add any physical effect to the calculation model. In AC/DC Module, all modelling formulations are
based on Maxwell’s equations or subsets and special cases of these together with material laws like
Ohm’s for low charge transport. In summary, the AC/DC interfaces formulate and solve the
differential form of Maxwell’s equations together with initial boundary conditions. The equations are
solved using the finite element method with numerically stable edge element discretization in
combination with state-of-the-art algorithms for preconditioning and solution of the resulting sparse
equation systems [4-3].
4.2.2 Equations Employed
The numerical calculation presented in this chapter was done under a charge-free region of space;
which is given by the Laplace equation, ∇ ∙ 𝐄 = 0. Equations employed in the numerical calculation
are as follows,
𝐄 = −∇∅ ,
(4-1)
𝒊 = σ𝐄,
(4-2)
𝒊 = σ𝐄 +
∂𝐃
∂t
,
(4-3)
where 𝐄 : electric field [V/m], ∅ : electric potential [V], 𝒊 : current density [A/m2], and 𝐃 :
electric displacement field [C/m2]. Eq. 4-1 is for both the stationary and time-dependent calculation.
The next two are the same equations, where Eq. 4-2 is for stationary calculation and Eq. 4-3 is for
time-dependent calculation. In the calculation, the field intensity and current (conduction and
displacement current) were calculated after adding the boundary condition and the water properties
to the model. The process is as shown in the flowchart in Fig. 4-1.
For better calculation results, changes of the water properties due to the field intensity which
promotes the change of mobility should also be concluded. The liquid form of water also suggests
calculation using a fluid model; or a combination of electrical model and fluid model. However, in
order to obtain a simple calculation of the current distribution, only the minimal process for the
calculation of current distribution is concluded in this work.
65
Boundary condition
Water properties
Field intensity
calculation
Conduction current
calculation
Displacement current
calculation
Evaluation
between
experimental and
calculation results
Fig. 4-1 Calculation flowchart
66
4.2.3 Calculation Parameters
In this numerical calculation, the conductivity and relative permittivity are the important
parameters as water is a dielectric matter. However, up until now, the relative permittivity of water is
often generalized as 80, regardless of the conductivity [4-4, 4-5]. Thus, in this work, the permittivity
of tap water and saline solutions with different DC-conductivities (0.2, 0.5, 1.0, 2.5, 5.0 S/m), were
measured [4-6].
The measurement was done using impedance analyzer (4294A, Agilent Technologies) (IA) and
vector network analyzer (N5230C, Agilent Technologies) (VNA) in the frequency ranges of 40 Hz ~
110 MHz and 10 MHz ~ 50 GHz, respectively. For measurements using IA, a coaxial cylindrical
capacitance electrode with geometrical capacitance of 0.185 pF was used. The measurements using
VNA employed an open ended coaxial probe (85070E, Agilent Technologies) electrode. Open, short,
and load (50 Ω resistance) was used for the calibration from the measurement head of IA through
coaxial cable to the cylindrical electrode. The calibration of VNA was performed using air, mercury,
and pure water with dc conductivity of 0.89 μS/m.
Fig. 4-2 shows the logarithmic frequency dependences of (a) permittivity, 𝜀 ′ and (b) losses, 𝜀 ′′
for water and saline solutions. From this figure, it can be seen that the permittivity is a function of
frequency. From these data, the frequency dependency of (a) real and (b) imaginary parts of complex
conductivity as in Fig. 4-3 were obtained from the following relationship 𝜎 ∗ (𝑓) = 2𝜋𝑓𝑗𝜀0 𝜀 ∗ (𝑓),
where 𝜀 ′ (𝑓) = 𝜎 ′′ (𝑓)/2𝜋𝑓𝜀0 and 𝜎 ′ (𝑓) = 2𝜋𝑓𝜀0 𝜀 ′′ ; given that 𝜎 ∗ : complex permittivity and
permittivity of vacuum, 𝜀0 = 8.854 × 10−12 F/m. The DC permittivity (static permittivity) of the
solutions are given by the plateau of permittivity at the lower frequency, observed between 100 MHz
and 1GHz is given in Fig. 4-4. It can be seen that DC permittivity decreased with the increase in DC
conductivity, where pure water is 78.5, and seawater is 68.3. This is expected due to the increase in
NaCl content, where the water content decrease.
In this numerical calculation, only tap water and seawater was considered based on the results
obtained in previous chapters. The properties of the two water needed in the calculation is
summarized in Table 4-1. In this work, only the DC values of conductivity and permittivity were
employed to simplify the calculation, and presenting the minimal condition for the calculation. This
is also coherent to the impulse voltage used in the experiments, which the impulse time is in the
range of μs. Furthermore, the lightning impulse voltage used in the experiment was also in the range
of MHz in frequency, which is coherent to the frequency where the plateau of permittivity was
observed.
67
Fig. 4-2 Frequency dependences of (a) real
Fig. 4-3
and
complex
and (b) imaginary parts of ac complex
permittivity of pure water, tap water, and
conductivities of pure water, tap water, and
sodium chloride aqueous solutions with
sodium chloride aqueous solutions with
various DC conductivity at 22.0 °C.
various DC conductivity at 22.0 °C.
(b)
imaginary
parts
of
Frequency dependences of (a) real
Fig. 4-4 Plots of permittivity of water at 100 MHz ( = static permittivity) against dc conductivity of
pure water, tap water, and sodium chloride aqueous solutions with various DC conductivity at
22.0°C.
68
Table 4-1 Properties of tap water and seawater (DC-values)
Property
tap water
seawater
Conductivity, σ [S/m]
0.07
5
Relative permittivity, εr
78.5
68.3
69
In this 1D calculation, 4 calculation model with different input boundary condition; A, B, C and D
as shown in Fig. 4-5 ~ Fig. 4-5 were employed. The calculation models were square-shaped models
with ground, where
Ø
= 0 V at the bottom side and right side, imitating the grounding electrodes’
placement of the 1D electrode system. Tap water and seawater were distinguished by the
conductivity, σ and relative permittivity, εr as notated in Table 4-1.
The input boundary conditions were the experimentally measured electric potential, Vw (x, y) as in
Fig. 2-13 for tap water and Fig. 2-14 for seawater. Only the potential on the water surface, Vw (x, 0);
and potential at the y-axis, Vw (0, y) were employed in this calculation. The input of these electric
potential was lessen accordingly from A to D.
For model A, both Vw (x, 0) in the range 0 < x < 200 [mm]; and Vw (0, y) in the range 0 < y < 200
[mm] were employed as shown in Fig. 4-5. For model B in Fig. 4-6, only the Vw (x, 0) in the same
range to model A was employed. For this absence of Vw (0, y), the boundary condition for y-axis was
modified to n·i = 0 which means that no electric current flows across the boundary with n direction
is perpendicular to the boundary. For model C as shown in Fig. 4-7, only the Vw (x, 0) in the range of
0 < x < 90 [mm] for tap water and 0 < x < 30 [mm] for seawater was employed. This range is
represented as lcalc in the figure. For tap water, the lcalc was determined from the length of filamentary
discharge on water surface. For seawater with no filamentary discharge, the lcalc length was set to the
second x point which is the smallest after x = 0 mm. This is also the position where the measured Vw
(0, y) started to stay at a constant value. As model B, other boundaries were modified to n·i = 0 with
the absent of Vw (x, y). As minimal input was anticipated, model D shown in Fig. 4-8 which only use
the potential at the local discharge point (x = y = 0 mm) as the input boundary condition was also
considered. For this model, both the boundary conditions for upper side and right side were n·i = 0,
where the electric potential Vw (0, 0) was set as a point value. The meshes for these models are 898
triangle elements as shown in Fig. 4-9.
70
y
x
ø = Vw (x, 0)
ground;
ø=0V
200 mm
ø = Vw (0, y)
ground;
ø=0V
200 mm
water with σ , εr
ø=0V
200 mm
Fig. 4-5 Calculation model A
y
x
ø = Vw (x, 0)
water with σ , εr
ø=0V
200 mm
Fig. 4-6 Calculation model B
71
ø = Vw (x, 0)
y
x
water with σ , εr
ground;
ø=0V
200 mm
lcalc
ø=0V
200 mm
Fig. 4-7 Calculation model C
y
x
water with σ , εr
ground;
ø=0V
ø=0V
200 mm
Fig. 4-8 Calculation model D
72
200 mm
ø =Vw (0, 0)
y [mm]
x [mm]
Fig. 4-9 Mesh for 1D model
73
Fig. 4-10 to Fig. 4-13 show the calculation results of electric potential compared to the
experimental results for model A, B, C and D respectively, where (a) is the tap water and (b) is the
seawater. The potential on water surface is shown in (i), while potential on y-axis is shown in (ii).
The current density at the grounding electrodes are shown in Fig. 4-14. From the figures, it can be
concluded that the calculation model with the optimum minimal input is model C.
Calculation results of electric potential for model A showed an expected result, where it agrees well
with the calculation results. However, this does not fulfill the objective of this work to visualize the
current distribution using a minimal input of experimental results as the boundary condition. Results
for model B showed almost similar to model A, suggesting that the Vw (0, y) can be removed from
the input boundary conditions. The results for model C did not showed much difference to model B,
despite the smaller range of Vw (x, 0). The potential gradient at the water surface and y-axis had
shown a comparable result to the experimental values, for both tap water and seawater. For model D
which has the minimum input among the four models, the calculated potential showed a drastic
decrease compared to the experimental result. Thus, it is concluded that one-point input of Vw (0, 0)
is insufficient for this calculation.
The calculated current density, igi obtained from model C and D showed the same pattern to that of
obtained from the experiment. The difference in magnitude should be related to the difference in the
potential gradient.
From these results of potential and current distribution, it can be concluded that the optimum
boundary condition for this calculation is as in model C for both tap water and seawater, where the
filamentary discharge on water surface was taken into consideration.
74
20
20
Calculation
Calculation
Experiment
10
5
(ii)
Experiment
15
Vw (0, y)
15
Vw (x, 0)
(i)
10
5
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(a) Tap water
10
10
Calculation
Calculation
8
Experiment
6
Vw (0, y)
Vw (x, 0)
8
(i)
4
2
(ii)
Experiment
6
4
2
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(b) Seawater
Fig. 4-10 Calculation results of electric potential for model A, compared to the experimental results
20
20
Calculation
Calculation
Experiment
10
5
(ii)
Experiment
15
Vw (0, y)
15
Vw (x, 0)
(i)
10
5
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(a) Tap water
10
10
Calculation
Calculation
8
Experiment
6
Vw (0, y)
Vw (x, 0)
8
(i)
4
2
(ii)
Experiment
6
4
2
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(b) Seawater
Fig. 4-11 Calculation results of electric potential for model B, compared to the experimental results
75
20
20
Calculation
Calculation
Experiment
10
5
(ii)
Experiment
15
Vw (0, y)
15
Vw (x, 0)
(i)
10
5
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(a) Tap water
10
10
Calculation
Calculation
8
Experiment
6
Vw (0, y)
Vw (x, 0)
8
(i)
4
2
(ii)
Experiment
6
4
2
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(b) Seawater
Fig. 4-12 Calculation results of electric potential for model C, compared to the experimental results
20
20
Calculation
Calculation
Experiment
10
5
(ii)
Experiment
15
Vw (0, y)
15
Vw (x, 0)
(i)
10
5
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(a) Tap water
10
10
Calculation
Calculation
8
Experiment
6
Vw (0, y)
Vw (x, 0)
8
(i)
4
2
(ii)
Experiment
6
4
2
0
0
0
50
100
x [mm]
150
200
0
50
100
-y [mm]
150
200
(b) Seawater
Fig. 4-13 Calculation results of electric potential for model D, compared to the experimental results
76
1E+6
1E+5
1E+4
1E+3
Exp
A
B
C
D
1E+2
1E+1
1E+0
1
2
3
4
5
6
7
8
No. of grounding electrodes
(a) Tap water
9
10
1E+6
1E+5
1E+4
1E+3
Exp
A
B
C
D
1E+2
1E+1
1E+0
1
2
3
4
5
6
7
8
(b) Seawater
9
10
Fig. 4-14 Current distribution at the grounding electrodes for 1D model calculation;
compared to the experimental results
77
For the calculation of 2D model, a two-dimensional axial-symmetry model was used. Two models
were employed in this 2D calculation; without-air-model and with-air-model as shown in Fig. 4-15
(a) and (b), respectively. As the names suggest, the two models were employed in considering the
existence of the air phase and its effect to the current distribution.
The meshes of the models shown in Fig. 4-16 were triangular elements, with finer elements at the
boundaries which are representing the water surface and grounding electrodes. For with-air-model,
the meshes were coarser as it getting further from the water surface. There were 12634 elements and
for without-air-model and 15685 elements for with-air model.
As the 1D calculation model, the lower side and right side of the model are set as ground with Ø = 0
V, imitating the grounding electrodes’ placement of the experimental model. The σ and εr for water
and seawater employed in this calculation are as notated in Table 4-1. The dot-dash line represents
the symmetry axis. The dashed line in with-air-model represents the air phase area, stretched far
enough from the water surface at 10000 mm. The boundary for this air phase was set as Ø = 0 V.
As concluded in section 4.3, the input boundary condition of this calculation is considering the
filamentary discharge on water surface, where only the Vw (r, 0) in the discharge range was
employed. For with-air-model, n·i = 0 was replaced with a boundary of air and water. The lcalc for
tap water was set to 100 mm for tap water and 20 mm for seawater. The values for V w (r, 0) are the
measured potential on water surface in Chapter 3 (see Fig. 3-12). The Vw (r, 0) with time, t constant
for time-dependent calculation is as shown in Fig. 4-17 (a) and (b).
78
325 mm
ø = Vw (r, 0)
z
r
0
ground;
ø=0V
water with σ, εr
130 mm
lcalc
ground; ø = 0 V
306 mm
(a) without-air-model
325 mm
ø=0V
air
ø = Vw (r, 0)
z
10000 mm
ø=0V
r
ground;
ø=0V
water with σ, εr
ground; ø = 0 V
306 mm
(b) with-air-model
Fig. 4-15 Calculation models for 2D model
79
130 mm
0
z [mm]
r [mm]
z [mm]
(a) without-air-model
r [mm]
(b) with-air-model
Fig. 4-16 Meshes for 2D model
80
[kV]
16
Vw (r, 0) [kV]
14
12
12
8
10
4
8
0
100
16
6
4
r [mm]
50
2
40
0
0
0
20
time, t [μs]
(a) Tap water
[kV]
1.4
Vw (r, 0) [kV]
1.2
1.2
1.0
0.8
0.8
0.6
0.4
0.4
40
0
20
15
10
5
r [mm]
0 0
0.2
20
time, t [μs]
(b) Seawater
Fig. 4-17 Boundary condition for time-dependent calculation of 2D model
81
0
(i) Calculation under stationary condition
Fig 4-18 shows the electric field distribution to underwater expressed by vector arrows and color
map in log scale (log10 E [kV/m]). From this figure, it can be seen that the electric field are mainly
consisted of Ez-component at the positions where r < lcalc at z = 0 mm (which represent the
filamentary discharge on water surface), with small Er-component. At the position r > lcalc, the
electric field are mainly consisted of Er-component, where the vectors are mostly pointing sideward
towards the ground.
At the y-axis which is also the symmetry-axis, the arrows are mostly pointing downwards, which
means that the electric field is mostly consisted of Ez-component, with almost no Er-component.
From these results, it can be concluded that the filamentary discharge on water surface (or (Vw (r, 0)
in the model) is influencing the electric field distribution. This distribution of electric field to
underwater also suggests that the areas which are affected by the filamentary discharge are different
for both conductivities. The E for tap water is more affected than seawater, considering the longer
lcalc of tap water.
Fig. 4-19 shows the current distribution to underwater. The streamlines indicate the current vectors,
while the color map indicates the current density magnitude in log scale (log10 i [A/m2]). A similarity
to the E shown in Fig. 4-18 can be seen in this current distribution, where the effect of filamentary
discharge can be seen. The streamlines are mainly originating from the position where the Ø = Vw (r,
0) was added as the input boundary condition. It also can be seen that the current streamlines are
denser at the range 0 < r < 100 [mm] for tap water and 0 < r < 20 [mm] for seawater, where denser
current streamlines indicates higher current magnitude which can also be seen from the color range.
This is coherent with results obtained from the experimental result in Chapter 2, as concluded by
Matsuo et al. which states that most of the discharge current flows from the tip part of the local
discharge regardless of the propagation length [4-7].
Fig. 4-20 shows the current distribution at the grounding electrodes, of the two models compared
with the experimental results. The current density for both models did not show any significant
difference to each other, suggesting that the one phase model (without-air-model) is adequate for this
calculation, for both tap water and seawater. The current vector streamlines and color map also had
shown a very small current distribution to the air phase, thus can be neglected. The comparison
between the calculation and experimental value show a same pattern of distribution. However, the
differences observed in tap water, which is not more than one power order is thought to be caused by
the influence of electric fields generated by the residual space charge during the experiments, which
then accentuated or weakened the total electric field. For seawater, a comparable current density
values were obtained, suggesting less effect of residual space charge due to the high conductivity.
82
z [mm]
log10(E [kV/m])
r [mm]
(a) Tap water
z [mm]
log10(E [kV/m])
r [mm]
(b) Seawater
Fig. 4-18 Electric field distribution
83
z [mm]
log10(i [A/m2])
r [mm]
(a) Tap water
z [mm]
log10(i [A/m2])
r [mm]
(b) Seawater
Fig. 4-19 Current distribution to underwater
84
10000
1000
100
10
Experiment
without-air-model
with-air-model
1
1
2
3
4
5
6
7
8
9
8
9
(a) Tap water
10000
1000
100
10
Experiment
without-air-model
with-air-model
1
1
2
3
4
5
6
7
(b) Seawater
Fig. 4-20 Current distribution at the grounding electrodes for with-air-model and without-air-model;
compared to the experimental results
85
(ii) Calculation under time-dependent condition
Fig. 4-21 shows the discharge current waveforms at the grounding electrodes obtained from the
time-dependent calculation. These waveforms resemble the current waveforms that were obtained
from the experiments as can be seen in Fig. 3-7. As the calculation model in this work is only
considering the water phase (instead of the water and air phase of the experimental model), it can be
concluded these current waveform is not directly affected by the current at the discharge electrode
(which is at the air phase), or in other words, the Vw (r, 0) is enough to obtain the waveforms.
Fig. 4-22 shows the comparison of discharge current distribution to the grounding electrodes
between stationary and time-dependent calculation. The current density values for time-dependent
were obtained from the highest value of the current density calculated, which is equal to the peaks of
waveforms in Fig. 4-21. The times for the highest value to occur are different according to the
electrode number especially for tap water, where a time lag is observed as the grounding electrode
number shifted from 1 to 9. This was also observed in the experimental values which were also
obtained from the current waveform’s peak. From these figures, it can be seen that the distribution
patterns of stationary calculations agree well with time-dependent calculations. The slight difference
between the two calculation values is considered due to the effect of electric displacement field D
[C/m2] in time-dependent calculations, as suggested by Eq. 4-2 and Eq. 4-3. For tap water, the
time-dependent calculation results are 15% smaller than that of stationary calculation results. On the
other hand, a difference of 20% was observed for seawater. The 5% difference between the two
conductivities is considered to be as an effect of the difference in the relative permittivity, where
∂𝐃
∂t
𝜕𝐄
= 𝜀𝑟 𝜕𝑡 [4-4].
Fig. 4-23 and 4-24 show the current vectors’ change with the time of tap water and seawater,
respectively. For tap water, the change of current vectors is mostly visible during the first 2.5 μs.
This is coherent to the current waveform that showed sudden increase, then gradually decreases with
the change in time. For seawater, the change of current is faster compared to tap water, consistent
with the waveform which showed sudden increase and decrease in the first 2.0 μs. The changes are
mostly obvious at where Vw (r, 0) was available.
86
50
E1
E2
40
E3
Current, Igi [A]
E4
30
E5
E6
20
E7
E8
10
E9
0
0
2
4
6
8
10
12
Time [μs]
14
16
18
20
(a) Tap water
50
E1
E2
40
E3
Current, Igi [A]
E4
30
E5
E6
20
E7
E8
10
E9
0
0
2
4
6
8
10
12
Time [μs]
14
16
18
(b) Seawater
Fig. 4-21 Current waveforms at the grounding electrodes
obtained from the time-dependent calculation
87
20
10000
1000
100
10
Experiment
stationary
time-dependent
1
1
2
3
4
5
6
7
8
9
8
9
(a) Tap water
10000
1000
100
10
Experiment
stationary
time-dependent
1
1
2
3
4
5
6
7
(b) Seawater
Fig. 4-22 Current distribution to the grounding electrodes for stationary
and time-dependent calculation; compared to the experimental results
88
z [mm]
z [mm]
log10(i [A/m2])
0 μs
log10(i [A/m2])
0.5 μs
r [mm]
z [mm]
r [mm]
z [mm]
log10(i [A/m2])
1.0 μs
log10(i [A/m2])
1.5 μs
r [mm]
z [mm]
r [mm]
log10(i [A/m2])
z [mm]
2.0 μs
log10(i [A/m2])
2.5 μs
r [mm]
z [mm]
r [mm]
z [mm]
log10(i [A/m2])
5.0 μs
log10(i [A/m2])
10.0 μs
r [mm]
r [mm]
Fig. 4-23 Time-variable current distribution to underwater for tap water
(time for each distribution is notated at the upper left of the frame)
89
z [mm]
z [mm]
log10(I
(i [A/m2])
0 μs
log10(i [A/m2])
0.5 μs
r [mm]
z [mm]
r [mm]
z [mm]
log10(i [A/m2])
1.0 μs
log10(i [A/m2])
1.5 μs
r [mm]
z [mm]
r [mm]
z [mm]
log10(i [A/m2])
2.0 μs
log10(i [A/m2])
2.5 μs
r [mm]
z [mm]
r [mm]
z [mm]
log10(i [A/m2])
5.0 μs
log10(i [A/m2])
10.0 μs
r [mm]
r [mm]
Fig. 4-24Time-variable current distribution to underwater for seawater
(time for each distribution is notated at the upper left of the frame)
90
4.4.3 Remarks on the Prediction of Current due to Natural Lightning based on the Calculation
Results
The end of the lightning leader or the leader tip was reported to be an access of 10 MV with respect
to the earth [4-8]. This is about 103 times higher than the Vw (0, 0) observed in the experiment for tap
water, and 104 times for seawater. Electric fields from positive lightning flashes are apparently
similar to that of negative flashes, where the polarity and field change rate are different, which
results to the difference in current. Current for negative lightning was reported in the average of 30
kA, while for positive lightning is between 200 to 300 kA [4-8 ~ 4-10]. This current value of positive
lightning is in a large difference with the discharge current observed in this work, which are around
50 A for tap water and 150 A for seawater.
From the results of the current calculation which are comparable to the experimental results; in
considering lightning discharge on water surface in a relatively large area, it can be predicted that
lightning on the seawater surface could bring larger current to location distant away from the strike
point. Compared to fresh water, this large current in seawater seems to be highly distributed to the
water surface, which is the area where human activities are mostly concentrated such as at the beach
areas. Under the potential of 10 MV in a condition where the depth is in smaller ratio than the
distance on water surface, in can be expected that a higher current is distributed to the water surface.
With this estimated current of natural lightning which surpass the quantity of current that can be
tolerate by human body, this would be a silent threat to human if there is no information on lightning
at distant areas (i.e. far from the human activity areas) is provided. Because of that, the information
obtained from the developed lightning detection and prediction technology should be taken seriously
and spread to not only at the involved area, but also to the areas with a distance from it which shared
the same water area.
However, this does not indicate that lightning on fresh water surface is less dangerous. As the
filamentary discharge also plays a role in current distribution, and the length increased under higher
voltage [4-11]; the danger due lightning is also comparably high. Furthermore, unlike the sea, fresh
water areas are mainly a limited space of water, which eliminates the privilege of distance for the
electric potential to decrease.
91
4.5 Summary
Evaluation of current distribution to underwater due to spark discharge on water surface by the
mean of numerical calculation was done, using COMSOL Multiphysics’ AC/DC Module.
Calculation models similar to the experimental models were employed, under a charge-free region of
space. The calculation was done using tap water and seawater considering the significant difference
in experimental results, which were differentiate by the different conductivity and relative
permittivity in the calculation models.
The optimum minimal input of boundary condition for the calculation was determined by
calculation using the 1D model, where the boundary condition was varied to four types. Comparison
of calculated electric potential to the experimental results shows that boundary condition that are
considering the filamentary discharge (for tap water) and luminous area (for seawater) gave the
optimum calculation result.
From there, the calculation of current distribution of 2D model was done by employing boundary
condition considering the filamentary discharge (or luminous area). The results show that the current
was mostly originating from the position with input boundary condition, with higher magnitude at
those areas. This is coherent with the obtained electric field vector. Comparison to the experimental
results showed same pattern of distribution, with some difference thought to be due to the residual
charge during the experiments. For this 2D calculation model, the air phase was also considered by
employing two calculation model, with-air-model and without-air-model. The calculation results
show that there was no significant difference between the two models, where current at the air phase
was comparatively small and could be neglected. Comparison between stationary and
time-dependent calculation did not showed any obvious difference apart from the difference due to
the displacement field and also the relative permittivity of tap water and seawater. This confirms the
reliability of the stationary calculation results for a quick spatial evaluation of the current quantities.
The change in current distribution obtained from the time-dependent calculation showed a noticeable
change during up to 2.5 μs, especially at the areas of input boundary condition.
The results obtained from this calculation are consistent to the results obtained in chapter 2 and 3,
where it was observed that filamentary discharge had occurred on the water surface during the
discharge, and this is affecting the current distribution. Thus, it is assumed that the electric potential
at the filamentary discharge circumference is critical and should be considered as the boundary
condition for the calculation.
92
References
[4-1]
N.S. Midi, M.K.A. Muhamad, R. Ohyama, “Numerical Calculation of Current Distribution
due to Spark Discharge on Water Surface with Surface Potential as Boundary Condition”,
Proc. Schl. Eng. Tokai Univ. Ser. E, vol. 39, pp. 1-6, 2014.
[4-2]
M.A. Cooper, R.L. Holle, C. Andrews, “Distribution of Lightning Injury Mechanisms”,
20th Int. Lightning Detection Conf., pp. 1-4, 2008.
[4-3]
COMSOL, 2011. Introduction to COMSOL Multiphysics : Version 4.2a
[4-4]
H. Momma and T. Tsuchiya, “Undersea Communication by Electric Current”, Technical
Reports of Japan Marine Science and Technology Center, pp. 19-25, 1977. (in Japanese)
[4-5]
P.C. Sirles, Use of Geophysics for Transportation Projects, Transportation Research Board,
Washington, 2006.
[4-6]
N.S. Midi, K. Sasaki, R. Ohyama, N. Shinyashiki, “Broadband Complex Dielectric
Constants of Water and Sodium Chloride Aqueous Solutions with Different DC
Conductivities”, IEEJ Trans. Electrical and Electronic Engineering, vol. 9, no. s1, pp.
s8-s12, 2014.
[4-7]
H. Matsuo, T. Yamashita, and T. Fujishima, “Shape of Contacting Surface between an
10, no. 4, pp. 634-640, 2003.
[4-8]
A.M. Hussein, W. Janischewskyj, J.-S. Chang, V. Shostak, W.A. Chisholm, P. Dzurevych,
Z.-I. Kawasaki, “Simultaneous Measurement of Lightning Parameters for Strokes to the
Toronto Canadian National Tower”, J. Geophys. Res., vol. 100, no. D5, pp. 8853-8861,
1995.
[4-9]
M.A. Uman, 2001, The Lightning Discharge, Orlando : Academic Press.
[4-10]
A. Borghetti, C.A. Nucci, M. Paolone, “Estimation of the Statistical Distributions of
Lightning Current Parameters at Ground Level from the Data Recorded by Instrumented
Towers”, IEEE Trans. Power Del., vol. 19, no. 3, 2004.
[4-11]
N.S. Midi, M.K.A. Muhamad, R. Ohyama, “Experimental Studies on Electrical
Characteristics of Spark discharge on Water Surface of Tap Water”, 2013 Ann. Rep. Conf.
on Electrical Insulation and Dielectric Phenomena, vol. 1, pp. 647-650, 2013.
93
Chapter 5 Conclusion and Future Prospect
5.1 Conclusion
Building wind power generators at the coastal areas of sea and large lakes is one of the energy
growth strategies in countries with limited ground areas and insular countries such as Japan and
Malaysia. However, the Hokuriku region of Japan and South East Asia are known to be as lightning
prone areas, exposing the power generators to damages. In general, the power generators are
equipped with a designated path for the lightning current to travel to underwater in an event of a
direct strike.
In the case of lightning to ground areas, the knowledge for the development of protection is widely
available, which includes protection against both the primary (due to direct strike) and secondary
(due to the discharge current) effect of lightning. However, this is still limited in the case of lightning
to sea or water areas. As water is a dielectric matter with attribution of conductivity and permittivity,
secondary damages due to the lightning discharge current need to be focused, apart from the direct
strike as mentioned above.
In this work, investigations on current distribution in water circumference under spark discharge on
water surface were done. This is as an evaluation of lightning phenomenon on water surface
especially in sea areas. The outcomes of each chapter are summarized as follow:
In chapter 1, the background of lightning on water area and the problems regarding the protection
measures were described. Besides that, the social significance of this work was explained. The
outline of the research content was made clear by explaining the objective and the methodology of
this work. In correspondence to that, a literature review on electrical discharge in dielectric
two-phase gas-liquid system applied on this study was presented.
In chapter 2, the electrical discharge on water surface of a 1D model was investigated in order to
understand the lightning phenomenon on water surface. The model was consisted of a discharge
electrode placed with an air gap from the water surface, and multiple underwater grounding
electrodes fixed in the water reservoir. The water reservoir was a square-shape acrylic box with the
same horizontal and vertical length, where the side depth was kept to a minimum length. Impulse
lightning discharge was applied to the discharge electrode to generate spark discharge on the water
surface in order to imitate the lightning discharge. Two types of water, tap water and saline solution
with the same conductivity to seawater were used in the experiments. From there, the electrical
properties were observed and the findings are as follow :
1.
The discharge on tap water and seawater had shown different breakdown properties to
each other. This can be seen from the voltage and current waveforms at the discharge
94
electrode. The discharge condition on the water surface also had shown significant
difference, where filamentary discharge was observed sprouting on the tap water surface.
For discharge on seawater surface, the discharge only localized at the local discharge
point.
2.
The filamentary discharge on tap water surface was observed to influence the current
distribution to the water surface, which was not observed in seawater. The current
distribution was also affected by the distance of electrode from the local discharge point.
3.
The effect of the filamentary discharge also can be observed from the potential distribution
which was coherent to the current distribution.
In chapter 3, a 2D model was introduced to investigate the effect of water properties to the
discharge and current distribution. The water reservoir for this 2D model is a cylindrical plastic tub
of larger scale than the 1D model, with the same discharge electrode and multiple underwater
electrodes. The parameter of water property was varied by changing the conductivity of water. The
findings obtained from this chapter are as follow :
1.
The increase in the conductivity of water had shown a significant difference between tap
water and saline solutions in general. This was observed even with a slight difference of
conductivity between them, and can be seen from the voltage and current waveforms.
2.
The length of filamentary discharge on water surface decreased with the increase in
conductivity.
3.
Changes in voltage and current can be seen as conductivity increase, but exhibit a
tendency to saturate at higher conductivity.
4.
As the 1D model, the current distribution depends on the distance from the local discharge
point, and shows different pattern between the tap water and saline solutions. The effect of
filamentary discharge length due to the change in conductivity can be seen, and was
confirmed from the potential distribution.
5.
The relation between filamentary discharge and current distribution was also observed in a
different manner to the 1D model, suggesting an effect of the model geometry.
In chapter 4, evaluation of current distribution to underwater due to spark discharge on water
surface by the means of numerical calculation was done. Calculation models similar to the
experimental model were employed with the measured electric potential as the boundary condition
under stationary and time-dependent condition. Comparable results to the experimental results with a
minimal input of boundary condition were anticipated. The findings from the evaluation are as
follow:
1.
Boundary condition which considered the filamentary discharge on water surface was
identified as the optimum minimal input boundary condition for tap water. As for seawater
95
which no filamentary discharge was observed, the potential gradient before it stays at a
constant value is enough as the boundary condition to obtain a comparable result.
2.
From the comparisons, it can be concluded that the discharge occurred on water surface is
critical in determining the current distribution to underwater.
From the findings above, the current distribution to a limited underwater circumference due to
spark discharge on water surface and the accompanying electrical characteristics were made cleared
and evaluated. In relation to the lightning on water surface, it is anticipated that these findings are an
important component in developing an evacuation measure during an event of such. Combined with
the technology in lightning prediction and detection, an indicator for the critical areas of action
should be able to be determined.
96
5.2 Future Prospect
Considering the vast scale of natural lightning, analysis using numerical calculation is the
preferable method, and therefore the quality in future works needs to be increased in order to comply
with the natural phenomenon.
For this present calculation of current conduction, the discharge in air phase as the input boundary
condition should be considered to achieve the minimum dependency to the experimental values. This
is preferably with further details on the ions from the water itself and the interaction with the
lightning spark at the air gap. From the results which showed difference between the models, it is
also necessary for flexibility in the geometry as this might influence the spatial distribution of
current, considering the irregularity of the seabed and beach geography.
For a better understanding of the discharge phenomenon, further calculation analysis of the
equivalent circuit and the corresponding transient phenomenon should also be considered. In
addition, as the conductivity and permittivity of water are both a function of frequency should also
be included, add to that the lightning itself is consisted of various frequency component.
Despite the promising potentials in numerical calculations, laboratory experimental works is still
practical in some aspects. For example, a variation of experimental model will improve the database,
which then should be an advantage in the numerical calculation with geometry flexibility. Besides
that, investigation on the space charge in two-phase liquid-gas environment and the residual space
charge.
97
Acknowledgment
In the name of Allah, the Most Beneficent, the Most Merciful.
I would like to express my sincere appreciation to my supervisor, Prof. Dr. Ryu-ichiro Ohyama for
his valuable guidance and generous support throughout my doctor course.
My special thanks to the members of Ohyama Laboratory, Department of Electrical and Electronic
Engineering, Tokai University; and to the department as whole.
I express my warm thanks to fellow co-researchers and papers’ co-authors involved in this work. I
also would like to thank the professors involved in the inspection of this thesis.
Next, I would like to thank International Islamic University of Malaysia and Ministry of Education
Malaysia for the opportunity for me to further my study in Tokai University in order to gain more
knowledge and experience that will soon be used in my career.
Last but not least, thanks to my parents, family and friends for the warm support throughout the
three years of my doctor course.
98

Studies on Current Distribution in Water Circumference under Air

Transcription

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