Simulations of the Propagation of Streamers in Electrical Discharges in a 5mm Water Filled Gap
Thamir H Khalaf1* and Duaa A Uamran1,2
1Department of Physics, College of Science, University of Baghdad, Iraq
2Department of Physics, College of Science, University of Kerbala, Iraq
Submission: August 09, 2017; Published: September 27, 2017
*Corresponding author: Duaa A Uamran, Department of Physics, College of Science, University of Baghdad, Iraq, Email: duaa)firstname.lastname@example.org
How to cite this article: Thamir H Khalaf, Duaa A Uamran. Simulations of the Propagation of Streamers in Electrical Discharges in a 5mm Water Filled
Gap. Curr Trends Biomedical Eng & Biosci. 2017; 9(4): 555767. DOI: 10.19080/CTBEB.2017.09.555767
This work is devoted to the modeling of streamer discharge, propagation in liquid dielectrics (water) gap using the bubble theory. This of the electrical discharge (streamer) propagating within adielectric liquid subjected to a divergent electric, using finite element method (in two dimensions). Solution of Laplace’s equation governs the voltage and electric field distributions within the configuration, the electrode configuration a point (pin) - plane configuration, the plasma channels were followed, step to step. That shows the streamer discharge bridges the dielectric liquid gap and indicates the minimum breakdown voltage required for a 5mm atmospheric pressure dielectric liquid gap as 22KV. The initiated streamer grows and branches toward all elements that satisfy the required conditions. The electric potential and field distributions shown agreement with the streamer growth, according to the simulation development time.
The breakdown of insulating liquids is not simple to explain and the mechanism responsible for the initiation of breakdown is still open to controversy. Many breakdown theories have been put forward since the start of research on this subject. Experimental data on the electric breakdown of liquids that were accumulated, confirm that there are several different breakdown mechanisms that cannot be described in the context of a unified theory [1-4].
The ignition of an electric discharge in the liquid phase leads to the generation of non-thermal plasma, which can be utilized in various processes and technologies. An application of high electric energy into the system initiates an intensive movement of charged particles resulting in frequent collisions [5,6]. The discharge generation depends on the environment in which the plasma is ignited. There are at least three main factors distinguishing the liquid phase from gasses. The first one is a substantially higher density inducing a higher collision frequency and low mobility of charged particles. The second problem appearing in aqueous solutions comes up from a high polarity and dielectric strength of liquid molecules. These properties lead to the creation of dipole momentum in the applied electric field, and cause inhomogeneous areas in the vicinity of an electrode surface. The third factor influencing the discharge creation in the liquid phase is a presence of ions and their different mobility in a solution. In particular, fast electrons
and slow, heavy ions alter the propagation of discharge channels [7-9].
Kao  derived a mathematical model of the breakdown mechanism based on the formation of gas bubbles in liquids. He assumed that bubbles might be formed in a liquid for the reasons such as, the gas which accumulates in microscopic cavities and hollows on the electrode surface. From the liquid itself by local evaporation on the surface of the electrodes due to the action of electrical current, dissociation of molecules through collisions with electrons or impurities. Due to electrostatic forces overcoming the surface tension. The electrostatic force effect causes elongation of the bubble in the electric field. The streamer mechanism in liquids occurs if the electric field is strong enough, it is assumed that electron avalanches can initiate in the liquid .
This paper is aimed at the modeling of the streamers propagating within a dielectric liquid (water) submitted to a divergent electric field (point-plane electrode configuration). The aim is to determine the initiation propagation and branching of streamers in this liquid gap (water).
Many theories have been put the initiation the growth of a streamer in dielectric liquid [10,12-17]. Confirm that there are several different breakdown mechanisms that cannot be described in the context of a unified theory [2,18].
This model, here, was built based on several assumptions
to initiating the growth of a streamer within the buffer liquid.
Many conditions have suggested to the start and growth of the
Following are the basic assumptions of the proposed model:
The simulation was implemented in the two dimensional
region of finite elements. Some nodes of some elements represent
the electrodes, while the others represent the dielectric liquid
between the electrodes.
The electric potential at all nodes of all elements that
belongs to the dielectric is calculated by solving the Laplace
equation with the boundary conditions on the electrodes and
the streamer discharge pattern.
The likelihood of initiation and growth of a streamer
can be satisfied when
The local electric field (in the center of finite element)
is greater that a threshold value . The local electric field will
be calculated according to the values of the voltage at the nodes
of each element. Also, The heat of liquid evaporation (Ws) is
greater than the latent heat (L) [1,20].
Ws=R s Is2 Δτ……………………………….…(1)
L=ρ .Vab .Cp (T).ΔT……….…………….(2)
When Rs is resistance streamer, Is is current streamer, Δτ
time duration of jump, L is the energy to heat liquid [J], ρ is the mass density
Vab is the Volume of bubble [m3], Cp(T) is the heat capacity
of liquid (J/kg.K) and ΔT is the temperature change (K).
The electric field value (Etip) at the streamer tip is
greater than a threshold value .
Etip= 2V0/(r0 ln4(d-Ɩs/r0 )………………….…(3)
Where V0 is the applied voltage, d is the gap length and Ɩs
is the length of the streamer channel and r0 is the radius of the
The electric field of the bubble (Eb) is greater that a
threshold value .
When Eloc. is the local electric field and εr is the relative
permittivity of the dielectric
All the streamer branches were followed for one step only,
because they, at all conditions, will decay. And only the main will
bridge the gap between electrodes.
To validate our model, (Figure 1) consider a pin-plane
electrode geometry, submerged in an insulating (water) of
permittivity 78.6 and submitted to different applied voltages,
the radius of streamer channel r0=5μm and the conductivity of
channel =0.1(Ω.m)-1. The model to be implemented, a computer
simulation must be executed within a pin-plane electrode
arrangement, Figure 1. The pin (anode) is of 10mm length. The
plane (cathode) is about (15) mm diameter, and the distance
between the electrodes is the liquid gap length of 5mm. A
positive DC high voltage was applied to the pin (V0=22, 25, 27,
30 and 33kV) while the plane was grounded.
Laplace’s equation governs the voltage and electric field
distributions within the arrangement. So, finite element method
(in two dimensions) was used as a good tool to solve Laplace’s
equation in the complicated arrangement (the solution region as
in Figure 2). The program was written with Fortran 77 language.
It was used to do the calculations that are needed to predict
the voltage and electric field distributions within the water gap
between the electrodes (Figure 2). As well as and to simulate the
path and branching of the streamer within the simulation area.
The simulation was carried out within the electrode
arrangement of a water gap of 5mm length to show the initiation
and growth of the streamer from the anode (pin) to the cathode
(plane). The aim is to determine the breakdown voltage of the
water gap, show the streamer branching and the effect applied
voltage V0 on the branching streamer and the time (Δτarr)
required to arrive the plain pole.
The streamer initiation and development was followed within
the solution region between the two electrodes. A streamer is
initiated at the elements that have values that consensus with
the conditions; First, the local electric field is greater than the
threshold value (7.4KV/mm)  and the energy injected by the
electric field is sufficient to cause the evaporation of the liquid
then formation the bubble [1,18]. Second, the electric field wit
in the bubble is greater than the threshold (10kV/mm) , the
last condition the electric field at the head streamer greater than
the threshold (200kV/mm) [24,25].
The gap breakdown voltage was expecting at the minimum
applied voltage value that grows streamer pattern to channel the
gap. The value of the water gap of 5mm in this work was achieved
at 22KV. Figure 3 shows the streamer initiation and development
between the two electrodes for the minimum breakdown voltage.
The figure shows the initiation of the streamer at the head of the
pin because of the highest values of the electric field. It is found
that the initiation time is 0.5435μsec and the required time for
the streamer growth to embankment the gap between the two
electrodes and reach the plane is 3.04μsec. Also, the streamer
path was traced by trend the center of the opposite electrode
Initially, the solution of Laplace’s equation gives the
voltage at every node on the gridand then we know the
voltage distribution as well as the field distribution. Figure 4
& 5 show our simulation pictures of the voltage and electric
field distributions development with time. Also, we observe
corresponds to the growth streamer path in the previous item.
These figures suggest obviously the locomotion of the region of
the highest voltages and the highest electric field agrees to the
streamer growth. The plots for the magnitude of the electric field
can attain the weak region where the breakdown may begin. In
this case, the weak region was identified to be the region where
the magnitude of the electric field is the highest and from this
region the breakdown will initiate.
The simulation was reiterated at the same mesh, but with
different applied voltages (22, 25, 27, 30 and 33 KV). That is
to clarification the effect of applied voltage on the streamer
branching as in Figures 6. From the Figure 6 the one can notice
that, the number of branches increases with the increasing of the
applied voltage due to the increased number of elements inside
mesh that is realized condition of the growth of streamers inside
liquid. Also, the streamer growth with the shortest distance
between the electrodes with the increase of the voltages on the
anode (pin), which leads to a decrease (Δτarr). This is consistent
with studied many experiential and theoretical researches [26-
28]. Table 1, shows the number of branches and arriving time at
each applied voltage.