A tutorial demonstration of streamer physics via fluid simulations

In this paper, an improved air discharge fluid model under non-uniform electric field is constructed based on the plasma module COMSOL Multiphysics with artificial stability term, and the boundary conditions developed in the previous paper are applied to the calculation of photoionization rate. Based on the modified model, the characteristics of low temperature sub-atmospheric air discharge under 13 kV direct current voltage are discussed, including needle-plate and needle-needle electrode structures. Firstly, in order to verify the reliability of the model, a numerical example and an experimental verification were carried out for the modified model respectively. Both verification results show that the model can ensure the accuracy and repeatability of the calculation. Secondly, according to the calculation results of the modified model, under the same voltage and spacing, the reduced electric field under low temperature sub-atmosphere pressure is larger than that under normal temperature and atmospheric pressure. The high electric field leads to the air discharge at low temperature and sub atmospheric pressure entering the streamer initiation stage earlier, and has a faster propagation speed in the streamer development stage, which shortens the overall discharge time. Finally, the discharge characteristics of the two electrode structures are compared, and it is found that the biggest difference between them is that there is a pre-ionization region near the cathode in the needle-needle electrode structure. When the pre-ionization level reaches 1013 cm−3, the propagation speed of the positive streamer remains unchanged throughout the discharge process, and is no longer affected by the negative streamer. The peak value of electric field decreases with the increase of pre-ionization level, and tends to be constant during streamer propagation. Based on the previous paper, this paper constructs the air discharge model under non-uniform electric field, complements with the previous paper, and forms a relatively complete set of air discharge simulation system under low temperature and sub atmospheric pressure, which provides a certain reference for future research.

The influence of humidity and applied voltage on negative streamer discharge in air gaps exhibits a nonlinear synergistic effect. Numerical simulation and experimental investigation were conducted on negative streamer discharges in a 3 mm needle–plane air gap. A fluid model was established that simultaneously accounts for both humidity and the applied voltage. The validity of the model was confirmed by comparison with experimental data. The electron density and electric field at the streamer head increase with increasing humidity, and both quantities continue to intensify as the streamer propagates toward the plane electrode. The magnitude of the applied negative DC voltage and its influence become more pronounced in the vicinity of the plane electrode. The applied voltage has almost no effect on the streamer channel radius, whereas the channel radius increases with increasing humidity. When the applied voltage amplitude is below 10 kV, an increase of 30% in relative humidity leads to approximately a 10% reduction in streamer propagation velocity, while the discharge current exhibits only minor variation. In contrast, when the applied voltage amplitude exceeds 10 kV, every 30% increase in relative humidity causes the electric field at the streamer head, the streamer channel radius, and the streamer propagation velocity to increase by 7.8%, 10%, and 50%, respectively, and the discharge current nearly doubles. At constant relative humidity, every additional 1 kV in applied voltage increases the electric field at the streamer head, the streamer propagation velocity, and the discharge current by approximately 5%, 25%, and 30%, respectively. Moreover, these increasing trends become more pronounced at higher relative humidity. However, the increase in applied voltage has no significant effect on the streamer channel radius.

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 a dielectric liquid subjected to a divergent electric field, 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. The results show that, the electrical discharge (streamer) indicates the breakdown voltage required for a 3mm atmospheric pressure dielectric liquid gap as 13 kV. Also, the electric potential and field distributions shown agreement with the streamer growth, according to the simulation development time.

SF6 is commonly used as gaseous insulation media in high voltage equipment, but it has high global warming potential and urgently needs to be replaced with eco-friendly alternatives. CO2-based mixtures have shown promising results as SF6 alternatives. Streamers that form the initial phase of electrical breakdown have become important for the reliable design of high-voltage equipment based on gaseous insulation. In this paper, the influence of concentration ratio (90% CO2/10% O2, 80% CO2/20% O2, and 70% CO2/30% O2), applied voltage (±8 kV, ±10 kV, and ±12 kV), pressure (1.5, 2.0, and 2.5 bars), and gap distance (4, 4.5, and 5 mm) on positive and negative streamer formation and propagation is investigated in detail using a 2D axis-symmetric simulation model. Considering the low probability in gas mixtures with higher concentrations of CO2, photoionization is excluded, and background ionization is used for generating free electrons along with the Townsend ionization equation and the Gaussian approximation for the initial electron density distribution. The simulation results show that by increasing the O2 concentration in CO2, the electron density, electric field, and streamer velocity increase under positive and negative polarities. The σ (collision cross section) value of O2 is greater than CO2 at the specific ionization energy, indicating that O2 molecules in a gas mixture have a higher reactivity and a lower molecular stability. The negative streamer has an overall high electron density as compared to the positive streamer. To understand the effect of applied voltage, pressure, and gap distance, only 80% CO2/20% O2 concentration ratio was chosen. By increasing the applied voltage, the electron density, electric field, and streamer velocity increase. Furthermore, a decreasing trend of electron density, electric field, and streamer velocity was observed by increasing the gas pressure and the electrode distance.

The non-thermal, chemically active plasma is one of the promising technologies for the removal of the hazardous environmental pollutants. Pulsed streamer discharges in atmospheric pressure gases have received a great deal of interest for many years. It is very important to know the propagation mechanism of streamer discharges in order to improve the energy efficiency of pulsed discharge systems. In the present work, a Blumlein generator that has a pulse width of 100 ns was used to investigate the streamer discharge propagation. The propagation images in a coaxial reactor were taken by a streak camera for both positive and negative polarities of the applied voltage. From the results, primary and secondary streamers were observed propagating from the inner wire electrode to the outer cylinder electrode, and the maximum propagation velocity of the streamer head were 0.6 - 1.2 mm/ns in the range of 43 - 93 kV of the absolute value of the applied voltage. The propagation velocity of the positive streamer was faster than that of the negative polarity. The electric field at the wire electrode for streamer onset was 12 MV/m for the positive streamer and 20 MV/m for the negative streamer.

The effect of cellulose particles on streamer and breakdown phenomena in a synthetic ester and a mineral oil was investigated using a non-uniform point-plane electric field and a uniform plane-plane electric field under standard lightning impulse voltages. Oil samples were prepared to be low and high contamination levels according to CIGRE brochure 157. A multi-frame high-speed camera was used to record the streamer phenomena. By analysing the breakdown voltage and streamer characteristics, i.e. length, velocity, initiation time and propagation time under both positive and negative polarities, the particle effect on streamer development and breakdown in liquids is revealed. The results show that the increase of cellulose particle contamination level does not affect streamer propagation in non-uniform electric field, but promotes the streamer initiation leading to lower breakdown voltages in uniform electric field.

Submarine cables are widely used in submarine power grid systems, and the operating environment is complex and harsh. Anchor damage is the most fatal factor affecting the safe and stable operation of submarine cable lines. In this paper, the finite element analysis is used to study both the electric and magnetic field distribution of submarine cables to evaluate the degree of anchor damage. Process principles of the two working conditions, anchor drop and anchor drag, are considered and described respectively. In the simulation environment, the 2D finite element model of 110 kV single-core AC submarine cable is built, simulating the anchor damage through longitudinal compression and overall deformation of the stressed section. After solving the electric and magnetic field distribution of the insulation layer, the correlation between the electric field distribution, magnetic field distribution and the deformation degree of anchor damage are finally established. Results show that the deformation of submarine cables caused by anchor damage lead to uneven distribution of both electric field strength and magnetic flux density in the insulation layer. The compression of the cable in the stress direction results in the thickness reduction of the material, thus weakening its magnetic shielding ability. With the simulation conclusion, the internal electric and magnetic field contribution of the submarine cable insulation layer can be inferred according to the insulation deformation degree, which contributes to the status evaluation of the submarine cable after the anchor damage and further ensures the safety and reliability of submarine cable operation.

A Monte Carlo simulation technique has been used to model the electron transport behavior, especially the electron diffusion motion, in the cathode fall region of a glow discharge under the influence of a non-uniform electric field and a transverse magnetic field perpendicular to the cathode sheath electric field. Three types of collisions (elastic, excitation and ionization) are taken into account in our model. The electron free flying time is determined by the electron-neutral atom collision frequency. We focus attention on the electron diffusion distance and velocity. The electron-neutral atom collision processes and the electron drift velocity are also studied. The results indicate that with the increase of the magnetic field the electron diffusion distance increases and the electron diffusion velocity decreases. The results also show that the collision processes are enhanced by the magnetic field, this is in agreement with the experimental result. However, the axial magnetic field does not affect the electron transport behavior.

PurposeIn high-voltage direct current (HVDC) cable systems, space charges accumulate because of the constant applied voltage and the nonlinear electric conductivity of the insulating material. The change in the charge distribution results in a slowly time-varying electric field. Space charges accumulate within the insulation bulk and at interfaces. With an operation time of several years of HVDC systems, typically the stationary electric field is of interest. The purpose of this study is to investigate the influence of interfaces on the stationary electric field stress and space charge density.Design/methodology/approachAn analytic description of the stationary electric field inside cable insulation is developed and numerical simulations of a cable joint geometry are applied, considering spatial variations of the conductivity in the vicinity of the electrodes and interfaces.FindingsWith increasing conductivity values toward the electrodes, the resulting field stress decreases, whereas a decreasing conductivity results in an increasing electric field. The increased electric field may cause partial discharge, resulting in accelerated aging of the insulation material. Thus, interfaces and surfaces are characterized as critical areas for the reliability of HVDC cable systems.Research limitations/implicationsThis study is restricted to stationary electric field and temperature distributions. The electric field variations during a polarity reversal or a time-varying temperature may result in an increased electric conductivity and electric field at interfaces and surfaces.Originality/valueAn analytical description of the electric field, considering surface effects, is developed. The used conductivity model is applicable for cable and cable-joint insulations, where homo- and hetero-charge effects are simulated. These simulations compare well against measurements.

The earlier experimental setup for the study of a multi-streamer single pulse sliding discharge was supplemented by a photoelectric system for recording streamer radiation with a time resolution of 1.5 ns. Measurements of streamer delay and propagation velocity in Ne of atmospheric pressure at two supply voltage polarities were performed. The results showed that during each discharge pulse, regardless of its polarity, streamers of two types propagate across the gap in opposite directions. The first ones, primary streamers, start from a high-voltage electrode and move to a grounded electrode. The other type of streamers, reverse streamers, propagate in the opposite direction from a grounded electrode only after primary streamers have reached it. The experiments were carried out using voltage amplitude of 3 and 3.5 kV applied to plane-parallel electrodes on an alumina ceramic substrate with a rectangular discharge area of 9.5×11.6 cm2 in size. The total delay time range of the streamers was up to 2500–2700 ns and their motion velocity up to (3.5−5.6)×107 cm/s, depending on the discharge voltage and polarity. The dependence of delay time and velocity of the streamers' head motion on their position in the gap is presented. A qualitative explanation of the primary streamer characteristics is proposed, while the obtained experimental data are not sufficient for a similar explanation with respect to reverse streamers. The presented results are significant for studying the physical mechanisms of counterpropagating surface streamer/ionization wave dynamics, while the experimental methodology allows recording their spatiotemporal evolution in the gap.

Head‐on collisions between negative and positive streamers have been proposed as a mechanism behind X‐ray emissions by laboratory spark discharges. Recent simulations using plasma fluid and particle in cell models of a single head‐on collision of two streamers of opposite polarities in ground pressure air predicted an insignificant number of thermal runaway electrons >1 keV and hence weak undetectable X‐ray emissions. Because the current available models of a single streamer collision failed to explain the observations, we first use a Monte Carlo model coupled with multiple static dielectric ellipsoids immersed in a subbreakdown ambient electric field as a description of multiple streamer environment and we investigate the ability of multiple streamer‐streamer head‐on collisions to accelerate runaway electrons >1 keV up to energies ∼200–300 keV instead of just one single head‐on collision. The results of simulations show that the streamer head‐on collision mechanism fails to accelerate electrons; instead, they decelerate in the positive streamer channel. In a second part, we use a streamer plasma fluid model to simulate a new streamer‐electron acceleration mechanism based on a collision of a large negative streamer with a small neutral plasma patch in different Laplacian electric fields |E0|= (35, 40, 45) kV/cm, respectively. We observe the formation of a secondary short propagating negative streamer with a strong peak electric field >250 up to 378 kV/cm over a time duration of ∼0.16 ns at the moment of the collision. The mechanism produces up to 106 runaway electrons with an upper energy limit of 24 keV.

This paper investigates the behaviour of partial discharge (PD) in transformer insulation paper based on the Finite Element Method (FEM). The three-dimensional (3D) FEM model consists of conductor and insulation paper, representing part of a transformer’s high voltage winding. The conductor’s width, height, and length used in this study were 2.4 mm, 11.5 mm, and 16 mm. An insulation paper thickness of 1 mm was modelled around the conductor. An internal cavity with a diameter of 0.5 mm cavity was introduced within the insulation paper. This study introduced two locations of the spherical cavities at the centre and left corner of the insulation paper: Location 1 (L1) and Location 2 (L2). An AC voltage of 33 kV, 50 Hz, was applied to the conductor while the bottom of the insulation paper was grounded. The model was used to study the electric field distribution within the insulation paper and its effect on PD current and charge magnitude. The influence of cavity location on the charge magnitude was also examined. It is found that the electric field distribution is influenced by the conductor configuration as well as the location of the cavity. The electric field in the cavity is the highest at L1 compared to L2. The first PD occurs faster for the cavity with a high electric field. Due to the PD occurrence at the same inception field, the real PD current and charge magnitude is similar at different locations. The apparent PD current and charge magnitude induced at the ground electrode is slightly higher at L1 than at L2.

The development of high-voltage DC cables is mainly limited by the properties of insulating materials. Adding an appropriate amount of nanoparticles can improve the dielectric properties of materials. To study the effect of high temperature and nano-filler concentration on the conductivity characteristics of the dielectric, LDPE/Sio <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> nanocomposites with the particle size of 7 nm and mass fraction of 0.5wt%, lwt%, and 3wt% were prepared by filling LDPE with nano- Sio <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> particles. The DC conductance at 90°C and 100°C was measured at the electric field strength of1-100 kV/mm, and the temperature sensitivity of the samples were analyzed. The results show that in the condition of high temperature and low electric field, the nanocomposite can effectively reduce the conductivity current density and improve the conductivity performance, and the first threshold electric field increases with the increase of nano-filling concentration. Under the high electric field at high temperatures, temperature becomes one of the main factors that affect the carrier transport process. Among all samples, the LDPE/Sio <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> nanocomposite with a mass fraction of 3wt% has the best conductivity and the lowest temperature sensitivity.

Discharge processes such as glow, streamer, and leader inception among others take place before an upward leader can be launched from a grounded structure during thunderstorms. Electrostatic fields below the thundercloud could lead to the formation of glow charge from grounded objects. if the electric field is high enough and ionization keeps expanding into the gap, streamers can be incepted. Depending on the available charge and the thermodynamic properties of the gas, there is a possibility to incept or not a positive upward leader towards the cloud. Usually, the inception of positive upward leaders is directly related with the appearance of a downward coming leader from cloud towards the grounded object. Such a downward leader will intensify the electric field in such a way that the streamer discharges could thermalize and produce an unstable upward leader channel. However, experimental observations have indicated the inception of upward leaders from grounded structures without registering connecting downward leaders towards the structure. The present paper intends to explain the inception of positive upward leaders from the top of a rod, whenever the electric field produced by the cloud suddenly changes e.g. due to intra-cloud discharges or distance cloud to ground flash. A two dimensional model based on the gas-dynamic equations, the main processes responsible for gas heating such as vibrational excitation and transfer of energy into electronic, rotational and translational excitation, coupled with Poisson equation is presented in this paper. Rods of different lengths under thundercloud electric field were studied. Simulation results indicate that positive upward leaders can be incepted from long rods under certain conditions of thundercloud electric field without the need of a coming downward leader. However, for rods of tenths of meters the thundercloud electric field is not enough to incept positive upward leaders and an intensification of the electric field is required in order to incept a positive upward leader from the structure, e.g., a coming downward leader.

The over 9 million deaths in 2018, and 10 million in 2020, worldwide, due to cancer, indicates that the current standard of treatments is inadequate; there is an urgent and critical need for additional/alternate physical therapies. Towards this, electroporation-based chemotherapy, known as Electrochemotherapy is emerging. This involves application of high intensity, short duration pulses at the tumor site, which enhances the biopotential across the phospholipid bilayers of the cell plasma membrane and hence opens up pores for enhanced uptake. The electric field intensity and distribution is shaped by the electrode geometry, size, material and the tissue treated. In this research, we investigated the influence of different electrodes on the electric field intensity and distribution. For this purpose, platinum and surgical steel needle array hexagonal and pentagonal electrodes were used. ANSYS, the industry standard software that uses finite element method was used to study the electric field distribution, intensity and contour. Both, healthy tissue and tumor tissue were used to identify the electric field intensity and distribution using these various electrode configurations and materials, for unipolar and bipolar voltages were studied. The results indicate that the electric field distribution, both in magnitude and pattern is similar for both electrodes, for both configurations and materials, which is desired from the clinical aspect. The electric field intensities for the hexagonal and pentagonal needle electrodes were 1280V/cm and 1180V/cm respectively in the case of tumor tissue (correlating well with the desired level of 1200V/cm). They were 835V/cm and 843V/cm for these electrodes in the case of healthy tissues. The values were same in the case of bipotential and negative voltages too.