Determination of Electric Field Distributions Along Fluid-Solid Dielectric Interfaces Using a Schlieren Technique

The Kerr electro-optic technique is used to investigate electric field and space charge effects using large Kerr constant propylene carbonate as the dielectric liquid with Kerr constant B≈1.22×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> m/V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . However, improved accuracy of this technique to measure space charge distributions remains an important goal. This paper describes inversion algorithm research on obtaining accurate space charge distributions from Kerr measurements. The original charge-coupled device (CCD) image of light intensity was converted into grayscale values for improved calculation. The grayscale CCD image was transformed into the frequency domain through a two-dimensional Fourier transformation. Butterworth filtering techniques were employed for edge enhancement algorithms. The most important parameter for calculation of space charge distributions are the integer fringe numbers n in the sequence of light and dark fringes measured by the CCD camera. Comparison of the improved algorithm and traditional methods for calculating electric field and space charge distributions between a pair of stainless steel parallel plate electrodes was investigated. The space charge dynamics were also calculated after processing the CCD images with some improvements. The results showed the electric field was essentially uniform at early times of pulsed high voltages. This uniformity indicated the absence of space charge during the early transient interval, while a bipolar charge injection was found in the central region between electrodes at later times. For longer times the electric field and space charge distributions slowly became uniform again. Grayscale processing and Butterworth filtering played an important role in the improvement of the algorithm for better image quality and edge enhancement.

Homocharge, particularly, positive charge near anode has been observed inside low-density polyethylene (LDPE) by many researchers. However, the phenomenon is yet to be understood theoretically and mathematical analysis is pending, although, simulations have been reported. Simulation of evolution of space charge in LDPE, with time and space, using bipolar charge transport model considered only drift component of charge carriers inside the dielectric. The experimental results suggest significant concentration gradient in space charge distribution. The authors derived a comprehensive drift and diffusion based analytical models, for the time/space evolution of space charge and electric field in dielectrics using Maxwell's equations, current continuity equation, conduction and injection mechanisms. The proposed analytic models of electric field and space charge distribution entwines charge injection at electrodes and charge transport inside the medium, which seem to have not been reported until now. Remarkable, believed to be unprecedented, agreement between the analytical and experimental results has been observed. Using the model, the role of conduction, injection, diffusion on homocharge accumulation has been investigated. Pulsed electroacoustic method is used for the measurements of the space charge dynamics.

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.

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.

Polypropylene laminated paper (PPLP) is an important composite insulation which has been successfully used in oil filled (OF) cable, mass impregnated (MI) cable and high temperature superconductor (HTS) cable. PPLP is an improved insulation based on conventional cellulose Kraft paper. It is made of one PP film sandwiched between two Kraft papers. The space charge distribution in DDB oil impregnated PPLP sample under DC electric field has been investigated by the pulsed electroacoustic (PEA) technique in this paper. The electric field distribution and distortion have been discussed based on the results obtained from one, two and three layers of PPLP sample. The results show that space charges start to accumulate at the interfaces between paper and PP with time. As a result, the electric field created by the accumulated space charge within the PP film has been enhanced while the electric field in paper reduced. The more the charge accumulated, the higher the electric field distortion in the PP film. The charge distribution and electric field distortion present repeatable pattern in multilayered PPLP sample.

Many high voltage conduction models assume drift dominated conduction where each charge carrier has a constant mobility with negligible diffusion effects. Then the charge carrier velocities are proportional to the local electric field while in turn the electric field is related to the net local charge density through Gauss's law. Recent work has developed general transient time and spatial solutions of the electric field and space charge distributions and the terminal voltage - current characteristics for any initial and charge injection boundary conditions and for any type of terminal excitation or constraint (1).

A drift dominated conduction model is often used in the analysis of charge transport through a dielectric where the velocities of charge carriers are proportional to the local electric field through their mobilities. In return the electric field is also related to the carrier charge densities through Gauss's law. Using this conduction model recent work has developed a generalized method which solves for the electric field and space charge distributions and the time dependence of the terminal current for any initial and boundary conditions with any terminal excitation or constraint.1–5 While this past work has emphasized the transient response to a step voltage, in this study we consider a sinusoidally varying applied voltage for bipolar conduction including Langevin recombination6 and also consider the effects of a lossy dielectric with ohmic conductivity. Analytical solutions for the terminal current are compared to preliminary experiments.

A complete finite-element analysis method for corona discharge process, which is governed and coupled by charge transport equation and electric field equation, was presented. The charge transport equation of first order was transformed into second order by utilizing the artificial diffusion scheme. The two second-order equations were analyzed by the finite-element formulation which is well-developed for second-order equations. The Fowler-Nordheim injection boundary condition was adopted for charge transport equation. After verifying the numerical results by comparing to the analytic solutions using parallel plane electrodes with one carrier system, we extended the result to blade-plane electrodes in 2-D xy geometry with three carriers system. Radius of the sharp tip was taken to be 50 mum. When this sharp geometry was solved by utilizing the space discretizing methods, the very sharp tip was found to cause a singularity in electric field and space charge distribution around the tip. To avoid these numerical difficulties in the finite-element method, finer meshes, a higher-order shape function, and artificial diffusion scheme were employed

The current continuity equation is usually applied to solve DC electric field distribution when there is inhomogeneous material conductivity due to temperature gradient or multi‐layer dielectrics. However, in the presence of charge accumulation, which may result from the process of electrode injection, impurity ionisation or charge trapping, the material conductivity is in tangled relationship with local field strength, and the current continuity equation can be hardly applied due to the ignorance of conductivity distribution. Thus, quantitative analysis on the effect of space (surface) charge for DC apparatus with inhomogeneous material conductivity has been a difficult problem, which requires a complicated physical model to solve. This paper has proposed a simple method to compute the synergetic influence of inhomogeneous conductivity and the space charge on the DC field distribution; through assigning bulk (interface) charge as functions of local material conductivity and field strength, the effect of inhomogeneous conductivity can be incorporated in Gauss' law and the space charge accumulation can be further included in the equation. The effect of space (surface) charge on electric field distribution in DC apparatus with temperature gradient as well as multiple‐layer dielectrics is simulated through the proposed method, which shows that the method has offered a convenient approach for investigating the effect of charge accumulation on DC field distribution under various insulation structure and working conditions.

In this paper, electric field, potential and temperature distributions of normal and fog type insulators were examined. These insulators were modeled in 3D. Simulations were made with COMSOL Multiphysics program using Finite Element Method. The pollution layer was modeled by a layer of 0.5 mm thickness on the insulator surface and the conductivities of the insulator's upper and bottom layers were varied from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup> and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> S/m values. Potential and electric field distributions at 11 kV (rms) for clean, uniform and non-uniform pollution conditions and the temperature distributions at 11-15-20 kV (rms) for clean and uniform pollution conditions were examined. The results showed that when the pollution layer conductivity increased, the potential distribution approached the linear state and the electric field strength decreased. The temperature values increased with the applied voltage and conductivity increase.

This paper presents the results of electric field and potential distributions simulation along surface of silicone rubber polymer insulators.Finite element method (FEM) is adopted for this paper.Identification of the electrical field and the potential distributions at the dielectric insulation has always been important; The water droplets increase the electric field strength at the insulator surface because of their high permittivity and conductivity, at first the results of water droplets existing on the surface of silicone rubber materials has been investigated and electric field distribution along the surface are shown.Then Different Thickness and conductivity of pollution layer on polymer insulator has been considered and electrical field distribution has been analyzed.

Under the HVDC condition, the formation of the space charge in the oil paper system could affect the electric field distribution for converter transformers. Therefore, it is important to analyze the factors that determine the space charge behavior such as the temperature, moisture, electric field, oil paper thickness ratio and multilayers such as (Oil+Paper+Oil+Paper) structure. This paper focuses on the space charge distribution affected by the multilayers (O+P+O+P) oil paper structure and different oil paper thickness ratios. The pulsed electroacoustic method (PEA) was used to measure space charge distributions. It is found that increasing oil thickness could facilitate charge injection. However, the increase of pressboard thickness could prevent the charge injection. It is also found that the same oil paper thickness ratio could lead to similar space charge injection within the oil paper sample under the same 10 kV/mm electric field. Therefore, based on the same oil paper thickness ratio, space charge measured from the thinner thickness sample were further applied to the thicker thickness sample to estimate electric field distribution using COMSOL software, which cannot be measured by the PEA system directly.

When sufficiently high voltages are applied to electrical insulators, electrical breakdown occurs at some time after the voltage is applied. This time delay to breakdown coupled to time of flight measurements of charge carrier mobilities obtained from peaks in the current waveform, provides information on insulation and conduction characteristics of the dielectrics. In addition, the bulk electric field and space charge distributions can be measured using the Kerr electro-optic effect for those dielectrics which become birefringent when stressed by high voltages, such as water <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and nitrobenzene. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> A short circuit analysis applied during the post breakdown period.

We present investigations of the distribution of space charges in thin films of conjugated polymers. A thermal wave method (LIMM) has been used to resolve the depth profile of space charges and the distribution of the internal electric field in 3–4 µm films of poly(2,5‐pyridinediyl), the poly(p‐phenylenvinylene) derivative poly[2‐methoxy,5‐(2′‐ethyl‐hexyloxy)‐1,4‐phenylenvinylene] (MEH‐PPV) and polyfluorine (PFO). The results demonstrate that in conjugated polymers, space charges cannot only be created but can also be stored permanently. The electric field in the bulk of the film is significantly reduced because of the existence of two space charge layers: a narrow, positively charged layer at the front electrode, and a broader, negatively charged layer at about 500 nm. We assign the positive layer to the injection of positive charge carriers from the anode into near surface traps, and the second hetero‐charge layer to bulk charges that have been separated within the external electric field and accumulated in the trapping zone. The dynamics of the accumulation and poling of the space charge layers has been investigated by means of measurements of the temporal evolution and temperature dependence of the pyroelectric response.© 2002 Society of Chemical Industry

“Giant” undulations on the equatorward boundary of the evening diffuse aurora, occasionally observed during a substorm, are numerically simulated. A “giant” undulation is defined as a waveform having the crest‐to‐trough amplitude comparable to the wavelength. The two‐dimensional particle code is used for studying the motion of magnetospheric plasma perpendicular to the geomagnetic field. Based on the observational facts, it is assumed that in the auroral magnetosphere there exist azimuthally aligned sheets of enhanced density, which are called arc sheets. (Arc sheets inside the inverted‐V structure can actually be responsible for discrete arcs.) The simulation model for giant undulations assumes the presence of an arc sheet equatorward of the proton diffuse aurora. Anomalous cross‐field diffusion of the arc sheet protons leads to polarization of the arc sheet. The polarized arc sheet is such that a negative charge sheet is sandwiched between two positive charge sheets. The polarized arc sheet is subject to a Kelvin‐Helmholtz (K‐H) instability due to a velocity shear generated in the arc sheet. The K‐H waves associated with the arc sheet can spatially modulate the equatorward boundary of the proton diffuse aurora. In the actual simulation, the temporal evolution of the diffuse auroral pattern, as displayed in photographs from the satellites, can be visualized by following the cluster of the energetic protons. The outstanding indentations characteristic of observed giant undulations are successfully reproduced. There have been a few examples of the satellite measurements of electric fields, field‐aligned currents, and fluxes of precipitating particles around the undulating diffuse auroral boundaries. The distributions of electric fields and space charges obtained from the simulation are found to be consistent with these observations. Therefore, giant undulations on the equatorward diffuse auroral boundary can be identified with spatial modulation of the energetic protons by the K‐H waves arising from the polarized arc sheet.