Modelling of corona discharge in cylinder-wire-plate electrode configuration

Numerical computation of the electric field strength and ionic space charge density in electrode systems consisting of ionizing wire and non-ionizing cylinder, connected to the same DC high-voltage supply and facing a grounded plate, is a difficult problem, which is of interest to several electrostatic processes applications. In a previous study a simple numerical method has been proposed to calculate the spatial distributions of electric field and ionic space charge in a case of a continuum and uniform corona discharge originating at the surface of the wire. The aim of the present paper is to improve the physical model of the corona discharge in this particular electrode configuration, by assuming a more realistic law of charge injection on the wire circumference. The computations were carried out for an ionizing wire of radius r=0.1 mm, located at different distances h from a metallic tubular support of radius R=13.4 mm.The initial conditions of the corona discharge took into account the non-uniformity of the charge injection around the ionizing wire electrode. The computational results were compared with those obtained under the assumption of uniform corona discharge. The comparison pointed out that neither the non-uniformity of the electric field nor that of the charge injection can be neglected. They depend on the geometry of the electrode system and affect the distribution of the electric field and of the space charge density in the inter-electrode gap.     

Modeling of corona under positive lightning surges

A novel corona model for predicting the corona characteristics under positive lightning surges is proposed. The ionization process is described by a series of successive generations of electron avalanches. A simplified method is presented for computing the electric field in the ionization zone. With a discrete treatment for the ionization process in time and space, the proposed model computes the total charge of corona from the applied surge voltage and so the q–u curves can be obtained. A laboratory measurement of q–u curves is also made by a coaxial cylindrical electrode to check the validity of the proposed model.     

Impulse breakdown characteristics of the plane-to-plane electrode system with a needle-shaped protrusion in SF6

This paper presents the impulse pre-breakdown and breakdown characteristics of the plane-to-plane electrode system with a needle-shaped protrusion in SF₆ gas. The breakdown voltage–time (V–t) characteristics and the breakdown voltage–gas pressure (V–p) characteristics of a highly non-uniform SF₆ gas gap under positive and negative lightning impulse voltages are investigated in the pressure range between 0.1 and 0.5 MPa. The pre-breakdown developments are examined by the corona current and light emission measurements with high time resolution. As a result, the dielectric strengths versus time-to-breakdown of SF₆ gas gap under positive lightning impulse voltages were nearly independent of the gas pressure. The first streamer corona was initiated at the tip of the needle electrode, and the streamer corona pulses developed with a stepwise propagation. The discharge paths were zigzag, and the branches of the discharge channel for positive polarity were created. On the other hand, the leader channel in the negative polarity was thicker and brighter than that in the positive polarity.     

Sliding discharge in air at atmospheric pressure: electrical properties

Several studies have shown that a surface non-thermal plasma may be used as an electrofluidodynamic actuator for airflow control. For few years, we has been working on this subject, especially in the case of DC corona discharges and AC barrier discharges established at the wall of profiles. The present paper deals with a new type of surface plasma using a sliding discharge. This discharge, excited here by a negative AC voltage with a positive DC component, is created in a three-electrode geometry: one DC positive electrode and two negative AC electrodes at the same voltage. Then a barrier discharge is established between the positive electrode and the first negative one when a surface corona discharge or sliding discharge is generated between the positive electrode and the second negative one. In this preliminary study, the goal is to obtain a stable sliding discharge. Then the electrical properties of this discharge are observed and briefly discussed.     

真实人体鼻腔三维重建和气流特性的数值模拟

为研究人体鼻腔内的气体流动和颗粒沉积状况,基于19岁男志愿者的螺旋CT医学图像,采用医学有限元方法和逆向工程技术,重构了真实人体鼻腔的三维几何模型.采用RNG k-ε湍流模型和有限差分数值方法对志愿者在Q=15 L/min(人体平静时刻)、Q=30 L/min(小负荷运动时刻)、Q=60 L/min(大负荷运动时刻)三种呼吸强度下的鼻腔内的气体流动特性进行了数值模拟与分析,得到了呼吸时鼻腔内的压力和气流分布规律,并在拉格朗日框架下跟踪了颗粒的运动和沉积.以3μm粒径颗粒为研究对象,可视化显示了其在鼻腔内的沉积位置.本研究对呼吸时人鼻腔中气体流动特性、气雾剂治疗等问题深入探讨具有参考价值.     

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k–? turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.     

Visualization of the local ionic wind profile in a DC corona discharge field by laser-induced phosphorescence emission

Experimental visualization for ionic wind motion originated from DC corona discharges in a needle-plate electrode system has been investigated. A vapor-phase biacetyl tracer with laser-induced phosphorescence emission is used for optically characterizing the ionic wind profile. The ionic wind blows the excited biacetyl molecules away in continuing the visible phosphorescence emission for a long radiative lifetime. The captured image with elapsing time from the excitation presents the shifting location of radiative tracer along the ionic wind direction. The experimental results show the ionic wind profile enhanced in the electric field direction corresponding to the corona discharge progress. Especially, the ionic wind near an initiating point of corona discharges is focused as an advantage of this optical technique. The ionic wind velocity along the electrode axis can be obtained at the location close enough to the corona discharge initiation point, and the velocity at 0.5 mm from the discharge point is figured out as 9.3 to 19.2 m/s under the condition of the EHD Reynolds number of 0.95×10³ to 2.1×10³.     

Flow distribution and pressure of air due to ionic wind in pin-to-plate corona discharge system

An electrohydrodynamic investigation has been carried out in a pin-to-plate gas discharge system to clarify the mechanism of repulsive force generation between a pin and plate electrode at corona discharge. Numerical calculations have been conducted in two steps. First, the axi-cylindrical static corona discharge field was calculated with the finite-element method to deduce the Coulombic body force ρ E applied to the air, where ρ is the charge density and E is the electric field, and then the induced ionic wind was calculated with the finite differential method. The calculated pressure distribution on the plate electrode was on the order of 10 Pa which was in good agreement with the measured pressure distribution. The calculated air velocity at the center was several m/s and was confirmed by a time-of-flight experiment and the velocity distribution near the pin electrode also agreed with measurements using a laser Doppler velocimeter. Pressure and wind velocity were increased at high-applied voltage. These results confirm that the ionic wind is the cause of the repulsive force to the pin electrode at the corona discharge.     

Numerical study of EHD-enhanced water evaporation

A numerical model has been developed for the investigation of water evaporation enhanced by corona wind. The corona wind is generated by a wire electrode charged at a high dc voltage. Only positive corona discharge is considered in the present study. The effect of cross-flow on EHD-enhanced water evaporation is also examined. The results show that water evaporation can be greatly enhanced by corona wind. However, a cross-flow with a high velocity may diminish the effect of corona wind. The numerical results are also compared with experimental data reported in the literature. A satisfactory agreement is found between these results.     

Corona “impedance” in a pin-to-plane geometry

Our work focuses on the analysis of binary hydrocarbon mixtures, namely cyclopentane, 1-pentene and pentane. The purpose is to describe, analyze, and model the conduction properties of selected hydrocarbons, as well as to find a method for modifying the composition of hydrocarbon mixtures in order to obtain the desired discharge properties. Data analysis is performed in terms of the corona “impedance” of the discharge medium. In a logarithmic coordinate system, experimental data show a first-order dependence of the corona “impedance” of the electrode gap on the corona current, which appears to be more general in nature. Starting from a conic approximation of the geometry of the effective discharge area, we have derived a model where the mentioned linearity can be reduced to an expression that closely matches experimental data.     

Unipolar model of negative corona discharge: Comparison of calculated and experimental <Emphasis Type="Italic">I–V</Emphasis> characteristics for the sphere–plane electrode system

Substantial computational resources and time are needed for computer simulation of the corona discharge with allowance for the sheath processes. This circumstance necessitates a search for and development of simplified models in which the processes in the sheath of corona discharge are reduced to the boundary condition at the surface of active electrode. A unipolar model that takes into account only one type of carriers is considered, and the boundary condition on the discharge electrode describes the rate of variations in the electron-flux density from the sheath. The calculated I–V characteristics are compared with experimental data for interelectrode distances ranging from several millimeters to several centimeters to reveal the applicability of the model. The simulated and experimental results are in good agreement at interelectrode distances of greater than 1 cm.     

An efficient finite volume method for electric field–space charge coupled problems

The goal of this paper is to introduce some recently developed finite volume schemes to enable numerical simulation of electric field–space charge coupled problems. The key features of this methodology are the possibility of handling problems with complex geometries and accurately capturing the charge density distribution. The total variation diminishing (TVD) scheme and the improved deferred correction (IDC) scheme are used to compute the convective and diffusive fluxes respectively. Our technique is firstly verified with the computation of hydrostatic solutions in a two coaxial cylinders configuration. The homogeneous and autonomous injection from the inner or outer electrode is considered. Comparison has been made with the analytical solution. The numerical technique is also applied to the problem of corona discharge in a blade-plane configuration. The good agreement between our numerical solution and the one obtained with a combination approach of Finite Element Method (FEM) and Method of Characteristics (MoC) is shown.     

Three-dimensional EHD simulation for point corona electrostatic precipitator based on laminar and turbulent models

The three-dimensional flow interaction for tuft or point corona for industrial electrostatic precipitators was investigated using both laminar and turbulent flow models. The secondary flow distribution based on laminar flow model forms a pair of organized donut-shaped rings generated from every corona or tuft points, while a pair of rings is less organized for turbulent flow model. When the primary flow exists, the organized spiral motion for turbulent model is further diffused in the direction of gas flow and increased N_EHD, which leads to turbulent flow. Turbulent model appears to be more appropriate for predicting the wire-plate ESP based on experimental investigation.     

A numerical analysis on flow field and heat transfer by interaction between a pair of vortices in rectangular channel flow

This paper is a numerical study of the effect of flow field and heat transfer created by interactions between a pair of vortices generated by a vortex generator in a rectangular channel flow. In order to analyze the vortices produced by the vortex generator, the pseudo-compressibility method is introduced into the Navier–Strokes (NS) equation of a three-dimensional unsteady, incompressible viscous flow. A two-layer k–ε turbulence model is used on the flat plate three-dimensional turbulence boundary to predict the turbulence characteristics of the vortices. The computational results accurately predict the vortex characteristics, which are related to Reynolds stress, turbulent kinetic energy, and flow field. Also, in the prediction of thermal boundary layers, skin friction characteristics, and heat transfers, the present results are reasonably close to the experimental results obtained by other researchers.     

A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell

Using Kirchhoff transformation, we develop a Dirichlet–Neumann alternating iterative domain decomposition method for a 2D steady-state two-phase model for the cathode of a polymer electrolyte fuel cell (PEFC) which contains a channel and a gas diffusion layer (GDL). This two-phase PEFC model is represented by a nonlinear coupled system which typically includes a modified Navier–Stokes equation with Darcy’s drag as an additional source term of the momentum equation, and a convection–diffusion equation for the water concentration with discontinuous and degenerate diffusivity. For both cases of dry and wet gas channel, we employ Kirchhoff transformation and Dirichlet–Neumann alternating iteration with appropriate interfacial conditions on the GDL/channel interface to treat the jump nonlinearities in the water equation. Numerical experiments demonstrate that fast convergence as well as accurate numerical solutions are obtained simultaneously owing to the implementation of the above-described numerical techniques along with a combined finite element-upwind finite volume discretization to automatically control the dominant convection terms arising in the gas channel.     

Improved fictitious charge method for calculations of electric potential and field generated by point-to-plane electrodes

In the framework of standard tip-to-plane electrode geometry favorable to corona streamer discharge development at atmospheric pressure, this work is devoted to the improvement of fictitious charge method for calculations of electric potential and field repartition when the tip is powered by a DC voltage. It is in fact dedicated to implement the image charge method (generally used in plane-to-plane electrodes) in the case of a point-to-plane geometry. The numerical method is based on the solution an open system of n equations with m unknowns (n >> m) where m is the number of fictitious charges and n the number of contours at the surface of the tip electrode defining the boundary conditions. This numerical technique can accurately interpolate the shape of the electrode tip whatever its geometry and hence allows us to accurately calculate the electric potential and field even at a position very close to the electrode. It is noteworthy that the solution of such open system of equations cannot be obtained from conventional techniques (Cramer, Gauss, matrix inversion, etc.). We used the method of least squares which enables us to close the equation systems and to find the optimal solution fulfilling all the required boundary conditions. The present method is therefore based on the coupling between the conventional method of fictitious charges using image charge method and the optimization by the Least Squares Method. The results of simulation show that the punctual fictitious charges have given the most accurate results when the electrode has symmetry of revolution like the present geometry of a pen shape anode cylinder ended by a sharp tip set in front of cathode plane.     

Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry

The gas-kinetic numerical algorithm solving the Boltzmann model equation is extended and developed to study the three-dimensional hypersonic flows of spacecraft re-entry into the atmosphere in perfect gas. In this study, the simplified velocity distribution function equation for various flow regimes is presented on the basis of the kinetic Boltzmann–Shakhov model. The discrete velocity ordinate technique and numerical quadrature methods, such as the Gauss quadrature formulas with the weight function 2/π^1/2exp(?V²) and the Gauss–Legendre numerical quadrature rule, are studied to resolve the barrier in simulating complex flows from low Mach numbers to hypersonic problems. Specially, the gas-kinetic finite-difference scheme is constructed for the computation of three-dimensional flow problems, which directly captures the time evolution of the molecular velocity distribution function. The gas-kinetic boundary conditions and numerical procedures are studied and implemented by directly acting on the velocity distribution function. The HPF (high performance fortran) parallel implementation technique for the gas-kinetic numerical method is developed and applied to study the hypersonic flows around three-dimensional complex bodies. The main purpose of the current research is to provide a way to extend the gas-kinetic numerical algorithm to the flow computation of three-dimensional complex hypersonic problems with high Mach numbers. To verify the current method and simulate gas transport phenomena covering various flow regimes, the three-dimensional hypersonic flows around sphere and spacecraft shape with different Knudsen numbers and Mach numbers are studied by HPF parallel computing. Excellent results have been obtained for all examples computed.     

An approach for unipolar corona discharge in N2/O2 gas mixture by considering townsend conditions

In this study (α/p) = f(E/p) functional relation is derived for the gas mixture of N₂/O₂ by considering Townsend approach, and formation mechanism of corona discharge is investigated for the coaxial electrode system located in this gas medium. The electron energy distribution function (EEDF) which is required for estimation of ionization coefficient, is determined by considering probability distribution function of inelastic electron collisions versus energy. An algorithm for determining ionization coefficient for binary gas mixture is presented. The development and motion of the electron avalanche in inter-electrode gap are studied by considering the effect of positive space charges. It is determined by considering the derived mathematical expressions that the formation of corona discharge is related with the variation of the current characteristics in inter-electrode gaps depending on the change of potential of central electrode.     

Modelling of ions for seeding technique to electrify the atmosphere

There are number of ways in which weak electrification can affect the microphysics of clouds, with consequences for cloud lifetime, radiative properties, and precipitation efficiency. Kauffman [2011] suggested ions produced by direct current generators will add to and enhance the catalysing effects that cosmic ray ions are now known to produce in among other things, lowering nucleation barriers, stimulating charged particle growth and stability and increasing the scavenging rate in clouds. Thus to electrify the atmosphere ions can be generated artificially in abundance along with large electric field.Ions can be generated by the corona effect using Atmospheric electrifiers (a device used to generate negative ions) which makes use of corona discharge phenomenon to charge the air particles. Exact assessment of electric field and charge density distributions and the flow dynamics inside the electrifiers is essential to understand the particle behaviour inside the electrifiers.In this paper, a novel model of governing equations to evaluate the space charge density, electric field intensity and velocity of ionized airflow is suggested as a function of applied voltage. The Poisson and charge conservation equations are derived and hence can be used to estimate the electric field and charge density distributions. Navier stokes equation can be used to get the velocity of ionized airflow because of electric force on the air. Simulation is carried out to validate the proposed model and verify that velocity is function of input voltage and is proportional to it.     

Mechanism of electrohydrodynamically induced flow in a wire-non-parallel plate electrode type gas pump

An experimental investigation and one-dimensional modeling have been conducted to study the mechanism of net flow direction induced by electrohydrodynamic (EHD) forces in a wire-non-parallel plate electrode type EHD gas pump. The experiments were conducted with various different locations of corona wire electrode for negative and positive applied voltage from 0 to 14 kV at atmospheric pressure and room temperature, where air was used as the working fluid. A one-dimensional cross-sectional averaged model based on mass and momentum conservation as well as Poisson electric field and ion transport equations was also developed. The results show that the net flow direction of electrohydrodynamically induced gas flow in a wire-non-parallel plate electrode system significantly depends on the location of the corona wire electrode relative to the grounded electrode position. The effect of conversion angle of non-parallel plate electrode on the net flow direction and pressure drop also was investigated and discussed in detail.