On the Stability of Electric Arc Discharges

The stability of electric arc discharges has been explored through the use of an energy balance coupled with charge conservation. In order to facilitate this analysis, a new model for the electrical conductivity function has been proposed. Asymptotic solutions for the arc governing equations have been obtained. Stability criteria have been developed from both the linear theory (infinitesimal size disturbance) and from a minimizing solution point of view for finite size disturbances. The results delineate an open region in the stability diagram where arc instabilities may be possible

Charged Particle Distributions and Heat Transfer in a Discharge Between Geometrically Dissimilar Electrodes: From Breakdown to Steady State

The low-current electric discharge from a fine wire anode to a planar cathode in atmospheric pressure air is numerically simulated from high-voltage prebreakdown through electron temperature growth, then ionization and consequent current growth to steady state, limited by a ballast resistor in the external circuit. Conservation of number ~mass! for ions and electrons, Gauss’ law for the self-consistent electric field, and energy conservation for electrons have been solved from breakdown to steady state in a body fitted coordinate system generated specifically for these two geometrically dissimilar electrodes. To facilitate the discussion of the results, the discharge has been categorized under ~a! electron acceleration period, ~b! charged particle generation period, ~c! current increase and voltage drop period, and ~d! current and voltage stabilization period. Results are given for transient electron, ion, and temperature distributions in the gap as well as current growth and voltage drop across the gap. Heat flux from the discharge to the wire is calculated. The numerical simulations were compared with experiments performed under the same conditions on a wire bonding machine with very close correspondence

Effect of Negative Ions on Electrical Breakdown in a Nonuniform Air Gap Between a Wire and a Plane

Electrical breakdown of an axisymmetric, atmospheric pressure air gap between a wire and a plane has been investigated for a gap length of 0.5 mm. 0- and 02- have been identified as the negative ions affecting the discharge development in air, besides electrons and positive ions, and have been included in the electrical breakdown model. Five coupled two-dimensional transient partial differential equations describing the discharge evolution in the air gap have been solved using a finite difference algorithm developed earlier. Temporal development of the charged particle number densities, electrostatic potential, electric field, and current at both the electrodes is presented when the wire is negatively biased at 2500 V. The impact of negative ions on gap breakdown has been assessed by comparing the results of analyses with and without negative ions. It is concluded that the negative ions have negligible effect during the early stages of the discharge development. However, as the discharge evolves, the negative ions cause a net loss of electrons from the discharge. The effect is most pronounced away from the discharge axis, where peaks in the electron density occur as breakdown proceeds. Radial spread of discharge and current growth rate are relatively unaffected by the presence of negative ions, but the magnitude of total current at the electrodes has been found to decrease by a decade when the negative ions are present

Two-Dimenslonal Analysis of Electrical Breakdown in a Nonuniform Gap Between a Wire and a Plane

Electrical breakdown of a gap between a wire (modeled as a hyperboloid) and a plane has been investigated numerically by solving the two-dimensional form of the diffusion flux equations for the charged particle number densities and Poisson\u27s equation for the self-consistent electric field. Electron impact ionization, thermal ionization, and three-body recombination have been considered as the charged particle production and loss mechanisms. The electrode surfaces are considered to be absorbing and the initial density of the particles is small, but nonzero, A gap length of 0.5 mm is investigated and the gas medium is air or argon at atmospheric pressure. The temporal development of the profiles of ion and electron number densities, potential and electric field, and current growth on both the electrodes are presented when the applied voltage is 1500 and 2500 V for both positive and negative wires. When the wire is negatively biased, the peaks in the radial distribution of both of the charged particle densities near the wire occur off the axis except during the very early part of the breakdown. With positive polarity, the electron density maximum always occurs on the discharge axis, while for ions it moves away from the axis, later in the transient, due to the reverse particle drift in the electric field from the negative polarity case, The discharge spreads farther out into the ambient (almost two times the gap length) when the wire is negatively biased than with positive polarity. The effect of charge separation on the externally applied electric field is significant at voltages 2500 V and higher. Ionization is greater in argon than in air for a fixed potential difference between the electrodes

Electrode Heating in a Wire-to-Plane Arc

A steady wire-to-plane electric discharge has been modeled in a prolate spheroidal coordinate system with the wire shape taken as a hyperboloid of revolution. A set of continuum conservation equations for the charged particle densities and temperatures together with Poisson’s equation for the self-consistent electric potential describe the steady electric discharge process. These equations have been solved numerically to obtain ion and electron densities, temperature distribution, and electrode heat fluxes. Particle densities show the main body of the arc is quasineutral bounded by space charge sheaths at both electrodes. The temperature is greatest in a region around the discharge axis about one-third of the distance from the wire to the plane. Strong electric fields are concentrated in the electrode sheaths. The heat flux to the wire is sharply peaked near the tip but on the plane it decays slowly away from the discharge axis. The knowledge of heat transfer from the arc to the electrodes is useful in determining arc parameters that govern the ball formation process used in wire bonding of microelectronic semiconductor chips as well as welding processes

Thermal and electrical characteristics of a two‐dimensional tanh‐conductivity arc

The two-dimensional variable-property arc has been studied through the use of the tanh-conductivity model. Results that describe the thermal and electric arc characteristics for various values of the electrode temperatures and aspect ratios are given. The numerical evaluation is carried out by the use of a Galerkin technique. The results exhibit several novel and interesting features depending on the arc parameters. For large aspect ratios (ratio of the interelectrode distance to that between the bounding walls) and small electrode temperatures, the current---electric-field characteristics tend toward those of a slender arc. However, at a given aspect ratio with large enough electrode temperatures, the distinct minimum noted in the slender-arc characteristics does not occur. Also, for a given aspect ratio and large enough differences in electrode potential, the electric-field-current characteristic is nearly linear and is independent of the electrode temperature. The transverse electrostatic potential is found to have no significant variation in cross-sectional planes. The qualitative nature of the thermal characteristics are similar to those of a constant-property arc although significant differences in quantitative results exist. Wall and electrode heat transfer rates are provided

Oscillatory enhancement of the squeezing flow of yield stress fluids: A novel experimental result

The extrusion of a yield stress fluid from the space between two parallel plates is investigated experimentally. Oscillating the magnitude of the squeezing force about a mean value (F = f[1+αcos(ωt)]) was observed to significantly enhance the flow rate of yield stress fluids, while having no effect on the flow rate of Newtonian fluids. This is a novel result. The enhancement depends on the magnitude of the force, the oscillatory frequency and amplitude, the fluid being squeezed, and the thickness of the fluid layer. Non-dimensional results for the various flow quantities have been presented by using the flow predicted for the constant-force squeezing of a Herschel-Bulkley yield stress fluid as the reference. In the limit of constant-force squeezing, the present experimental results compare very well with those of our earlier theoretical model for this situation (Zwick, Ayyaswamy & Cohen 1996). The results presented in this paper have significance, among many applications, for injection moulding, in the adhesive bonding of microelectronic chips, and in surgical procedures employed in health care

Evaporation and Combustion of a Slowly Moving Liquid Fuel Droplet: Higher-Order Theory

The evaporation and combustion of a single-component fuel droplet which is moving slowly in a hot oxidant atmosphere have been analysed using perturbation methods. Results for the flow field, temperature and species distributions in each phase, interfacial heat and mass transfer, and the enhancement of the mass burning rate due to the presence of convection have all been developed correct to second order in the translational Reynolds number. This represents an advance over a previous study which analysed the problem to first order in the perturbation parameter. The primary motivation for the development of detailed analytical/numerical solutions correct to second order arises from the need for such a higher-order theory in order to investigate fuel droplet ignition and extinction characteristics in the presence of convective flow. Explanations for such a need, based on order of magnitude arguments, are included in this article. With a moving droplet, the shear at the interface causes circulatory motion inside the droplet. Owing to the large evaporation velocities at the droplet surface that usually accompany drop vaporization and burning, the entire flow field is not in the Stokes regime even for low translational Reynolds numbers. In view of this, the formulation for the continuous phase is developed by imposing slow translatory motion of the droplet as a perturbation to uniform radial flow associated with vigorous evaporation at the surface. Combustion is modelled by the inclusion of a fast chemical reaction in a thin reaction zone represented by the Burke-Schumann flame front. The complete solution for the problem correct to second order is obtained by simultaneously solving a coupled formulation for the dispersed and continuous phases. A noteworthy feature of the higher-order formulation is that both the flow field and transport equations require analysis by coupled singular perturbation procedures. The higher-order theory shows that, for identical conditions, compared with the first-order theory both the flame and the front stagnation point are closer to the surface of the drop, the evaporation is more vigorous, the droplet lifetime is shorter, and the internal vortical motion is asymmetric about the drop equatorial plane. These features are significant for ignition/extinction analyses since the prediction of the location of the point of ignition/extinction will depend upon such details. This article is the first of a two-part study; in the second part, analytical expressions and results obtained here will be incorporated into a detailed investigation of fuel droplet ignition and extinction. In view of the general nature of the formulation considered here, results presented have wider applicability in the general areas of interfacial fluid mechanics and heat/material transport. They are particularly useful in microgravity studies, in atmospheric sciences, in aerosol sciences, and in the prediction of material depletion from spherical particles

Breakdown of a Wire-to-Plane Discharge: Transient Effects

A wire-to-plane discharge during the early phases of breakdown has been studied. The discharge has been modeled in a prolate spheroidal coordinate system with the wire shape taken as a hyperboloid of revolution. Four simultaneous coupled, time-dependent, nonlinear partial differential equations describe the electrical discharge. These are the conservation equations for ion and electron densities, the energy equation for electron temperature, and Poisson’s equation for the self-consistent electric field. By solving this formulation subject to appropriate initial and boundary conditions, charged particle densities and temperature variations have been obtained as the ionization progresses in the discharge. The results show that both the electron temperature and the charged particle densities increase with the progress of ionization. The effect of different wire polarities is also examined. With a positive wire polarity, the increases in electron temperature and charged particle densities are confined to regions of the discharge in the vicinity of the wire tip. With a negative wire polarity, the breakdown occurs in the entire gap at a faster rate than with a positive wire polarity. The wire polarity affects the magnitude of energy transfer between the particles

An Evaluation of the Various Short Forms of the Wechsler-Bellevue Test

The need for a rapid and efficient method of estimating adult intellectual level on an individual examination basis has been felt with increasing urgency in the past few years. An instrument of this type should include, to as great an extent as possible, the statistical advantages of a well standardized individual test along with the advantage of administrative economy. A brief scale meeting these criteria should be useful as a clinical screening device. It should be of some service as a method of sifting out of a large group those individuals who should be given further examination. Such an instrument should also be useful for various placement problems where large groups must be dealt with, and as an aid in research where groups or individuals need to be matched for intelligence