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- Detailed numerical simulation of cathode spots in vacuum arcs: Interplay of different mechanisms and ejection of dropletsPublication . Kaufmann, H. T. C.; Cunha, M. D.; Benilov, M. S.; Hartmann, W.; Wenzel, N.A model of cathode spots in high-current vacuum arcs is developed with account of all the poten tially relevant mechanisms: the bombardment of the cathode surface by ions coming from a pre existing plasma cloud; vaporization of the cathode material in the spot, its ionization, and the inter action of the produced plasma with the cathode; the Joule heat generation in the cathode body; melting of the cathode material and motion of the melt under the effect of the plasma pressure and the Lorentz force and related phenomena. After the spot has been ignited by the action of the cloud (which takes a few nanoseconds), the metal in the spot is melted and accelerated toward the periph ery of the spot, with the main driving force being the pressure due to incident ions. Electron emis sion cooling and convective heat transfer are dominant mechanisms of cooling in the spot, limiting the maximum temperature of the cathode to approximately 4700–4800 K. A crater is formed on the cathode surface in this way. After the plasma cloud has been extinguished, a liquid-metal jet is formed and a droplet is ejected. No explosions have been observed. The modeling results conform to estimates of different mechanisms of cathode erosion derived from the experimental data on the net and ion erosion of copper cathodes.
- Space-resolved modeling of stationary spots on copper vacuum arc cathodes and on composite CuCr cathodes with large grainsPublication . Benilov, Mikhail S.; Cunha, Mário D.; Hartmann, Werner; Kosse, Sylvio; Lawall, Andreas; Wenzel, NorbertA self-consistent space-resolved numerical model of cathode spots in vacuum arcs is realized on the computational platform COMSOL Multiphysics. The model is applied to the investigation of stationary spots on planar cathodes made of copper or composite CuCr material with large ( 20 µm) chromium grains. The modeling results reveal a well defined spot with a structure, which is in agreement with the general theory of stationary cathode arc spots and similar to that of spots on cathodes of arcs in ambient gas. In the case of CuCr contacts with large chromium grains, spots with currents of the order of tens of amperes on copper coexist with spots on chromium with currents of the order of one or few amperes. The main effect of change of the cathode material from copper to chromium is a reduction of thermal conductivity of the cathode material, which causes a reduction of the radius of the spot and a corresponding reduction of the spot current.
- A simple model of distribution of current over cathodes of vacuum circuit breakersPublication . Cunha, Mário D.; Wenzel, Norbert; Almeida, Pedro G. C.; Hartmann, Werner; Benilov, Mikhail S.There are several hundreds of spots operating simultaneously on cathodes of vacuum arcs in high-power vac uum circuit breakers. In this work, the spot distribution along the contact surface is simulated by means of an approach that is based on the concept of surface density of spots and represents a natural alternative to tracing individual spots. An equation governing the evolution of the surface density of the spots or, equivalently, the distribution of macroscopic (averaged over individual spots) current density over the cathode is obtained by generalizing the concept of random walk of a single cathode spot in low-current vacuum arcs. The model relies on empirical parameters characterizing individual spots (the diffusion coefficient of the random motion of cathode spots and the velocity of drift superimposed over the random motion), which may be taken from experiments with low-current arcs, and does not involve adjustable parameters. The model is simple and physically transparent and correctly reproduces the trends observed in the experiments under conditions where the cathode arc attachment is diffuse. The distribution of the macroscopic current density on the cathode, given by the model, represents the boundary condition that is required for existing numerical models of vacuum arcs in high-power vacuum circuit breakers.
- Detailed numerical simulation of cathode spots in vacuum arcs—IPublication . Cunha, Mário D.; Kaufmann, Helena T. C.; Benilov, Mikhail S.; Hartmann, Werner; Wenzel, NorbertA model of cathode spots in high-current vacuum arcs is developed, with account of the plasma cloud left over from a previously existing spot, all mechanisms of current transfer to the cathode surface, including the contribution of the plasma produced by ionization of the metal vapor emitted in the spot, and the Joule heat generation in the cathode body. The simulation results allow one to clearly identify the different phases of life of an individual spot: the ignition, the expansion over the cathode surface, and the thermal explosion. The expansion phase is associated with a nearly constant maximum temperature of the cathode, which occurs at the surface and is approximately 4700–4800 K. Thermal explosion is a result of thermal instabil ity (runaway), which develops below the cathode surface when the Joule heating comes into play. The development of the spot is interrupted if the plasma cloud has been extinguished: the spot is destroyed by heat removal into the bulk of the cathode due to thermal conduction. Therefore, different scenarios are possible depending on the time of action of the cloud: the spot may be quenched before having been formed or during the expansion phase, or even at the initial stage of thermal explosion.
- Modeling cathode spots in vacuum arcs burning on multi-component contactsPublication . Benilov, M. S.; Benilova, L. G.; Cunha, M. D.; Hartmann, W.; Lawall, A.; Wenzel, N.A self-consistent space-resolved numerical model of cathode spots in vacuum arcs is developed on the basis of the COMSOL Multiphysics software. The model is applied to cathode spots on copper-chromium (CuCr) contacts of vacuum interrupters. In the limiting case of large grains, the main effect of change in cathode material from Cu to Cr is the reduction of thermal conductivity of the cathode material, which causes a reduction of spot radius and spot current. Hence, the model indicates that spots with currents of the order of tens of amperes on Cu coexist with spots on Cr with currents between one and two amperes. The parameters of spots on small Cr grains of the order of 10 µm size are rather close to those of spots on pure Cu, whereas the parameters for spots on medium-size Cr grains of around 20 µm are quite different from those of spots on both pure Cu and pure Cr. The power flux is directed from the cathode into the plasma, i.e., it is the cathode that heats the plasma – and not the other way round. What maintains the spot is a substantial Joule heating inside the cathode bulk. About 70 percent of the heat is generated in the grain and 30 percent in the surrounding copper. One may hypothesize that such grains are highly unstable, leading to explosive-like behavior with a consequent additional loss of cathode material, and a severe limitation in spot lifetime.
- Simulation of thermal instability in non-uniformities on the surface of cathodes of vacuum arcsPublication . Cunha, M. D.; Benilov, M. S.; Hartmann, W.; Wenzel, N.Instability stemming from the strong dependence of electron emission current on the local surface temperature plays an important role in current transfer to hot cathodes of arc discharges. In the case of vacuum arcs, this instability may lead to micro explosions on cathode surface even if the surface is planar. This work is concerned with numerical simulation of effect produced by surface non-uniformities. It is found that the effect is non-trivial: the presence of surface non-uniformities can not only accelerate the development of the instability, which is what one would expect intuitively, but also slow it down and even suppress.