Browsing by Author "Hartmann, Werner"
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- 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 spots on composite copper-chromium contacts of vacuum arcs and their stabilityPublication . Benilov, Mikhail S.; Cunha, Mário D.; Hartmann, Werner; Kosse, Sylvio; Lawall, Andreas; Wenzel, NorbertCathode spots on copper–chromium contacts of vacuum interrupters are simulated by means of a self-consistent space-resolved numerical model of cathode spots in vacuum arcs developed on the basis of the COMSOL Multiphysics software. Attention is focused on spots attached to Cr grains in the Cu matrix in a wide range of values of the ratio of the grain radius to the radius of the spot. In the case where this ratio is close to unity, parameters of spot are strongly different from those operating on both pure-copper and pure-chromium cathodes; in particular, the spot is maintained by Joule heat generation in the cathode body and the net energy flux is directed from the cathode to the plasma and not the other way round. An investigation of stability has shown that stationary spots are stable if current controlled. However, under conditions of high power circuit breakers, where the near-cathode voltage is not affected by ignition or extinction of separate spots, the spots are unstable and end up either in explosive-like behavior or in destruction by thermal conduction. On the other hand, spots live significantly longer-up to one order of magnitude-if the spot and grain sizes are close; else, typical spot lifetimes are of the order of 10 µs. This result is very interesting theoretically and may explain the changes in grain size occurring in the beginning of the lifetime of contacts of high-power current breakers. A sensitivity study has shown that variations in different aspects of the simulation model produce quantitative changes but do not affect the results qualitatively.
- Near-cathode plasma layer on CuCr contacts of vacuum arcsPublication . Almeida, Nelson A.; Benilov, Mikhail S.; Benilova, Larissa G.; Hartmann, Werner; Wenzel, NorbertA model of near-cathode layers in vacuum arcs is developed. The model relies on a numerical solution of the problem of near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface, and allows the selfconsistent determination of all parameters of the near-cathode layer, including the ion backflow coefficient. The dependence of the density of energy flux from the plasma to the cathode surface on the local surface temperature is nonmonotonic with a maximum, a feature that plays an important role in the physics of plasma–cathode interaction. The developed model may be used for a variety of purposes, including as a module of complex nonstationary multidimensional numerical models of plasma– cathode interaction in vacuum arcs. As a simple example, an analytical evaluation of parameters of stationary spots on copper and chromium is given. In the case of composite CuCr contacts with large grains, spots with current of several tens of amperes burning on the copper matrix coexist with spots with currents of the order of 1 A burning on the chromium grains.
- Revisiting theoretical description of the retrograde motion of cathode spots of vacuum arcsPublication . Benilov, Mikhail S.; Kaufmann, Helena T. C.; Hartmann, Werner; Benilova, Larissa G.A fresh attempt to develop a self-consistent descrip tion of the retrograde motion of cathode spots on volatile cathodes is undertaken. Three potential mechanisms of effect of transversal magnetic field on the distribution of parameters in the spot are studied: the effect of magnetic field on hydrodynamics processes in the spot, in particular, on the formation of liquid-metal jet and the droplet detachment, and the effect of transversal magnetic field over the motion of ions and emitted electrons in the near-cathode space-charge sheath. It is found that for typical conditions of cathode spots in vacuum arcs the effect of magnetic field over the formation of liquid-metal jet and the droplet detachment is negligible; the motion of the ions in the near-cathode space-charge sheath is not disturbed; and the motion of the emitted electrons is disturbed only marginally. Thus, the above-mentioned potential mechanisms are hardly relevant and the first-principle understanding is still missing. A phenomenological description of the retrograde motion is developed as an alternative. The description employs general considerations without relying on specific assumptions and the (only) unknown parameter can be determined from comparison with the experiment.
- 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.
- 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.