Sylvio Kosse

Space-Resolved Modeling of Stationary Spots on Copper Vacuum Arc Cathodes and on Composite CuCr Cathodes With Large Grains

A 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

Numerical simulation of multi-component arcs in high-current vacuum interrupters

({\gtrsim}{\rm 20}~\mu{\rm m})

Modeling Spots on Composite Copper–Chromium Contacts of Vacuum Arcs and their Stability

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.

Simulation of spots on Cu-Cr cathodes of vacuum arcs and of their stability

A transient three-dimensional numerical model has been developed to describe a diffuse multi-component vacuum arc between copper-chromium (CuCr) electrodes under the influence of an axial magnetic field (AMF). The model is based on a two-temperature magneto-hydrodynamic approach of the plasma and is realized with commercial simulation software (CFX) and in-house extensions. The quasi-neutral plasma is described as a two-fluid system distinguishing between electrons and multiply ionized heavy particles. The heavy particles are treated as a multi-component fluid containing Cu ions and Cr ions. The model incorporates balance equations for the ion momentum, balance equations for the ion and electron energy, and transport equations for the magnetic flux density and the radiation. The plasma parameters near the cathode are specified in terms of a self-consistent space-resolved numerical model of the cathode spot on CuCr contacts taking into account the granular structure of the contact material. The simulation is performed at different times during a 50 Hz electrical current cycle. Results are presented for plasma flows under realistic conditions referring to the geometry (140 mm diameter, 11 mm gap), the material (CuCr), and the spatio-temporal AMF profiles of a cup-shaped AMF contact system in an industrial high-current vacuum interrupter (72 kA). Depending on the characteristics of the mass flow near the cathode, distinct features of the energy transport onto the anode are calculated.

Modeling spots on copper and copper-chromium cathodes of vacuum arcs

Cathode 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.

TAP CHANGER AND VACUUM INTERRUPTER FOR SUCH A TAP CHANGER

Summary form only given. This work is concerned with simulation of cathode spots on copper-chromium contacts of vacuum interrupters in the framework of a self-consistent space-resolved numerical model of cathode spots in vacuum arcs developed earlier1. Results reported in this work refer to the case where the grain has a hemispherical shape and the cathode surface is flat; a convenient test case for elucidating the underlying physics. The 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, which is the case typical for low-current arc devices and small-scale experiments. However, under conditions of high-power circuit breakers, where the near-cathode voltage is not significantly affected by ignition or extinction of separate spots, the spots are unstable and end up in either explosive-like behavior or destruction by thermal conduction. On the other hand, the time of development of the instability is significantly longer in the case where the grain radius is close to the spot radius. This result is very interesting theoretically and may explain the changes in grain size occurring in the beginning of 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.

Device for splitting a chemical compound, and associated method

Summary form only given. A variety of approaches have been developed in the literature towards modelling of cathode spots in vacuum arcs. These include space-resolved descriptions based on numerical solution of 1D or 2D partial differential equations, both stationary and non-stationary. However, the simplest model, namely, a stationary spot on an infinite planar cathode, has been studied mostly in the 0D approximation, where the spot is described only on the integral level. Some authors even presumed that due to thermal runaway steady-state solutions describing a stationary spot on an infinite planar vacuum arc cathode do not exist or are unstable. The lack of a mathematically accurate solution of the most basic problem of the theory of plasma-cathode interaction in vacuum arc discharges is unfortunate and detrimental to the theory.The aim of this work is to obtain axially symmetric numerical solutions describing spots on cathodes of vacuum arcs and to investigate their stability. Also investigated will be the effect produced on these solutions by a granular structure of the cathode; a question which is of significant interest in connection with contacts of high-power vacuum circuit breakers. To this end, a self-consistent space-resolved numerical model of cathode spots in vacuum arcs is realized on the computational platform COMSOL Multiphysics. Distributions of temperature and electrostatic potential in the cathode body are calculated by means of the time-dependent heat conduction equation and the current continuity equation. Boundary conditions on the cathode surface are generated by means of a model simulating the near-cathode plasma layer. Modelling results reveal a well-defined spot with a virtually constant temperature of the cathode surface, negligible current outside the spot, and a maximum of the density of energy flux from the plasma being positioned at the spot edge; features familiar from the general theory of stationary cathode arc spots and from modeling of spots on cathodes of high-pressure arcs. A spot on pure copper-cathode is stable if it operates at a fixed current. A spot is unstable due to thermal explosion or exponential decay if it operates at a fixed voltage, however it may be stabilized by a chromium grain.