Modelling and Simulation of Air and SF6 Switching Arcs in High Voltage Circuit Breakers

This thesis is concerned with the modelling of switching arcs in air in high voltage circuit breakers and with a comparative study of interruption capability of air and SF6 switching arcs. Emphasis is given to the identification of dominant energy transport processes for arc interruption and the material properties associated these processes. There have been renewed interests in air arcs because of its possible use in a mixture with other gases as a replacement for SF6 in circuit breakers for environment protection. Computer simulation of the switching air arc has been carried out using arc models based on laminar flow and on turbulent flow for the experimental set up of Fang et al [41] under DC current and that of Frind and Rich [66] for the current zero period. DC arc voltages predicted by arc model assuming laminar flow (LAM) are much lower than those measured. Thus, turbulence is introduced to account for additional power loss mechanism not included in the laminar flow model. Two turbulence models have been used to take into account of turbulence enhanced momentum and energy transport: the Prandtl mixing length model (PML) and the standard k-epsilon model or its modified version. For the DC air nozzle arc of Fang et al [41] the value of the turbulence parameter, c= 0.06, in PML has been chosen to match the predicted arc voltage with that measured at 1 kA DC and a stagnation pressure of 10 bar. PML can give satisfactory agreement with experiments over a DC current range from 250 A to 3 kA. When the standard k-epsilon model is used, the predict arc voltage is much higher than that measured indicating that turbulence cooling is too strong. One of the turbulence parameters of the standard k-epsilon model which controls the dissipation rate of turbulent kinetic energy is adjusted to match the predicted arc voltage with the experimentally measured arc voltage under the same discharge conditions as those for finding the value of c in PML. With this chosen value of 1 = 1.62, the modified k-epsilon model (MKE) gives similar results to those of PML. Three arc models (LAM, PML and MKE) are used to compute the critical rate of rise of recovery voltage (RRRV) for the air nozzle arc of Frind and Rich [66]. The presence of the shock inside the nozzle in the presence of the arc prevents the optimisation of the value of turbulence parameter for PML due to numerical convergence problems. RRRV predicted by PML and LAM are much lower than the experimental value. MKE with 1 = 1.65 is successful in predicting satisfactorily the RRRV at di/dt= 13.5 A/μs for several stagnation pressures. However, it has been found that a single value of 1 chosen for one value of di/dt cannot give satisfactory prediction of RRRV for other values of di/dt. A comparative computational study of SF6 and air switching arcs based on MKE has been carried out for the experimental conditions of Frind and Rich [66] for di/dt= 13.5A/μs at several stagnation pressures. Under the same discharge conditions RRRV of SF6 switching arc is one order of magnitude higher than that of air switching arc. Such large difference in the interruption capabilities of SF6 and air is due to the different dominant energy transport processes responsible for the arc cooling during current zero period. Two material properties of the arc plasma, the product of density and specific heat at constant pressure (ρCP) and that of density and enthalpy (ρh) are responsible for the distinctive arc features for SF6 and air. SF6 switching arc has a distinctive arc core surrounded by a thin region with steep temperature gradient. Under the same discharge conditions as those of SF6 air switching arc has no distinctive core structure. Its radial temperature profile is very broad and arc radius is much bigger than that of SF6. Such broad radial temperature profile of air arc is due to the peaks of turbulent thermal conductivity at 4,000 K and 7,000 K produced by the corresponding peaks of the material property of ρCP of air. For SF6 ρCP has a peak just below 4,000 K, which ensures rapid temperature decay above 4,000 K and a gentle temperature tail below 4,000 K. In comparison with SF6 under the same pressure difference across the nozzle the velocity inside air arc is much higher than that of SF6. With ρh of air being greater than that of SF6 for temperature higher than 7,000 K together with higher velocity enthalpy transport capability of air arc is much higher than that of SF6. Energy balance calculation for the current carrying core indicates that after the breakdown of quasi-steady state turbulent thermal conduction is the dominant energy transport process for SF6 while for air arc axial convection is dominant. As a consequence the rates of decay of arc temperature and arc radius for air arc a few microseconds before current zero are much slower than those of SF6, thus resulting in a large difference between RRRVs for the two gases under the same discharge conditions. To find an alternative arc quenching gas with similar interruption capability to that of SF6 one should aim at ρCP and ρh of the alternative gas with similar features to those of SF6.