Modelling of turbulent SF6 switching arcs

• Main Author: Zhang, Quan
• Published: University of Liverpool 2014
• Subjects: 621.3; Q Science (General)
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.666721

There is an overwhelming experimental and theoretical evidence indicating SF6 arc burning in a supersonic nozzle (known as the switching arc) is turbulent and in local thermodynamic equilibrium (LTE). Such an arcing arrangement is commonly used as the interrupter in gas blast circuit breakers. In order to reduce the development cost of gas blast circuit breakers, it is highly desirable to predict the arc behaviour under the operational conditions encountered in a power system. The major difficulty in achieving full computer aided predictive design of gas blast circuit breakers is the satisfactory prediction of the thermal interruption capability of an arc under turbulent conditions. Mathematical modelling of turbulent SF6 switching arcs, thus, forms the subject matter of this thesis. The approach for the modelling of turbulent switching arcs is similar to that for turbulent shear flows due to a direct resemblance between a nozzle arc and a round free jet both of which are dominated by shear flow. The conservation equations for switching arcs are, therefore, derived using Reynolds’s approach. The closure of these equations is based on the adoption of Boussinesq assumption to relate Reynolds stress to the time averaged velocity gradients through eddy viscosity. The turbulent heat flux is assumed to be related to Reynolds stress through a constant turbulent Prandtl number. Additional equations are introduced to determine the turbulence length scale and velocity scale required by eddy viscosity, which are provided by turbulence models. There are numerous turbulence models but none of them are specifically devised for switching arcs. The objective of the present investigation is, therefore, to choose relevant turbulence models to model turbulent SF6 switching arcs. Our choice of turbulence models is restricted to those which have been applied with success to similar flow conditions as those of a switching arc as well as their suitability for engineering application. We therefore choose the standard k-epsilon model and its two variants (the Chen-Kim model and the RNG model) for the modelling of SF6 turbulent switching arc. Since the application of the Prandtl mixing length model to SF6 switching arcs has met considerable success, this turbulence model is included in our investigation for comparison. In order to demonstrate the effects of turbulence, results based on laminar flow model are presented. Therefore, altogether five flow models have been used to study the nozzle arcs. Computational results are obtained by the five flow models under a wide range of discharge conditions in terms of different nozzle geometries, the rate of change of current (di/dt) before current zero and the stagnation pressure (P0). A detailed analysis of the physical mechanisms encompassed in each flow model is given to show the adequacy of a particular model in describing the rapidly varying arc during current zero period. The computed values of the critical rate of rise of recovery voltage (RRRV) are compared with corresponding measurements. It is found that RRRV predicted by laminar flow model is a few orders of magnitude lower than that measured, which indicates that turbulence plays a decisive role in the determination of thermal interruption capability of a nozzle arc. Of the four turbulence models, the Prandtl mixing length model gives the best prediction of RRRV when compared with experimental results. The drawback is that the value of the turbulence parameter of the Prandtl mixing length model needs to be derived from one test result for a given geometry. With our current understanding of the physics of turbulent arcs, the Prandtl mixing length model is the only turbulence model which can be used to predict the thermal interruption capability of a nozzle arc arrangement.