Study on the bifurcation of the shock wave in SF6 circuit breaker

For studying the effect of the pressure on the breaking performance during the cold gas interruption of a SF₆ circuit breaker (CB), 1D compressive gas flow field mathematical model was deduced by replacing the mass equation with the pressure equation based on the mathematic transformation. And the distribution of Mach number in gas flow field under different opening strokes were simulated using finite volume method (FVM), and the density, the pressure, the velocity, and the temperature distribution of the gas flow were obtained and especially the above gas flow parameter variations at the region of the shock wave formed have been calculated. And the fundamental solution of the equations describing the gas flow in the SF₆ CB has been resolved using separation of variables method, and 1D differential equations with constant coefficient were derived. Based on the proposed model, the bifurcation diagrams at different opening strokes have been calculated. The results show that for the gas flow with different velocity, the system exhibits periodic, quasi-periodic or even chaotic behavior in the arc quenching chamber. And the instability of the shock wave may be one of the origins of the complex phenomena.