Turbulence and Magnetic Field Calculations in High-Voltage Circuit Breakers

In high-voltage circuit breakers (HVCBs), the representation of convection is essential to provide a satisfactory description of the pressure increase in the heating volume or thermal expansion chamber. The plasma flow is mainly governed by Lorentz forces and turbulence effects. The Lorentz forces depend on the self-induced magnetic field which can be calculated by several approaches. A mixing formulation based on resolving the potential vectors and a Biot-Savart integral for the boundary condition is applied. The difference between this formulation and a null flux boundary condition is illustrated. The mixing formulation gives similar results to the use of Biot-Savart over the entire domain but is much less time consuming. To represent turbulence, one of the most frequently used models is the Prandtl mixing length model (PMLM). Nevertheless, recent works have demonstrated that the realizable model (RM) must represent the flow behavior in the heating volume. Such a model was applied and compared to the PMLM over the entire HVCB domain. The RM is clearly suitable to describe the turbulence in HVCB geometry.