Mathematical model using macroscopic and microscopic scales of an electrical arc discharge through a porous medium in HBC fuses

We introduce a model to describe the mechanical interaction and the energy transfer mechanisms from arc column toward to porous medium occuring in the HBC fuse. The model is built on a macroscopic and microscopic approach in order to evaluate more accurately the thermal evolution of the solid phase and the vaporization and condensation processes of the silica sand. We consider a thermal model at the scale of a sand grain to determine the temperature evolution of the sand grains. The gas flow is based on the compressible homogenized Euler equations with two species coupled with a porous media model. The governing equations are discretized following a finite volume scheme coupled with a fractional step technique