A Fast Multiscale Numerical Algorithm for Coupling Dynamics of the Bubble in Insulating Oil Under the Electric Field

The presence of bubbles in the transformer oil is very prone to cause partial discharges in the oil, which affects the insulation characteristics. Therefore, it is of vital importance to study the severity of the electric field distortion and the dynamic characteristics of the bubble under this physical model of gas-liquid two-phase flow. In this paper, a multiscale finite element method of electric field coupled with the dynamic characteristics of the bubble is proposed. The coupling between the electrostatic field and the hydrodynamic field is established through the level set function. The level set function is an output of data from the hydrodynamic field for the position of the bubble and at the same time an input of data for the description of the interpolation function when solving for the electric field by the extended finite element method. Unlike the conventional finite element method, this algorithm eliminates the need to re-dissect the elements at each time step, and thus can greatly reduce the solution time while maintaining accuracy.