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Lattice Boltzmann model for simulation of the electric breakdown in liquids
We investigate pre-breakdown hydrodynamic ﬂows and initial stages of the electric breakdown in dielectric liquids. Three models are considered. The ﬁrst one represents the purely thermal mechanism. Here, the liquid is simulated by a single-phase lattice Boltzmann equation (LBE) method. The temperature and the electric charge density are described by additional LBE components with zero mass. The permittivity is assumed to be constant. The conductivity increases with the increase of temperature. Electric force acting on a charged liquid is coupled with the hydrodynamics by the exact difference method [Kupershtokh, 2004; Kupershtokh & Medvedev, J. Electrostatics, 2006]. The last process in the model is the Joule heating.
In the second model, a possible phase transition is included. To simulate a ﬂuid with an arbitrary two-phase equation of state (such as van der Waals or Carnahan-Starling EOS), the method proposed by Kupershtokh is used [Kupershtokh, 2005; Kupershtokh et al., 2007]. The conductivity increases with the decrease of the ﬂuid density. When the voltage is applied, the charge injection from the surface of electrode begins. The electric force acting on the charged ﬂuid produces negative pressure near electrode leading to a phase transition (evaporation). Conductivity increases leading to enhanced evaporation and growth of a conducting bubble. Thus, the bubble mechanism of breakdown is realized.
The last model includes the density-dependent permittivity. For non polar liquids, the dependence is given by the Clausius – Mosotti law. In this case, several additional processes are possible. First, dielectrics is pulled into regions with higher electric ﬁeld which produces rarefaction waves. Second, an anisotropic instability [Kupershtokh & Medvedev, Phys. Rev. E, 2006] can develop producing low-density channels along the electric ﬁeld. Since these channels can easily become conducting, another mechanism of the breakdown is realized.