# Abstract

Abstract of report at 1998 IEEE International Symposium on Electrical Insulation, 7-10 June 1998, Washington, DC, USA. Full text of presentation.

## Simulations of Gas-dynamic Flows During Streamers Propagation at Liquid Dielectrics Breakdowns A. L. Kupershtokh, D. A. Medvedev

In the present work a new model is realized in which two-dimensional flow of liquid dielectrics is simulated with the immiscible lattice gas (ILG) method [1] and the transition of dielectric to conductive phase is described by fluctuation field criterion (FFC) [2,3].

The hydrodynamic flow was computed taking into account the electric pressure $\varepsilon$ E2/8$\pi$ acting on the interface. Then, the Laplace equation $\Delta \varphi =0$ was solved in the region occupied by dielectric. The conductive phase was considered equipotential ($\varphi =0$). When the growth criterion E > E* + $\delta$ is satisfied for a node adjacent to the interface, this node and its neighbors become conductive and some energy is released (the pressure increases).

In a high electric field the boundary of the conductive phase moves because of action of the electric forces. In addition, the conductive region expands due to the higher pressure in it. As a result, the streamer grows due to both hydrodynamic movement and the breakdown of new portions of dielectric (transition to the conductive state). The relative role of these two mechanisms of conductive structure development can be modified by changing the ratio between the streamer growth velocity and the hydrodynamic velocity of viscous flow.

The numerical calculations were performed in the rectangular area between two "plane" electrodes to which an electric potential difference $\varphi (t)$ was applied. Periodic boundary conditions in the X direction were used. Transition between two mechanisms of conductive structure development was demonstrated.

In the present work, simulation of linear conductive channel propagation between the "plane" electrodes was also carried out. An eight-directional ILG model with three velocity values 0, 1, $\sqrt{2}$ is used [1]. It allows one to describe the energy release at the streamer tip.

Simulations using the lattice Boltzmann equation method were also performed. In this model, real numbers are utilized to represent the ensemble-averaged particle distribution functions. Thus, statistical noise is eliminated, and the averaging step needed in ILG simulations is completely bypassed.

The expansion of conductive channel and formation of compression waves, which propagate with sound velocity in liquid dielectric C, were observed. If the velocity of the streamer tip is greater than C, then a divergent wave with approximately conic shape was generated. Such waves were clearly observed in experiments [4].

This work was supported in part by the Russian Foundation for Basic Research under grant No. 97-02-18416.

### References

1. A.L. Kupershtokh, S.M. Ishchenko, A.P. Ershov, Instability of Interface between Conductive Liquid and Non-conductive One in Electric Field. // Proc. of the 12th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Roma, Italy, pp. 107--110, 1996.
2. A.L. Kupershtokh, Fluctuation model of the breakdown of liquid dielectrics. // Sov. Tech. Phys. Lett. v. 18(10), pp. 647--649, 1992.
3. A.P. Ershov, A.L. Kupershtokh, Fluctuation Model of Liquid Dielectric Breakdown with Incomplete Charge Relaxation. // Proc. of the 11th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Baden-Dattwil, Switzerland, pp. 194--198, 1993.
4. P. Gournay, O. Lesaint, Study of the Dynamics of Gaseous Positive Streamer Filaments in Pentane. // Proc. of the 11th Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Baden-Dattwil, Switzerland, pp. 289--293, 1993.
Full text of presentation.

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