Lattice Boltzmann Model for Simulation of Avalanche Formation and Streamer Discharge in Breakdown of Gaseous Dielectrics
Keywords:
Lattice Boltzmann method, numerical simulation, streamer dischargeAbstract
Gas discharges play a central role in the electrical breakdown of matter, both in nature and technology. Therefore, accurate modeling and simulation of streamers in gaseous discharge processes are of particular interest. This study presents the formulation of computationally efficient models of the charge density and electric field produced by the lattice Boltzmann method. The propagation of double-headed streamers is described in 1-cm plane-to-plane geometry in pure nitrogen at atmospheric pressure by 1.5D and 2D models. The lattice Boltzmann method was successfully applied to the simulation of streamer discharges. Therefore, this scheme is a potential way of simulating gaseous discharge problems.
Downloads
References
C. Wu and E. Kunhardt, “Formation and propagation of streamers in N2 and N2-SF6 mixtures,” Physical Review A, vol. 37, no. 11, pp. 4396-4406, Jun. 1988.
G. E. Georghiou, et. al., “Numerical modelling of atmospheric pressure gas discharges leading to plasma production,” Journal of Physics D Applied Physics, vol. 38, no. 20, pp. 303-328, Sep. 2005.
D. A. Medvedev, “Lattice Boltzmann model for simulation of the electric breakdown in liquids,” Procedia Computer Science I, vol. 1, no. 1, pp. 811-818, Apr. 2010.
A. L. Kupershtokh, “Lattice Boltzmann equation method in electrohydrodynamic problems,” Journal of Electrostatics, vol. 64, no. 7-9, pp. 581-585, Nov. 2006.
H. Huang, L. Wang, and X-Y. Lu, “Evaluation of three lattice Boltzmann models for multiphase flows in porous media,” Computers and Mathematics with Applications, vol. 61, no. 12, pp. 3606-3617, 2011.
Y. L. He and Y. Wang, Lattice Boltzmann Method Theory and Application, Science Press, China, 2009.
S. Chen and G. D. Doolen, “Lattice Boltzmann method for fluid flows,” Annu. Rev. Fluid Mech., vol. 30, no. 5, pp. 329-364, Aug. 1998.
Y. Qian and D. d’Humieres, “Lattice BGK models for Navier-Stockes equation,” Europhys, vol. 17, no. 6, pp. 479-484, Jan. 1992.
Z. Li. Guo and C. G. Zheng, Theory and Application of Lattice Boltzmann Method, Science Press, China, 2009.
J. M. Buick and C. A. Greated, “Gravity in a lattice Boltzmann model,” Physical Review E, vol. 61, no. 5, pp. 5307-5320, May 2000.
N. Wang, Q. Lei, and X. Wang, “Lattice Boltzmann model for simulation of the electric charge flow and calculation of electrorheology,” International Journal of Digital Content Technology and its Applications, vol. 6, no. 17, pp. 135-143, Sep. 2012.
L. B. Loeb and J. M. Meek, “The mechanism of spark discharge in air at atmospheric pressure,” J. Appl. Phys, vol. 11, no. 6, pp. 438-47, Nov. 1940.
A. J. Davies and C. S. Davies, “Computer simulation of rapidly developing gaseous discharges,” PROC. IEE., vol. 118, no. 6, pp. 816-823, 1971.
M. B. Zheleznyak, A. K. Mnatsakanian, S. V. Sizykh, “Photoionization of nitrogen and oxygen mixtures by radiation from gas discharge,” High Temperature, vol. 20, no. 3, pp. 357-362, 1982.
J. Roger-Riba, P. Casals-Torrens, and R. Bosch, “Defects identification in XLPE medium-voltage cables by applying multivariate methods,” DYNA, vol. 89, no. 6, pp. 633-641, 2014.
G. W. Penney and G. T. Hummert, “Photoionization measurements in air oxygen and nitrogen,” Journal of Applied Physics, vol. 41, no. 2, pp. 572-577, Aug. 1970.
A Bourdon, et. al., “Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations,” Plasma Sources Science and Technology, vol. 16, no. 3, pp. 656- 678, Aug. 2007.
W. J. Yao and S. P. Chen, “Elastic-plastic analytical solutions of deformation of uplift belled pile,” Tehnicki Vjesnik-Technical Gazette, vol. 21, no. 6, pp. 1201-1211, Dec. 2014.
R. Benzi, S. Succi, M. Vergassola, “The lattice Boltzmann equation theory and applications,” Phys. Rep., vol. 222, no. 3, pp. 145-97, 1992.
P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision processes in gases: small amplitude processes in charged and neutral one component system,” Phys. Rev., vol .94, no. 3, pp. 511-525, Jan. 1955.
Y. Zhang, High Voltage and Insulation Technology, China Power Press, Beijing, 2002.
A. Boretti and S. Jiang, “Development of a two stroke direct injection jet ignition compressed natural gas engine,” Journal of Power Technologies, vol. 94, no. 3, pp. 145-152, Mar. 2014.
D. Bessieres, J. Paillol, A. Bourdon, and P. Segur, “A new one-dimensional moving mesh method applied to the simulation of streamer discharges,” Journal of Physics D: Applied Physics, vol. 40, no. 21, pp. 6559-6570, Apr. 2007.
C. Zhuang and R. Zeng, “Discountinuous Galerkin method for short air gap discharge simulations and its applications,” High Voltage Engineering, vol. 39, no. 4, pp. 970-978, Apr. 2013.
Y. Zhang and R. Zeng, X-C. Yang, and B. Zhang, “Study on photoionization produced by discharge in atmospheric air by numerical method,” Proceedings of the CSEE, vol. 29, no. 4, pp. 110- 116, Feb. 2009.
