3D numerical simulation of the electric arc motion between bus-bar electrodes

Transcription

1 3D numerical simulation of the electric arc motion between bus-bar electrodes M. Lisnyak 1 *, M. Chnani 2, A. Gautier 2, J-M. Bauchire 1 1 GREMI, UMR 7344, CNRS/Université d Orléans, 14 Rue d'issoudun, Orléans, 45067, France 2 Zodiac Aerospace, 7 Rue des Longs Quartiers, Montreuil, 93108, France *marina.lisnyak@univ-orleans.fr

2 Thermal plasmas Plasmas classification [1]: Thermal plasma applications: Thermal plasma in nature: Thermal plasmas characteristics: n e ~ m 3 and T e ~10 4 K Local Thermodynamic Equilibrium (LTE) 2 [1] M. I. Boulos, P. Fauchais, and E. Pfender, Thermal Plasmas Fundamentals and Applications. Boston, MA: Springer US : Imprint: Springer, 1994.

3 S Objective Bus-bars electrodes construction, dimensions: L~ mm and h ~ 10 mm Supplied with AC or DC currents in range A Working conditions: atm B I v I L In case of fault the electric arc takes place and propagates along the electrodes. Goal: to investigate arc propagation using numerical simulation 3

4 Mathematical description Arc column description and electrodes: The system of MHD equations in the LTE approximation is solved for arc bulk plasma: ρ + ρu = 0, t ρu T + ρu u = p + η u + u 2 η u + j B, t 3 T ρc p t + u T + q = j φ Q rad, q = λ T 5 kt 2 e j, j = 0, j = σ φ, 1 μ 0 B = j, In the electrodes: B = A. ρ s c p T s t (λ s T s ) + σ s φ 2 = 0, (σ s φ) = 0. 1 μ 0 B = j, B = A. The system is solved with respect to variables: u, p, T, φ, A in the arc plasma and φ, T s, A in the electrodes. 4

5 v Heat transfer in fluids j j, φ Arc model in COMSOL Temperature Magnetic fields Electric currents Electric conductivity σ(t) Thermal conductivity λ(t) Specific heat C p (T) B j Viscosity η(t) Density ρ(t) Laminar flow 5

6 3 20 Calculation conditions Ar [1 atm] I Electrodes: Plane electrodes made of copper Power: Direct current I = 200 A I Conditions: Atmospheric pressure Gas: argon Initial conditions: Stationary arc with, fixed spots positions. Initial conditions 6

7 Temperature (in K) distributions Impact of the magnetic field Without external (from the electrodes) magnetic field(mf) cathode 0,5 ms 1 ms 1,5 ms anode With external (from the electrodes) magnetic field(mf) 0,5 ms 1 ms 1,5 ms cathode anode 7

8 Arc displacement Arc temperature (in K) evolution with the time 8

9 Experiment I = 1.5 ka peak, h = 20 mm, fr/s 9

10 Arc displacement velocity [1] [2] [1] M.Lisnyak, M. Chnani, A. Gautier, J-M. Bauchire, Behavior of a short electric arc between plane electrodes:numerical and experimental study, contributions to ICPIG congress, July [2] B. Swierczynski, J. J. Gonzalez, P. Teulet, P. Freton, and A. Gleizes, Advances in low-voltage circuit breaker modelling,

11 Stabilization Discretization: Solver : Convergence criteria: Mesh: Laminar flow Heat transfer in fluids Calculation time: Numerical aspects Linear or quadratic basic functions. Streamline diffusion Crosswind diffusion Segregated (φ, A, u, p, T) Direct (MUMPS) and Iterative (GMERS). Relative tolerance is Number of DOF 10 6, refined near the electrodes with Δx max = 0.6 mm. 7 days with 8 cores, Xeon 3.2 GHz, 32 Gb. 12

12 Summary COMSOL Multiphysics allows to perform 3D time-dependent model of the electric arc. The good numerical stability for highly nonlinear problems is achieved. The calculation time is reasonable, that makes the model interesting for engineering applications. The physical aspects of the model corresponds to the experimental observations. 13

13 For more details I would like to invite you to the poster 84. Thank you! 14

14 Plasma properties Thermodynamic properties Argon 1 atm Transport coefficients: 15 [1] K. C. Hsu, K. Etemadi, and E. Pfender, Study of the free burning high intensity argon arc, J. Appl. Phys., 1983.

15 Convergence control Mass conservation Integration over external surface of the model: ρv ds 0 2 D case R ρv ds = 2πρ v z o rdr + ρr h v r 0 dh = 0 3 D case ρv ds = ρ v x n x + v y n y + v z n z ds = 0 Where n x, n y, n z are normal vectors (directed externally to the surface), R model radius, h model height Current conservation j ds cathode = j ds anode In COMSOL MF Results Derived values Surface integration 16

16 Fluxes calculations 17

17 Arc electrodes interaction Plasma near the electrodes is not in equilibrium. Goal: To include plasma-electrodes interaction without implementing non-equilibrium plasma description. Plasma anode interaction: attachment is constricted (spot mode), R as = 0.8 mm. anode heating is calculated according to: 5 q a = 2 kt j δ pl + A f e Plasma cathode interaction: spot mode on the cathode with the fixed radius [1, 2]: R cs = 1 mm. temperature in the cathode spot is uniformly distributed [1]: T av = 3200 K. The current continuity is imposed between plasma and electrodes. [1] W. L. Bade and J. M. Yos, Theoretical and Experimental Investigation of Arc Plasma-generation Technology, [2] M. S. Benilov and A. Marotta, A model of the cathode region of atmospheric pressure arcs, J. Phys. Appl. Phys., vol. 28, no. 9, p. 1869, Sep