Simulating the Spontaneous Formation of Self-Organized Anode Spot Patterns in Arc Discharges

Transcription

1 Simulating the Spontaneous Formation of Self-Organized Anode Spot Patterns in Arc Discharges Juan Pablo Trelles Department of Mechanical Engineering and Energy Engineering Graduate Program University of Massachusetts Lowell 66 th Annual Gaseous Electronics Conference Princeton, New Jersey, September 30 - October 4,

2 Electrode spot formation Motivation & Background Fundamental phenomena (self-organization, bifurcation, stability,...) Critical for electrode erosion, process uniformity Abundant in electrical discharges (DC, AC, DBD, Glow,...) Mechanisms in Arc Discharges less understood Harsh conditions: high heat & current flux Coupled interactions: fluid dynamic, thermal, chemical, electromagnetic Computational observation for the first time in the present work 1 Purwins H-G and Berlemeier J 2011 IEEE Trans Plasma Sci Schoenbach K H, Moselhy M and Shi W 2004 Plasma Sources Sci Technol Abolmasov S P and Tachibana K 2011 IEEE Trans Plasma Sci Almeida P G C, Benilov M S and Faria M J 2011 IEEE Trans Plasma Sci

3 Canonical Arc Discharge Free Burning Arc Extensively studied: Experimentally & Numerically 1 cathode 2 3 anode Used as benchmark for thermal plasma models Simple geometry, steady, axi-symmetric, LTE,??? Anode spot patterns? 1 Hsu K C and Pfender E 1983 J Appl Phys Murphy A B 1999 IEEE Trans Plasma Sci Tashiro S, Tanaka M, Ushio M, Murphy A B and Lowke J J 2006 Vacuum

4 Nonequilibrium Plasma Flow Model Transport System: Transient + Advective + Diffusive + Reactive = 0 Chemical equilibrium Thermodynamic nonequilibrium (Non-LTE) Monolithically coupled: Fluid - Electromagnetic ~ Simplest NLTE model 4

5 Numerical Model Transport System: A 0 t Y + A Y (K Y) i i i ij j (S Y + S ) 1 0 = L Y S 0 = R (Y) = 0 transient advective diffusive reactive transport operator residual Variational Multiscale Finite Element Method (VMS-FEM): Variational form: Scale decomposition: total = large + small Solve: large = f(small) Model: small =f(large) Solution Approach: W R (Y)dΩ = 0 Ω Y = Y + Y' and W = W + W' W R (Y) dω Ω + L W Y' dω Ω = 0 large Y' = τr (Y ) small τ L 1 TransPORT solver (TPORT) Implicit Alpha Method Globalized Inexact Newton-Krylov Parallel Preconditioned GMRES Consistent & complete Second-order Space & Time 5

6 Computational Domain & Discretization Standard free-burning arc geometry Structured meshes base: ~ 2.6 M unknowns fine: ~ 2X base Complete Zoom 2X Zoom 10X Anode mesh 6

7 Validation Temperature fields: Complete domain Experimental * Equilibrium temperature This work Heavy-species temperature ~ stronger cooling anode BC: κ (h w = 10 5 [W/m 2 h n T h = h w (T h T w ) -K]) κ h n T h = 0 T h = T w (r) (common: or ) * Hsu K C and Pfender E 1983 J. Appl. Phys

8 Dependence on total current I tot : Validation (cont.) 2X finer mesh ~ linear 1 ~ linear 1 u zmax (J qcath I tot ) 1 2 ~ sublinear 2 ~ linear 2 1 Boulos M I, Fauchais P and Pfender E 1994 Thermal Plasmas: Fundamentals and Applications 2 Lowke J J, Morrow R and Haidar J 1997 J. Phys. D: Appl. Phys

9 Self-Organized Anode Patterns Heavy-species temperature 0.2 [mm] above anode: 300 [A] 275 [A] 250 [A] 225 [A] 200 [A] 175 [A] 150 [A] 125 [A] 100 [A] Convergent steady results from transient 3D simulations 9

10 Pattern Validation & Sensitivity Experimental* (100 [A]) Major center spot, satellite minor spots Computational base 2X finer (200 [A]) Solution dependent on discretization * Yang G and Heberlein J 2007 Plasma Sources Sci. Technol

11 Anode Patterns & Nonequilibrium Th and θ = Te/Th 0.2 [mm] above anode: 300 [A] 275 [A] 250 [A] 225 [A] 200 [A] 175 [A] 150 [A] 125 [A] 100 [A] 100 [A] 100 [A] nonequil. rings Spots not correlated with discretization nodes Current transfer heavily relies on θ 11

12 Summary and Conclusions Nonequilibrium arc discharge simulations can capture spontaneous formation of anode attachment patterns Patterns qualitatively agree with experimental anode erosion marks, analytical studies Results sensitive to spatial discretization Further information: J. P. Trelles, Formation of Self-Organized Anode Patterns in Arc Discharge Simulations, Plasma Sources Science and Technology (2013) Vol. 22, Thank You! 12

13 Additional 13

14 Abstract: NR : Simulating the Spontaneous Formation of Self- Organized Anode Spot Patterns in Arc Discharges Session NR2: Plasma-surface Interactions 10:00 AM 12:15 PM, Thursday, October 3, 2013, Room: Ballroom II Self-organized pattern formation is a captivating phenomenon common in numerous biological, chemical and physical systems. The experimental observation of selforganized anode patterns in diverse types of electrical discharges, including atmospheric-pressure arc discharges, has been well reported and characterized in the plasma literature. Nevertheless, the capturing of anode pattern formation in arc discharges by fluid flow models has proven exceedingly elusive. For the first time computational simulations, based on a time-dependent three-dimensional thermodynamic nonequilibrium model, reveal the spontaneous formation of selforganized anode attachment spots patterns in a free-burning arc. The characteristics of the patterns depend on the total arc current and on the resolution of the spatial discretization, whereas the main properties of the plasma, such as maximum temperatures, velocity, and voltage, depend only on the former. The obtained patterns qualitatively agree with experimental observations and confirm that the spots originate at the fringes of the arc - anode attachment. The results imply that heavy-species - electron energy equilibration, in addition to thermal instability, has a dominant role in the formation of anode spots in arc discharges. 14

15 Thermodynamic Properties Argon, Chemical Equilibrium & Thermodynamic Nonequilibrium: Ar, T h T e, (θ = T e /T h ) 15

16 Transport Properties Argon, Chemical Equilibrium & Thermodynamic Nonequilibrium: Ar, T h T e, (θ = T e /T h ) 16

17 Boundary Conditions Conditions ~ simplest & standard in arc discharge simulations Heat transfer to water-cooled anode h w = 10 5 [W/m 2 -K] 17

18 Solution Fields I tot = 200 [A] 18