2D Modelling of HID lamps using PLASIMO: Electric field calculation

1. 2D Modelling of HID lamps using PLASIMO:Electric field calculation D.A. Benoy Philips Lighting, CDL

2. Contents • Introduction • HID development and lamp design • HID modeling • HID plasma model • PLASIMO sub-model: E-field • Conclusions

3. COST “standard” MH Na + Hg radiation Observation: color non-uniformity  axial segregationefficiency loss (vert.)  color depends on burning position Goal: understanding, optimizing effects of de-mixing. Na + RE + Hg radiation Introduction: examples of MH-lamps Commercial CDM

4. HID development and lamp design (1) • AIM • To get a reliable relation between lamp design parameters and • physical and chemical processes, and • radiation transport. • To provide accurate temperature information for lifetime prediction. • Reduction throughput time of: • Future development of new types, • Improvement of existing types. • Finding design rules by virtual DOE’s. • Understanding HID plasma physical processes is enabler for new lamp types.

5. Radiation spectrum HID development and lamp design (2) Development: New products: Light Technical Properties (LTP) • Colour temperature • Colour rendering • Efficacy • Colour stability (dimmable) • Spatial uniformity (burning position)

6. HID development and lamp design (3) • Lamp design: • Improvement existing products: Lifetime • Stresses in burner • Failure modes • Wall corrosion Design rules? Relation with: burner, electrode geometry, buffer gas, salt, etc…? Influence of lamp design parameters on LTP? Get answers by using models.

7. Life time ? LTP ? Thermo-mechanical modeling Wall stresses Temperature distribution Radiation spectrum Wall corrosion Particle distribution Plasma modeling HID lamp design  model Lamp design parameters Materials Geometry Buffer gas Salt Operating conditions PLASMA Thermo-mechanical, and plasma modeling are complementary.

8. HID modeling (1) • Focus on modeling detailed discharge properties: • Local chemical equilibrium (LCE) for species composition in liquid (salt-pool) and gas phase, i.e. determination of local partial pressures of radiating species. • Transport of minority species by diffusion, and convection. • Radiation transport: • Absorption, and self-absorption, • Include line broadening mechanisms. • Ohm’s law for electric field, and current density (electrode end effects). • Gravity drives natural convection solve flow field • Model constraints: • Transport coefficients calculated from plasma composition, • Number of “fit” parameters (in radiation, and transport coefficients) as small as possible.

9. HID plasma model: power balance (requires flow field) Work by expansion Energy transport by convection Heat conduction Ohmic dissipation Radiation term: emission, absorption (UV, visible, IR) (requires flow field ) (requires electron densities and E) (requires additives density distribution) • To be calculated: • Flow field u, , and p additional balance equations • Transport coefficients • E-field • Radiation transport, and losses • Minority density distribution • Chemical composition • Transport of minority species additional balance equations

10. HID plasma model: other balance equations Vertical burning position Momentum balance Bulk flow field Mass balance Elemental diffusion Species flux Elem. densities Elemental flux Stoichiometric coefficient Electric field

11. HID plasma model: sub-models • Chemical composition • Guldberg-Waage-Saha balance relations: • Open source, • Only 1 phase (gas). • Commercial library • Gibbs minimiser, commercial package  only DLL available) • Multi-phase composition possible  vapor pressures above saltpool. • Extended species database • Radiation transport • Expression for local energy loss by radiation: • Solution techniques: • Ray tracing • “Full” radiation transport treatment: • including line broadening, • limited number of lines

12. HID model: PLASIMO • Axis-symmetry  2-dimensional  Vertical position when gravity is included • Stationary • LTE • Academic approach: • “First principles” • “No calculation time limits” • Pragmatic approach: • Use of data fits • Pressure on calculation time • PLASIMO offers both approaches

13. Interaction between plasma and electrodes Electrode Plasma is “decoupled” From electrodes HID plasma sub-models: E-field and geometry (1) HID-burner

14. HID plasma sub-models: E-field and geometry • 1- Dimensional: • E(R)  Ez(z): Constraints: • Current I is given • Power is given • Ez is constant Computational geometry model: 1D-electric field • 2-Dimensional: • Solve electric potential with finite electrodes: • div J = 0,J = E, E = - • - = 0, Power is given • new EM plug-in needed. • Make use of “standard”  equation. Computational geometry model: 2D-electric field

15. HID plasma sub-models: E-field interface

16. 1 0.75 0.5 0.25 Axis Potential 0 wall electrode edge -0.25 -0.5 -0.75 -1 0 0.004 0.008 0.012 0.016 0.02 0.024 z-axis HID plasmas modeling: E-field calculations (1) Electrode distance (Z): 24mm Burner radius (R): 6mm Electrode radius: 0.5mm DF 2V s constant NZ 40 NR 40 Regular grid Large E-field  Large DT  Source of difficulties

17. HID plasmas modeling: E-field calculations (2) Electrode distance (Z): 32mm Burner radius (R): 4mm Electrode radius: 0.5mm s F(T) Total power 70W Electrode temperature 2900K NZ 120 NR 40 Regular grid selectrode = s(lte) selectrode = s(n-lte) > s(lte) Profiles not realistic

18. HID plasmas modeling: E-field calculations (3) Estimation of gradient length: First grid point regular grid at 1.6x10-4m (120 Z-points)  Is too large. If equidistant grid  1000 axial points needed!  Axial grid transform (2-point stretch)

19. HID plasmas modeling: grid-transformation Computational grid: equi-distant control volumes Electrode Physical grid: transformed control volumes Fine mesh at tip required, First gridline at 10mm

20. HID plasmas modeling: E-field calculations (4) Electrode distance (Z): 32mm Burner radius (R): 4mm Electrode radius: 0.5mm s F(T) Total power 70W NZ 120 NR 40 Transformed grid selectrode = s(lte) selectrode > s(lte)

21. HID plasmas modeling: E-field calculations (5) • Estimated electrode heat loss • Heat flux at middle of electrode • q=kDT/Dx • q  0.09×1000/10-5 = 0.09×108W/m2  Total electrode loss 7.8W • q  0.11×1900/10-5 = 0.21×108 18.2W • q  2.90×5700/1.6×10-4 = 1.03×108 66W • Is 8.5×larger! • Much higher heat lost through electrode = unrealistic Power input = 70W Rule of thumb:  10 ~ 15% electrode losses. Values for s(n-lte), Telectrode? Near electrode (e-source) there is deviation from equilibrium. Plasma model: equilibrium  s(n-lte), and Tinput are input data. Coupling with electrode model for self-consistent calculation of s(n-lte), and Tinput.

22. No 2-nd order polynomial curve fitting Ez(boundary, not electrode) = 0. HID plasmas modeling: E-field calculations (6)

23. HID plasmas modeling: E-field calculations (7) Gravity Temperature Ohmic dissipation (log scale) P=10Bar P=40Bar P=60Bar

24. Influence of E-field model on vmax. 2D E-field • 1D E-field • Underestimation of vmax • Overestimation of segregation

25. Summary and conclusions • PLASIMO as a “grand model” is a powerful, “flexible”, and modular tool for understanding, and optimizing HID lamps (calculating plasma physical, and radiation properties) • For 2D-electric field model: • Non-LTE electric conductivity at electrode • Quantification non-LTE needed • Very fine grid needed at electrode  transformed grid (still a large number grid points needed) • Has huge impact on radiation transport calculation if calculated on same grid. •  Use of separate radiation grid.