Computational plasma physics: HID modeling with Plasimo

1. Computational plasma physics:HID modeling with Plasimo D.A. Benoy Philips Lighting, CDL, MD&HT

2. Contents • Introduction • Modelling HID burners • HID plasma modelling • Why Plasimo • Plasimo extensions • Results: computational analysis • Conclusions

3. Introduction (1) • Discharges for lighting: • Low pressure: • Hg: fluorescent (TL) • Na: Sox • High pressure: • Hg: UHP (radiation source) • Hg: CDM, MH, … (buffer gas) • …

4. 1. Introduction (3): vertical burning MH lamps top Observation: axial segregation=> efficiency loss (vert.) => color depends on burning position Na + Hg radiation Goal: understanding, optimizing effects of de-mixing. Na + RE + Hg radiation bottom

5. 2. Modeling HID (1): Global energy balance Pin Pdischarge=Pin-Pelect Pelect Prad Pcond/conv PUV Pbulb Pvis rad PIR Multi-component discharge Electrode modeling Burner + bulk discharge

6. Nb wire sealing glass Cermet ceramic vessel electrode Plasma arc: global properties salt pool 2. Modeling HID (2) Focus on burner during lamp operation: Thermal modeling With commercial package: e.g. ANSYS (finite elements) Emphasis on geometry details. Total radiation: Empiric expression Different colors represent different materials

7. 2. Modeling HID (3) • Thermo-mechanical modeling: • Study mechanical behaviour (stresses) of CDM (PCA) burners as result of plasma heating: Global plasma modelling is included for calculating thermal wall load. • Optimise burner design. • Detailed properties of discharge not needed. • Detailed description of burner geometry, and burner material properties needed. • Use of commercial packages: ANSYS

8. Focus on discharge modeling for lighting properties electrode Plasma arc: detailed properties Radiation transport Side-on spectrum Buffer + additive salt salt pool 2. Modeling HID (4)

9. 3. HID plasma modeling (1) • Discharge modelling: What? • Study physical processes in the plasma of the burner (radiation, lamp voltage, local composition (de-mixing), heat transfer, …). • Optimise design rules for gas discharge lamps w.r.t. light-technical properties (Colour Rendering Index [properties of spectrum], efficacy, colour temperature) • Detailed properties of discharge are needed. High pressures discharge  continuum approach

10. 3. HID plasma modeling (2) In this lecture: focus on modeling detailed properties of discharge. • Plasmas in MH discharge lamps are complex systems: • Which physical processes? • Plasma as a light source:  solve energy balance, • Light properties are determined by salt additives:  solve chemical, and transport balance of minority species (i.e. multi-component plasma), • For vertical burning position: gravitation influences local chemical composition by means of natural convection:  solve flow-field.  Understanding, optimizing effects of de-mixing of minority species (MH)

11. 3. HID plasma modeling (3) • Physical model assumptions for mass, and energy transport balances: • 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 broadening mechanisms. • Ohm’s law for electric field, and current density (electrode end effects). • Model constraints: • Transport coefficients calculated from plasma composition, • Number of “fit” parameters (in radiation, and transport coefficients) as small as possible.

12. 3. HID plasma modeling (4) • Plasma simulation model requirements: • Calculation chemical composition, • Transport of minority species by diffusion, and convection: • Not limited by #species • Not limited by #diffusion - convection mechanisms • Radiation transport, • Flow-field solver, • Thermal k, electric s conductivity, viscosity, and diffusion coefficients: function of plasma state, and composition, • 2-dimensional E-field.

13. 3. Plasma balance equations Bulk, ambipolar, reactive Mass balance Elemental flux Elemental diffusion Species flux Stoichiometric coefficient Vertical burning position Momentum balance Energy balance Electric field Ohmic dissipation Radiation term

14. 4. Which simulation package? • Flaws of commercial packages: • Non-local radiation transport, • Limited number of species, • Limited number of diffusion mechanisms, • Limited functionality of user sub-routines (no source code) • PLASIMO does not have these short-comings • Flaw of PLASIMO • Limited freedom in modeling electrode geometry. For detailed modeling of discharge: not serious problem. • Additional issues: • Flexibility w.r.t. “minor” extensions, and modifications, • Nearby support, including implementation “major” extensions, • Cheap

15. 5. Plasimo extensions (1) Computational geometry electrode 2D-electric field HID-burner 1D-electric field • Electric potential solver for finite electrodes: • div J = 0,, J = E, E = - • - = 0 • new EM plug-in needed. Make use of “standard”  equation.

16. 1. Add new constructor class grdEXP plPoissonVariable : public plPhiVariable { class ConstTerm : public plDoublePhiTermContribution { public: void Update() {} plGridVar<REAL> m_field; ConstTerm( plModelRegion *reg, REAL val ); }; public: plPoissonVariable( plModelRegion *reg, const std::string & Aname, const plNode & node ); plPoissonVariable( plModelRegion *reg, const std::string & Aname, const plNode & node, plRememberingGridVar<REAL> &sig ) ; }; 2. Add new class class plEME2dCurrentData : public plBaseEMData { private: REAL m_power; … public: plEME2dCurrentData( plModelRegion *reg, const plNode & node ); virtual void CalculateFields(REAL acc ); REAL Accuracy() const { return m_potential.Accuracy(); } protected: plPoissonVariable m_potential; };

17. 3. Implement constructor of new class plEME2dCurrentData::plEME2dCurrentData( plModelRegion *reg, const plNode & emnode ) : plBaseEMData( reg, emnode ), m_potential( reg, "Potential", emnode["EMPotentialFromCurrent"], sig ) { … } 4. Instruct how to calculate fields void plEME2dCurrentData::CalculateFields( REAL acc ) { … m_potential.Update( acc ); // calculate the electric fields gradient( & m_potential.tbcimat(), m_Eimposed1.tbcimat(), m_Eimposed2.tbcimat(), m_potential.fdgrid() ); … } 5. Export plug-in class plEME2dCurrent: public plBaseEMProxy<plEME2dCurrentData> { … } REGISTER_PROVIDER( plBaseEM, plEME2dCurrent, "E2dCurrent");

18. 5. Plasimo extensions (2): Composition • PLASIMO has own solver for calculation of composition: • E.g. 8 species: Hg (buffer), Hg+, Na, Na+, I, I+, NaI, e: • 3x ionisation ( X + e  X+ + 2e) • 1x dissociation (Na + I  NaI) • Charge neutrality • Pelemental = Pbulk •  • 2x elemental diffusion balance

19. 5. Plasimo extensions (2): Composition • 2. At CDL and PFA a chemical database is already available.  • Plasimo needs to call external library for calculating species partial pressures. CHEMAPP (Gibbs minimizer, commercial package  only DLL available) • Windows version of Plasimo required. • New composition plug-in. Hg (buffer), elements: Na, I, Ce, e CHEMAPP called for each grid point  2x elemental diffusion balance

20. 5. Plasimo extensions (2): chemapp initialization Initialization Geometry, grid Plasma parameters Buffer gas pressure (for Hg: based on dose and, effective temp. Cold spot temperature Salt doses, CHEMAPP returns initial values for elemental pressures. These values must be transferred to “Elemental function node”  Install again (input data is “constant”) CHEMAPP Cold spot elemental partial pressures: Apply to whole plasma Local temperature (init distribution) Transport coefficients User fit models, or Different interaction potentials Start main loop

21. 5. Plasimo extensions (3): • Implementing various line broadening mechanisms in radiation transfer module (ray tracing method): data from CDL. • Pressure • Stark • Doppler

22. 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 6. Results: 2D – Electric potential Electrode distance (Z): 24mm Burner radius (R): 6mm Electrode radius: 0.5mm DF 2V s constant NZ 40 NR 40 Electrode Large E-field  Large DT  Source of difficulties

23. 6. Results:2D – Electric potential, and temperature (1) Electrode distance (Z): 32mm Burner radius (R): 4mm Electrode radius: 0.5mm s F(T) (Fit from PFA data: Hg (buf) + Na + I) Total power 70W Electrode temperature 2900K NZ 120 NR 40 Regular grid selectrode = s(lte) selectrode= s(n-lte) > s(lte) Profiles not realistic

24. 6. Results: estimation thermal gradient at electrode First grid point regular grid at 1.6x10-4m Is too large. If equidistant grid  1000 axial points needed!  Axial grid transform (2-point stretch)

25. 6. Grid transformation Computational grid: equi-distant control volumes Electrode Physical grid: transformed control volumes Fine mesh at tip required, First gridline at 10mm

26. 6. 2D – Electric potential, and temperature (2) 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)

27. Heat flow analysis at electrode tip

28. 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 = 0.14×1900/10-5 = 0.27×108 23.5W • 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.

29. Checking E, and current density 3-rd axial gridpoint Radial integrated Jx is obviously overestimated. What is the reason? (physical, or numerical background?)

30. No 2-nd order polynomial curve fitting Ez(boundary, not electrode) = 0.

31. 6. Buffergas calculation (1): E, T, flow field, Hg • Influence of buffer gas pressure: • on flow field (maximum velocity) • Temperature distribution • Convergence

32. 6. Buffergas calculation (2): Flow field Gravity Only buffer gas (10 bar) Only buffer gas (40 bar) Only buffer gas (80 bar)

33. 6. Buffer gas calculation (3): temperature Gravity Only buffer gas (10 bar) Only buffer gas (40 bar) Only buffer gas (80 bar)

34. 6. Buffer gas calculation (4): temperature

35. 6. Convergence buffer gas calculations Only buffer gas (40 bar) Only buffer gas (80 bar)

36. (Fischer, 1976) Convection dominates (high pHg,R) Diffusion dominates (low pHg,R) pi 0 0 r r 6. Results (5) pi Axial velocity saturates? Na-I-Hg discharge ID = 14 mm IL = 32 mm Parabolic T-profile Hard-spheres diffusion 1D-Electric field (large radius electrode) ID = 8 mm IL = 32 mm Calculated T-profile 2D-Electric field (small radius electrode)

37. Buffer gas (10 bar) Na, and I additive (10mbar) 6. Results (4) Gravity

38. 6. Results (4) Only buffer gas (10 bar) Buffer gas (10 bar) Na minority (10mbar)

39. 7. Conclusion, and future work • Plasimo is powerful, and “flexible” tool for optimizing discharges used for lamps (calculating plasma physical, and radiation properties  light properties) • 2-D electric field has significant influence on flow field, • Flexible • can be linked with “third party” (commercial) libraries, • Small modifications can be implemented at CDL, • Large modifications implemented by TUE. Current and future work • Electrode boundary conditions (F), • Implementation radiation transport for rare-earth radiators (C, solution algorithm is free, radiation data is not free) , • Calculation “wall loads” (F)