Computational plasma physics: HID modeling with Plasimo D.A.

Computational plasma physics: HID modeling with Plasimo D.A.

Computational plasma physics: HID modeling with Plasimo D.A. Benoy Philips Lighting, CDL, MD&HT Contents Introduction Modelling HID burners HID plasma modelling Why Plasimo Plasimo extensions Results: computational analysis Conclusions Lighting, CDL, D. Benoy, 4 November, 2003 2 Introduction (1) Discharges for lighting: 1. Low pressure: Hg: fluorescent (TL) Na: Sox 2. High pressure: Hg: UHP (radiation source) Hg: CDM, MH, (buffer gas) Lighting, CDL, D. Benoy, 4 November, 2003 3

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 Lighting, CDL, D. Benoy, 4 November, 2003 4 2. Modeling HID (1): Global energy balance Pin Pdischarge=Pin-Pelect Pelect Pcond/conv

Pbulb Electrode modeling Burner + bulk discharge Lighting, CDL, D. Benoy, 4 November, 2003 Prad PUV Pvis rad PIR Multi-component discharge 5 2. Modeling HID (2) Focus on burner during lamp operation: Thermal modeling With commercial package: e.g. ANSYS (finite elements) Emphasis on geometry details. Nb wire sealing glass Cermet ceramic vessel electrode Plasma arc:

global properties Total radiation: Empiric expression salt pool Different colors represent different materials Lighting, CDL, D. Benoy, 4 November, 2003 6 2. Modeling HID (3) 1. 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 Lighting, CDL, D. Benoy, 4 November, 2003 7 2. Modeling HID (4)

Focus on discharge modeling for lighting properties electrode Plasma arc: detailed properties Radiation transport Side-on spectrum Buffer + additive salt salt pool Lighting, CDL, D. Benoy, 4 November, 2003 8 3. HID plasma modeling (1) 2. Discharge modelling: What? Study physical processes in the plasma of the burner (radiation, lamp voltage, local composition (demixing), 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 Lighting, CDL, D. Benoy, 4 November, 2003

9 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) Lighting, CDL, D. Benoy, 4 November, 2003 10 3. HID plasma modeling (3) Physical model assumptions for mass, and energy transport balances: 1. Local chemical equilibrium (LCE) for species composition in liquid (salt-pool) and gas phase, i.e. determination of local partial pressures of radiating species. 2. Transport of minority species by diffusion, and convection. 3. Radiation transport: Absorption, and self-absorption, Include broadening mechanisms.

4. Ohms 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 Lighting, CDL, D. Benoy, 4 November, 2003 11 3. HID plasma modeling (4) Plasma simulation model requirements: 1. Calculation chemical composition, 2. Transport of minority species by diffusion, and convection: Not limited by #species Not limited by #diffusion - convection mechanisms 3. Radiation transport, 4. Flow-field solver, 5. Thermal , electric conductivity, viscosity, and diffusion coefficients: function of plasma state, and composition, 6. 2-dimensional E-field. Lighting, CDL, D. Benoy, 4 November, 2003 12 3. Plasma balance equations Mass balance Elemental diffusion

Momentum balance Energy balance Electric field ( u) 0 t Elemental flux Bulk, ambipolar, reactive D p kT p kT c 0 Species flux Ri i 0 i Stoichiometric

coefficient Vertical burning position ( u) ( uu) p g t ( CV T ) ( CV Tu) T p u E 2 Qrad t ( ) 0 Lighting, CDL, D. Benoy, 4 November, 2003 Ohmic dissipation Radiation term 13 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 Lighting, CDL, D. Benoy, 4 November, 2003 14 5. Plasimo extensions (1) 1. Electric potential solver for finite electrodes: div J = 0,, J = E, E = - - = 0 new EM plug-in needed. Make use of standard equation. ( f u) S electrode HID-burner

Lighting, CDL, D. Benoy, 4 November, 2003 Computational geometry 1D-electric field 2D-electric field 15 1. Add new constructor class grdEXP plPoissonVariable : public plPhiVariable { class ConstTerm : public plDoublePhiTermContribution { public: void Update() {} plGridVar 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 &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; }; Lighting, CDL, D. Benoy, 4 November, 2003 16 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 { } REGISTER_PROVIDER( plBaseEM, plEME2dCurrent, "E2dCurrent"); Lighting, CDL, D. Benoy, 4 November, 2003 17 5. Plasimo extensions (2): Composition 2. 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 Lighting, CDL, D. Benoy, 4 November, 2003 18 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 Lighting, CDL, D. Benoy, 4 November, 2003 19 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 Cold spot elemental partial pressures: Apply to whole plasma Local temperature (init distribution) CHEMAPP returns initial values for elemental pressures. These values must be transferred to

Elemental function node Install again (input data is constant) Transport coefficients User fit models, or Different interaction potentials Start main loop Lighting, CDL, D. Benoy, 4 November, 2003 20 5. Plasimo extensions (3): 3. Implementing various line broadening mechanisms in radiation transfer module (ray tracing method): data from CDL. Pressure Stark Doppler Lighting, CDL, D. Benoy, 4 November, 2003 21 6. Results: 2D Electric potential Electrode distance 24mm Burner radius (R): Electrode radius:

constant NZ NR 1 (Z): 6mm 0.5mm 2V 40 40 Electrode 0.75 0.5 Potential 0.25 Axis 0 wall electrode edge -0.25 -0.5 -0.75

-1 0 Large E-field Large T Source of difficulties 0.004 0.008 0.012 0.016 0.02 0.024 z-axis Lighting, CDL, D. Benoy, 4 November, 2003 22 6. Results:2D Electric potential, and temperature (1) Axial temperature profiles electrode= (lte)n-lte) > (lte)lte) Lighting, CDL, D. Benoy, 4 November, 2003

9000 8000 7000 Temperature (K) Electrode distance (Z): 32mm Burner radius (R): 4mm Electrode radius: 0.5mm F(T) (Fit from PFA data: Hg (buf) + Na + I) Total power 70W Electrode temperature 2900K NZ 120 NR 40 electrode Regular grid= (lte)lte) 6000 5000 4000 3000 2000 1000 0

0.004 0.008 0.012 0.016 0.02 0.024 0.028 0.032 Axial position (m) Profiles not realistic 23 6. Results: estimation thermal gradient at electrode th T E 2 1 dimensional gridtransform 0.0002

0.5 2000 5 3 . 3 10 m 2 40 (150000) First grid point regular grid at 1.6x10-4m Is too large. If equidistant grid 1000 axial points Axial grid transform (2-point needed! stretch) 0.00015 transformed x 5 7.5 10 0.0001

12.5 15 no tr 0.00005 0 0 0.0002 0.0004 0.0006 0.0008 0.001 z-position Lighting, CDL, D. Benoy, 4 November, 2003 24 6. Grid transformation Computational grid: equi-distant control volumes Electrode Physical grid: transformed control volumes

Lighting, CDL, D. Benoy, 4 November, 2003 Fine mesh at tip required, First gridline at 10m 25 6. 2D Electric potential, and temperature (2) Axial temperature profiles electrode = (lte)lte) electrode > (lte)lte) 6000 5500 5000 4500 Temperature (K) Electrode distance (Z): 32mm Burner radius (R): 4mm Electrode radius: 0.5mm F(T) Total power 70W NZ 120 NR 40

Transformed grid 4000 3500 3000 2500 2000 1500 1000 0 0.004 0.008 0.012 0.016 0.02 0.024 0.028 0.032 Axial position (m) Lighting, CDL, D. Benoy, 4 November, 2003 26

Heat flow analysis at electrode tip Axial temperature profiles 9000 Temperature (K) 8000 7000 6000 5000 4000 Thermal conductivity (LU) 3000 2000 10 0.0005 0.001 axial position (m) 0.0015 Thermal conductivity (W/mK) 0 0.002 1

0.1 0.01 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Temperature (K) Lighting, CDL, D. Benoy, 4 November, 2003 27 Estimated electrode heat loss Heat flux at middle of electrode q=T/x q = 0.091000/10-5 = 0.09108W/m2 Total electrode loss 7.8W

-5 8 q = 0.141900/10 = 0.2710 23.5W q = 2.905700/1.610-4 = 1.03108 66W Axial temperature profiles Is 8.5larger! 9000 Much higher heat lost through electrode = unrealistic Power input = 70W Rule of thumb: 10 ~ 15% electrode losses. Temperature (K) 8000 7000 6000 5000 4000 3000 alues for (n-lte), Tn-lte), Telectrode? 2000 0 0.0001 0.0002 0.0003

0.0004 axial position (m) ear electrode (e-source) there is deviation from equilibrium. asma model: equilibrium (n-lte), and Tinput are input data. oupling with electrode model for self-consistent calculation of (n-lte), and Tinput . Lighting, CDL, D. Benoy, 4 November, 2003 28 Checking E, and current density Current (axial, and radial) (electrode radius = 0.5mm) 1.0 #Z-gridpoints: 100 0.5 0.0 -0.5 Ix(lte)100,0.5) -1.0 Iy(lte)100,0.5) -1.5

0.0020 -0.50 0.0015 -1.00 0.0010 -1.50 0.0005 -2.00 0.008 0.016 0.024 0.032 Axial position [m] 3-rd axial gridpoint Radial integrated Jx is obviously overestimated. What is the reason? (physical, or numerical background?) 0.0000

Current -2.5 0.000 Axial physical coordinate [m] -2.0 Transf. rel Ix(lte)100,0.5) -2.50 0 0.05 0.1 0.15 0.2 Comp. Z-axis Lighting, CDL, D. Benoy, 4 November, 2003 29 Axial electric component Axial potential distribution

100000 -80 50000 0 -85 R=0.57mm -90 R=0.36mm R=0.46mm R=0.57mm Ez Potential [V] -50000 R=0.46mm -100000 R=0.36mm R=0.25mm R=0.0mm R=0.00mm

-150000 -200000 -95 -250000 -300000 -100 0 0.00005 0.0001 0.00015 0 0.0002 0.00005 0.0001 0.00015 0.0002 Axial pos [m] Axial pos [m]

Axial electric field 100000 50000 0 -50000 R=0.00mm R=0.25mm E No 2-nd order polynomial curve fitting Ez(boundary, not electrode) = 0. -100000 R=0.36mm R=0.46mm R=0.57mm -150000 -200000 -250000 -300000 0 0.00005 0.0001 0.00015 0.0002

axis Lighting, CDL, D. Benoy, 4 November, 2003 30 6. Buffergas calculation (1): E, T, flow field, Hg Influence of buffer gas pressure: on flow field (maximum velocity) Temperature distribution Convergence Lighting, CDL, D. Benoy, 4 November, 2003 31 6. Buffergas calculation (2): Flow field Gravity Only buffer gas (10 bar) Only buffer gas (40 bar) Only buffer gas (80 bar) Lighting, CDL, D. Benoy, 4 November, 2003 32 6. Buffer gas calculation (3): temperature Gravity

Only buffer gas (10 bar) Only buffer gas (40 bar) Only buffer gas (80 bar) Lighting, CDL, D. Benoy, 4 November, 2003 33 6. Buffer gas calculation (4): temperature Axial temperature distribution 5500 Temperature 5000 4500 20bar 40bar 60bar 4000 3500 3000 0 0.008

0.016 0.024 0.032 Axial position [m] Lighting, CDL, D. Benoy, 4 November, 2003 34 6. Convergence buffer gas calculations Only buffer gas (40 bar) Lighting, CDL, D. Benoy, 4 November, 2003 Only buffer gas (80 bar) 35 6. Results (5) Z=32mm, R=4mm, 60W 50 p( z ) p0 exp( z ) 45 (Fischer, 1976) 40

pi pi r 0 r 0 35 V-axial max [cm/sec] Convection dominates (high pHg,R) Diffusion dominates (low pHg,R) 30 25 20 15 segregation coefficient (m^-1) 10 40

5 35 0 Axial velocity saturates? 0 30 ID = 14 mm IL = 32 mm Parabolic T-profile Hard-spheres diffusion 1D-Electric field (large radius electrode) 20 15 10 5 0 0 10 20 30

40 20 30 40 50 60 70 80 Pressure [bar] Na-I-Hg discharge 25 10 50 ID = 8 mm IL = 32 mm Calculated T-profile 2D-Electric field (small radius electrode) 60

pressure (Bar) Lighting, CDL, D. Benoy, 4 November, 2003 36 6. Results (4) Buffer gas (10 bar) Na, and I additive (10mbar) Gravity Lighting, CDL, D. Benoy, 4 November, 2003 37 6. Results (4) Only buffer gas (10 bar) Lighting, CDL, D. Benoy, 4 November, 2003 Buffer gas (10 bar) Na minority (10mbar) 38 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) Lighting, CDL, D. Benoy, 4 November, 2003 39

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