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

13 April, Contents Introduction HID development and lamp design HID modeling HID plasma model PLASIMO sub-model: E-field Conclusions

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

13 April, HID development and lamp design (1) AIM To get a reliable relation between lamp design parameters and 1.physical and chemical processes, and 2.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.

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

13 April, HID development and lamp design (3) Lamp design: Improvement existing products: Lifetime o Stresses in burner o Failure modes o 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.

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

13 April, Focus on modeling detailed discharge properties : 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 line broadening mechanisms. 4.Ohm’s law for electric field, and current density (electrode end effects). 5.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. HID modeling (1)

13 April, Ohmic dissipationRadiation term: emission, absorption (UV, visible, IR) Heat conduction Work by expansion Energy transport by convection (requires flow field )(requires electron densities and E) (requires flow field) (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 o Chemical composition o Transport of minority species  additional balance equations HID plasma model: power balance

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

13 April, HID plasma model: sub-models Chemical composition 1.Guldberg-Waage-Saha balance relations: Open source, Only 1 phase (gas). 2.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

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

13 April, HID plasma sub-models: E-field and geometry Computational geometry model: 1D-electric field 1- Dimensional: E(R)  E z (z): Constraints: Current I is given Power is given E z is constant 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

13 April, HID plasma sub-models: E-field interface

13 April, Electrode distance (Z): 24mm Burner radius (R):6mm Electrode radius:0.5mm  2V  constant NZ40 NR40 Regular grid HID plasmas modeling: E-field calculations (1) Large E-field  Large  T  Source of difficulties

13 April, Electrode distance (Z):32mm Burner radius (R):4mm Electrode radius:0.5mm  F(T) Total power70W Electrode temperature2900K NZ120 NR40 Regular grid  electrode =  (lte) HID plasmas modeling: E-field calculations (2) Profiles not realistic  electrode =  (n-lte) >  (lte)

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

13 April, HID plasmas modeling: grid-transformation Fine mesh at tip required, First gridline at 10  m Electrode Computational grid: equi-distant control volumes Physical grid: transformed control volumes

13 April, Electrode distance (Z):32mm Burner radius (R):4mm Electrode radius:0.5mm  F(T) Total power70W NZ120 NR40 Transformed grid  electrode =  (lte) HID plasmas modeling: E-field calculations (4)  electrode >  (lte)

13 April, Estimated electrode heat loss Heat flux at middle of electrode q=  T/  x q  0.09×1000/10 -5 = 0.09 × 10 8 W/m 2  Total electrode loss 7.8W q  0.11×1900/10 -5 = 0.21× W q  2.90×5700/1.6×10 -4 = 1.03× W Is 8.5 ×larger!  Much higher heat lost through electrode = unrealistic Power input = 70W Rule of thumb:  10 ~ 15% electrode losses. Values for  (n-lte), T electrode ? Near electrode (e-source) there is deviation from equilibrium. Plasma model: equilibrium   (n-lte), and T input are input data. Coupling with electrode model for self-consistent calculation of  (n-lte), and T input. HID plasmas modeling: E-field calculations (5)

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

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

13 April, Influence of E-field model on v max. 1D E-field  Underestimation of v max  Overestimation of segregation 2D E-field

13 April, 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.