2D Modelling of HID lamps using PLASIMO:

Electric field calculation

D.A. BenoyPhilips Lighting, CDL

13 April, 2005 2

Contents

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

13 April, 2005 3

Introduction: examples of MH-lamps

Commercial CDM Na + Hg radiation

Na + RE + Hg radiation

COST “standard”

MH Observation: color non-uniformityaxial segregation efficiency loss (vert.) color depends on burning positionGoal: understanding, optimizing effects of de-mixing.

13 April, 2005 4

HID development and lamp design (1)

AIM• To get a reliable relation between lamp design parameters

and1. 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, 2005 5

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, 2005 6

HID development and lamp design (3)

Lamp design:•Improvement existing products: Lifetime

o Stresses in burnero Failure modeso 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, 2005 7

HID lamp design model

PLASMA

Thermo-mechanical, and plasma modeling are complementary.

MaterialsGeometry SaltBuffer 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, 2005 8

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, 2005 9

2( )( )V

V rad

C TC T T p E U

t

u u

Ohmic dissipation Radiation 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 compositiono Transport of minority species additional balance equations

HID plasma model: power balance

13 April, 2005 10

HID plasma model: other balance equations

( ) 0t

u

( )( ) p

t

τ

uuu g

Vertical burning position

{ }

0

0

bulkambipolar term reactive term

i ii

i e ii i i i

i ie e

D pkT kTp

R

q P PR D R D

q P P

c

c u

JJJJJJJJJJJJJJ

Massbalance

Elementaldiffusion

Momentumbalance

Stoichiometric coefficientElemental flux

Species flux

Bulk flow field

Elem. densities

0)(

Electric field

13 April, 2005 11

HID plasma model: sub-models

Chemical composition1. 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 transportExpression for local energy loss by radiation:

Solution techniques:• Ray tracing• “Full” radiation transport treatment:

• including line broadening,• limited number of lines

.

4

( ) ( , ) ( ) ( , )

( ) exp( ( ))

( ) ( ') '

R

R

R

r

U r r B r L r s d d

L r r dr

r r dr

13 April, 2005 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 April, 2005 13

HID plasma sub-models: E-field and geometry (1)

HID-burner

Electrode

Interaction between plasmaand electrodes

Plasma is “decoupled”From electrodes

13 April, 2005 14

HID plasma sub-models: E-field and geometry

( ) Sf

u

Computational geometry model: 1D-electric field

1- Dimensional:E(R) Ez(z):

Constraints:• Current I is given• Power is given• Ez 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, 2005 15

HID plasma sub-models: E-field interface

13 April, 2005 16

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

0 0.004 0.008 0.012 0.016 0.02 0.024

z-axis

Po

ten

tial Axis

wall

electrode edge

Electrode distance (Z): 24mmBurner radius (R): 6mmElectrode radius: 0.5mm 2VconstantNZ 40NR 40Regular grid

HID plasmas modeling: E-field calculations (1)

Large E-field Large T Source of difficulties

13 April, 2005 17

Axial temperature profiles

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.004 0.008 0.012 0.016 0.02 0.024 0.028 0.032

Axial position (m)

Tem

per

atu

re (

K)

Electrode distance (Z): 32mmBurner radius (R): 4mmElectrode radius: 0.5mmF(T) Total power 70WElectrode temperature 2900KNZ 120NR 40

Regular grid

Axial temperature profiles

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.004 0.008 0.012 0.016 0.02 0.024 0.028 0.032

Axial position (m)

Tem

per

atu

re (

K)

electrode = (lte)

HID plasmas modeling: E-field calculations (2)

Profiles not realistic

electrode = (n-lte) > (lte)

13 April, 2005 18

HID plasmas modeling: E-field calculations (3)

m

E

Tx th

52

2

103.3)150000(40

20005.0

First grid point regular grid at 1.6x10-

4m(120 Z-points) Is too large.

If equidistant grid 1000 axial pointsneeded! Axial grid transform (2-point stretch)

Estimation of gradient length:

1 dimensional gridtransform

0

0.004

0.008

0.012

0.016

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

z-position (computational space)

tra

ns

form

ed

(p

hy

sic

al s

pa

ce

) 5

7.5

10

15

no tr

0

0.00005

0.0001

0.00015

0.0002

0 0.0002 0.0004 0.0006 0.0008 0.001z-position

tran

sfo

rmed

5

7.5

10

12.5

15

no tr

13 April, 2005 19

HID plasmas modeling: grid-transformation

Fine mesh at tip required,First gridline at 10m

Electrode

Computational grid: equi-distant control volumes

Physical grid: transformed control volumes

13 April, 2005 20

Axial temperature profile

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.004 0.008 0.012 0.016 0.02 0.024 0.028 0.032

Axial position (m)

Tem

pera

ture

(K

)

Electrode distance (Z): 32mmBurner radius (R): 4mmElectrode radius: 0.5mmF(T)Total power 70WNZ 120NR 40

Transformed grid

Axial temperature profiles

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

0 0.004 0.008 0.012 0.016 0.02 0.024 0.028 0.032

Axial position (m)

Tem

pera

ture

(K

)

electrode = (lte)

HID plasmas modeling: E-field calculations (4)

electrode > (lte)

13 April, 2005 21

Axial temperature profiles

2000

3000

4000

5000

6000

7000

8000

9000

0 0.0001 0.0002 0.0003 0.0004

axial position (m)

Tem

pera

ture

(K

)

Estimated electrode heat lossHeat flux at middle of electrodeq=T/x

q 0.09×1000/10-5 = 0.09×108W/m2 Total electrode loss 7.8Wq 0.11×1900/10-5 = 0.21×108 18.2Wq 2.90×5700/1.6×10-4 = 1.03×108 66WIs 8.5×larger!Much higher heat lost through electrode = unrealistic

Power input = 70WRule of thumb: 10 ~ 15% electrode losses.

Values for (n-lte), Telectrode?Near electrode (e-source) there is deviation from equilibrium.Plasma model: equilibrium (n-lte), and Tinput are input data.

Coupling with electrode model for self-consistent calculation of (n-lte), and Tinput .

HID plasmas modeling: E-field calculations (5) Thermal conductivity (LU)

0.01

0.1

1

10

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Temperature (K)

Th

erm

al

co

nd

ucti

vit

y (

W/m

K)

13 April, 2005 22

Axial potential distribution

-100

-95

-90

-85

-80

0 0.00005 0.0001 0.00015 0.0002

Axial pos [m]

Po

ten

tia

l [V

]

R=0.46mm

R=0.57mm

R=0.36mm

R=0.0mm

Axial electric component

-300000

-250000

-200000

-150000

-100000

-50000

0

50000

100000

0 0.00005 0.0001 0.00015 0.0002

Axial pos [m]

Ez

R=0.46mm

R=0.57mm

R=0.36mm

R=0.25mm

R=0.00mm

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

Axial electric component

-300000

-250000

-200000

-150000

-100000

-50000

0

50000

100000

0 0.00005 0.0001 0.00015 0.0002

Axial pos [m]

Ez R=0.46mm

R=0.57mm

R=0.36mm

R=0.25mm

R=0.00mm

HID plasmas modeling: E-field calculations (6)

13 April, 2005 23

HID plasmas modeling: E-field calculations (7) Gravity

P=60Bar

P=40Bar

P=10Bar

Ohmic dissipation (log scale)Temperature

13 April, 2005 24

2 2

maxv ~gas axis

gr PM gr

R T

Z=32mm, R=4mm

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80

Pressure [bar]

V-a

xial

max

[cm

/sec

]

Influence of E-field model on vmax.

1D E-fieldUnderestimation of vmax

Overestimation of segregation

2D E-field

13 April, 2005 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.