Computational plasma physics: HID modeling with Plasimo

Computational plasma physics:HID modeling with Plasimo

D.A. BenoyPhilips Lighting, CDL,

MD&HT

Lighting, CDL, D. Benoy, 4 November, 2003 2

Contents

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


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)• …


Na + Hg radiation

Na + RE + Hg radiation

top

bottom

Observation:axial segregation => efficiency loss (vert.) => color depends on burning position

1. Introduction (3): vertical burning MH lamps

Goal: understanding, optimizing effects of de-mixing.


2. Modeling HID (1): Global energy balance

Pin

Pdischarge=Pin-PelectPelect

Prad

PUV

Pcond/conv

Pbulb Pvis rad PIR

Electrode modelingBurner + bulk discharge

Multi-componentdischarge


2. Modeling HID (2)Focus on burner during lamp operation:Thermal modeling

Cermet

sealing glass

ceramic vessel

electrode

salt pool

Nb wire

Plasma arc:global properties

Total radiation:Empiric expression

Different colors represent different materials

With commercial package: e.g. ANSYS (finite elements)Emphasis on geometry details.


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


2. Modeling HID (4)

Focus on discharge modelingfor lighting properties

Buffer + additive salt

electrode

Plasma arc:detailed properties

salt pool

Radiation transportSide-on spectrum


3. HID plasma modeling (1)

2. 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


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)


In this lecture: focus on modeling detailed properties of discharge.


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. 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.



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.



3. Plasma balance equations

( ) 0t

u

( )( ) p

t

τ

uuu g

2( )( )V

V rad

C TC T T p E Q

t

u u

Vertical burning position

0

0i ii

D pkT kTp

R

c

Massbalance

Elementaldiffusion

Momentumbalance

Energybalance

Stoichiometric coefficient

Elemental flux

Species flux

Ohmic dissipationRadiation term

Bulk, ambipolar, reactive

0)(

Electric field


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)

Additional issues:• Flexibility w.r.t. “minor” extensions, and modifications,• Nearby support, including implementation “major”

extensions,• Cheap

PLASIMO does not have these short-comingsFlaw of PLASIMO• Limited freedom in modeling electrode geometry. For

detailed modeling of discharge: not serious problem.


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.

( ) Sf

u

electrode

HID-burner 1D-electric field 2D-electric field

Computational geometry


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 ) ;};

1. Add new constructor

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;};

2. Add new class


plEME2dCurrentData::plEME2dCurrentData( plModelRegion *reg, const plNode & emnode ) : plBaseEMData( reg, emnode ), m_potential( reg, "Potential", emnode["EMPotentialFromCurrent"], sig ){

…}

3. Implement constructor of new class

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() );…}

4. Instruct how to calculate fields

class plEME2dCurrent: public plBaseEMProxy<plEME2dCurrentData>{…}REGISTER_PROVIDER( plBaseEM, plEME2dCurrent, "E2dCurrent");

5. Export plug-in


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 neutralityPelemental = Pbulk2x elemental diffusion balance


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


5. Plasimo extensions (2): chemapp initializationInitialization

Geometry, grid

Buffer gas pressure (for Hg: based on dose and, effective temp.Cold spot temperatureSalt doses,

CHEMAPP

Cold spot elemental partial pressures:Apply to whole plasma

Local temperature (init distribution)

Plasma parameters

Transport coefficients

User fit models, orDifferent interaction potentials

Start main loop

CHEMAPP returns initial values for elemental pressures. These values must be transferred to “Elemental function node” Install again (input data is “constant”)


5. Plasimo extensions (3):

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


-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 40

6. Results: 2D – Electric potential

Electrode

Large E-field Large T Source of difficulties


Electrode distance (Z): 32mmBurner radius (R): 4mmElectrode radius: 0.5mmF(T) (Fit from PFA data: Hg (buf) + Na + I)Total power 70WElectrode temperature2900KNZ 120NR 40Regular 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)electrode= (n-lte) > (lte)

6. Results:2D – Electric potential, and temperature (1)

Profiles not realistic


6. Results: estimation thermal gradient at electrode

1 dimensional gridtransform

0

0.00005

0.0001

0.00015

0.0002

0 0.0002 0.0004 0.0006 0.0008 0.001

z-position

tra

ns

form

ed 5

7.5

10

12.5

15

no tr

m

E

Tx th

52

2

103.3)150000(40

20005.0

First grid point regular grid at 1.6x10-4mIs too large.

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


6. Grid transformation

Fine mesh at tip required,First gridline at 10m

Electrode

Computational grid: equi-distant control volumes

Physical grid: transformed control volumes


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


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

per

atu

re (

K)

electrode = (lte)electrode > (lte)

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


Thermal conductivity (LU)

0.01

0.1

1

10

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Temperature (K)

Th

erm

al c

on

du

ctiv

ity

(W/m

K)


2000

3000

4000

5000

6000

7000

8000

9000

0 0.0005 0.001 0.0015 0.002

axial position (m)

Tem

per

atu

re (

K)

Heat flow analysis at electrode tip


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 = 0.14×1900/10-5 = 0.27×108 23.5Wq = 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 .


2000

3000

4000

5000

6000

7000

8000

9000

0 0.0001 0.0002 0.0003 0.0004

axial position (m)

Tem

per

atu

re (

K)


Current (axial, and radial)(electrode radius = 0.5mm)

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0.000 0.008 0.016 0.024 0.032

Axial position [m]

Ix(100,0.5)

Iy(100,0.5)

#Z-gridpoints:100

0.0000

0.0005

0.0010

0.0015

0.0020

0 0.05 0.1 0.15 0.2

Comp. Z-axis

Axi

al

ph

ysi

cal

co

ord

ina

te [

m]

-2.50

-2.00

-1.50

-1.00

-0.50

Cu

rren

t

Transf. rel

Ix(100,0.5)

3-rd axial gridpointRadial integrated Jxis obviously overestimated.What is the reason? (physical,or numerical background?)

Checking E, and current density


Axial potential distribution

-100

-95

-90

-85

-80

0 0.00005 0.0001 0.00015 0.0002

Axial pos [m]

Pot

enti

al [

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

Axial electric field

-300000

-250000

-200000

-150000

-100000

-50000

0

50000

100000

0 0.00005 0.0001 0.00015 0.0002

axis

ER=0.00mm

R=0.25mm

R=0.36mm

R=0.46mm

R=0.57mm

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


6. Buffergas calculation (1): E, T, flow field, HgInfluence of buffer gas pressure:

•on flow field (maximum velocity)•Temperature distribution•Convergence


6. Buffergas calculation (2): Flow field

Only buffer gas (10 bar)

Gravity




6. Buffer gas calculation (3): temperature


Gravity




Axial temperature distribution

3000

3500

4000

4500

5000

5500

0 0.008 0.016 0.024 0.032

Axial position [m]

Tem

per

atu

re 20bar

40bar

60bar

6. Buffer gas calculation (4): temperature


6. Convergence buffer gas calculations

Only buffer gas (40 bar) Only buffer gas (80 bar)


6. Results (5)

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60

pressure (Bar)

seg

reg

atio

n c

oef

fici

ent

(m^

-1)

pi

(Fischer, 1976)

Diffusiondominates(low pHg,R)

Convectiondominates(high pHg,R)

r0

r0

pi

)exp()( 0 zpzp

Na-I-Hg discharge

ID = 14 mmIL = 32 mmParabolic T-profileHard-spheres diffusion1D-Electric field (large radius electrode)

Z=32mm, R=4mm, 60W

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

]

ID = 8 mmIL = 32 mmCalculated T-profile2D-Electric field (small radius electrode)

Axial velocity saturates?


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

Gravity


6. Results (4)

Buffer gas (10 bar)Na minority (10mbar)



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 workElectrode boundary conditions (F),Implementation radiation transport for rare-earth radiators (C, solution algorithm is free, radiation data is not free) ,Calculation “wall loads” (F)

Documents

Computational plasma physics: HID modeling with Plasimo