Post on 22-Dec-2015
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.