Upload
lita
View
45
Download
0
Embed Size (px)
DESCRIPTION
Radiation flux density in short lamp arcs. David Wharmby Technology Consultant [email protected]. COST 529 12-16 April 2005. Outline. Why is radiation flux density (RFD) important? Line-of-sight radiation transport Optical depth Absorption coefficient Radiation flux density - PowerPoint PPT Presentation
Citation preview
1
Radiation flux density inshort lamp arcs
David WharmbyTechnology Consultant
COST 529 12-16 April 2005
2
Outline
• Why is radiation flux density (RFD) important?• Line-of-sight radiation transport• Optical depth• Absorption coefficient• Radiation flux density• RFD in cylindrical geometry• Jones and Mottram net emission coefficient• Calculation of RFD in arbitrary geometry• Galvez’ method• Summary
3
Compact arcs need models for development
Tbottom= 1255K
= 1305KTtop
Tmax= 9095K
Tmin = 1325K
gas temperature velocity
outsidewall temperature
Short arcs have strong flows, no symmetry, dominant electrode effects
Time-dependence models are needed
Materials are very highly stressed
Source Miguel Galvez, LS10 Toulouse, 2004
~mm
4
• 50% of power may escape as radiation • High pressures mean that most of spectrum is at medium optical depth• But . . .LTE is usually OK, thankfully• Chemistry, conduction, convection and radiation must be included• Short arcs have radial and longitudinal temperature gradients, non-uniform
E field• Steady state energy balance
– all terms depend on temperature– solution gives the temperature field
• Satisfactory treatment of radiation flux density vector FR (W m-2) is critical because radiation is so dominant
Compact 3D arc models
Source M. Galvez, paper P-160 LS10 Toulouse, 2004
W m-3termsconvectionFdivFdivE CR _)()(2
conductionradiationpower in
5
Role of radiation
• E field accelerates electrons• electrons collisions produce excited states• emitted photons may escape or may be absorbed • absorption determines excited state densities• photons can travel throughout the plasma & affect excited state
densities elsewhere• non-linear & non-local system
– electron and excited state densities depend exponentially on T– absorption and emission processes depend very strongly on
frequency– absorption depends on emission from rest of plasma
Radiation transport requires massive computer resourcesMost approaches are unsatisfactory for short HID lamps
6
Line of sight radiation transport
7
Line of sight radiation transport• Spectral intensity (spectral radiance) of ray direction u at position r in the
plasma (W m-2 sr-1 nm-1)
• LTE (& Kirchhoff), no scattering, no incoming radiation
• Only data needed is local value of (,T)• Total intensity in just one direction needs triple
integration over s, ,
sdsdsTTTBsIs
s
s
so
))(,(exp),()()(
Planck
absorptioncoefficient
optical depth
s
plasma
I(s)
so
ss
u
r
8
Example calculation
• SR intensities are a guide to maximum temperature
– independent of oscillator strength, number density
– slightly dependent of T(r)
• SR dips can give some information about T(r)
Across diameter 100 torr Na plasma, parabolic profile 4200K-1500K, Stark & resonance broadening
0
2000
4000
6000
500 600 700 800
wavelength (nm)
spec
tral
rad
ianc
e
wall radiance
Planck
0
2000
4000
6000
585 590 595
wavelength (nm)
spec
tral
rad
ianc
e
wall radiance
Planck
centerradiance
0
2000
4000
6000
816 818 820 822
wavelength (nm)
spec
tral
rad
ianc
e
wall radiance
Planck
9
Is plasma optically thin?
• Information needed for experiment and model
• Measurement of transmittance is unreliable in lamps
– t>0.95 (say)
• Better guide
– compare measured spectral radiance with line-of-sight radiation transport calculation using assumed temperature distribution
• At given plasma is thin when
– measured spectral radiance << Planck radiance at highest T
• For energy balance calculation
– radiation that is neither thick nor thin affects temperature profile
– needs full RFD calculation.
Source Griem “Plasma Spectroscopy”, 1964
10
How do we know that a plasma is optically thin?
1. Make spectral radiance measurement2. Calculate [radiance/BB radiance] at Tmax, assuming T(r)
0.0
0.2
0.4
0.6
0.8
1.0
550 600 650wavelength (nm)
tra
nsm
itta
nce
0.00
0.01
0.02
rad
ian
ce fr
act
ion
spectralradiance (asfraction of BB)
11
How do we know that a plasma is optically thin?
1. Make spectral radiance measurement2. Calculate ratio radiance/BB radiance at Tmax, assuming T(r)3. Calculate transmittance t = exp(-)
0.0
0.2
0.4
0.6
0.8
1.0
550 600 650wavelength (nm)
tra
nsm
itta
nce
0.00
0.01
0.02
rad
ian
ce fr
act
ion
plasmatransmittance
spectralradiance (asfraction of BB)
12
How do we know that a plasma is optically thin?
1. Make spectral radiance measurement2. Calculate ratio radiance/BB radiance at Tmax, assuming T(r)3. Calculate transmittance t = exp(-)4. Where is t > 0.95
0.0
0.2
0.4
0.6
0.8
1.0
550 600 650wavelength (nm)
tra
nsm
itta
nce
0.00
0.01
0.02
rad
ian
ce fr
act
ion
transmittance
95%transmittance
spectral radiance(as fraction ofBB)
13
Absorption coefficient (,T) data example
• Example– High pressure Hg at
8000K• Absorption from
– lines: resonance, van der Waals & Stark
– e-a and e-i Brems.– e-i recombination – molecular
• Omission of molecular wing of lines gives imperfect line profile
10
100
1000
10000
100000
1000000
540 580 620 660 700
wavelength (nm)
ab
sorp
tion
co
effi
cie
nt (
1/m
)
total
lines
electron-atom Brems.(Lawler)
electron-ion Brems.
Source Lawler, J. Phys. D: Appl. Phys. 37, 1532-6, 2004 (e-a data for Hg)Hartel, Schoepp & Hess, J. App. Phys 85, 7076-7088, 1999 (line broadening)
14
8.0
8.5
9.0
546
436
405
6 3,1D 1S0
365 group
313 group
297
X
G
D
F
E
B A
185
Molecular absorption
Source A Gallagher in “Excimer Lasers”
• Green transitions give absorption in UV 254nm resonance line
• Blue transitions affect extreme wing profile of non-resonance lines
• Upper levels are completely unknown
• Generally bb, ff, fb and bf emission from molecules will be important
254
?
15
100
80
60
40
20
0
relative intensity %
wavelength (nm)
530 534 542538
Molecular effects in the wing of the Tl lineMeasurements of Tl resonance line broadened by Tl and Hg
Note strongly curtailed red wing
Time dependent spectra on 50Hz operation
16
Radiation flux density
17
Radiation flux density (RFD)
• Integrate intensity (vectorially) passing through area at r in directions u
• Two more integrations over and
• This vector is radiation powerFRthrough unit area at r (W m-2 nm-1)
• Total RFD FR(W m-2) needs 5th integration over
• For a uniform element, div(FR) (W m-3) gives radiation power (W m-3) in element for calculation of energy balance
• net emission coefficient div(FR) = 4N
– difference between emission and absorption in element of plasma
durIrF R ),()(
r
I(r,u2)
FR(r)
I(r,u1)
I(r,u4)
I(r,u3)
plasma
18
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
19
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
often hopeless
20
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
many examples – Lowke, TUe
often hopeless
21
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
many examples – Lowke, TUe
Jones & Mottram?
often hopeless
22
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the RFD integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
many examples – Lowke, TUe
Jones & Mottram?
control of approx?
often hopeless
23
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
many examples – Lowke, TUe
Jones & Mottram?
control of approx?will examine in detail
often hopeless
24
Treating radiation complexity – in order of increasing computer time
• Ignore it by unphysical approximations
– >>1 (diffusion)
– <<1 (optically thin)
• Reduce complexity of RFD integral using symmetry
– e.g cylindrical
• Find a realistic way to express N as a local quantity
• Find ways to pre-tabulate some of the integral
– Sevast’yanenko (pre-tabulate integration over )
– Galvez (pre-tabulate geometry)
• Use Monte Carlo methods
• Full-blooded numerical integration
Remember RFD must be evaluated many times during energy balance
many examples - Lowke
Jones & Mottram?
control of approx?will examine in detail
useful for checking
out of sight
often hopeless
25
Infinite cylindrical geometry • treated by Lowke for Na arcs• shows contribution from various rays to RFD in
blue element
J J Lowke JQRST 9, 839-854, 1969
r
s()
wall
26
-5
0
5
10
15
20
25
0.0 0.2 0.4 0.6 0.8 1.0
radial position-5
0
5
10
15
20
F R (MW m-2) N (MW m-3 sr-1)
Infinite cylindrical geometry • shows contribution at r to RFD from ray in
direction u • reduce evaluation of to 4 integrations by
projecting variation onto horizontal plane using pre-tabulated function G1(s)
• FR only has a radial component
J J Lowke JQRST 9, 839-854, 1969
Sodium arc
Jones & Mottram FR
after Lowke (1969)
N = (1/4)div(FR)
r
u
s()
wall
27
Jones and Mottram - N as an approximate local function
• Guess temperature to start to energy balance and calculate RFD FR exactly
• Calculate N(r) from div FR
• Represent N(r) as a function (T)- Emission part depends on depends on upper state number density- Absorption part depends on FR and lower state number density
• Use Nfit to represent radiation
until energy balance converges
• Recalculate Nfit
• Converge energy balance again
))(/exp()())(/exp()(
)]([rTdrcrTba
rT
rTpRNfit F
Jones BF & Mottram DAJ J. Phys. D: Appl. Phys. 14, 1183-94, 1981
For HPS in cylindrical geometry requires only 3 RFD evaluations
-5
0
5
10
15
1000 2000 3000 4000 5000
temperature (K)
net
emis
sion
coe
ffici
ent
Jones and Mottram data
estimated from empirical formula
28
• Makes N seem local as long as conditions do not change too much
• The closer the arc temperature profile is to the guessed profile used to
calculate Nfit, the more rapid the solution of energy balance
• Particularly applicable to calculating effect of
– a sequence of changes of pressure or power
– time-dependent solutions of energy balance
because from previous input values can be used
• Can this be used in 3D???
– do full RFD calculation using Galvez or other method
– fit Nfit(T(u), P, FR) to FR one or more directions u
Jones and Mottram - Nfit as an approximate local function
This could be a powerful aid but needs to be tested
29
Radiation flux in asymmetric 3D plasma
30
Radiation flux in asymmetric 3D plasma
Green cell A receives radiation from all other cells(e.g. n = 1 . .6)
• Amount of radiation from cell n is TnB(Tn)
• Absorption at A depends TAThese depend on local values of temperature
The heavy computation occurs because the spectrum emitted cell n is selectively absorbed in the path to A
temperature contours
1
2
3
4
56
A
31
Galvez method – geometrical precalculation
• 2D picture of 3D process, showing finite volumes in calculation mesh• From a starting cell (green) take rays to other parts of the plasma
wallwall
32
Galvez method – geometrical precalculation
• 2D picture of 3D process, showing finite volumes in calculation mesh• From a starting cell (green) take rays to other parts of the plasma
wallwall
33
Galvez method – geometrical precalculation
• 2D picture of 3D process, showing finite volumes in calculation mesh• From a starting cell (green) take rays to other parts of the plasma
wallwall
34
• 2D picture of 3D process, showing finite volumes (FV) in calculation mesh• From a starting cell (red) take rays to other parts of the plasma
• For each ray tabulate – which FV is emitting ray– which FV the ray crosses– Distance traversed in each FV– Which FV is the exit volume
wallwall
Galvez method – geometrical precalculation
geometry only!
35
How many rays are needed?
• FV mesh
• Rays emitted from a single cell chosen at random
• Let cell emits N rays isotropically
• N increased until the rays visit at least 95% of the cells
• N used by Galvez is typically 100
• So solid angle element for each ray – 4/N =4/100
• Repeats checks using other FV for emission confirm 100 is about enough for a good representation of the radiation field
36
Pre-tabulate following
wall
ray 3
9
2345678
10j =
3 4 5 6 7 8 9210k =
Start cell s(j,k) s(4,3) Ray number r 3 Cells visited n(j,k) n(3,4) n(3,5) n(2,6) n(2,7) n(1,7) n(1,8) n(1,9) n(0,9) Distance in cell d(j,k) d(3,4) d(3,5) d(2,6) d(2,7) d(1,7) d(1,8) d(1,9) d(0,9) Exit cell e(j,k) e(0,9)
For each ray in from each start cell
s
s kj
kjdkjTsdsTss,
),()],(,[))(,(),,(
Geometrically complicated integral for then becomes a simple sum based on pre-tabulated geometry & absorption coefficients
37
Results
• Galvez at LS10 gave an example of a MH short arc energy balance calculation with
– 7400 finite volumes
– 100 rays per finite volume
– 19000 wavelengths
• Used in design study of ceramic metal halide lamps
– calculates inner wall temperature
– bulge shape avoids corrosion at corners of cylinder
– salt temperature is more independent of orientation – better color
– bulge shape reduces mechanical stress by factor 2
Source S Juengst, D Lang, M Galvez, LS10 Toulouse, Paper I-14 2004
Inner WallTemperature Distribution
Molten salts
Molten salts
Inner Wall Temperature Distribution
Inner WallTemperature Distribution
Molten salts
Molten salts
Inner WallTemperature Distribution
Inner WallTemperature Distribution
Molten salts
Molten salts
Inner Wall Temperature Distribution
38
Advantages of Galvez method
• Straightforward evaluation of div(FR)
– In the course of energy balance FR is updated every 10 to 20
iterations
– Look up tables for geometry and absorption coefficients used to calculate non-local part of integral
• Spectral flux from finite volumes adjacent to wall
– summed to give the spectral flux (power) distribution
– this can be compared with measurements in an integrating sphere
• Accuracy approaches that of full integration as number of rays N increases
• As with many RFD calculations it can be parallelized
• Applicable to time-dependent solutions
Source M Galvez, LS10 Toulouse, Paper P-160 2004
39
Conclusions
• Ray tracing precalculation of Galvez is a major advance
– provides a practical solution to RFD calculations in arbitrary geometry• Computational speed means that it can be applied to arbitrary geometry with
convection • Has been applied to time-dependent calculations
• Example is ultra high mercury pressure video projection lamp showing gas temperature, combined with electrode sheath model
Tmax = 9095K
Tmin = 1325K
Source M Galvez, LS10 Toulouse, Paper P-137 2004
3684K
3602K
3556K
3511K
3465K
40
• Galvez method will prove to be method of choice for asymmetric arcs
• Iteration will be further speeded up by Jones & Mottram semi-
empirical N approach (or something like it)
• This will make radiation modelling of time-dependent short arcs practical
• But– Better data on high temperature absorption coefficients will
be needed, especially for bb, bf, ff molecular processes
The future?
41