1/24 Optical Thermometry Haiqing Guo Dept. of Fire Protection Engineering [email protected] Lab Methods Day June 25, 2014
Jan 11, 2016
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Optical Thermometry
Haiqing Guo
Dept. of Fire Protection Engineering
Lab Methods Day
June 25, 2014
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Introduction
• Optical thermometry, i.e. soot pyrometry, provides soot temperature and soot concentration information in flames.
• Soot radiance in flames was detected and converted to soot temperature (K) and soot volume fraction (ppm).
• This technique is nonintrusive.
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For hot regions in the visible or near-IR:
• Choose wavelength
Soot Radiance
1)/exp(
25
2
kThc
hcBW
The spectral radiance of hot soot is:
Blackbody spectral radianceSpeed of lightPlanck’s constantBoltzmann’s constantTemperatureEmissivityWavelength
Bλ
chkTελ
1)/exp( kThc
• Measure radiance (e.g., with filtered digital camera)
• Determine emissivity
wikipedia.org
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Bandpass Filters
• Choose two or more bandpass filters, e.g., at 450, 650, and 900 nm.• Bandwidth choice involves a tradeoff between error and signal
strength. A FWHM of 10 nm is most common.• Avoid chemiluminescence spectra (e.g., Swan Bands) and should be
far separated.
newport.com
wikipedia.org
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Soot Emissivity
• Determine emissivity
dyyxKdyyxKyx absabs ),()),(exp(1),(
/)(6 sextabs fmEKK Assume:
/),()(6),( dyyxfmEyx s
Refractive index absorption functionSoot volume fractionAbsorption coefficientExtinction coefficient
E(m)fs
Kabs
KextNotes:
• The variation of E(m) with soot morphology, soot age, and other conditions is not fully understood.
• Soot volume fraction fs is unknown.
Rayleigh scattering can be assumed because soot primary particles (dp 30 nm) are smaller than the Rayleigh limit.
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Camera Signal
• Measure soot radiance
0
dWI
aIGS
CCD/CMOS cameras are attractive owing to high bit depth (e.g, 14), higher pixel counts (12M), larger sensor arrays (36 x 24 mm), and decreased noise.
Irradiance incident on the CMOS sensor I:
a Constant that accounts for pixel size, fill factor, and sensitivityGS Grayscale divided by shutter time Constant that accounts for magnification and lens light losses Bandpass filter transmissivity
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Camera Calibration
• Constant a obtained from blackbody furnace calibration.– Emissivity of ε = 0.99 ± 0.01– Uniform and stable temperature
T range: 900 − 1200 ºCT increment: 25 ºCT accuracy: ± 0.1 ºC
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Line-of-Sight Radiance
x
y
Bandpass Filter
x
(x,y)dy
dydyyxfmE
yxTkhc
yxfhcmE
dydyyxKyxByxKxI
y
ss
yextabs
')',()(6
exp)],(/exp[
),()(12
')',(exp),(),()(
6
22
The exponent term describes the extinction effect from soot. For optically thin cases, it is negligible.
Flame cross section
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)],(/exp[
),()(12),(6
22
yxTkhc
yxfhcmEyxI s
GS to T Conversion
dy
yxTkhc
yxfhcmExI s
)],(/exp[
),()(12)(6
22
Tomography can convert the line-of-sight integrated irradiance I(x) into the local irradiance I(x,y).
a
yx ),GS(
For optically thin conditions:
From measured grayscale, blackbody calibration, and tomography
From filter manufacturer
High uncertainty
Required
Objective
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Ratio Pyrometry
• With multiple bandpass filters, ratio pyrometry allows fs and E(m) to be cancelled:
)/exp(
)/exp(
),(GS
),(GS
16
122
26
211
1
2
2
1
Tkhc
Tkhc
a
a
yx
yx
and
),(GS),(GSln
/1/1),(
1221
21
yxCyxCk
hcyxT
where C = a τ Δλ / λ6 is a constant for each filter and camera that does not vary with T or E(m).
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fs from Emissions
• The pyrometry determined temperature can be used to obtain the soot volume fraction for each filter.
• A soot refractive index of m = 1.57 – 0.56 i is commonly assumed, which yields E(m) = 0.26.
• Any uncertainty in T is amplified in determining fs.
CmEhc
yxTkhcyxyxf s
)(12
),(/exp),GS(),(
22
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Camera Tradeoffs
• Digital cameras require considering:– Response linearity (gamma correction must be avoided)– Parallel light collection (small aperture)– Sufficient depth-of-field (small aperture)– High spatial resolution (big sensor, small object distance)– High temporal resolution (fast shutter)– High signal resolution (high color bit-depth)– Ideal exposures should have high GS but not be
saturated in any color plane. This presents tradeoffs with aperture, shutter, and ISO.
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Deconvolution
• 3D tomographic reconstruction requires multiple imaging at different locations.
• For axisymmetric flames, tomography from I(x) to I(r) can be simplified and requires only one image.
• Commonly used deconvolution algorithms:– Abel transform– Onion peeling– Filtered back projection
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Abel Transform
• Based on an exact solution• Requires discretization
dyrfxp )()(
xdr
xr
rrfxp
22
)(2)(
rdx
rx
xprf
22
)('1)(
Line-of-sight integration of the flame property f(r) is:
Substituting y with x and r following r2 = x2 + y2 yields:
Analytical inverse of the above equation yields:
Sensitive to noise
Singularity at x = r
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Abel Transform
• Alternatively, a discretized form is simpler and more commonly used.
)2(
)()(1)()(1)(
2/3222/322 hrh
rpxdx
rx
xpxdx
rx
rpxprf
L
hr
hr
r
Lower integration limit region, solved with a open type numeric integration (e.g. Steffensen’s formula).
Solved with a regular closed type integration scheme (e.g. Simpson’s rule).
2/1222/122
1
1
221
)()1(2)( ijij
L
ij jj
i rrrrrr
jpjprf
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Onion Peeling
• Based on numerical approximation.• The domain is divided into a series of
concentric rings.• Within each ring, the value of the
spatial function f(r) is assumed to be constant.
• For the i-th cord and the j-th ring:
ijjjjjiji rrfsxp 1)()(
sij is a geometric matrix
ji
jjjijij rrxpsf 11 )()(
Deconvolve Form:
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Deconvolution
0 0.5 1 1.5 2 2.5 3 3.5 40E+00
1E+18
2E+18
3E+18
4E+18
5E+18
0.0E+00
5.0E+18
1.0E+19
1.5E+19
2.0E+19
TRUE
Onion peeling
Abel transform
Projection
r (mm)
Dec
onvo
luti
on
Pro
ject
ion
Deconvolution results from prescribed projection data. Spatial resolution is 0.05 mm/pixel.
• Sufficient spatial resolution is required for enough accuracy.
• Due to the differentiation, deconvolution is very sensitive to noise. Data smoothing can help: Low-pass filter Gaussian filter Savitzky-Golay filter
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Laminar Jet Diffusion Flame
• A Santoro coflow burner was used.
• The flame was steady and axisymmetric.
• Fuel tube: 11.1 mm ID
• Air tube: 101 mm IDAir
Fuel
Glass beads
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C2H4 Flame
• Fuel: ethylene
• Oxidizer: coflowing air.
• Flame height: 88 mmSteadyOptically thinAxisymmetric
Visible(a)
632.8 nm(c)
650 nm(b)
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Soot Temperatures
0 0.5 1 1.5 2 2.5 30
500
1000
1500
2000
2500
z = 50 mm
450/650 450/900 650/900
r (mm)
T (
K)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
z = 15 mm
450/650 450/900 650/900
r (mm)
T (
K)
Visible(a)
632.8 nm(c)
650 nm(b)
Low soot concentration
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T Contours
• T range: 1600-1850 K.
• Spatial resolution: 23 µm
• Longest shutter time: 125 ms
• Precision: ± 0.1 K
• Uncertainty: ± 50 K (95% confidence)
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Soot Emission Concentrations
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.0
0.5
1.0
1.5
2.0
2.5
3.0
fs450
fs650
fs900
r (mm)
fs (
pp
m)
Visible(a)
632.8 nm(c)
650 nm(b)
0 0.5 1 1.5 2 2.5 30
2
4
6
8
10
12
fs450
fs650
fs900
r (mm)
fs (
pp
m)
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Resultsfs results
Emission Extinction
fs (ppm) 0.1-10 0.2-10
Res. (µm) 23 34
t (ms) 125 167
Precision (ppm)
± 4×10-4 ± 6×10-4
Uncertainty ± 30% ± 10%
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Limitations
• Only applicable for sooting flame.• Needs to be optically thin (otherwise
complicated corrections are required).• Needs to be steady.• Needs to be axisymmetric.
For detailed information, please refer to “H. Guo, J.A. Castillo, P.B. Sunderland, Digital Camera Measurements of Soot Temperature and Soot Volume Fraction in Axisymmetric Flames, Applied Optics 52 (2013) 8040-8047.”