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Optical Thermometry

Haiqing Guo

Dept. of Fire Protection Engineering

hguo@umd.edu

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.”