Quantifying the Effects of Combustion Gases' Radiation on Surface

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Quantifying the E#ects of Combustion Gases Radiation on Surface Temperature Measurements Using Two-Color Pyrometry Yunwei Huang, Mujun Long, Helin Fan, Lintao Gui, Dengfu Chen, and Huamei Duan Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b00257 • Publication Date (Web): 11 Mar 2019 Downloaded from http://pubs.acs.org on March 18, 2019

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Energy & Fuels

Quantifying the Effects of Combustion Gases Radiation

1 2

on Surface Temperature Measurements Using Two-Color

3

Pyrometry

4

Yunwei Huang a,b, Mujun Long a,b,*, Helin Fan a,b, Lintao Gui a,b, Dengfu Chen a,b,*,

5

6 7 8 9

Huamei Duan a,b

a

State Key Laboratory of Coal Mine Disaster Dynamics & Control, College of Materials

Science and Engineering, Chongqing University, Chongqing 400044, P.R. China. b. Chongqing

Key Laboratory of Vanadium-Titanium Metallurgy and New Materials,

Chongqing University, Chongqing 400044, P. R. China

10

Email of authors:

11

Yunwei Huang: [email protected]

Mujun Long: [email protected]

12

Helin Fan: [email protected]

Lintao Gui: [email protected]

13

Dengfu Chen: [email protected]

Huamei Duan: [email protected]

14 15

Correspondence authors:

16

Mujun Long

17

Address: College of Materials Science and Engineering, Chongqing University, Chongqing

18

400030, P.R. China.

19

Phone: +86-023-65102467

20

Email: [email protected]

21

Dengfu Chen

22

Address: College of Materials Science and Engineering, Chongqing University, Chongqing

23

400030, P.R. China.

24

Phone: +86-023-65102467

25

Email: [email protected] 1

ACS Paragon Plus Environment

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Page 2 of 33

1

Abstract

2

This paper developed an analytical two-color thermometry model combined with

3

a mathematical radiative heat transfer model. The proposed model was used to

4

investigate the performance of two-color pyrometry affected by absorption bands in

5

hot combustion gases. This model was validated by comparing with a range of

6

measured data and the results of other numerical solutions. The analysis of the

7

temperature errors produced by high-temperature H2O-CO2-N2 mixture in three

8

measurement

9

H2O-CO2-N2 mixture greatly affected the measurement accuracy of two-color

10

pyrometry. Minimizing the absorption and emission effect by selection of the

11

instrument spectral band is useful when interfering combustion gases are at low

12

concentrations. The results showed that the measured temperature had an apparent

13

oscillatory phenomenon due to combustion gaseous absorption and emission effect.

14

This phenomenon tended to further strengthened with thicker hot interfering gas layer.

15

Through an analysis of the mechanism of the oscillatory behavior, a correction

16

strategy to minimize the temperature error was presented. Theoretical temperature

17

shifts at some selected wavelength pairs produced by changes in the model input

18

parameters were estimated to provide at least a basis for an uncertainty analysis, as

19

well as a sensitivity analysis of the impact factors was performed. The calculated

20

temperature error was nearly exponential growth with increase of combustion gas

21

temperature when gas temperature is greater than target temperature, and it was

22

linearly growth in magnitude with both gas mixture concentration and viewing path

23

length increasing. The analyses presented in the paper may provide valuable

24

descriptions of measurement errors produced by combustion gases and necessary

25

theoretical supports for the design and application of a two-color pyrometer in the

26

presence of combustion gases.

27 28

situations

was

presented.

The

presence

of

high-temperature

Keywords: Two-color pyrometry, Surface temperature measurement, Hot combustion gases, Radiative heat transfer.

29

2


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Energy & Fuels

1

1. Introduction

2

The measurement and control of surface temperature in manufacture procedure is

3

significant from the viewpoints of energy management, process control and product

4

quality1. Accurate surface temperature measurements of critical components operating

5

in harsh environment are quite vital as far as their lifetime is concerned2 and are

6

required for energy saving. As Saunders pointed out that surpassing the designed

7

temperature by just 15 K will halve the life expectancy of a furnace tube3 and

8

preventing an event of furnace tubes being exposed to a very high temperature will

9

save about 100 million dollars4. Advanced and effective surface temperature

10

measurement methods have scientific significance and practical value for maintaining

11

high product quality and energy effectiveness in plant furnaces5.

12

Radiation thermometry is of great industrial importance and is the widely used

13

methods of measuring surface temperature in the severe environment of

14

high-temperature industrial processes where resistance thermometers, thermocouples,

15

or other contact-type sensors are found to be inappropriate1, 6. An significant

16

application of radiometric temperature measurement is the measurement of surface

17

temperature of parts in gas turbines and furnaces where the combustion gas

18

environment is often at a higher temperature than the target surface7. The main

19

problem in this application is the large error arising from the absorption and emission

20

of intervening combustion gases. The radiation from the target surface must spread

21

some distances through the hot combustion gases layer to the thermometer. Any

22

interplay between the combustion gases and the radiation in the form of emission and

23

absorption will change the radiation received by the pyrometer. Scattering of radiation

24

by particles, e.g. soot, can also be a puzzle. Nonetheless, gas-fired furnaces do not

25

generally incur scattering problems. For oxy-combustion applications, combustion gas

26

concentrations of CO2 and H2O are greater than in gas-fired systems and increase

27

gaseous absorption and emissions8. The capability to correctly predict the influence of

28

combustion gases on the surface temperature measurement is practically significant to

29

the forecasting, understanding, and minimizing or prevention of the measurement

30

errors.

31

The method applied in most previous research to address this issue involves

32

either restricting the optical pass-band to spectral regions in which the combustion

33

gases are considered to be transparent9-11 or multiplying a spectral transmittance of the

34

gases between the target and the thermometers6, 12. It should be emphasized that this 3


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Page 4 of 33

1

method may be effective in certain limited situations where the interfering

2

combustion gases are at low concentrations. If the high-temperature combustion gases

3

present in high concentrations, the absorption and emission of radiation by the gases

4

can have deeply harmful impacts on radiometric temperature measurements, such as

5

that of measuring surface temperature in combustion chamber and gas turbines. In

6

such cases, a more sophisticated understanding the fundamentals of the radiation

7

augmentation and attenuation in the combustion gases and the mechanism of the

8

measurement error caused by combustion gases is essential to the proper selection and

9

application of radiometric temperature measurement techniques to industrial

10

processes.

11

In industrial processes when there is extra radiation attenuation or augmentation

12

because of intervening participating media, it is not uncommon to employ a two-color

13

pyrometer to compensate for the radiation losses13. Because two-color pyrometers

14

determine target temperature from the ratio of the detected radiation in two different

15

operating wavebands, the decrease in electrical signal caused by extra attenuation

16

cancels in part by ratioing the outputs from the two different channels14, 15. Therefore,

17

two-color pyrometry is a very potential technique for accurate surface temperature

18

measurement when the sight path of thermometer is filled with high concentration

19

combustion gases. Though scholars have done some researches on gaseous absorption

20

and emission effects on single-color pyrometry4,

21

widely been used for the measurement of the temperature and concentration of soot or

22

gas present in combustion flames18-22, few investigations have attempted to study

23

these effects on surface temperature measurement using two-color pyrometry. On the

24

basis of the latest high-temperature molecular spectroscopic database, HITEMP

25

201023, exploration of the performance of two-color radiation thermometers affected

26

by absorption bands in the interfering combustion gases is attainable. A majority of

27

such influences can be eliminated if one has a fundamental knowledge of their

28

origins.

16, 17

and two-color pyrometry has

29

Instigated by these observations, the first goal of the present study is to

30

investigate the performance of two-color radiation thermometers affected by

31

absorption bands in hot combustion gases. The second goal is to correct for the

32

temperature errors due to combustion gases obscuring the measurement sight path by

33

understanding the nature and origin of the errors. In present work, a radiative heat

34

transfer model linked with a two-color pyrometry model was proposed. The radiative 4


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Energy & Fuels

1

properties of the interfering combustion gases, which is an input parameter to the

2

radiative heat transfer model, was obtained by adopting statistical narrow-band (SNB)

3

model and grey-band approximation method. Subsequently, to validate this model, its

4

parameters and predictions were compared with both relevant experimental

5

measurements and the other numerical model calculations in references. The analysis

6

of the temperature errors produced by the H2O-CO2-N2 mixture in three measurement

7

situations was presented. Through an analysis of the mechanism of this error, a

8

methodology for selecting wavelength pairs to minimize the error was discussed.

9

Furthermore, theoretical temperature shifts at some selected wavelength pairs

10

produced by changes in the model input parameters are estimated to provide at least a

11

basis for an uncertainty analysis, as well as a sensitivity analysis of the impact factors

12

was performed. Finally, the primary conclusions of this study were presented in brief.

13

2. Model formulation

14 15

2.1 Basic theory of the surface temperature measurement affected by interfering combustion gases

16

The planar geometry studied in the present work is outlined in Fig. 1. It is

17

composed of an infinite, blackbody target boundary and a hot combustion gases layer

18

of thickness L between the boundary and a two-color pyrometer. The target surface is

19

considered to be a blackbody to eliminate the influences of extraneous reflection and

20

target surface emissivity. The pyrometer normal to target surface is assumed to

21

receive the radiation energy emitted by the target surface, as shown in Fig 1.

22 23

Fig. 1 Physical model of radiative temperature measurement in hot combustion gas 5


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1 2

Page 6 of 33

The total radiative energy in two different wavebands detected by the two-color pyrometer can be expressed as, E 

3

 I

in

cos  d 

(1)

2

4

where Iin is the incident radiative intensity toward the pyrometer. θ is the angle

5

between the incident direction and the normal direction of the target surface. Ω is the

6

solid angle of the measured surface relative to the pyrometer. The incident radiative

7

intensity Iin depends on the target surface temperature and the absorption coefficient

8

of the interfering combustion gases, which can determined by radiative transfer

9

equation and boundary condition: I ( x,  )  k I b  k I  ( x,  )   x

10

(2)

11

I b (0,  )  I b (T1 ),

 0

(3a)

12

I  ( L,  )  0,

 0

(3b)

13

where subscripts λ and b stand for wavelength and blackbody, respectively. kaλ is the

14

absorption coefficient of the interfering combustion gas, x stands for x-coordinate,

15

x=0 and x=L correspond to the locations of the target boundary and the pyrometer,

16

respectively. μ is the direction cosine of polar angle 𝜃, μ=cos𝜃, and T1 is the surface

17

temperature of the target. n is refractive index, σ is known as Stefan-Boltzmann

18

constant. I  ( x,  ) is the radiative intensity at position x, and direction μ. I b denotes

19

the radiative intensity of interfering gas. I b (0,  ) and I  ( L,  ) are radiative

20

intensities projects to the internal interfering gas from the measured surface and

21

detected surfaces, respectively.

22

Through solving equations (1)–(3), the received radiative energy in waveband Δλ

23

( E ) can be determined. In two-color pyrometry, temperature is inferred by

24

measuring the ratio of the incoming radiation in two different wavebands Δλ1 and Δλ2.

25

The calculated temperature of the target can be determined by the following equation

26

on the basis of Planck's law if the slope of the instrumental emissivity set to 1:

27

E1 (T ) E2 (T )



2 hc02  n215[ehc0 / n1kT  1] d  1

2 hc02  n225[ehc0 / n2kT  1] d  2

6


(4)

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Energy & Fuels

1

where h=6.626×10-34 J·s, which is Plank’s constant, c0=2.998×108 m/s, which is the

2

speed of light in vacuum, k=1.3806×10-23 J/K, which is Boltzmann’s constant.

3

Before detected by the ratio radiation thermometer, the intensity of radiation

4

initially emitted by the target surface is absorbed partially by the combustion gases

5

existing in a light path between the target and the thermometer. In order to

6

quantitatively determine the error in radiation temperature measurement due to the

7

interfering gases, there are two key issues need to be addressed: One is the

8

determination of the radiative physical properties of the combustion gases; the other is

9

calculation of the incident radiative intensity.

10

2.2 Radiative properties of the interfering combustion gases

11

The radiation from fully burnt combustion products of most conventional gas

12

and oil fuels is mainly due to the vibration rotation spectra of carbon dioxide and

13

water vapor. Thus, we consider these two representative interfering gases mixture

14

ordinarily encountered in engineering applications in the present work: H2O-CO2-N2

15

mixture. N2 is assumed to be a transparent gas. Considering the radiometric reading

16

will display some sort of an “average” temperature, a statistical narrow-band (SNB)

17

model linked with a gray-band approximation method is selected herein to calculate

18

the radiative properties of interfering combustion gases averaged on a narrowband.

19

With regard to a uniform column of path-length L having a single absorbing gas

20

species at a total pressure p and molar fraction X, the SNB model gives a

21

transmissivity averaged on a narrowband of width Δλ as24:

22

 2   XpLk   1   1      

  = exp  

(5)

23

where 𝛿 and 𝑘 are averaged narrowband parameters, which have been reported for

24

H2O and CO2 by Rivière and Soufiani25 on the basis of HITEMP 2010 high resolution

25

spectroscopic database. The database covers a large temperature scope from 300 to

26

5000 K for H2O and CO2 with a consistent bandwidth of 25 cm-1. The containing

27

spectral wavenumbers and number of wavebands are provided in Table I. Further

28

details regarding this database could be found in reference published by Rivière and

29

Soufiani25. 𝛾 (in cm-1) is a classic averaged collisional half-width of Lorentz line

30

profiles. The expressions of 𝛾 for H2O and CO2 are:

7


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1

H O 

2

 CO 

2

2

p ps

Page 8 of 33

 Ts Ts   0.462 X H 2O  0.079(1  X CO2 )  0.106 X CO2    T T  

p Ts 0.7 ( ) 0.07 X CO2  0.058(1  X H 2O  X CO2 )  0.1X H 2O  ps T

(6)

(7)

3

where pS = 1 atm, and TS = 296 K. T is temperature of the intervening gas. For a

4

inhomogeneous and non-isothermal sight path, the averaged transmissivity is

5

achieved

6

transmissivity of the gases mixture of absorbing species can roughly be estimated as

7

the product of separate transmissivities, which was examined and confirmed in

8

previous study (see Ref.27).

9

by

applying

the

Curtis–Godson

approximation26.

The

averaged

Table I. Minimum and maximum SNB wavebands centers and number of wavebands25 Molecule

νmin(cm-1)

νmax(cm-1)

Number of bands

H2O

50

11,250

449

CO2

250

8300

323

10

Given the input parameter of Eq. (3) is the absorption coefficient of combustion

11

gas, therefore the achieved averaged narrowband transmissivity should be

12

transformed into a absorption coefficient averaged on a narrowband through applying

13

gray-band approximation method28,

14

participating medium is gray within a narrowband and employs Beer’s law to obtain

15

an absorption coefficient from the achieved averaged transmissivity. An averaged

16

narrowband absorption coefficient is achieved as:

29.

k 

17

This approximation method assumes the

ln   ( LNB ) 1 k d       LNB 

(8)

18

where the parameter LNB is mean beam length, which is 1.9L for the planar slab

19

indicated in Fig. 1.30

20

2.3 Calculation of the incident radiative intensity

21 22

Integrating Eqs. (5) and (6) over a spectral waveband Δλ produce the coming equations:



23 24

I  ( x,  )  ka I b  ka I  ( x,  ) x

with boundary conditions 8


(9)

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Energy & Fuels

1

I  (0,  )  I b (T1 ),

 0

(10a)

2

I  ( L,  )  0,

 0

(10b)

3

where I  ( x,  ) 

 I  ( x,  )d  ,



I b 

1

 I  d  . k      k d  . 

b





4

Eq. (9) can be figured out by employing discrete ordinates method together with

5

S8 quadrature scheme31. Further details regarding these methods could be found in our

6

previous studies5, 32. Once the model input parameters, i.e., the true target temperature

7

T1, the concentration X and temperature of the combustion gas mixture Tg,, and the

8

thickness of the combustion gases layer L, are known, the radiative intensity

9

distribution in the gas layer can be obtained by solving the combustion gas radiative

10

properties model and Eq. (9).

11

2.4 Determination of the surface temperatures

12

Note that the incoming heat flux received by the two-color radiation

13

thermometer at x=L is positive since cos   0 . Sum over all N incoming directions

14

(subject to cos   0 ) at x=L gives the total incoming heat flux in each narrow band33,

15

i.e., E ( x  L) 

16

N



j 1,

j 0

w j  j I  ( L, j )

(11)

17

The ratio of the incoming heat flux in two different wavebands is the left term of Eq.

18

(4). Then the surface temperature of the target can be obtained by using bisection

19

method to solve Eq. (4).

20

3. Model Validation

21

To evaluate the validity of the current temperature calculation model, the

22

predictions were compared with previous results in two different aspects: one is the

23

radiative property of combustion gases as an input parameter to the radiative heat

24

transfer model; the other one is radiant heat flux, which can be used to calculate the

25

target surface temperature through Eq. (4). We also verified the accuracy of the model

26

solver as following.

27

3.1 Validation of combustion gases radiative property 9


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Page 10 of 33

1

The calculated H2O transmissivities by the present model were compared to the

2

experimental results of Modest34, 35 and Phillips36. The measurements of Modest were

3

made at a spectral resolution of 4 cm−1 employing a FTIR spectrometer. Phillips has

4

made high-resolution H2O transmission measurements (0.06 cm−1) for the 2.7 um

5

band with a Nicolet 8000 FTIR spectrometer. Further details regarding their

6

experimental setup can be found in the reference34,

7

data of H2O transmissivities by Modest and Phillips were degraded to 25 cm-1 to

8

permit comparisons with current calculation results.

36.

The experimental measured

9

Comparisons of the model calculations with the calculated transmissivities using

10

HITEMP database34 and the degraded measured transmissivities for the 2.7 um band

11

of H2O at two temperatures of 600 K and 1000 K and two optical depths: L=20cm and

12

40cm were shown in Fig. 2. At a temperature of 600 K, the proposed model seemed to

13

obtain a rational compromise of transmissivity measurements by Modest and Phillips.

14

At a temperature of 1000 K, the model calculations corresponded well to the

15

experimental data over most of the investigated band, except for wavenumber ranges

16

of 3125~3475 cm-1 in which the model prediction displayed slight inconsistencies at

17

the optical depth of 40cm. As a whole, the agreements between the model prediction

18

and the experimental data were satisfactory. This validation applied to an individual

19

combustion species. However, combustion products usually are mixtures of several

20

gas species. Therefore, further comparisons concerning the transmissivity of

21

combustion gases mixture with experimental data were expected, although accessible

22

precise data were very few.

23 24 25

Fig. 2 Comparison of current model calculations with experimental data of Phillips36 and Modest34, 35 (2.7 μm band of H2O)

10


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Energy & Fuels

1

Fig. 3 showed comparisons between column transmissivities for a combustion

2

gas mixture containing 10% CO2+10% H2O+5% CO at a temperature of 1500 K and

3

atmospheric pressure for a 100 cm gas column, obtained from the “measured” and

4

calculated data of Ren37 and present calculations, respectively, in spectral interval

5

1800~2350 cm-1. Noted that the “measured” transmissivities at a resolution of 4 cm-1

6

were synthesized with 5% of artificial random noise. The comparisons between the

7

“measured” and calculated results and proposed model calculations showed an

8

excellent agreement illustrating the good quality of present model parameter.

9 10

Fig. 3 Comparison of present model calculations with “measured” and calculated data of Ren37 at

11

the given temperature T=1500 K for a combustion gases mixture of 10% CO2+10% H2O+5% CO

12

in the spectral interval 1800~2350 cm-1

13

3.2 Validation of radiant heat flux

14

In order to verify the accuracies of the detected heat flux by the two-color

15

pyrometer, numerical calculations were performed for the four test cases shown in

16

Table II which have been selected as examined cases by Zhang et al.38, Kim et al.30,

17

Liu et al.39,

18

property models. In all the four cases, the radiation calculations were performed in a

19

one-dimensional parallel-plates enclosure containing a H2O/N2 mixture at a total

20

pressure of 1 atm and the two plates surfaces were assumed to be black. In cases 1 and

21

2, the gas mixture is isothermal and homogeneous and the length between the two

22

plates is 0.1 and 1.0 m, respectively. The H2O concentration in case 3 follows a

23

parabolic profile and the temperature profiles in case 4 are of a boundary layer type,

24

respectively. The four examination cases provided good test bench to assess

25

individually the influences of path-length and gas concentration and temperature

26

distributions on the predictions and were chosen herein so that the results obtained

27

from this work can be compared to their published results.

40,

and J.G. Marakis41 utilizing diverse solution means and gas radiative

11


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1

Page 12 of 33

Table II. Detailed information about the four test cases Case

Concentration profile

Temperature profile

L [m]

1

Pure water vapor (1 atm)

Uniform (1000 K)

0.1

2


Uniform (1000 K)

1.0

3

Parabolic H20 profile30

Uniform (1000 K)

1.0

4


Boundary layer type30

0.5

2

Table III showed the net radiative wall fluxes obtained by using different models

3

for the cases presented in Table II. The proposed model employing SNB method with

4

gray-band approximation, which is easier to formulate and therefore much quicker

5

computationally, gave almost the same wall heat fluxes as the other solutions. The

6

minor inconsistencies are ascribed to the disparate angular discretization applied in

7

calculation. Kim pointed out that the slight discrepancies would vanish, if the

8

absorption coefficient in Eq. (8) was the real path-length for each angle rather than the

9

average sight length.30 Their results indicated that this proposed model predicts

10

accurate wall heat flux.

11

Table III. Comparison of predicted net heat fluxes with different models Model

Case 1

Case 2

Case 3

Case 4

Present model

-13.914

-29.77

-26.4

276.531

Kim et al., Malkmus correlated30

-14.3

-28.2

-25.4

277.4

Marakis et al., LMRT, Goody correlated41

-13.7

-28.5

-25.3

276.0

Liu et al., SNB39

-14.2

-30.3

-27.0

271.5

Liu et al., SNBCK739

-14.0

-30.0

-26.6

271.3

Marakis et al., HL2ST, Goody correlated41

-15.1

-29.0

-26.4

277.6

12 13 14 15

Note: LMRT and HL2ST are databases developed by (Ludwig, Malkmus, Reardon, Thompson)24

16

To validate the correctness of present model and its solver, we calculated the

17

target surface temperature using the proposed model with a known real target

18

temperature T1 on the assumption of no combustion gases existing between the target

19

and the pyrometer. The other parameters were fixed as L= l00 cm, ε1=1.0. The two

20

wavebands for thermometry model in this confirmation were selected as a two

21

adjacent bands. The assumed target surface temperature is T1, and the predicted

and (Hartmann, Levi Di Leon, Soufiani, Taine)42, 43, respectively.

3.2 Validation of the model solver

12


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Energy & Fuels

1

temperature by employing present thermometer model is TR. Table IV presented TR

2

for different T1. From this, we can see the calculated temperature TR displays

3

ignorable differences with T1.

4

Table IV. The calculated temperature TR for different real temperature T1 T1, K

TR, K

1000.00

1000.00

1100.00

1099.99

1200.00

1200.00

1300.00

1299.99

1400.00

1400.00

1500.00

1500.00

5

From the validations above, we could draw conclusions that the model

6

calculations are reliable, and the combustion gases radiative property applied in the

7

present calculation is correct.

8

4. Results and Discussion

9

In this section, the feature of intervening combustion gases in the present system

10

was discussed as far as their effects on the measurement error of a ratio radiation

11

thermometer were concerned. Through an analysis of the mechanism of this error, a

12

methodology for selecting wavelength pairs to minimize the error was discussed.

13

Furthermore, theoretical temperature shifts at some selected wavelength pairs

14

produced by changes in the model input parameters were estimated to provide at least

15

a basis for an uncertainty analysis, as well as a sensitivity analysis of the influencing

16

factors was carried out.

17

4.1 Error analysis

18

Fig. 4 represented that the calculated temperature for ratio radiation thermometry

19

was a function of detection wavenumbers in the range of 50-11250 cm-1 with a target

20

temperature of 1200 K and XH2O, XCO2, L, and Tg at three different values. The three

21

conditions of (XH2O=0.1, XCO2=0.1, L=10 cm, Tg=1000 K), (XH2O=0.3, XCO2=0.3,

22

L=100 cm, Tg=1400 K) and (XH2O=0.5, XCO2=0.5, L=1000 cm, Tg=1800 K) were

23

chosen herein because they were believed to represent weak, medium and strong

24

combustion gaseous absorption and emission effect in the present system, 13


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

respectively. Note that the separation of the two wavebands for two-color

2

thermometry model herein was chosen as a two adjacent bands and the data points in

3

which the calculated temperatures are greater than 2100 K were not shown in Fig. 4.

4

As Fig. 4 indicated, temperature errors approaching several hundred degrees

5

have been found in most instances, which indicated that the existence of hot

6

combustion gases (H2O-CO2-N2 mixture) in the sight path notably affect the

7

measurement accuracy of two-color thermometry. The methods to reduce or eliminate

8

these effects through careful selection of the instrument spectral pass-band, such as

9

wavebands near 1.0, 1.6, 1.25 and 2.2 μm, are limited to conditions in which the

10

medium concentration is at a low level and the layer of hot combustion gas is not very

11

thick. As depicted in Fig.4, when the high-temperature H2O-CO2-N2 mixture

12

presented in significant concentrations, the absorption and emission of radiant flux by

13

high-temperature combustion gas can have deeply harmful impacts on radiometric

14

temperature measurements.

15

It was interesting to note from the lower part of Fig. 4 that the predicted

16

two-color radiometer reading at some specific wavebands, such as wavenumbers in

17

the ranges of 100-750 cm-1, 2200-2350 cm-1, and 3500-3725 cm-1, was the

18

temperature of hot combustion gases (1800 K), when the high-temperature gases were

19

present in significant concentrations (XH2O=0.5, XCO2=0.5, L=1000 cm, Tg=1800 K).

20

This indicated that in these wavenumber ranges the received radiation mainly came

21

from the hot interfering gas emission, while the radiation emitted by the target surface

22

were mostly absorbed by the high-concentrated gases. These wavenumber ranges

23

were not reported by previous researches, but may be good selections for the

24

temperature measurement of high-concentration combustion gases. Further detailed

25

investigations on the optimal wavelength ranges for the ratio radiation temperature

26

measurement of high-concentration combustion gases will be summarized in our next

27

study.

14


Page 14 of 33

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Energy & Fuels

1 2 3 4 5

Fig. 4 The calculated temperature for two-color thermometer as a function of wavenumber with T1=1200 K and XH2O, XCO2, L, and Tg at different values. (a) XH2O=0.1, XCO2=0.1, L=10 cm, Tg=1000 K. (b) XH2O=0.3, XCO2=0.3, L=100 cm, Tg=1400 K. (c) XH2O=0.5, XCO2=0.5, L=1000 cm, Tg=1800 K.

6

As shown in Fig. 4, for two-color thermometry, whether the predicted

7

temperature was higher or lower than the real target temperature was dependent on

8

the choice of work wavelength pairs. Fig. 4 obviously displayed this oscillatory

9

phenomenon because of the absorption and emission effect of combustion gases. The

10

fluctuation behavior of temperature profiles obtained by the proposed two-color

11

thermometer model was consistent with the experimental observations reported in

12

references44-46. This phenomenon tended to farther strengthened with thicker gas

13

layer. Detailed explanation about the origin of the oscillatory phenomenon was given

14

as follows.

15

If the radiation energy emitted by the target and the attenuated/augmented

16

radiation in narrow band Δλ caused by H2O-CO2-N2 mixture are denoted as

17 18

E (T ,  ) and E (T ,  ) , respectively, then the received radiation energy can be expressed as E (T ,  )+E (T ,  ) . In this way, Eq. (4) can be converted into

19

the following Eq. (12) considering the effects of interfering combustion gases.

15


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

E1 (T , 1 )+E1 (T , 1 )

1

2

E2 (T , 2 )+E2 (T , 2 )



2 hc02  n215[ehc0 / n1kT  1] d  1

2 hc02  n225[ehc0 / n2kT  1] d  2

(12)

Let ϕΔλ be the ratio of the attenuated/augmented radiation to the true radiation in band

Δλ.

E1 (T , 1 )=1 E1 (T , 1 )

3

narrow

4

E2 (T , 2 )=2 E2 (T , 2 ) converts Eq. (12) into

5

Page 16 of 33

Replacing

1+1 E1 (T , 1 )   1+2 E2 (T , 2 )

2 hc02  n215[ehc0 / n1kT  1] d  1

2 hc02  n225[ehc0 / n2kT  1] d  2

and

(13)

6

Depending on the levels of ϕΔλ1 and ϕΔλ2 approaching -1, the predicted

7

temperature will fluctuate between zero and values approaching infinity. That is

8

because the denominator or numerator of the left term of Eq. (13) will approach

9

illimitably to zero, and then the model calculation will generate huge temperature

10

errors. The amplitude of fluctuation increases with the departure between ϕΔλ1 and ϕΔλ2

11

increasing, and comes to zero when ϕΔλ1 = ϕΔλ2.

12 13 14 15

Fig. 5 The attenuated/augmented energy ratio ϕΔλ due to combustion gaseous absorption and emission as a function of wavenumber with T1=1200 K and XH2O, XCO2, L, and Tg at different values 16


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Energy & Fuels

1

The ϕΔλ under the three conditions mentioned above were plotted in Fig. 5. For

2

two-color thermometer operating at two adjacent spectral bands, comparison of the

3

Figs. 4 and 5 unveiled that the discrepancy between the true temperature and the

4

predicted temperature enlarges as the departure between ϕΔλ1 and ϕΔλ2 or the separation

5

between ϕΔλ and 0 increases, and vice versa. For example, when the interfering

6

combustion gas was at a low level (XH2O=0.1, XCO2=0.1, L=10 cm, Tg=1000 K) and

7

the operating wavebands of two-color thermometer were in the spectral regions of

8

1.08~1.0 μm, the temperature errors were very small since the ϕΔλ were quite small

9

and almost kept constant in those spectral ranges. In contrast, large temperature errors

10

will produce if the two-color thermometer operates in the spectral regions of 2.5~3.7

11

μm owing to the large departure between ϕΔλ1 and ϕΔλ2.

12

The upper part of the Fig. 5 showed the absorption by the gases reduce the

13

radiative emission of target when the combustion gases temperature was lower than

14

the radiance temperature of target. Conversely, if the combustion gases temperature

15

was greater than the radiance temperature of the target as shown in the lower part of

16

the Fig. 5, then the emission term would dominate and increase the emissivity of the

17

target. Because two-color thermometers infer temperature from the ratio of the

18

measured radiance in two different wavebands, something that makes a change to the

19

surface radiance does not necessary cause the thermometer to be in error. According

20

to the above analysis, if the ϕΔλ are identical across the two wavebands, it is suitable to

21

select them as the working wavebands of two-color pyrometer interfered with

22

combustion gases.

23 24

Table V. The calculated temperature errors for two-color thermometer operating at some selected wavenumber pairs for T1=1200 K and different values of XH2O, XCO2, L, and Tg Wavenumber pairs (η1, η2)

XH2O=0.1, XCO2=0.1,

XH2O=0.3, XCO2=0.3,

XH2O=0.5, XCO2=0.5,

L=10 cm, Tg=1000 K

L=100 cm, Tg=1400 K

L=1000 cm, Tg=1800 K

ϕΔλ

η1=9275 cm-1

ϕΔλ1=-1.7E-05

cm-1

ϕΔλ2=6.2E-06

η1=6100 cm-1

ϕΔλ1=-2.7E-05

cm-1

ϕΔλ2=-0.00027

η1=6275 cm-1

ϕΔλ1=-9.7E-06

cm-1

ϕΔλ2=-1.6E-05

η2=11250 η2=7650 η2=10025

Error ΔT 0.004 K -0.06 K 0.01 K

ϕΔλ ϕΔλ1=0.0016 ϕΔλ2=0.0012 ϕΔλ1=0.0111 ϕΔλ2=0.0144 ϕΔλ1=0.0127 ϕΔλ2=0.0179

Error ΔT -0.18 K 2.14 K -1.37 K

ϕΔλ ϕΔλ1=0.5734 ϕΔλ2=0.5744 ϕΔλ1=1.8386 ϕΔλ2=1.8343 ϕΔλ1=3.0881 ϕΔλ2=3.0856

Error ΔT 0.35 K -0.98 K 0.16 K

25

Table V showed the calculated temperature errors by using the proposed

26

two-color thermometry model with the two working wavebands selected as: (9275 17


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Page 18 of 33

1

cm-1, 11250 cm-1), (6100 cm-1, 7650 cm-1), and (6275 cm-1, 10025 cm-1). From the

2

Table, we can find that although the value of ϕΔλ1 and ϕΔλ2 are very high, the minor

3

temperature errors still can be achieved so long as the separation between the ϕΔλ1 and

4

ϕΔλ2 is small enough. These wavebands are not in general employ at present.

5

However, they seem to be good candidates for industrial applications involving

6

high-concentration H2O-CO2-N2 mixture. This selection method not only provides

7

solid reference information for the proper selection of wavelengths combination, but

8

also helps one to better understand the fundamentals of measurement errors for

9

two-color pyrometer interfered with participating media.

10

Two aspects are particularly important for practical two-color radiation

11

thermometry. First, the relative combustion gases and target temperature plays a

12

crucial role in determining whether the radiation emitted by target attenuates or

13

augments when it goes through the interfering combustion gas layer. Second, the

14

amount of the attenuation/ augmentation depends on the concentration of the

15

interfering combustion gas and the distance from an object to the thermometer. In the

16

two following subsections, we will briefly discuss the influence of the three input

17

parameters on ratio radiometric temperature measurements.

18

4.1.1 Effect of gas temperature Tg

19

Temperature readings at different combustion gas temperatures Tg were

20

calculated for two-color thermometry having a spectral responsivity near 3.9, 1.25,

21

1.0 and 0.9 μm with other system parameters set as XH2O=0.3, XCO2=0.3, L=100 cm.

22

The selection of wavenumber pairs for these spectral bands was listed in Table VI.

23

The spectral bands appearing in Table VI were selected because they correspond to

24

commercially available radiation thermometers designed for special applications

25

requiring a very narrow bandwidth at a particular wavelength in an atmospheric

26

window.

27

Table VI. The wavenumber pairs (η1, η2) for selected spectral bands used in the calculations Spectral bands

Wavenumber pairs (η1, η2)

Spectral bands

Wavenumber pairs (η1, η2)

3.9 μm

1.0 μm

η1=2575 cm-1

1.25 μm

η2=2675 cm-1 η1=9500 cm-1

0.9 μm

η2=9600 cm-1 18


η1=7950 cm-1 η2=8050 cm-1 η1=10900 cm-1 η2=11000 cm-1

Page 19 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1

The results were given in Fig. 6. The data points in which the temperatures errors

2

are greater than 4000 K were not shown in Fig. 6. They indicated that the value of the

3

ΔT is less than 30 K when Tg < T1, whereas it increases almost exponentially with gas

4

temperature further increases.

5 6 7 8 9 10

Fig. 6 Influence of gas temperature Tg on predicted temperature deviations ΔT for ratio thermometer operating at selected spectral bands with different target temperature; a) T1 = 1000 K, b) T1 = 1200 K, c) T1 = 1400 K

4.1.2 Effect of gas mixture concentration and viewing path length L

11

Fig. 7 and Fig. 8 showed that the influence of the concentrations of H2O-CO2-N2

12

mixture characterized by the same ratio XH2O:XCO2=1:1 and path lengths on the

13

calculated temperature error with T1=1200 K, Tg=1600 K, respectively. It can be seen

14

that the effect of gaseous absorption and emission depends on the concentrations of

15

the absorbing gas and the viewing path length through the interfering combustion

16

gases. The errors are the linearly growth in magnitude with both of these quantities

17

increasing, which agree with the numerical results reported in reference32. The rate of 19


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

the increase of ΔT for waveband 3.9 μm is fastest, followed by 0.9 μm and 1.25 μm,

2

and the slowest growth of ΔT occurred at waveband 1.0 μm. Therefore, ratio

3

thermometer operating at 1.0 μm waveband can be less susceptible to the variation in

4

gas mixture concentration and viewing path length.

5 6 7 8

Fig. 7 The predicted temperature deviations ΔT for ratio thermometer operating at selected spectral bands with different concentrations of H2O-CO2-N2 mixture characterized by the same ratio XH2O:XCO2=1:1

9 10 11

Fig. 8 The predicted temperature deviations ΔT for ratio thermometer operating at selected spectral bands with different L. 20


Page 20 of 33

Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1

4.2 Measurement sensitivity analysis

2

Based on the aforementioned analysis and discussion, we could find gas mixture

3

temperature and concentration, and path length have significant effects on the

4

predicted target temperature. To diagnose which impact factors contribute the most to

5

the present model output behavior and which are non-influential input parameters, a

6

sensitivity analysis method was employed herein as a tool for the evaluation of the

7

impact factors. The means of this assessment was described as follows. The calculated

8

temperature is a function of the three factors without considering the influences of

9

other impacts factors:

P  f ( 1 ,  2 , 3 )

10

(14)

11

where P stands for the calculated temperature, and β1, β2, β3 represent model input

12

parameters of Tg, X, and L, respectively. To assess the percentage of the individual

13

contribution of αk to the calculated temperature P, the sensitivity index of parameter αk

14

(Sk) defined as the ratio of the relative error of P (δP =ΔP/P) to the relative error of

15

parameter βk (δβk =Δβk/βk) was adopted, while maintaining other input parameter

16

βm(m≠k) fixed at a given central value. Sk  (

17

 P )/( k ) k P

(15)

18

The results of sensitivity index of parameter αk (Sk) were shown in Table VII. It

19

showed that the gas temperature did have a relative strong influence on the predicted

20

target temperature, whereas the gas concentration and viewing path length had a weak

21

influence on it. These consequences indicated that gas temperature must be known

22

very precisely for good assessment of target surface temperature. In contrast, large

23

uncertainties on the gas concentration and on the viewing path were acceptable, since

24 25

they had little influence on the assessment of the target surface temperature. Table VII. Sensitivity index of parameters (Sk) for selected spectral bands Gas temperature Parameter

Tg=600 K

Tg=1600 K

Gas concentration

Path length

XH2O=0.3, XCO2=0.3

L=100 cm

variation

+100 K

-100 K

+100 K

-100 K

+10%

-10%

+10%

-10%

3.9 μm

-11.2%

60.6%

66.6%

44%

11.8%

11.4%

11.6%

11.3%

1.25 μm

20.6%

24.1%

81.9%

49.5%

10.4%

10.4%

10.4%

10.4%

1.0 μm

34.2%

39.9%

126.3%

63.2%

10.1%

10.1%

10.1%

10.1%

0.9 μm

47.2%

89.7%

52.3%

42.4%

8.1%

8.4%

8.1%

8.4%

21


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

5. Summary

2

This paper established an analytical two-color thermometry model linked with a

3

mathematical radiative heat transfer model. The radiative property of combustion gas

4

mixture, which is the input parameter to the proposed model, was calculated by

5

employing SNB model and grey-band approximation method. The narrowband

6

parameters of SNB model adopted the data reported by Rivière and Soufiani25. The

7

model was utilized to investigate the influence of hot combustion gas on surface

8

temperature measurement using two-color radiation thermometry. The main

9

conclusions for the effects of hot combustion gas reveal the following:

10

(1) The presence of hot H2O-CO2-N2 mixture greatly affects the measurement

11

accuracy of two-color radiation thermometry. Minimizing the absorption and

12

emission effect by selection of the instrument spectral band-pass is useful when

13

interfering combustion gases at low concentrations.

14

(2) Through an analysis of the mechanism of the temperature error due to

15

combustion gaseous effect, we presented a selection methodology of spectral

16

pass-band of two-color radiation thermometer to minimize the influences of the

17

participating medium.

18

(3) When the high-temperature interfering gas presents in significant

19

concentrations, the ratio radiometer reading at some specific wavebands, such as

20

wavenumbers in the range of 100-750 cm-1, 2200-2350 cm-1, and 3500-3725 cm-1, is

21

the temperature of interfering gas rather than of target temperature.

22

(4) The calculated temperature error is the exponential growth with the increase

23

of gas mixture temperature when gas temperature is greater than target temperature,

24

and it is the linearly growth in magnitude with both gas mixture concentration and

25

viewing path length increasing. Gas temperature does have a relative strong influence

26

on the predicted target temperature, relative to gas concentration and viewing path

27

length.

28

These conclusions may provide valuable descriptions of temperature

29

measurement errors produced by high-temperature combustion gases and the

30

necessary theoretical supports for the design and application of a two-color pyrometer

31

in the presence of combustion gases. 22


Page 22 of 33

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Energy & Fuels

1

Acknowledgements

2

The work is financially supported by the Natural Science Foundation of China,

3

Project No. 51504048, 51374260 and 51611130062, and the Fundamental Research

4

Funds for the Central Universities of China, Project No. 2018CDPTCG0001/35. The

5

authors acknowledge Philippe Rivière and Anouar Soufiani, CNRS, for their useful

6

database about H2O and CO2 radiative properties.

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

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16. Feijt, A. J.; Kohsiek, W., The effect of emissivity variation on surface temperature determined by infrared radiometry. Boundary-Layer Meteorology 1995, 72, (3), 323-327. 17. Gao, S.; Wang, L.; Feng, C.; Kipngetich, K. D., Analyzing the influence of combustion gas on a gas turbine by radiation thermometry. Infrared Physics & Technology 2015, 73, 184-193. 18. Bäckström, D.; Johansson, R.; Andersson, K.; Johnsson, F.; Clausen, S.; Fateev, A., Measurement and modeling of particle radiation in coal flames. Energy & Fuels 2014, 28, (3), 2199-2210. 19. Zabrodiec, D.; Hees, J.; Massmeyer, A.; vom Lehn, F.; Habermehl, M.; Hatzfeld, O.; Kneer, R., Experimental investigation of pulverized coal flames in CO2/O2-and N2/O2-atmospheres: Comparison of solid particle radiative characteristics. Fuel 2017, 201, 136-147. 20. Ayling, A.; Smith, I., Measured temperatures of burning pulverized-fuel particles, and the nature of the primary reaction product. Combustion and Flame 1972, 18, (2), 173-184. 21. Molina, A.; Shaddix, C. R., Ignition and devolatilization of pulverized bituminous coal particles during oxygen/carbon dioxide coal combustion. Proceedings of the combustion institute 2007, 31, (2), 1905-1912. 22. Yan, W.; Zhou, H.; Jiang, Z.; Lou, C.; Zhang, X.; Chen, D., Experiments on measurement of temperature and emissivity of municipal solid waste (MSW) combustion by spectral analysis and image processing in visible spectrum. Energy & Fuels 2013, 27, (11), 6754-6762. 23. Rothman, L. S.; Gordon, I. E.; Barber, R. J.; Dothe, H.; Gamache, R. R.; Goldman, A.; Perevalov, V. I.; Tashkun, S. A.; Tennyson, J., HITEMP, the high-temperature molecular spectroscopic database. Journal of Quantitative Spectroscopy & Radiative Transfer 2010, 111, (15), 2139-2150. 24. Ludwig, C. B.; Malkmus, W.; Reardon, J.; Thomson, J.; Goulard, R., Handbook of infrared radiation from combustion gases. 1973. 25. Rivière, P.; Soufiani, A., Updated band model parameters for H 2 O, CO 2 , CH 4 and CO radiation at high temperature. International Journal of Heat & Mass Transfer 2012, 55, (13-14), 3349-3358. 26. Godson, W., The evaluation of infra‐red radiative fluxes due to atmospheric water vapour. Quarterly Journal of the Royal Meteorological Society 1953, 79, (341), 367-379. 27. Taine, J.; Soufiani, A., Gas IR radiative properties: from spectroscopic data to approximate models. Advances in heat transfer 1999, 33, 295-414. 28. Modest, M. F.; Sikka, K. K., The stepwise gray P -1 approximation for multi-dimensional radiative transfer in molecular-gas—particulate mixtures. Journal of Quantitative Spectroscopy & Radiative Transfer 1992, 48, (2), 159–168. 29. Liu, F.; Gülder, Ö. L.; Smallwood, G. J., Three-dimensional non-grey gas radiative transfer analyses using the statistical narrow-band model. Revue générale de thermique 1998, 37, (9), 759-768. 30. Kim, T. K.; Menart, J. A.; Lee, H. S., Nongray radiative gas analyses using the SN discrete ordinates method. Human Relations 1991, 56, (5), 587-607. 31. Liu, F.; Becker, H.; Pollard, A., Spatial differencing schemes of the discrete-ordinates method. Numerical Heat Transfer 1996, 30, (1), 23-43. 32. Huang, Y.; Long, M.; Chen, D.; Tan, K.; Duan, H.; Xu, P., Effect of hot water vapor on strand surface temperature measurement in steel continuous casting. International Journal of Thermal Sciences 2019, 138, 467-479. 33. Chu, H.; Liu, F.; Zhou, H., Calculations of gas radiation heat transfer in a two-dimensional rectangular enclosure using the line-by-line approach and the statistical narrow-band correlated-k model. International Journal of Thermal Sciences 2012, 59, 66-74. 34. Bharadwaj, S. P.; Modest, M. F.; Riazzi, R. J., Medium resolution transmission measurements of water vapor at high temperature. Journal of heat transfer 2006, 128, (4), 374-381. 24


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35. Alberti, M.; Weber, R.; Mancini, M.; Modest, M., Comparison of models for predicting band emissivity of carbon dioxide and water vapour at high temperatures. International Journal of Heat and Mass Transfer 2013, 64, 910-925. 36. Phillips, W., Band-model parameters of the 2.7-μm band of H2O. Journal of Quantitative Spectroscopy and Radiative Transfer 1990, 43, (1), 13-31. 37. Ren, T. Determination of temperature and concentration from radiometric measurements in combustion systems. UC Merced, 2015. 38. Zhang, L.; Soufiani, A.; Taine, J., Spectral correlated and non-correlated radiative transfer in a finite axisymmetric system containing an absorbing and emitting real gasparticle mixture. International Journal of Heat and Mass Transfer 1988, 31, (11), 2261-2272. 39. Liu, F.; Smallwood, G. J.; Gülder, Ö. L., Application of the statistical narrow-band correlated-k method to low-resolution spectral intensity and radiative heat transfer calculations—effects of the quadrature scheme. International Journal of Heat and Mass Transfer 2000, 43, (17), 3119-3135. 40. Liu, F.; Gülder, Ö.; Smallwood, G.; Ju, Y., Non-grey gas radiative transfer analyses using the statistical narrow-band model. International journal of heat and mass transfer 1998, 41, (14), 2227-2236. 41. Marakis, J., Application of narrow and wide band models for radiative transfer in planar media. International journal of heat and mass transfer 2001, 44, (1), 131-142. 42. Hartmann, J.; Di Leon, R. L.; Taine, J., Line-by-line and narrow-band statistical model calculations for H2O. Journal of Quantitative Spectroscopy and Radiative Transfer 1984, 32, (2), 119-127. 43. Soufiani, A.; Hartmann, J.; Taine, J., Validity of band-model calculations for CO2 and H2O applied to radiative properties and conductive-radiative transfer. Journal of Quantitative Spectroscopy and Radiative Transfer 1985, 33, (3), 243-257. 44. Zhang, B.; Xu, C.; Wang, S., An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation. Measurement Science and Technology 2016, 27, (7), 074002. 45. Liu, D.; Duan, Y.-Y.; Yang, Z., Effects of participating media on the time-resolved infrared measurements of wall temperature in a coal-fired combustor. Experimental Thermal and Fluid Science 2012, 39, 90-97. 46. Sun, Y.; Lou, C.; Zhou, H., A simple judgment method of gray property of flames based on spectral analysis and the two-color method for measurements of temperatures and emissivity. Proceedings of the combustion Institute 2011, 33, (1), 735-741.

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Fig. 1 Physical model of radiative temperature measurement in hot combustion gas 118x99mm (150 x 150 DPI)


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Energy & Fuels

Fig. 2 Comparison of current model calculations with experimental data of Phillips and Modest (2.7 μm band of H2O) 405x147mm (300 x 300 DPI)


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Fig. 3 Comparison of present model calculations with “measured” and calculated data of Ren37 at the given temperature T=1500 K for a combustion gases mixture of 10% CO2+10% H2O+5% CO in the spectral interval 1800~2350 cm-1 375x117mm (300 x 300 DPI)


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Energy & Fuels

Fig. 4 The calculated temperature for two-color thermometer as a function of wavenumber with T1=1200 K and XH2O, XCO2, L, and Tg at different values. (a) XH2O=0.1, XCO2=0.1, L=10 cm, Tg=1000 K. (b) XH2O=0.3, XCO2=0.3, L=100 cm, Tg=1400 K. (c) XH2O=0.5, XCO2=0.5, L=1000 cm, Tg=1800 K. 316x192mm (300 x 300 DPI)


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Fig. 5 The attenuated/augmented energy ratio ϕΔλ due to combustion gaseous absorption and emission as a function of wavenumber with T1=1200 K and XH2O, XCO2, L, and Tg at different values 315x191mm (300 x 300 DPI)


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Energy & Fuels

Influence of gas temperature Tg on predicted temperature deviations ΔT for ratio thermometer operating at selected spectral bands with different target temperature; a) T1 = 1000 K, b) T1 = 1200 K, c) T1 = 1400 K 146x123mm (220 x 220 DPI)


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The predicted temperature deviations ΔT for ratio thermometer operating at selected spectral bands with different concentrations of H2O-CO2-N2 mixture characterized by the same ratio XH2O:XCO2=1:1 215x176mm (300 x 300 DPI)


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Energy & Fuels

The predicted temperature deviations ΔT for ratio thermometer operating at selected spectral bands with different L. 215x178mm (300 x 300 DPI)


Quantifying the Effects of Combustion Gases' Radiation on Surface

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