行政院國家科學委員會專題研究計畫 成果報告

行政院國家科學委員會專題研究計畫 成果報告

低成本之光學感測器研發及應用於碳氫火焰量測(第 2 年) 研究成果報告(完整版)

計 畫 類 別 ： 個別型

計 畫 編 號 ： NSC 95-2221-E-216-018-MY2

執 行 期 間 ： 96 年 08 月 01 日至 97 年 08 月 31 日 執 行 單 位 ： 中華大學機械與航太工程研究所

計 畫 主 持 人 ： 鄭藏勝

計畫參與人員： 碩士班研究生-兼任助理人員：鄭雅云 碩士班研究生-兼任助理人員：簡毓倩 碩士班研究生-兼任助理人員：陳瑜偉 碩士班研究生-兼任助理人員：陳永軒 博士班研究生-兼任助理人員：李約亨 博士班研究生-兼任助理人員：張智國 博士班研究生-兼任助理人員：周中祺 博士後研究：吳志勇

報 告 附 件 ： 出席國際會議研究心得報告及發表論文

處 理 方 式 ： 本計畫涉及專利或其他智慧財產權，2 年後可公開查詢

中 華 民 國 97 年 11 月 11 日

行政院國家科學委員會補助專題研究計畫 ■ 成 果 報 告

□期中進度報告

低成本之光學感測器研發及應用於碳氫火焰量測

Development of Low Cost Optical Sensors for Hydrocarbon Flame Measurement

計畫類別：▓ 個別型計畫 □ 整合型計畫

計畫編號：NSC 95－2221－E －216－018－MY2

執行期間： 95 年 8 月 1 日至 97 年 8 月 31 日

計畫主持人：鄭藏勝 教授 共同主持人：

計畫參與人員：趙怡欽 教授、吳志勇(博士後研究員)、李約亨(博士生)、

張智國(博士生)、鄭雅云(碩士生)、簡毓倩(碩士生)、陳 瑜偉(碩士生)、周中祺(博士生)、陳永軒(碩士生)

成果報告類型(依經費核定清單規定繳交)：□精簡報告 ■完整報告

本成果報告包括以下應繳交之附件：

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

■出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

處理方式：除產學合作研究計畫、提升產業技術及人才培育研究計畫、列 管計畫及下列情形者外，得立即公開查詢

□涉及專利或其他智慧財產權，□一年▓二年後可公開查詢

執行單位：中華大學機械與航太工程研究所

中 華 民 國 97 年 11 月 9 日

ACKNOWLEDGEMENTS

This research was supported by the National Science Council of Taiwan, Republic of China under the grant number NSC 95-2221-E-216-018-MY2. The computer time was provided by the National Center for High-performance Computing, Taiwan, ROC.

中文摘要

本計畫以二年的時間研發可同時量測紊流預混甲烷火焰當量比及溫度之低成本無 雷射光學感測器，為了研發低成本的量測工具，本研究重新設計卡塞格倫反射鏡之鏡座 使其具有微米級之焦聚調整精度，並與光纖集光器結合成一體。此外，也自行設計含有

二色鏡、濾光鏡及光電增倍管之 CH*、OH*及 C2*(0, 0)自然螢光分析儀並完成組裝測試。

除了自行設計的自然螢光分析儀之外，我們也利用光譜儀結合液態氮冷卻之 CCD 照相 機進行自然螢光量測。兩種自然螢光量測儀皆被應用於層流預混本生火焰的量測並進行

系統校正，而所量測之最大 C2*/CH*、C2*/OH*及 CH*/OH*螢光比值也皆隨著當量比呈

線性關係，惟吾人發現，雖然搭配光電增倍管之自然螢光分析儀具有快速的數據存取

率，但無法濾除因 CO2*螢光造成之訊號干擾，而光譜儀搭配液態氮冷卻之 CCD 照相機

雖然數據存取率較慢，但可同時量測波長從 250 nm 到 650 nm 之所有 OH*、CH*、C2*(1,

0)、C2*(0, 0)、C2*(0, 1)及 CO2*螢光光譜，所以由 CO2*螢光造成之訊號干擾可由後續之

數據處理中剔除，同時 C2*(1, 0)及 C2*(0, 0)之螢光比值亦可作為溫度量測。因此，本研

究最後採用卡塞格倫反射鏡及光纖集光器與光譜儀搭配液態氮冷卻之 CCD 照相機進行

系統校正，並將於層流預混本生火焰校正所得之最大 C2*/CH*、C2*/OH*及 CH*/OH*螢

光比值與當量比關係式及溫度較正常數應用於紊流預混甲烷火焰，以驗證本研究所研發 之感測器可同時量測紊流預混甲烷火焰之當量比及溫度，而本研究之最終目標則是發展 無雷射之光學感測器作為工業燃燒爐及焚化爐等之即時主動監控感測器。

關鍵詞：光學感測器、自然螢光、當量比、火焰溫度

Abstract

The objective of this research is to develop a low cost, robust, non-laser based optical sensor and to apply this sensor for simultaneous measurements of local equivalence ratio and temperature in turbulent premixed hydrocarbon flames. The sensor system uses Cassegrain optics to eliminate the chromatic aberrations and to improve the spatial resolution for light collection. Two types of light detection units, one is the spectroscopic unit with the PMT array and the other is the spectrometer with the LN-CCD camera, are tested in the experiments to verify their applicability. Both types of light detection units are applied to the laminar premixed flames to demonstrate the capability of the light detection units for chemiluminescence emission measurements. The PMT array provides fast data acquisition rate for chemiluminescence emission measurements but gives no information on the broadband CO2* emissions. On the other hand, the LN-CCD camera measures the entire spectral range of OH*, CH*, C2*(1, 0), C2*(0, 0), C2*(0, 1) as well as the broadband CO2* emissions but gives slow data acquisition rate (about 1.5 s per image frame). Although the LN-CCD camera gives slow data acquisition rate, the simultaneous measurements of C2*(1, 0) and C2*(0, 0) emissions provide a method for flame temperature measurement using the intensity ratio of C2*(1, 0)/C2*(0, 0). Therefore, the linear relationship between the C2*/CH*, C2*/OH*, and CH*/OH* intensity ratios and equivalence ratio as well as the instrument constant obtained by the spectrometer coupled with the LN-CCD camera are used for simultaneous measurements of equivalence ratio and flame temperature in turbulent premixed CH4-air flames to demonstrate the capability of the developed optical sensor. The final goal of the research is to apply the developed inexpensive, non-laser based optical sensor system for real-time active control in industrial burners and hazardous waste incinerators.

Keywords: Optical sensor, Chemiluminescence emission, Equivalence ratio, Flame

temperature

CONTENTS

ACKNOWLEDGEMENTS ... i

中 文 摘 要 ... ii

ABSTRACT ... iii

CONTENTS ... iv

LIST OF TABLES ... vi

LIST OF FIGURES...vii

CHAPTER I INTRODUCTION ... 1

1.1 Background ... 1

1.2 Motivations and Objectives ... 2

CHAPTER II RESEARCH METHODS ... 4

2.1 Experimental Setup ... 4

2.2 Bunsen Burner ... 5

CHAPTER III THEORETICAL BACKGROUND OF VIBRATIONAL TEMPERATURE MEASUREMENT ... 6

3.1 Vibrational Temperature Measurement ... 6

3.2 Theory of Vibrational Temperature Measurement ... 7

CHAPTER IV NUMERICAL SIMULATION... 10

4.1 Governing Equations ... 10

4.2 Numerical Method ... 11

4.3 Boundary Conditions ... 11

CHAPTER V RESULTS AND DISCUSSION ... 13

5.1 Characteristics of Cassegrain Mirror ... 13

5.2 Chemiluminescence Emission Spectra... 13

5.3 Chemiluminescence Emissions in Laminar Premixed Flames ... 15

5.3.1 Measurements Using PMT Array... 15

5.3.2 Measurements Using LN-CCD Camera ... 17

5.4 Numerical Simulation of Laminar Premixed Flames... 18

5.5 Measurements of Turbulent Premixed Flames... 19

CHAPTER VI SUMMARY AND CONCLUSIONS ... 22

SELF EVALUATION ... 25

REFERENCES... 26

TABLES ... 31

FIGURES ... 34

APPENDIX ... 71

LIST OF TABLES

Table 1. Operating conditions for laminar premixed CH₄-air Bunsen flames ... 31 Table 2. Physical properties of the C2* vibrational bands [51]... 32 Table 3. Reaction mechanism for the excited state species OH(A), CH(A), and C2(d) [50]

... 33

LIST OF FIGURES

Fig. 1. Schematic diagram of the Raman/Rayleigh/CO LIF line imaging and crossed PLIF imaging experiment [44]... 34 Fig. 2. Schematic diagram of Cassegrain optics ... 35 Fig. 3. Schematic diagram and photograph of the measurement system using the PMTs ... 36 Fig. 4. Photograph of measurement system using a spectrometer coupled with a

LN-CCD camera... 37 Fig. 5. Photograph of laminar (a) and turbulent (b) premixed CH4/air flames at φ = 1.0 ... 38 Fig. 6. Typical emission spectra of the two C2* bands between 460 and 520 nm for CH4

flame under conditions of T_{N2 + O2} = 20°C [51]. The numbers in the figure correspond to those given in Table 2 ... 39 Fig. 7. Computational domain with boundary conditions... 40 Fig. 8. The light-collection-rate distribution around the probe volume. (a) at the focal

point, (b) 2-D distribution, and (c) 3-D profile ... 41 Fig. 9. Effect of the different slit widths of the eye mask on the OH*

chemiluminescence intensity profiles (premixed CH₄-air jet flame, φ = 1.35) .. 42 Fig. 10. Flame emission spectra measured from laminar premixed methane-air flames at

φ = 0.85, 1.0, and 1.3... 43 Fig. 11. Radial distribution of the OH*, CH*, and C2* chemiluminescence intensities

at h = 3 and 9 mm for φ = 0.85 flame ... 44 Fig. 12. Radial distribution of the OH*, CH*, and C₂* chemiluminescence intensities

at h = 3 and 9 mm for φ = 1.0 flame ... 45 Fig. 13. Radial distribution of the OH*, CH*, and C₂* chemiluminescence intensities at

h = 3 and 9 mm for φ = 1.3 flame ... 46

Fig. 14. Variations of the maximum chemiluminescence intensities with the equivalence

ratio at h = 3 and 9 mm ... 47 Fig. 15. Correlation of the intensity ratios of C2*/CH*, C2*/OH* and CH*/OH* to

the equivalence ratios at h = 3 and 9 mm... 48 Fig. 16. Radial distribution of the OH*, CH*, and C2* chemiluminescence intensities at

h = 3 and 9 mm for φ = 0.85 flame... 49

Fig. 17. Radial distribution of the OH*, CH*, and C₂* chemiluminescence intensities at

h = 3 and 9 mm for φ = 0.95 flame... 50

Fig. 18. Radial distribution of the OH*, CH*, and C₂* chemiluminescence intensities at

h = 3 and 9 mm for φ = 1.0 flame ... 51

Fig. 19. Radial distribution of the OH*, CH*, and C2* chemiluminescence intensities at

h = 3 and 9 mm for φ = 1.2 flame ... 52

Fig. 20. Radial distribution of the OH*, CH*, and C2* chemiluminescence intensities at

h = 3 and 9 mm for φ = 1.35 flame... 53

Fig. 21. Radial distribution of the OH*, CH*, and C2* chemiluminescence intensities at

h = 3 and 9 mm for φ = 1.35 flame... 54

Fig. 22. Variations of the maximum chemiluminescence intensities with the equivalence

ratio at h = 3 and 9 mm ... 55 Fig. 23. Correlation of the intensity ratios of C2*/CH*, C2*/OH* and CH*/OH* to the

equivalence ratios at h = 9 mm ... 56 Fig. 24. Computed temperature isopleths for laminar premixed CH₄-air flames at φ =

0.85, 1.0, and 1.2 ... 57 Fig. 25. Computed OH* mass fraction isopleths for laminar premixed CH4-air flames at

φ = 0.85, 1.0, and 1.2... 58 Fig. 26. Computed CH* mass fraction isopleths for laminar premixed CH₄-air flames at

φ = 0.85, 1.0, and 1.2... 59 Fig. 27. Computed C₂* mass fraction isopleths for laminar premixed CH₄-air flames at

φ = 0.85, 1.0, and 1.2... 60 Fig. 28. Comparisons of measured and predicted radial distributions of OH*, CH*, and

C2* emissions in laminar premixed CH4-air flames (φ = 0.85, 1.0, and 1.2) at h = 3 mm ... 61 Fig. 29. Comparison of the measured and calculated adiabatic flame temperatures in

laminar premixed CH₄-air flames ... 62 Fig. 30. Radial distribution of the OH*, CH*, and C₂ emissions in turbulent premixed

stoichiometric CH₄-air flame at h = 10 mm ... 63 Fig. 31. Radial distribution of the OH*, CH*, and C2 emissions in turbulent premixed

rich CH4-air flame at h = 10 mm ... 64

Fig. 32. Histograms of measured equivalence ratio in turbulent premixed stoichiometric CH₄-air flame at h = 10 mm and r = -9 mm... 65 Fig. 33. Histograms of measured equivalence ratio in turbulent premixed rich CH₄-air

flame at h = 10 mm and r = -9.18 mm ... 66 Fig. 34. Radial distribution of average and rms equivalence ratios in turbulent premixed

stoichiometric CH₄-air flame measured by three different intensity ratios at h = 10 mm... 67 Fig. 35. Radial distribution of average and rms equivalence ratios in turbulent premixed

rich CH₄-air flame measured by three different intensity ratios at h = 10 mm .. 68 Fig. 36. Histograms of measured temperature in turbulent premixed stoichiometric and

rich CH₄-air flames at h = 10 mm and r = -9 mm ... 69 Fig. 37. Radial distribution of average and rms temperatures in turbulent premixed

stoichiometric and rich CH4-air flames at h = 10 mm ... 70

CHAPTER I INTRODUCTION

1.1 Background

According to the energy consumption report [1], the amount of energy (77,875 KLOE) consumed by the industrial and transportation sectors was 72.1% of the total annual energy consumption in Taiwan during the year of 2007. In these two sectors, about 90% of energy sources (fossil fuels) were used to generate power, process heat, and electricity through combustion. In order to burn the fuel more efficiently and effectively, the development of combustion heating and energy saving technologies is of vital importance. Although the Energy and Resources Laboratories (ERL), ITRI has devoted much efforts to improve the energy efficiency of industrial process heating [2], there are still many combustion related technologies that need to be developed. Also, from the academic point of view, the continuous support of fundamental scientific research and educating students is the essential way to achieve the goal of building up our own combustion technology.

Various types of turbulent flames, premixed, nonpremixed, or partially premixed, are employed in industrial boilers, process heating burners, internal combustion engines, hazardous waste incinerators, and both aircraft and land-based gas turbine engine combustors, etc. In order to control the turbulent combustion [3, 4] for reducing pollutant emission [5-7], increasing combustion efficiency [8], and obtaining stable flame holding [9-11], the detailed compositional structures at turbulent flame-front must be known. In addition, quantitative measurements of reaction zone structure, velocity, temperature, species concentration, flame curvature, and stretch rate in turbulent flames would provide valuable information that not only allow a better understanding of the physics underlines but also improve the applicability of combustion models. In order to quantitatively, spatially, and temporally resolve the turbulent flames, sophisticate laser diagnostic techniques are generally needed.

Laser-induced fluorescence (LIF) technique is a very powerful tool to visualize the reaction zone structures [12-14] and its time evolution [15] in turbulent flames through the excitation of OH and CH radicals from their ground electronic states. LIF can provide useful 2-D information on flame shape and flame front structure, but time-series analysis of the flame front motion is difficult because of the laser repetition rate. Velocity measurements in turbulent flames can be made using laser Doppler velocimetry (LDV) or particle imaging velocimetry (PIV) to acquire 1-D [16-18] or 2-D [19-22] velocity fields, respectively. Flame curvature and strain rate can be deduced using simultaneous OH and CH imaging and PIV techniques [23, 24]. It has been shown that the spontaneous vibrational Raman scattering coupled with LIF techniques can provide simultaneous

temperature, major, and minor species concentration measurements [25-28]. The effect of turbulence-chemistry interaction on finite-rate chemistry, pollutant emissions, and liftoff and blowout mechanisms can be understood from Raman/LIF measurements.

Literature survey indicates that more advanced instruments, such as high power lasers, spectrometers, intensified CCD (ICCD) cameras, fast data acquisition systems, and so on, are required in order to obtain more information non-intrusively from turbulent combustion.

These measurements are usually named as “noble experiments”. It is well known that the research budget would be cut more and more in the coming years due to an increased budget in Defense sector. Thus, the development of low cost, non-laser based optical sensors for turbulent hydrocarbon flames measurements is an alternative to continuous building up our own localized combustion technology.

1.2 Motivations and Objectives

There are a number of optical methods that can give information about the combustion process non-intrusively, e.g., optical emission, absorption, fluorescence, and other spectroscopic methods. The focus of this research is on the simplest of all these techniques, viz., observing the naturally occurring, optical emissions from the turbulent flames. While there are a number of sources for optical radiation from a flame, the source most directly connected to the combustion reactions is chemiluminescence. The chemiluminescence emissions are from electronically excited states of molecules (e.g.,

OH [^*

A

²Σ⁺ →

X

²Π], CH [^*

A

²Δ→

X

²Π], andC^*₂[

d

³

Π

→

a

²

Π

]) that are produced by chemical reactions. The excited molecules will transfer to lower energy states, in part by emitting light. This is known as chemiluminescence. Since the intensity of emission is proportional to the chemical production rate of the particular molecule, the chemiluminescence intensity can be related to chemical reaction rates [29]. For this reason, chemiluminescence has been used previously as a rough measure of reaction rate and heat release rate [30-35]. Thus, chemiluminescence can provide information on the presence and strength of the combustion process in a specific region of the combustor, making it well-suited for diagnostics and flame monitoring.

Since the chemiluminescence intensities are produced during the chemical reaction process, the light intensity is related to the rate of production/consumption of that species.

The reaction rate varies with reaction pathways which is a function of equivalence ratio, making it easier to deduce the equivalence ratio from the chemiluminescence intensity. It has been shown that the ratio of OH*/CH*, C2*/OH*, and C2*/CH* vary with equivalence ratio in laminar premixed flames [36]. This non-laser based diagnostic technique has been applied to turbulent premixed flames for local flame-front structure measurement [37], to

high-pressure laminar flame for local spectral measurement [38], to premixed-spray flame for observation of droplet group combustion behavior [39], to an atmospheric pressure micro-gas turbine combustor for detecting local equivalence ratio [40], to gas turbine combustors for developing optical equivalence ratio sensors [41], to turbulent premixed flames for flame-front motion analysis [42], and to gas turbine engines for active control [43].

Although the application of optical emission technique is being quite successful for various type of reacting flow measurements, simultaneous measurements of local equivalence ratio (mixture fraction) and temperature using chemiluminescence emissions from turbulent flames have not been reported. It has been the goal of considerable research effort to find universal state relationship for temperature and species concentrations as functions of a single variable, the mixture fraction, in order to create flamelet libraries for use in the modeling of turbulent combustion. However, in order that the comparison of experimental and computational data set is to be meaningful, both the mixture fraction and at least one additional variable, such as temperature, must be match in some fashion.

The objectives of this research project are to develop a low cost, robust, non-laser based optical sensor system and to apply this system for simultaneous temperature and equivalence ratio (mixture fraction) measurements in hydrocarbon flames.

CHAPTER II RESEARCH METHODS

2.1 Experimental Setup

In order to gain a better understanding of the physics of turbulent flames and their associated pollutant emission mechanisms, the thermophysical properties of the flames must be measured. Simultaneous multi-point measurements of temperature, species concentration, mixture fraction, and hence scalar dissipation rate have been made in turbulent jet flames using line-Raman/LIPF techniques [44, 45]. However, these techniques require expansive equipments such as narrowband excimer lasers, spectrometers, and ICCD cameras. For example, the Combustion Research Facility at Sandia National Laboratories, Livermore, California, USA used four lasers, one spectrometer, and six ICCD cameras (see Fig. 1) to measure flame orientation and scalar dissipation in turbulent partially premixed flames [46].

This type of experiment is out of our research funding capability. Thus in this work, a much simpler and cheaper method is used to accomplish the same job. That is chemiluminescence optical sensor.

In the past, most of the chemiluminescence measurements used typical collecting lenses to monitor global emissions along the line-of-sight, and hence there was insufficient spatial resolution to detect the local flame-front structure. The use of a 2-D chemiluminescence imaging system can overcome this problem [33, 48]. However, it is difficult to apply this technique to obtain chemical information about the local flame-front in turbulent premixed flames. Therefore, an optical measurement technique using spatially designed Cassegrain optics to detect local flame emissions has been reported [49]. The schematic diagram of the Cassegrain optics is shown in Fig. 2. The Cassegrain optics consists of a primary and a secondary mirror, which avoids the generation of chromatic aberrations for different wavelengths. The Cassegrain optics is designed by the ray-tracing method. The designed rms spot size of Cassegrain optics is 328 μm and the magnification ratio is 2.36. In order to improve the Cassegrain optics for a micro-level adjustment and to connect with the optical fiber for light collection, the optical holder is re-designed. In addition, a circular mask with different slit widths at the center can be placed in front of Cassegrain optics at the secondary mirror so that the background flame emission signals located away from the effective sample volume is minimized [50].

The schematic diagram and photograph of the measurement system are shown in Fig. 3.

Chemiluminescence signals emanating from the sample volume are collected and focused by the Cassegrain optics and relayed to the entrance slit of a spectroscopic unit through a 2-m

long optical fiber (core diameter = 100 μm). A collimated lens is coupled to the end of optical fiber for expanding the light rays. In the spectroscopic unit, three dichroic mirrors are used to separate different wavelengths of optical emissions. Particular regions of wavelength corresponding to OH*, CH*, and C2* are extracted through the narrowband interference filters and detected by the side-on type photomultiplier tubes (PMTs). The specifications (center wavelength/full width at half maximum) of the interference filters for OH*, CH*, and C2* are 307.3/22.2 nm, 432.1/10.5 nm, and 516.3/8.5 nm, respectively. The current output from the PMTs are simultaneously amplified and digitized with a 12-bit A/D converter. The output signals are stored in a personal computer for data reduction.

It is noted that although the use of PMTs for chemiluminescence measurements poses faster data acquisition rate than that of a 2D detector such as a CCD camera, the PMT provides no information on the emission spectra of OH*, CH*, and C2*. Therefore, in addition to the spectroscopic unit, a monochromator (Spectral Products, DSK 242, 1/4 m, f/#

= 3.9) coupled with liquid nitrogen cooled charge-coupled device (LN-CCD) is also employed in the present study. The photograph of measurement system is shown in Fig. 4.

2.2 Bunsen Burner

A Bunsen type jet burner (i.d. = 10 mm) is used to produce laminar premixed methane-air flames operated at several different equivalence ratios ranging from fuel-lean to fuel-rich conditions (φ = 0.85-1.5) for the emission measurements and system calibration.

To generate the laminar premixed flames, the exit velocity of the flow is kept at 1 m/s so that the flowrates of fuel and air are varied. The operation conditions of the laminar premixed flames are listed in Table 1. For turbulent premixed flames, a larger diameter jet burner (i.d.

= 20 mm) is employed. Typical flame features for laminar and turbulent premixed CH4/air flames at φ = 1.0 are shown in Fig. 5.

CHAPTER III

THEORETICAL BACKGROUND OF VIBRATIONAL TEMPERATURE MEASUREMENT

3.1 Vibrational Temperature Measurement

The flame temperature can be measured using the intensity ratio of C2* emission intensities at two vibrational bands as proposed by Ishiguro et al. [51]. Fig. 6 shows the typical emission spectra of the two C2* bands [51]. The intensity ratio I1/I2 of the two vibrational bands is given by

∑

∑

−

−

=

j

j j

, rel j i

i i

, rel u ip

kT / E A

v

kT / E A

v I

I

) exp(

) exp(

2

(1)

where v is the frequency, Arel the relative Einstein transition probability for spontaneous emission, E the upper vibrational energy (erg), k the Boltzmann constant, T the vibrational temperature (K), and p a constant for the instrument. The subscripts i and j indicate the individual emission lines of the two vibrational bands. The vibrational energy for the vibrational quantum number

υ

′, Eυ′ is given by the following [52]:

⎟ −

⎠

⎜ ⎞

⎝⎛ +

⎟ +

⎠

⎜ ⎞

⎝⎛ +

⎟−

⎠

⎜ ⎞

⎝⎛ +

′ =

3 2

2 1 2

1 2

1

ω υ ω υ

υ

υ

hc ω

e

hc

e

x

e

hc

e

y

e

E

--- (2)

Here

ω

e is the vibrational wave number, xe

and y

e are the anharmonicity constants. For υ′ → υ″, the transition probability Aυ′, υ″ is expressed by the following [52]:

[ _∫

^{′ ′′}

]

²

′′

′

∝ dx

A

_υ,υ ψ_υψ_υ (3) For a harmonic oscillator

ψ

_υ is given by [52]:

( ^x )

H x

N

^{2 1/ 2}

2

exp 1

α α

ψ

_{υ υ} ⎟ _υ

⎠

⎜ ⎞

⎝⎛−

= (4) where Nυ is the normalization constant,

( )

2 ! ^1/2

( / )

^1/4

N

_υ = ^υ

υ

⁻

α π

(5a)

( ) k / h h

/

^{1/ 2}

0

2

2

4 π μν π μ

α = =

(5b)

μ

is the reduced mass of the molecules and equals

m

₁

m

₂

/ ( m

₁

+ m

₂

)

, and Hυis the Hermite polynomial of the

υ

th degree and is given as

( )

1

0

X

=

H

( ) X X

H

₁

= 2

( )

4 ² 2

2

X

= X −

H

( ) X X X H

₃ =8 ³ −12

( ) X X X H

₃ =8 ³ −12

( )

16 ⁴ 48 ² 12

4

X

=

X

−

X

+

H

X = α

^1/2

x.

υ υ′, ′′

,

A

rel is calculated as the ratio of

A

_{υ′,υ′′} to

A

_0,0:

0 0, , ,

,

rel

A / A

A

_{υ′υ′′} = _{υ′υ′′} (6) The instrument constant p can be determined from the calibration and the values of λ,

( υ ′, υ ′′ )

,

υ υ′, ′′

E

and

A

_{rel,υ′,υ′′} for the band components are listed in Table 2.

The method of vibrational temperature measurement described by Ishiguro et al. [51]

involves many calculations of spectral properties. It seems that the summation of emission intensity for each vibration band has to be made by summing over all the vibrational state and the temperature is determined by comparing the calculated spectra with the measured ones.

Moreover, it is not clear where the calibration constant p is involved in Eq. (1). Therefore, we decided to derive the relation of intensity ratio with the flame temperature based on fundamental theory of emission.

3.2 Theory of Vibrational Temperature Measurement

The intensity of a spectral line in emission

I

_em^nm is defined as the energy emitted by the source per second. If there are Nn atoms in the initial state and if Anm is the fraction of atoms in the initial state carrying out the transition to m per second then [52]

nm nm n nm

em

N hc A

I

=

ν

(7) where h is the Planck constant, c is the speed of light, and

hc ν

_nm is the energy of each light quantum of wave number

ν

_nm emitted in the transition. Anm is the Einstein transition probability of spontaneous emission which is related to the matrix element of the transition as follows:

3 2 4

3

64 nm nm

nm

R

A π h ν

= (8) For the band emission from higher vibrational levels υ′ to lower vibrational levels υ″, Eq. (7) can be expressed as [52]:

( )

²

[ ]

²

4 4

3

64 ^{′ ′ ′′}

∫

^{′ ′′}

′′ =

N c R dr

I

_em^υ'υ

π

_υ

ν

_vib^υυ

ψ

_υ

ψ

_υ (9) where

N is the number of molecules in the upper vibrational levels,

_υ′

R

^υ_vib^′υ′′ is the vibrational transition moment, and

ψ

_υ is the vibrational eigenfunction. If we sum the transition probability over all transitions that can occur from a given vibrational level, we obtain on account of the sum rules [52]

2 1

∑

=

′

′′

′ υ

υ υ

R

vib ,

_{∑ ∫} [ ]

′ ′ ′′ =

υ

ψ

υ

ψ

υ

dr

² 1 (10) The total emission intensity from a band becomes

∑

∑

′ ′

′′

′′

′

=

=

υ υ

υ υ

υ

π

ν ^{c N}

I I

^em₄ ⁴

3

64

(11) In thermal equilibrium the number of molecules in the upper vibrational state is

( )hc/kT

e

G

Q

N N

^υ

υ

υ′ = ^{− 0 ′} (12) where

Q is the vibrational partition function and

_υ

G

₀

( ) υ

′ is the energy term value above the zero-point energy. The vibrational partition function is defined as:

( )

( ) ( )

( ) ( )

... x x

x

...

e e

e e

e e

Q

T / T T

/ T

T / T kT

/ hc kT

/ hc kT G

/ e

= − + + +

=

+ +

+

=

=

=

=

≡

−

−

∞

=

∞ −

=

∞ −

=

∞ −

=

−

−

∑ ∑ ∑

∑

1 1 1

1

2 2

0 0

0 0

0 0

υ υ

υ υ υ

υ

υ υ

υ ω υ

υ υ

ε ε υ

(13)

where

x

=

e

^−Tυ/T. Thus,

T /

e

T

Q

υ = − −υ

1

1 (14) where the characteristic vibrational temperature Tυ is defined as

k T hc ω

^e

υ = (15) Substituting Eqs. (12) and (13) into Eq. (11), it becomes

( )

∑

( )

∑

∑

′

− ′

′

− ′

′′

′′

′

=

=

=

υ υ υ υ

υ υ υ

υ

υ

π

ν

kT / hc G kT

/ hc em G

Q e e C

Q c N

I I

₄ ^{4 0 0}

3

64 (16) Note that C is the grouped constant.

Because the emission of C2*(1, 0) band starts from υ′ = 1 and that of C2*(0, 0) band starts from υ′ = 0, therefore the intensity ratio of the two vibrational bands can be expressed as:

( )

( )

( )

( )

T / T

T / T

T / T

T / T

kT / hc G

kT / hc G

kT / hc G

kT / hc G

e C e

e e

C C e

e C C e

C e C I

I

_υ

υ υ υ

υ

υ υ

υ

υ

υ υ

υ

υ Δ

υ

Δ −

−

−

−

∞

=

′

− ′

∞

′=

′

−

∞

=

′

− ′

∞

′=

′

−

=

= =

−

= −

−

=

=

∑

∑

∑

∑

3 2

1

0 0 2 1

0 2

1 1 0 1

1 1 1 1

0 0

0 0

(17)

( ) ( )

T C T

I

_ratio

= ln

₃

−

^υ

ln

(18)

( ) C ( I

_ratio

)

T T

ln ln

₃

−

=

^υ (19) where the characteristic vibrational temperature for C2 is Tυ = 2572.89 K and C3 is the instrument constant which can be determined from the calibration.

CHAPTER IV

NUMERICAL SIMULATION

4.1 Governing Equations

In the present study, numerical simulations of the laminar premixed CH4/air flames using a commercial package CFD-ACE are also performed to investigate the flame structures. The governing equations of mass, momentum, energy, and chemical species for a steady axisymmetric reacting flow can be written in the cylindrical (r, x) coordinate system as

0 )

( =

⋅

∇

ρ v

(20)

g

x

) v ( p ) v v

( ρ

=−∇ +∇⋅

μ

∇ +

ρ

⋅

∇ (21)

{ }

∑ ^{+ ∇ ⋅ ∇ + ∇}

−

∇

⋅

∇

=

⋅

∇

i

T i i

i i

i p p

T ln D Y

D w

c h ) T c (

) T v

( ρ 1 λ 1 [ ρ ρ ( )]

(22)

i T

i i

i

i

) D Y D ln T w

Y v

(

=∇⋅ ∇ + ∇ +

⋅

∇

ρ

[

ρ ρ

( )] (23) and the state equation

∑

=

i i

i

M T Y R

p ρ

₀ (24) where

ρ

, p, T, Y, cp, h, w, R0, M, gx, and v = (u,

υ

) are the density, pressure, temperature, mass fraction, specific heat capacity of the mixture, enthalpy, species production rate, universal gas constant, molecular weight, gravitational acceleration in x-direction, and velocity vector, respectively.

μ

,

λ

, and D are the viscosity, thermal conductivity, and mass diffusivity, respectively. The subscript i in equations (22)-(24) stand for the i-th chemical species. The second term in the bracket of equations (22) and (23) is the thermo-diffusion or Soret diffusion due to the effect of temperature gradient. The concentration-driven diffusion coefficient is calculated as:

i j N

j ij

j i i

D x D x

=

⎥ ⎥

≠

⎦

⎤

⎢ ⎢

⎣

⎡

= −

∑

1

1

(25)

where Dij is the binary diffusion coefficient. The binary mass diffusivity is determined by the Chapman-Enskog kinetic theory using Lennard-Jones parameters. The thermo-diffusion coefficient is calculated as:

i j N

j

j i j i j T i

i

k D

M M D M

=

⎥

≠

⎦

⎢ ⎤

⎣

= ⎡ ∑

1 2 (26) where M is the mixture molecular weight and kij is the thermo-diffusion ratio.

4.2 Numerical Method

The governing equations are solved using commercial package CFD-ACE. An orthogonal, non-uniform staggered-grid system is used for solving the discretized equations with a control volume formulation in accordance with the SIMPLEC algorithm. The momentum equations are solved using the second-order upwind scheme while the central difference method is used for the energy and species equations. The above equations are solved along the mesh lines in the computational domain using an iterative ADI and TDMA techniques. Input of the molecular transport data is obtained from the CHEMKIN package [53] and then the code calculates the thermal conductivity and viscosity of the mixture using Wilke’s formula. Thermal diffusion and buoyancy effects are included in this analysis but radiation heat loss is neglected. The GRI-Mech 3.0 chemical kinetic mechanisms (53 species, 279 elementary reactions) [54] are coupled to the CFD package. In order to calculate the OH*, OH*, and C2* emission intensities, additional CH*, OH*, and C2* kinetics (as shown in Table 3) in consideration of reaction rate, quenching rate, and spontaneous emission rate [50] are also included in the chemical mechanisms with GRI-Mech 3.0.

4.3 Boundary Conditions

The computational domain and the boundary conditions employed are shown in Fig. 7.

Uniform flow (1 m/s) of premixed methane/air mixtures is specified at the inflow boundary of the computational domain, which includes flow computation in the tube, and the velocity at the exit of burner port (tube exit) has been carefully checked and found to be in fully developed parabolic profile. As seen in the figure, the burner is placed inside the computational domain, and hence the property located inside as well as outside the burner is calculated. This takes into account the back-diffusion of species into the tube and the heat transfer between the tube and flame. The wall temperature is kept constant at 300 K. Far field boundary conditions are imposed to the open boundaries as shown in the figure.

Non-slip and non-catalytic reaction conditions are applied on the burner surface. Burner specifications (inner/outer diameter, conductivity etc.) and inlet velocity for the corresponding burner are set to meet the current experiments. Total number of meshes is 135 in the radial and 310 in axial direction for a physical domain of 30 mm × 250 mm.

The inner diameter and wall thickness of the tube are d = 10 mm and 1.5 mm, respectively.

The fuel tube exit plane is placed 50 mm downstream from the inflow boundary in the computational domain. Stretched meshes are applied in both directions; a minimum grid size of 0.1 mm is placed near the burner and an enlarged grid size is set forth toward the outer boundaries. The grid-independence study suggests that 0.1 mm grid spacing is sufficient for resolving the flame features. Convergence of solution is declared when the

ratio of change of the dependent variables to the maximum variables in that iteration is within 1 × 10^-4.

CHAPTER V

RESULTS AND DISCUSSION

5.1 Characteristics of Cassegrain Mirror

In order to understand the capability of the Cassegrain optics for “point” measurements of optical emissions, the spatial resolution of the Cassegrain optics is measured using an inverse ray tracing method. A diode laser is used to shine the red-light from the back-end of the optical fiber and to form a red spot at the focal point of the Cassegrain mirror. A CCD camera is directly placed at the focal point and moved along the optical axis to measure the light intensity profile. The measured light intensity distribution is depicted in Fig. 8. Fig.

8a shows the light-collection rate distribution at the focal point. It can be seen that the distribution of light intensity is not in a perfectly circular shape. This could be due to slightly misalignment between the laser light and the optical fiber or due to non-uniformity of the CCD chip. However, the high-intensity region indicates that a circular focal point with approximately 40 μm in diameter is achieved for the Cassegrain optics. The light intensity, defined by setting the threshold value at e^-2 times the peak value, along the optical axis and its 3-D distribution are shown in Figs. 8b and 8c, respectively. The effective probe volume determined from Fig. 8c is found to be 40 μm in diameter and 600 μm in length. The effective probe volume of the present Cassegrain optics is slightly better than that (100 μm in diameter and 800 μm in length) designed by Kojima et al. [50].

Prior to the chemiluminescence emission measurements using the spectroscopic unit with PMT array, the effect of the slit width of the eye-mask on the reduction of background flame emissions is examined. Fig. 9 shows that the measured OH* with the mask have narrower profiles, while that without the mask yields a broader profile due to a contribution from background flame emissions collected outside the effective probe volume. We also rotate the slit angles and found that the measured OH* has a narrower profiles when the slit centerline is parallel to the flame axis. This findings is in agreement with that observed by Kojima et al. [50]. After considering a trade-off relation between the slit width and the signal-to-noise ratio of the peak value, we found that the best performance of the eye-mask for the present study is a 5-mm-wide slit with the slit centerline arranged parallel to the flame axis (see Fig. 3).

5.2 Chemiluminescence Emission Spectra

Typical chemiluminescence emission spectra from the laminar premixed CH4/air Bunsen flames operated at φ = 0.85, 1.0, and 1.3 are shown in Fig. 10. These spectra are obtained by a double monochromator coupled with a LN-CCD camera (see Fig. 4). In order to obtain the

spectrum for wavelength covered from 208 to 835 nm, a 150 grooves/mm grating (12.8 nm/mm) is used. It can be seen from Fig. 10 that for φ = 0.85, the peak emissions of OH*(0, 0) at 307 nm, CH*(0, 0) at 430 nm, C2*(1, 0) at 470 nm, and C2*(0, 0) at 516 nm are visible in the spectrum. These emissions are due to following molecular transitions in the flame:

OH*(A²Σ⁺ −X²Π), CH*(A²

Δ

−X²Π), and C2*(d³Π−a³Π) [55, 56]. Previous studies [57, 58] have confirmed that the primary source of flame CH* is from the reaction C2H + O

→ CH* + CO, which might then provide a measure of the final steps in the C(2) reaction chain.

The formation of OH* is from the reaction CH + O2 → OH* + CO, which might provide a measure of the final steps in the CHx reduction chain. The formation mechanism of C2*, however, remains unclear. There are a couple of reactions proposed for the formation of C2* such as CH2 + C → C2* + H2, CH + C → C2* + H, CH + CH → C2* + H2, or O +C3 → C2* + CO. The reaction mechanisms and rate constants of OH*, CH*, and C2* have been recently investigated in low-pressure hydrocarbon flames [55, 56]. In addition to the peak emissions, there is also a broad underlying CO2* continuum [29] that extends from 280 nm throughout the sampled spectral region. This broadband emission varies with equivalence ratio and is especially significant when the spectral bandwidth of the detection system is broad [41].

Therefore, to obtain a more accurate measurement of chemiluminescence intensities, background correction based on the side bands must be made. The polynomial fits of the side bands used for background corrections are also shown in the figure (red dashed curves).

A linear or quadratic fit to the spectrum around the primary peak is employed, depending on the spectrum of side bands. The curve fit value at ~310 nm is subtracted from the intensity measured, to obtain a corrected OH* peak intensity, and likewise at ~430 nm for CH* and from ~450 to ~590 nm for C2*. In addition, the emission intensity varies with spectral location when the image is taken. This is due to that the grating has higher quantum efficiency at wavelength around visible and lower quantum efficiency near UV. During data processing, the emission intensity is corrected to compensate the quantum efficiency effect.

When the equivalence ratio is increased to 1.0, the peak intensities of OH*(0, 0), CH*(0, 0), and C2* Swan band all increase. The intensity of C2* Swan band reaches to a maximum value at φ = 1.3. Since the chemiluminescence intensity of OH*, CH*, and C2* varies with flame equivalence ratio, the ratio of CH*/OH*, C2*/OH*, and C2*/CH* can be used to determine flame local equivalence ratio. Generally, the strongest intensity of OH*, CH*, and C2* located at 306, 431.4, and 516.5 nm, respectively, is independently monitored when the spectroscopic unit coupled with PMT array is used for chemiluminescence measurements.

It should be noted that the detector gate time must be long enough to measure sufficient chemiluminescence light, but short enough to reject stray light from background, if a LN-CCD camera is used. However, the detector gate time is not an issue if a photomultiplier tube (PMT) is used.

5.3 Chemiluminescence Emissions in Laminar Premixed Flames

In the present study, two sensor systems are developed; one is the spectroscopic unit coupled with the PMT array, and the other is the double monochromator coupled with a LN-CCD camera. The use of PMT array provides prompt data acquisition rate which is more suitable for turbulent premixed flame measurements. However, the PMT array gives no information on the broadband CO2* emissions. The broadband CO2* emissions could affect the quantitative measurements of OH*, CH*, and C2* if they are not subtracted out from the measured total intensities. On the other hand, the use of a LN-CCD camera gives all the information including the OH*, CH*, and C2* peak intensities as well as the broadband CO2* emissions. But the data acquisition rate is very slow because each image requires about 1.5 s to store in the personal computer. In order to verify the applicability of the sensor system using the double monochromator coupled with a LN-CCD camera to turbulent flame measurement, we also perform some measurements in turbulent premixed flames.

5.3.1 Measurements Using PMT Array

Simultaneous measurements of OH*, CH*, and C2* chemiluminescence emissions using PMT array are made in laminar premixed methane-air jet flames (φ = 0.85-2.0) to examine the applicability of the developed sensor system. The radial distributions of normalized OH*, CH*, and C2* intensities at h = 3 and 9 mm for φ = 0.85, 1.0, and 1.3 flames are shown in Figs. 11-13, respectively. The measured maximum intensity of OH*, CH*, and C2* in the flames studied is used to respectively normalize each of emission signals, so that direct comparison of chemiluminescence intensity for different flame conditions can be made. It is noted that the radial location of local maximum chemiluminescence intensity is an indication of flame front position. In addition, the OH*, CH*, and C2* intensities of the hydrocarbon flames are functions of the relative heat release rate and their concentrations. Moreover, the profile of the OH* spectra has been correlated to the flame temperature and the CH* is an important indicator of the prompt NO formation [59].

Fig. 11 shows the radial distributions of OH*, CH*, and C2* intensities at h = 3 and 9 mm for φ = 0.85 flame. It can be seen that the peak OH* and CH* chemiluminescence signals occur at r = 3.51 mm and no C2* signal is detected near the burner exit (h = 3 mm).

At downstream location (h = 9 mm), the C2* signal increases and three emission signals peak at r = 2.25 mm. The shift of peak intensity location from r = 3.51 to 2.25 mm indicates that the flame front position moves towards the center of the flame with increasing downstream location. The low C2* emissions in lean flame conditions have also been observed by Kojima et al. [36]. Similar radial distributions of OH*, CH*, and C2* intensities at h = 3 and

9 mm for φ = 1.0 and 1.3 flames are shown in Figs. 12 and 13. It is noted that the high level of intensities between the two peaks is due to flame emissions coming from outside the probe volume. This fact suggests that although the present sensor is designed for “point”

measurement, the emissions outside the probe volume are not completely eliminated by the eye mask. Figs. 11-13 also indicate that the flame width is increased as the euqivalence ratio is increased from fuel-lean to fuel-rich conditions. For instance, the peak OH* intensity locates at r = 3.51 mm for the φ = 0.85 flame at h = 3 mm and it shifts to r = 4.14 mm for φ = 1.3 at the same height. The increase of the flame width in the richer flames indicates that it requires a broader region for the fuel to be consumed.

Comparisons of the measured maximum intensity for φ = 0.85-2.0 at h = 3 and 9 mm are shown in Fig. 14. Results indicate that at both heights the maximum OH*, CH*, and C2* intensities occur approximately at φ = 1.0, 1.1, and 1.2-1.25 respectively. These findings are in good agreement with experimental results of Kojima et al. [36], but depart from those measured by Jeong et al. [60]. Kojima et al. found that the peak OH* intensity occurred at φ

= 1.1, CH* at φ = 1.2, and C2* at φ = 1.3. Whereas Jeong et al. measured the peak intensities of OH*, CH*, and C2* at φ = 0.86, 0.91, and 1.06, respectively. The closer agreement between our results and the data of Kojima et al. could be due to that a similar Cassegrain light collection system was used for the measurements.

It has been suggested that the chemiluminescence intensity ratio of CH* to OH* or C2* to CH* or OH* and the equivalence ratio in hydrocarbob flames have a nearly linear relationship [36, 40, 61]. These suggestions were based on results showing that the chemiluminescence intensity was very sensitive to the equivalence ratio. In addition, the possibilities that the effects of temperature, pressure, and the size of the flame on the emission intensity could be canceled to detect the equivalence ratio. Therefore, the correlation between the chemiluminescence intensity ratio and euqivalence ratio at the flame front is investigated.

Fig. 15 shows the results of C2*/CH*, C2*/OH*, and CH*/OH* against the equivalence ratio for the local flame front of the laminar premixed methane-air jet flames at h = 3 and 9 mm. In Fig. 15, the peak emission intensities of OH*, CH*, and C2* shown in Fig. 14 are used to determine C2*/CH*, C2*/OH*, and CH*/OH*. It can be seen in Fig. 15b that near the burner exit (h = 3 mm) the fluctuational levels of C2*/CH* and C2*/CH* are higher than that of CH*/OH* due to low C2* emissions are produced at this downstream location. At h

= 9 mm (Fig. 15a), the scatter of the C2*/CH*, C2*/OH*, and CH*/OH* is greatly reduced because higher emission intensities of OH*, CH*, and C2* are generated. Figure 15 shows that the correlation of C2*/CH*, C2*/OH*, and CH*/OH* to the equivalence ratio is nearly linear when the equivalence ratio is less than 1.35. The high degree of correlation suggests

that the local flame stoichiometry at the flame front of premixed methane-air flames can be determined by the spatially resolved chemiluminescence measurements. However, it seems difficult to measure the equivalence ratio in methane-air flames for φ > 1.35 by using this system because nonlinear relationship is observed within this range. These findings are in excellent agreement with those obtained by Kojima et al [36].

Figure 15 also indicates that the variation of C2*/OH* curve is most sensitive to the equivalence ratio and C2*/CH* is the next most sensitive. However, the use of C2*/OH* and C2*/CH* correlations for determining the local equivalence ratio becomes less reliable for lean flame conditions, because the C2* emission intensity is very low at φ < 1.0, as shown in Fig. 11. On the other hand, the correlation of CH*/OH* can be used for determining the equivalence ratio in lean premixed flame conditions, because the CH* and OH* emissions can be observed clearly, as shown in Fig. 11. These results suggest that the spatially resolved emission intensity ratio of CH*/OH* can be used to determine the local flame stoichiometry in the reaction zone of premixed hydrocarbon flames for a wider range of equivalence ratios.

5.3.2 Measurements Using LN-CCD Camera

In order to validate the sensor system that consists of a double monochromator with a LN-CCD camera, chemiluminescence emission measurements of OH*, CH*, and C2* are also made in the similar laminar premixed methane-air flames (φ = 0.85-2.0). The radial distributions of normalized OH*, CH*, and C2* intensities at h = 3 and 9 mm for φ = 0.85, 0.95, 1.0, 1.2, 1.35, and 1.5 flames are shown in Figs. 16-21, respectively. It can be seen that for φ = 0.85 flame the peak OH* and CH* chemiluminescence signals occur at r = 4.14 mm and very low C2* signal is detected near the burner exit (h = 3 mm). At downstream location (h = 9 mm), the peak intensity location shifts from r = 4.41 to 3.06 mm that indicates the flame front position moving towards the center of the flame with increasing downstream location. Comparison of Figs. 16 and 11 indicates that the measured peak intensity locations are slightly different using both sensor systems. This could be due to that the scanning step (0.18 mm) used for Fig. 16 measurements are twice of that for Fig. 11.

Similar radial distributions of OH*, CH*, and C2* intensities at h = 3 and 9 mm for φ = 1.0, 1.2, 1.35, and 1.5 flames are shown in Figs. 17-21. It is noted that the high level of intensities between the two peaks is due to flame emissions coming from outside the probe volume. Figs. 17-21 also indicate that the flame width is increased as the equivalence ratio is increased from fuel-lean to fuel-rich conditions. In general, the measurements of chemiluminescence intensity using the double monochromator with a LN-CCD camera give better signal-to-noise ratio than those measured by the PMT array because the interferences due to broadband CO2* emissions can be subtracted out.