AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF BURNER-
GENERATED LOW STRETCH GASEOUS DIFFUSION FLAMES
by
BAI HAN
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Dissertation Adviser: Dr. Chih-Jen Sung
Department of Mechanical and Aerospace Engineering
CASE WESTERN RESERVE UNIVERSITY
May, 2005 CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the dissertation of
______
candidate for the Ph.D. degree *.
(signed)______(chair of the committee)
______
______
______
______
______
(date) ______
*We also certify that written approval has been obtained for any proprietary material contained therein.
Table of Contents 1
LIST OF TABLES ...... 6
LIST OF FIGURES ...... 7
ACKNOWLEDGEMENTS ...... 14
LIST OF ABBREVIATIONS ...... 15
ABSTRACT ...... 23
CHAPTER 1 INTRODUCTION ...... 25
1.1 Diffusion Flame Structure and Response 26
1.2 Effects of Stretch on Diffusion Flames 31
1.2.1 Flame Stretch 31
1.2.2 Counterflow Diffusion Flames 31
1.2.2.1 Counterflow Facilities 33
1.2.2.1.1 Opposed Jet Burner 34
1.2.2.1.2 “Tsuji” Burner 35
1.2.2.2 Studies of Counterflow Diffusion Flames 36
1.2.2.2.1 Steady Counterflow Diffusion Flames 36
1.2.2.2.2 Instabilities in Counterflow Diffusion Flames 38
1.3 Studies of Low Stretch Diffusion Flame 41
1.3.1 Low Stretch Diffusion Flame Behavior 41
1.3.2 Diffusion Flame under Micro-gravity 45
1.3.3 Alternative Low-Stretch Diffusion Flame Configuration 46
1
1.3.4 Flame Instabilities of Low Stretch Diffusion Flames 48
1.4 Motivations and Objectives of Study 50
1.4.1 Motivations 50
1.4.2 Objectives 51
CHAPTER 2 EXPERIMENTAL SETUP ...... 54
2.1 Definitions 54
2.1.1 Buoyancy-Induced Stretch Rate 54
2.1.2 Nominal Fuel Mixture Injection Speed 56
2.2 Burner Facility 57
2.2.1 Overview 57
2.2.2 Porous Burner 60
2.2.3 Burner Body 62
2.2.4 Experimental Operation 62
2.2.5 Demonstration of Quasi-1D Low-stretch Diffusion Flames 64
2.2.6 Uncertainty Analysis 66
2.2.6.1 Repeatability 66
2.2.6.2 Flow Rate Control 67
CHAPTER 3 OPTICAL DIAGNOSTICS SYSTEMS . . . . 68
3.1 Spontaneous Raman Spectroscopy 70
3.1.1 Experimental Setup and Capability 70
3.1.2 Quantitative Temperature Measurement 78
2
3.1.3 Qualitative Species Measurement 81
3.1.4 Uncertainty Analysis for Raman Temperature Measurements 82
3.1.4.1 Uncertainty of Spatial Location Determination 82
3.1.4.1.1 Mechanical Translation System 83
3.1.4.1.2 Steering Effect 83
3.1.4.2 Uncertainty of Temperature Measurement 84
3.2 OH-PLIF (Planar Laser-Induced Fluorescence) 86
3.2.1 Overview 86
3.2.2 Experimental Setup 88
3.2.3 Data Analysis 92
3.3 IR Imaging 93
3.3.1 Important Factors of IR Camera 94
3.3.2 Surface Temperature Measurement 97
3.4 Chemiluminescence Imaging 101
3.4.1 Experimental Facilities 101
3.4.2 Data Analysis 102
CHAPTER 4 NUMERICAL METHODOLOGY . . . . . 106
4.1 Justification of Stagnation-Point Boundary Layer Model 107
4.2 Flame Radiation Model 109
4.2.1 Overview 109
4.2.2 Radiation Modeling 110
4.3 Numerical Modeling 114
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4.3.1 Formulation 114
4.3.1.1 Assumptions 114
4.3.1.2 Governing Equations 114
4.3.2 Transformed Governing Equations 116
4.3.2.1 Similarity Transformation 116
4.3.2.2 Boundary Conditions 117
4.3.2.3 Heat Balance at Burner Surface 118
4.3.3 Numerical Method 120
CHAPTER 5 RESULTS AND DISCUSSION . . . . . 122
5.1 Uniformity of Quasi-1D Diffusion Flames 122
5.2 Flammability and Instability Map of Low Stretch Diffusion Flames 126
5.2.1 Sooting Flame Boundary 127
5.2.2 Extinction Limits Boundary 128
5.2.2.1 Burner Heat Loss Extinction 129
5.2.2.2 Radiative Extinction 130
5.3 Detailed Structure of Quasi-1D Diffusion Flames 131
5.3.1 Temperature Profiles 131
5.3.1.1 Thermocouple Measurement 131
5.3.1.1.1 Radiation Correction 132
5.3.1.1.2 Temperature Distributions of Steady Flames 134
5.3.1.2 Raman Scattering Measurement 136
5.3.1.3 Comparison of Measured Temperature Profiles 142
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5.3.2 Qualitative Species Distributions 155
5.4 Multi-Dimensional Flame Instabilities 163
5.4.1 Instability Patterns 163
5.4.2 Mechanisms of Instability of Low-stretch Diffusion Flames 171
5.4.2.1 Rayleigh-Taylor Instability 171
5.4.2.2 Thermal-Diffusive Instability 172
5.4.2.3 Instability Related to Heat Los 173
5.5 Computational Results 174
5.5.1 Effects of Three Controlling Parameter 174
5.5.2 Comparison of Experimental and Computational Temperature Profiles 178
5.5.3 Extinction Limits 182
CHAPTER 6 SUMMARY AND RECOMMENDATION FOR FUTURE WORKS 192
6.1 Summary 192
6.2 Future Works 195
APPENDIX A Fundamentals of Raman Scattering . . . . . 197
APPENDIX B Fundamentals of LIF/PLIF ...... 201
APPENDIX C Modeling for Spectral and Directional Radiative Heat Transfer . 206
BIBLIOGRAPHY ...... 211
5
List of Tables
Table 5.1 Five representative cases for Raman measurement
Table 5.2 Comparison of experimental data and simulated results for all five cases
Table 5.3 Heat flux analysis at two extinction limits
6
List of Figures
Figure 1.1 Flame response for an adiabatic diffusion flame system-“S-curve”
(Nanduri, 2002). It shows the extinction and ignition conditions.
Figure 1.2 Radiative diffusion flame response-“flame isola” (Nanduri, 2002). It
shows the radiative extinction limit and the blow-off extinction limit.
Figure 1.3 Schematic of opposed-jet burner configuration.
Figure 1.4 Schematic of Tsuji type burner configuration.
Figure 2.1 Schematic of present experimental setup. R is the radius of curvature of
burner surface.
Figure 2.2 Diagonal view from underneath of the present burner, including a quasi-
one dimensional low-stretch diffusion flame.
Figure 2.3 Side-views of steady quasi-1D flames under various nitrogen dilution
levels (in terms of mole fraction). It shows the uniformity of the quasi-1D
flames at different conditions.
Figure 3.1 Experimental setup of Raman scattering system.
Figure 3.2 Schematic of Raman scattering setup.
Figure 3.3 Picture showing the laser beam (green line in the middle) and a flame
(bottom) along with a burner head (top) and scale. For this demonstration
flame, the nitrogen dilution is 75% and the fuel mixture injection speed is
1.00 cm/s.
Figure 3.4 Picture of optical collection system.
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Figure 3.5 Comparison of experimental and theoretical spectra at the “best-fit”
temperature of 1530±25K. The experimental data are taken at 11.2 mm
away from burner surface in a diffusion flame (75% nitrogen/ 25%
methane burning in air), with fuel mixture injection speed of 1.10 cm/s.
Figure 3.6 Raman spectra for the diluted methane/air diffusion flame. The dilution
level is 75% nitrogen and the fuel mixture injection speed is 1.10cm/s. (a)
Spectra at different locations marked in (b). (c) Nitrogen spectra for this
case at different locations.
Figure 3.7 Comparison of experimental spectrum and theoretical Spectra at different
temperatures for a diffusion flame with 40%N2 /60%CH4 burning in air.
The fuel injection speed is 0.30 cm/s and the position of measurement is
6.0 mm away from the burner surface.
Figure 3.8 Schematic of OH-PLIF system.
Figure 3.9 Schematic of laser sheet generation optics.
Figure 3.10 Flow chart of controlling system for OH-PLIF measurements.
Figure 3.11 Emissivity of the bronze porous plate calibrated by an imbedded
thermocouple.
Figure 3.12 Direct IR images taken from the bottom of the burner. (a) IR image after
the flame is extinguished. (b) IR image for the combination of flame and
burner surface.
Figure 3.13 Time variation of the burner surface temperature after the flame is
extinguished at time=0. Symbols are the mean temperature in the core
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region (cf., Fig. 3.12) obtained by the IR camera. Line denotes the result
using linear regression.
Figure 3.14 Side chemiluminescence image across the flame. Nitrogen dilution is 75%
and fuel mixture injection speed is 1.10 cm/s.
Figure 3.15 Normalized chemiluminescence distribution across the flame. Nitrogen
dilution is 75% and fuel mixture injection speed is 1.10 cm/s.
Figure 4.1 Configuration of the present quasi-one-dimensional diffusion flame.
Figure 4.2 Schematic of energy balance at the burner surface.
Figure 5.1 (a) OH-PLIF image of a steady quasi-1D flame. (b) Comparison of OH-
PLIF intensity profiles at varying radial locations.
Figure 5.2 Steady diffusion flame standoff distance, OH-FWHM thickness, and
burner surface temperature as a function of fuel mixture injection speed:
(a) 25% CH4/75% N2 and (b) 60% CH4/40% N2.
Figure 5.3 Flammability and instability diagram for the present low-stretch methane
diffusion flames. Nitrogen dilution represents the nitrogen mole fraction
in fuel mixture. Shaded regions represent the flame instability conditions.
Figure 5.4 Schematic of the thermocouple configuration used in this study.
Figure 5.5 Comparison of thermocouple-measured temperature distributions at
different fuel mixture injection speeds for the 60%CH4/40%N2 mixture.
Figure 5.6 Five selected cases for detailed Raman scattering measurement.
Figure 5.7 Averaged (5000 shots) Raman spectra at varying distance from the burner
surface for Case A (40% nitrogen dilution and 0.55 cm/s fuel mixture
injection speed).
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Figure 5.8 Averaged (5000 shots) Raman spectra of nitrogen at varying distance from
the burner surface for Case A (40% nitrogen dilution and 0.55 cm/s fuel
mixture injection speed).
Figure 5.9 Temperature distribution across the flame for Case A. Both thermocouple-
measured and Raman-measured data are included. The shaded region
shows the observed bright luminous zone.
Figure 5.10 Temperature distribution across the flame for Case B. Both thermocouple-
measured and Raman-measured data are included. The shaded region
indicates the observed bright luminous zone in the flame.
Figure 5.11 Temperature distribution across the flame for Case C. Both thermocouple-
measured and Raman-measured data are included. The shaded region
shows the observed bright luminous zone.
Figure 5.12 Temperature distribution across the flame for Case D. Both thermocouple-
measured and Raman-measured data are included. The shaded region
shows the observed bright luminous zone.
Figure 5.13 Temperature distribution across the flame for Case E. Both thermocouple-
measured and Raman-measured data are included. The shaded region
shows the observed bright luminous zone.
Figure 5.14 (a) Comparison of the Raman-measured temperature profiles for Cases A
and B (40% nitrogen dilution). (b) OH-PLIF and chemiluminescence
profiles for Cases A and B. Symbols denote the OH concentration profiles,
while lines represent the chemiluminescence profiles.
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Figure 5.15 (a) Comparison of the Raman-measured temperature profiles for Cases C,
D and E (75% nitrogen dilution). (b) OH-PLIF and chemiluminescence
profiles for Cases C, D and E. Symbols denote the OH concentration
profiles, while lines represent the chemiluminescence profiles.
Figure 5.16 Raman spectra of Case A (40% nitrogen dilution, 0.55 cm/s fuel mixture
injection speed) at five different locations away from the burner surface:
3.7 mm, 7.1 mm, 11.2 mm, 12.1 mm, and 14.5 mm.
Figure 5.17 Raman spectra of Case B (40% nitrogen dilution, 0.30 cm/s fuel mixture
injection speed) at five different locations away from the burner surface:
3.0 mm, 5.2 mm, 8.0 mm, 10.9 mm, and 12.5 mm.
Figure 5.18 Raman spectra of Case C (75% nitrogen dilution, 1.30 cm/s fuel mixture
injection speed) at five different locations away from the burner surface:
3.0 mm, 9.6 mm, 12.5 mm, 14.4 mm, and 16.3 mm.
Figure 5.19 Raman spectra of Case D (75% nitrogen dilution, 1.10 cm/s fuel mixture
injection speed) at five different locations away from the burner surface:
3.1 mm, 8.9 mm, 11.2 mm, 13.3 mm, and 16.0 mm.
Figure 5.20 Raman spectra of Case E (75% nitrogen dilution, 0.75 cm/s fuel mixture
injection speed) at five different locations away from the burner surface:
3.3 mm, 7.1 mm, 9.0 mm, 11.1 mm, and 14.7 mm. Note that only the
spectra in the wavelength range of 560 nm-610 nm are shown in this
figure.
Figure 5.21 Diagram of flammability and instabilities. Nitrogen dilution represents the
mole fraction of nitrogen in the fuel mixture.
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Figure 5.22 Summary of multi-dimensional flame patterns observed in the present
study. Direct images show the view from underneath the burner.
Figure 5.23 OH-PLIF sequences showing the evolution of a single stripe or hole.
Figure 5.24 OH-PLIF sequences showing the evolution of multiple stripes.
Figure 5.25 Evolution of a periodic hole.
Figure 5.26 Comparison of computed temperature profiles for different stretch rates
with ξ =0.
Figure 5.27 Comparison of computed temperature profiles for different nominal fuel
-1 injection speeds with ab=2.25 s and ξ =0.
Figure 5.28 Comparison of computed temperature profiles at various burner heat loss
levels for fixed stretch rate and nominal fuel injection speed. Nitrogen
dilution level is equal to that of Case A.
Figure 5.29 Comparison of experimental and computational temperature profiles for
(a) Case A and (b) Case B.
Figure 5.30 Comparison of experimental and computational temperature profiles for
(a) Case C, (b) Case D, and (c) Case E.
Figure 5.31 Calculations performed near the upper extinction limit for a given stretch
rate 2.25 s-1. The maximum flame temperature is plotted for the case with
ξ =0.57, at two different nominal fuel injection speeds: 0.95 cm/s and 1.15
cm/s.
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Figure 5.32 Calculations performed near the lower extinction limit for a given stretch
rate 2.25 s-1 and ξ =0.91. The flame peak temperature and surface
temperature, as well as the flame location based on the location of peak
temperature, are plotted as a function of nominal fuel injection speed.
Figure 5.33 (a) Profiles of temperature and heat release rate for a flame near the upper
extinction limit with 87.9% nitrogen dilution and 1.15 cm/s nominal fuel
injection speed. (b) Profiles of radiative heat fluxes for this case.
Figure 5.34 (a) Profiles of temperature and heat release rate for a flame near the lower
extinction limit with 40% nitrogen dilution and 0.157 cm/s nominal fuel
injection speed. (b) Profiles of radiative heat fluxes for this case.
Figure A.1 Energy diagram of Raman scattering by molecules. v is the vibrational
quantum number. The solid lines denote the different rotational energy
levels. h is the Plank constant, ν is frequency.
Figure B.1 Energy level diagram for a simple two-level LIF case.
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ACKNOWLEDGMENTS
No words can express my gratitude to Professor Chih-Jen Sung, my advisor, for his support, guidance, expertise and patience during the course of my degree. I am so fortunate and extremely grateful to be a student and friend of Prof. Sung.
I’m also indebted to Prof. T’ien for his numeral precious advices. I appreciate the help of the other advisory committee members of my dissertation’s defense: Prof.
Kamotani and Prof. Martin.
All the members of the computational combustion lab gave me a lot of direct help and suggestions during this work. Additionally, I also want to thank Chris Mento, Megan
Browdie, and Yu Qiao Qu for their assistance in the experiments.
Especially, I want to thank Dr. Ibarreta for his great help on the experimental setup and image processing. The discussions with him on every detail make this work more comprehensive.
I appreciate Mr. Richard Pettegrew of National Center for Microgravity Research and
Dr. Steven Schneider of NASA Glenn Research Center for the assistance in the measurements and calibration involving the IR camera, as well as the useful discussions with Professor Volker Sick of University of Michigan on PLIF measurements.
Finally, I would like to acknowledge the financial support from the National Science
Foundation and the National Center of Microgravity Research.
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List of abbreviations
Symbols Quantities SI Units
a Mixed-convection stretch rate s-1
-1 ab Buoyancy-induced stretch rate s
-1 af Forced stretch rate s
2 Af Focal area of the laser beam m
-1 A21 Einstein coefficient for spontaneous emission s
-1 b12 Rate constant (coefficient) of absorption s
-1 b21 Rate constant (coefficient) of stimulated emission s
B Einstein coefficient for the stimulated emission m3/(J s2) c Speed of light m/s cp Specific heat at constant pressure kJ/(kg K) d Diameter of the bead of the thermocouple m dspot Spot diameter m d0 Initial diameter of the laser beam m
D Damköhler number N/A
Ei Energy at the i-th Energy state kJ f Focal length m f’ Derivative of the modified stream function N/A fw Non-dimensional fuel injection speed with “–” sign N/A
F Fluorescence signal power W g Gravitational acceleration m/s2
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Gr Grashof number N/A h Plank constant J s h Specific enthalpy kJ/kg
H Enthalpy kJ
2 Hw Burner heat loss flux W/m
I Total number of species N/A
I Intensity of Raman scattering W/m2
2 Iν Spectral radiation intensity (W s)/(m sr)
2 Iν Incident laser spectral irradiance (W s)/(m sr)
sat Saturation spectral irradiance (W s)/(m2 sr) Iν J Rotational quantum number N/A k Conductivity W/(m K) kB Boltzman constant kJ/K l Axial length along the laser beam m
L Length of the computational domain m
Ls Lens N/A m Mass kg
M Molecular weight kg/kmol
M Mirror N/A ni Number of molecules at the i-th energy state Ei N/A
nˆw Normal vector from the burner surface N/A
N Total number density of molecules m-3
Ni Population at the i-th energy level N/A
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Nt Total number of molecules N/A
N0 Total population N/A
Nu Nusselt number N/A p Pressure N/m2
Pr Prandtl number N/A
Q Radiative heat flux W/m2
2 Qa Absorbed radiative heat flux W/m
2 Qcond Heat conduction flux W/m
2 Qe Emitted radiative heat flux W/m
2 Qnet, w Net radiation flux out of the burner surface W/m
-1 Q12 Collisional excitation rate s
-1 Q21 Collisional quenching rate s
R Radius of the cylindrical/spherical burner or solid fuel m
R Rate coefficient s-1
Re or Re Reynolds number N/A
-3 -1 RF Fluorescence rate m s
Ri Richardson number N/A
Ru Universal gas constant kJ/(kg K) s and s’ Position variables along a path m t Time s tp Laser pulse duration s
T Temperature K
TA Adiabatic flame temperature K
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Te Ambient temperature, K
u Velocity component in x direction m/s
u Pressure path length. Pa m
U The forced oxidizer flow velocity for Tsuji’s burner m/s
v Velocity component in y direction m/s
v Vibrational quantum number N/A
vf Nominal fuel mixture injection speed m/s
vF Fuel mixture injection speed at the burner surface m/s
V or V Characteristic buoyant velocity m/s
V Fuel mixture mass flux in the y direction kg/(s m2)
2 VF Averaged fuel mixture mass flux at the burner surface kg/(s m )
Viy Diffusion velocity in the y-direction for the i-th m/s species x Tangent (radial) coordinate m
Xi Molar fraction N/A
y Transverse (axial) coordinate m
Y Mass fraction N/A
Yi,e Ambient mass fraction of the i-th species N/A
Greeks
β Thermal expansion coefficient K-1
βν Mean line width to spacing ratio N/A
γν Line half-width m
δ Thickness of boundary layer m
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δν Mean line spacing parameter m
∆ Change or difference of the quantity N/A
ε Emissivity N/A
εwν Spectral emissivity of the burner surface N/A
κ Geometric factor N/A
κν is the mean absorption coefficient
λ Thermal conductivity W/(m K)
λ Wavelength of the laser m
µ Dynamic viscosity coefficient kg/(m s)
ν or ν Momentum diffusivity (Kinetic viscosity) m2/s
ν Frequency s-1
ξ Burner heat loss fraction N/A
ρ Density kg/m3
3 ρf Fuel mixture density at far upstream kg/m
3 ρe Ambient air density kg/m
σ Stefan-Boltzman constant W/(m2 K4)
τ Time or time constant s
τν Spectrally averaged transmittance N/A
ω Molar rate of production kmol/(m3 s)
Ω Solid angle N/A
Φ Froude number N/A
χ i Incoming mass flux fraction for the i-th species N/A
χ2 The square of the residuals N/A
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ψ Direction cosine N/A
Subscripts
+ Positive y direction
- Negative y direction
A Property of air free stream
B Blackbody
B Blow-off condition comp Computational results
D Diameter of the bead of the thermocouple e Boundary on the air side, i.e. the ambience (y=L) e Equivalent band parameter. exp Experimental results f Property at far upstream, i.e. at ambient condition f Final state
F Gas phase quantities at the burner surface (y=0)
G Corrected gas phase temperature i Species i Initial state ig Property at ignition point
J Grid number
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L Incident laser max Maximum value of the variable min Minimum value of the variable net Net or total value of the property ss Steady state
S Stokes light
R Quenching condition by radiative heat loss
R Raman scattering
TC Thermocouple w Property in the solid phase at the burner surface (y=0)
X X-component of the vector
ν Property inside the spectral range (narrowband), ∆ν.
∞ Property of the free stream
0 Initial condition
Superscripts
- Bar over symbol denotes the mean value of the variable + Positive y direction
- Negative y direction
* Excited state for radicals
* Internal condition, chosen from the existing grid points of a convergent solution e Free stream or ambient property
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ext Extinction ign Ignition max Maximum
0 Initial value of the variable
0 Prior to the laser excitation
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An Experimental and Computational Study of Burner-Generated Low Stretch Gaseous Diffusion Flames
Abstract by
BAI HAN
The study of low-stretch flames is essential for the fundamental understanding of the
flame radiation effects on flame response and extinction limits. Low-stretch flames are
also relevant to fire safety in reduced gravity environment and large buoyant fires, where
localized areas of low stretch are attainable. An experimental study of the dynamics and
structure of low-stretched diffusion flames is carried out by using various advanced
optical diagnostics, along with a quasi-one-dimensional simulation with detailed
chemical kinetics, thermodynamic/transport properties, narrowband radiation model, and
gray surface radiation treatment.
In the present study, ultra-low stretch flames are established in normal gravity by
bottom burning of a methane/nitrogen mixture discharged from a porous spherically
symmetric burner of large radius of curvature. With the radius of curvature of ~400 cm,
quasi-one-dimensional diffusion flames of equivalent stretch rate as low as ~2 s-1 can be stabilized. Using this novel burner, the current study aims to improve our understanding of diffusion combustion, by expanding the available experimental data regarding the structure and response of diffusion flames to the previously-unexplored low-stretch rate regime. Several advanced non-intrusive optical diagnostics techniques are used to study
23
the flame structure. Gas phase temperatures are measured by Raman scattering, while the
burner surface temperatures are measured by infra-red imaging. OH-PLIF and
chemiluminescence imaging techniques are used to help characterize the reaction zone of
the flames.
A flame stability diagram mapping the response of the ultra-low stretch diffusion
flame to varying fuel injection speed and nitrogen dilution is explored. In this diagram,
the sooting and extinction limit boundaries are identified. Various near-extinction multi- dimensional flame patterns under different experimental conditions are observed, and their evolutions are studied using direct chemiluminescence and OH-PLIF imaging.
The experimental results on quasi-one-dimensional flame structure allow direct comparison with a detailed quasi-one-dimensional numerical model including the radiative interactions of flame and gray surface. The numerical modeling is demonstrated to be able to simulate the low-stretch flame structure. Using current modeling, the extinction limits under different conditions are also examined. The results are consistent with experimental observations.
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CHAPTER 1
INTRODUCTION
The study of combustion processes is motivated by its essential importance to
human’s life. Knowledge of fire and combustion has been built up since the very beginning of our civilization history. In modern societies, combustion is still the primary technology for many energy sources currently available, for example, heating, electric power, etc. It is not only playing an important role in everybody’s daily life, such as in cooking and transportation, but also widely used in many chemical processing and material synthesis technologies.
From the point view of chemistry, combustion process is a self-supported, exothermic reaction. The physical processes involved are principally transport of mass and energy.
The species involved in combustion process are fuel, oxidizer, intermediates, and final products, while the energy is released as heat and light from the flame zone.
One fundamental distinction in combustion is between premixed and non-premixed
(diffusion) systems. In contrast to the premixed flame in which the fuel and oxidizer are
mixed before entering the reaction zone and initiation of the chemical reaction, in the
non-premixed diffusion flame, fuel and oxidizer enter separately and diffuse into the
flame zone where reaction is occurring concurrently. Reactants usually mix together in a
reaction zone through molecular and turbulent diffusion (Glassman, 1996). Most practical
systems fall in the category of diffusion flames. Some examples of direct applications of
diffusion flames are candle flames, wood (forest) fires, diesel engines and fire spread. In
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classic diffusion flames, the mixing rate of fuel and oxidizer is generally slow compared to the chemical reaction rate and, thus the transport (mixing) process, instead of the chemical kinetics, is the major rate-controlling process. However, chemical kinetics are important in extinction and ignition of diffusion flames.
1.1 Diffusion Flame Structure and Response
Unlike premixed flames, diffusion flames do not have a burning velocity which is the intrinsic characteristic of the premixed flame system. Naturally, investigations of diffusion flames have been focused on the flame structure, flame dynamics, and the critical conditions of flame responses, such as ignition and extinction. The quantitative knowledge of detailed diffusion flame structure and flame response under different conditions can help us have a better understanding of the combustion processes. It has broad applications, including the design of combustion facilities, fire/explosion safety, combustion efficiency improvement, and pollution reduction.
As early as in 1928, Burke and Schumann carried out a seminal theoretical work on laminar diffusion flame. By using the “flame sheet model”, where chemical reaction rate is considered to be infinitely fast thereby the reaction zone becomes infinitely thin, they successfully analyzed the problem of fuel issuing from a cylindrical tube into concurrent airflow. It was shown that the flame sheet model is one useful tool for studying diffusion flames in certain extents. Since then, by employing this model, researchers have learned much about various laminar diffusion flames systems. However, this model has inherent limitations on the study of flame structure and flame response. In reality, the actual
26
reaction zone of a diffusion flame always has a finite thickness and the effect of finite rate chemistry cannot be neglected in those cases where the system residence time is comparable with chemical reaction time. So the flame sheet model cannot be applied to predict the detailed flame structure and certain flame responses, such as flame extinction.
Therefore, further quantitative investigations of the detailed structure of the diffusion flame should consider the finite-rate chemical kinetics and detailed thermodynamic/transport properties. In order to study the flame response, an appropriate controlling parameter is necessary to take into account the finite reaction time and residence time. The choice of the controlling parameter depends on the configuration being analyzed.
In classical theoretical treatments(Fendell, 1965; Liñán, 1974; Williams, 1985), the flame response for an adiabatic system is obtained by plotting a steady state solution such as the maximum temperature (Tmax) versus the Damköhler number, which is defined as the ratio of the characteristic gas residence time scale to the characteristic chemical reaction time scale. One example of the resulting “S-curve” is shown in Fig. 1.1.
27
TA
T1 UPPER BRANCH
Tmax
T2 MIDDLE BRANCH
LOWER BRANCH
T0 T3
Di Dext Dign Damköhler Number
Figure 1.1 Flame response for an adiabatic diffusion flame system-“S-curve” (Nanduri, 2002). It shows the extinction (Dext) and ignition (Dign) conditions.
It is seen from Fig. 1.1 that multiple solutions are possible due to the non-linearity of
the governing equation system. The non-monotonic variation of the maximum
temperature with Damköhler number in this regime gives three branches of flame
response. At the upper branch, a solution T1 for a given Damköhler number Di represents
the “stable” solution. A solution T2 in the middle branch is the “unstable” solution, and a solution T3 occurs in the lower “frozen” branch. However, only the solution along the
upper branch is of interest since the upper branch defines the actual “stable” flame
solution with a maximum temperature close to the adiabatic flame temperature of the system. Beyond the turning point of the convergence of the middle branch and the upper branch, namely when the Damköhler number is decreased below Dext, the only stable
solution that can be obtained is in the lower “frozen” branch. Hence this turning point is
28
referred as the extinction limit (Dext). Likewise, the other turning point near the
convergence of the lower branch and middle branch is referred as the ignition limit (Dign).
When the Damköhler number approaches Dext, the characteristic flow time becomes
too small as compared to the chemical reaction time and hence flame extinguishes. This
take places at low Damköhler number, and is called the “blow-off” extinction for this
system, which is denoted as Dext in Fig. 1.1. On the other hand, as Damköhler number becomes larger and larger, it refers to the limit of fast chemistry. At this limit a flame is
present with a maximum temperature close to the adiabatic flame temperature (TA) of the adiabatic system.
However, the practical flames are non-adiabatic due to the flame radiation and/or the presence of surface radiation. These inherent heat losses can reduce the maximum temperature of the combustion system, and consequently, induce flame extinction (e.g.,
Liu and Rogg, 1991; Sohrab and Williams, 1981).
Furthermore, because flame radiation is a volumetric phenomenon, the extent of radiative heat loss increases with increasing flame dimension. This is especially true for the flame with higher Damköhler number, because it leads to a thicker flame. When such a radiative heat loss becomes too large as compared to the heat generation by reaction, the reduction in temperature can cause extinction at high Damköhler number. This kind of extinction caused by excessive radiative heat loss is referred as “quenching” extinction. Therefore, in addition to the blowoff turning point, several recent studies (e.g.
T’ien, 1986; Chao et al., 1990) proposed a second extinction turning point in the one- dimensional (1D) flame response where the flame extinguishes due to the radiative heat
29
loss. Thus, the adiabatic “S-curve” response shown in Fig. 1.1 has to be modified if the
heat loss is considered in the combustion process, as shown in Fig. 1.2.
TA UPPER BRANCH T1
MIDDLE BRANCH
Tmax
T2
LOWER BRANCH
T0
T3
DB Di DR
Damköhler Number
Figure 1.2 Radiative diffusion flame response-“flame isola” (Nanduri, 2002). It shows the radiative extinction limit (DR) and the blow-off extinction limit (DB).
In Fig. 1.2 the radiative flame response, so-called flame isola, in which three branches
similar to the adiabatic “S-curve” flame response (Fig. 1.1) are displayed. In addition to
the blow-off extinction limit (DB), there is another extinction point in the high Damköhler
number region (DR), which is induced by the radiative heat loss.
Experimentally it has been observed by many researchers that there does exist a
“blow-off” extinction limit at low Damköhler number where the flame extinguishes due
to short residence time (e.g. Tsuji, 1982). However, experimental verifications on the extinction limit in the high Damköhler number region is relatively meager due to
30
difficultly of experimental setup under normal gravity. This issue will be discussed in detail later.
1.2 Effects of Stretch on Diffusion Flames
Since a combustion system is practically affected by the hydrodynamic aspects of the
flow, the effects of the flow field on flame is an essential part of combustion research.
The influence of hydrodynamics on the flame can be manifested in various forms, such as flow non-uniformity, flame curvature, and flame unsteadiness. These various influences have been collectively termed as stretch effects (Matalon, 1983; Chung and Law, 1984;
Sung, 1994), and a flame that is affected by one or more of these factors is said to be
stretched. Furthermore, in the stretched diffusion flames, the flow time scale or residence time of reactants can be determined by stretch rate.
One attractive feature of the flame stretch concept is that it can be applied locally and instantaneously in a flame. It is been recognized that in many situations the turbulent diffusion flames can be described as being composed of wrinkled, moving, laminar flame segments, or “flamelets” (Williams, 1985). This feature of the flamelets enables much of laminar flame structural analysis to be extended to the turbulent diffusion flame.
1.2.1 Flame Stretch
The effects of flame stretch have been of interest to combustion research for decades.
Since Karlovitz et al. (1953) first introduced the concept of flame stretch to study the
31
extinction, and stabilization in premixed turbulent flames, numerous studies on stretched
flames have been conducted.
Stretch rate is commonly defined as the logarithmic rate of increase of the area of an
infinitesimal element of flame surface with respect to time (Williams, 1985).
Consequently it has the unit of inverse second. It is further shown that stretch rate can be
equivalently given by the tangential gradient of the flow velocity over the flame surface
at which it is evaluated. This means that the flame surface suffers stretch when it has a
non-uniform tangential velocity, and it provides an alternate interpretation of the flame stretch (e.g., Matalon, 1983; Chung and Law, 1984; Sung, 1994).
Since the reciprocal of the stretch rate characterizes the flow time or residence time in a combustion system, Damköhler number and stretch rate are inversely proportional to each other. Thus, stretch rate is essentially related to the important controlling parameter,
Damköhler number, introduced in Section 1.1. Therefore, the concept of flame stretch was applied successfully to many practical flame phenomena, such as flame extinction, flame stabilization, and flame-front instability (e.g. Williams, 1985; Law, 1988).
Experimentally, structures of laminar diffusion flames have been studied for decades, especially by using a relatively simple configuration--- counterflow diffusion flame,
which will be addressed in the following section. It was proven by those earlier
investigations that structural study of diffusion flame is prefered in combustion science
due to its relatively thicker flame zone compared to the premixed flames with fast flame kinetics under normal pressure (Tsuji, 1982).
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1.2.2 Counterflow Diffusion Flames
To investigate diffusion flame structures it is desirable to establish a simple configuration that can be easily studied in detail. The counterflow diffusion flame represents such a configuration which can provide a quasi-one-dimensional diffusion
flame. Although counterflow configuration is widely used for gaseous fuels, this
approach can be readily applied to the diffusion flames with condensed phase (liquid or
solid) fuel.
Since the comprehensive review of Tsuji (1982), the counterflow configuration has been widely applied to study the dynamics and response of diffusion flames (e.g. Smooke et al., 1986, 2000; Puri et al., 1987; Sung et al., 1995; Atreya et al., 1996; Brown et al.,
1997). The relative simplicity of this flow field makes feasible the direct comparison of experiment and theoretical models. The level of sophistication of the investigations has
advanced to the point that discrepancies between the models and experiments have been
used to guide modifications to the fundamental properties used in the simulation, through
a combination of improved computational and diagnostic capabilities.
1.2.2.1 Counterflow Facilities
Based on the experimental burner setup, there are two types of counterflow facilities:
(A) Counterflow diffusion flame established between two opposed jets or
converged nozzles, one for fuel and the other one for oxidizer;
33
(B) Counterflow diffusion flame established in the forward stagnation point
region near a porous burner surface, which is the so-called Tsuji burner
(Tsuji and Yamaoka, 1967, 1969, 1971; Ishizuka and Tsuji, 1981; Tsuji,
1982).
1.2.2.1.1 Opposed-Jet Burner
Fuel flow
Flame Zone
Air flow
Figure 1.3 Schematic of opposed-jet burner configuration.
For opposed-jet flames, the fuel and oxidizer (normally air) are injected from two opposed converging nozzles or jets against each other. As shown in Fig. 1.3, the flame is established between those two jets and near the stagnation plane. The resulting diffusion flame can be located on either the fuel side or oxidizer side of the stagnation plane,
34
depending on the composition of the fuel and oxidizer. In addition, the imposed stretch rate depends on the impinging jet velocities and the separation distance between the two opposing jets.
1.2.2.1.2 “Tsuji” Burner
Figure 1.4 shows the “Tsuji” burner configuration. In this configuration, the diffusion flame is established in the forward stagnation region of a porous cylindrical/spherical burner immersed in a uniform oxidizer flow with given forced flow velocity. The imposed stretch rate is simply the forced-velocity gradient and can be varied by varying forced flow velocity (U) of oxidizer or the burner radius of curvature R (Tsuji and
Yamaoka, 1967, 1969, 1971; Ishizuka and Tsuji, 1981; Tsuji, 1982).
Gaseous Flame Fuel U
Oxidizer R
Figure 1.4 Schematic of Tsuji type burner configuration.
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1.2.2.2 Studies of Counterflow Diffusion Flames
In this section, some significant progresses in study of counterflow diffusion flames are briefly reviewed.
1.2.2.2.1 Steady Counterflow Diffusion Flames
Liñán (1974) first systematically studied the influence of stretch on counterflow diffusion flame structure and extinction. This definitive analysis of quasi-one- dimensional diffusion flames with one-step irreversible reaction yields explicit expressions for ignition and extinction for this configuration, and shows that extinction is achieved with increasing stretch. Since then, diffusion flames in a stagnation-point region have been intensively investigated by a number of theoretical and experimental studies
(e.g., Krishnamurthy et al., 1976; Seshadri and Williams, 1978; T’ien et al., 1978; Sohrab et al., 1982; Chung and Law, 1983; Dixon-Lewis et al., 1984; Puri and Seshadri, 1986;
Smooke, et al., 1986; Keyes and Smooke, 1987; Peters and Kee, 1987; Seshadri and
Peters, 1988; Chelliah et al., 1990; Papas et al., 1994; Sung et al., 1995; Maruta et al.,
1998; Rhatigan et al., 2002). In these studies, a wide range of aspects of diffusion flames have been investigated, including the flame structure, stability map, ignition and extinction criteria, etc.
One of the most significant observations of structural studies of stretched counterflow diffusion flames is the relatively thicker quasi-one-dimensional flame in this configuration. It was found that the zone of heat release is about ten times wider than
36
would be expected of an equivalent premixed flame (e.g. Pandya and Weinberg, 1964).
Furthermore, scaling method (Williams, 1985) showed that the flame thickness of diffusion flame is inversely proportional to the square root of stretch rate. It is implied that the detailed structural study is facilitated for low stretch diffusion flames than high
stretch diffusion flames. Therefore, the planar counterflow diffusion flame, especially the
low stretch diffusion flame, seems to be a very attractive flame configuration for the
experimental study of flame structure. This is also one important motivation of current
study.
Among those earlier experimental studies on counterflow diffusion flames, a number
of investigations have been done using Tsuji type burner (Tsuji and Yamaoka, 1967,
1969, 1971; Ishizuka and Tsuji, 1981; Tsuji, 1982). For example, the dilution limits
leading to extinction for various fuels have been investigated systematically (Tsuji,
1982). It was found that as the fuel concentration, which is defined as the mole fraction of
fuel in the fuel/inert mixture, is decreased, the flame luminosity becomes weak and
finally the flame extinguishes. There is a critical fuel concentration for a burner with
given geometry (i.e., stretch rate), below this fuel concentration the flame cannot be
stabilized, no matter how large is the mixture ejection velocity. Furthermore, it was also
pointed out by Tsuji and coworkers that this critical fuel concentration decreases
monotonically with stretch rate. Although their experiments did not extend to extremely
low stretch rates, their results seem to approach a constant limiting fuel concentration as
the stretch rate is extrapolated to zero.
It was also found that (Tsuji and Yamaoka, 1967, 1969; Tsuji, 1982) for a
hydrocarbon mixture, when air flow rate is very small and fuel injection speed is
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comparatively large, the flame thickness increases remarkably, and the flame shows a
luminous yellow inner zone (fuel side) and a blue outer zone (air side). The luminous yellow zone is the sooting layer of this type of diffusion flame. Consequently, the conditions leading to sooting flame, or so-called sooting limits, can be investigated using
the Tsuji type burner.
However, in those earlier literatures on the stagnation-point diffusion flames, the
effects of radiative heat loss on flame extinction, which is introduced in Section 1.1, have
not been considered as being remarkable, particularly when the stretch rates are
sufficiently high.
1.2.2.2.2 Instabilities in Counterflow Diffusion Flames
Contrast to the one-dimensional planar steady diffusion flame, the multi-dimensional
flame patterns are labeled as multi-dimensional flame instabilities in this study. “Cellular
flame” structures and separated individual “flamelets”, are examples to this category.
Near-extinction conditions are also shown to facilitate such flame instabilities. Since
quenching and re-ignition occurs at those edges of flamelets, these flame instabilities are
also related to the study of the “edge-flame” (Buckmaster, 2002).
There are some physical mechanisms may be responsible for the intrinsic flame
instabilities, such as buoyant effect, imbalance of heat and mass transport, and heat losses
(Williams, 1985). In particular, the buoyant effect can led to the so-called “Rayleigh-
Taylor instability” or “Bénard cells” (Rayleigh, 1916; Ostrach, 1964). With regard to a
horizontal layer of fluid heated from below, the fluid could result in a cellular type of
38
motion, either roll-shaped cells in enclosure with top cover plate or hexagonal cells in container without top plate (Burmeister, 1982).
In combustion systems, it was also found that the diffusional-thermal effects (e.g.
Turing, 1952; Shivashinsky, 1977; Cheatham and Matalon, 1996) play an important role for triggering instabilities. This type of instability is triggered by an imbalance between the diffusion of heat and the diffusion of species in the flame zone. For instance, in the presence of non-unity Lewis number reactants, the reactant of high-diffusivity diffuses preferentially to the reaction zone, thereby modifies the flame temperature. This effect can also lead to the reduction of flame temperature and local quenching (Kim et al.,
1996).
Other patterns of instability phenomena observed in experiments include fingering in smoldering (Olson et al., 1998), flame spread over a thin solid (Wichman and Olson,
1999), ceiling fires (Buckmaster, 2002), and rotating flames in von Karman swirling flows (Nayagam and Williams, 2000). However, it is unclear whether these kinds of multi-dimensional phenomena can be diffusional-thermal in nature.
It is not surprising that more theoretical and experimental efforts (e.g. Shivashinsky,
1977; Joulin and Clavin, 1979; Williams, 1985; Bechtold and Matalon, 1987; Sung et al.,
2002) are for the premixed flame instability than those for diffusion flame instability, because the coupling between the reaction and diffusion processes is much stronger in premixed flames than in diffusion flames. In general, it is found that the diffusional- thermal instabilities in premixed flames can be manifested through non-equidiffusion, non-adiabaticity, flame stretch, and near-extinction conditions (Sung et al., 2002).
39
Even though there are only few studies on the instabilities in diffusion flames,
diffusion flame instability phenomena have been identified by several experimental
studies (e.g. Garside and Jackson, 1953; Dongworth and Melvin, 1976; Ishizuka and
Tsuji, 1981; and Chen et al., 1992). In these literatures the observations of the diffusion
flame instability with negligible buoyancy effect were reported near the high stretch
“blow-off” conditions. Most of those experiments employed non-unity Lewis number fuels to demonstrate the diffusion-thermal effects, such as the (diluted) hydrogen as the fuel to approach the lower Lewis number (Ishizuka and Tsuji, 1981). Another recent study of a counterflow slot burner experiment by Kaiser et al. (2000), demonstrated the existence of a unique non-planar “flame tubes” with diluted hydrogen burning in air. As the Damköhler number was decreased by reducing the flame strength or by increasing the stretch rate, a two-dimensional flame transition from planar flames to moving flame tubes was observed in the study of Kaiser et al. (2000). Further decrease in the Damköhler number produced stationary flame tubes followed by extinction.
Some theoretical studies (Kirkby and Schmitz, 1966; Kim et al., 1996; Cheatham and
Matalon, 1996, 2000; Kim and Lee, 1999) confirmed that the diffusional-thermal instabilities also play an important role in diffusion flames, especially when the system is close to the extinction conditions. It was also found in these studies that the instability developed for non-unity Lewis number system was enhanced in the presence of heat loss.
Furthermore, Baliga and T’ien (1975) theoretically studied the possibility of near-limit oscillation for the unity Lewis number system with radiative heat loss from propellant surface. Kim (1997) showed analytically the diffusional-thermal instability in diffusion flames for Lewis number close to unity.
40
In closing this section we have to point out that, more experimental data need to be
collected particularly at the low stretch rates for further analyses of the diffusion flame
instability phenomena.
1.3 Studies of Low Stretch Diffusion Flame
1.3.1 Low Stretch Diffusion Flame Behavior
As discussed in the previous sections, a large number of experimental studies on gaseous diffusion flames have been performed under relatively high stretch rates.
Research on low-stretch flames has not been fully exploited, mainly due to the difficulty in establishing such flames in normal gravity. Recent studies have shown that the low- stretch flames can behave differently from the high-stretch ones both qualitatively and quantitatively (T’ien, 1986; Frate et al., 2000; Rhatigan et al., 2002). For example, as shown in Fig. 1.2, flame can be extinguished by excessive radiative heat loss at higher
Damköhler number (lower stretch rate).
Ohtani et al. (1983) studied the steady stagnation point flow near a cylindrical solid fuel sample including surface radiation and finite rate kinetics. They found that the flame temperature decreases and flame standoff distance increases, as the diameter of the cylinder increases, i.e. the stretch rate decreases for a given flow velocity.
The possibility of an upper and a lower limit of diffusion flames in term of extinction stretch rate was proposed by T’ien (1986). From his numerical solution of stagnation- point flow with surface radiation, an extinction limit was identified when the flame
41
stretch rate becomes sufficiently small. This limit occurs as a result of flame temperature
reduction when the rate of radiative heat loss from the solid fuel surface becomes
substantial compared with the rate of combustion heat release. Note that the complicated
flame-surface interaction is a vital part of the condensed-phase system since the fuel
pyrolysis process is determined by the heat transfer from the gas phase (cf. Kinoshita and
Pagni, 1981; Olson and T’ien, 2000).
Furthermore, the importance of gas phase radiative heat loss at low stretch rates has been recognized by a number of researchers. Negrelli et al. (1977) theoretically studied flame radiation in a methane/air diffusion flame. A non-gray wide-band radiation model and infinite fast kinetics are used in their modeling. The numerical results showed a good agreement with the experimental study with a porous burner in this work. They found a critical minimum fuel injection velocity for extinction limit. As the fuel injection velocity
increases, the flame moves away from the surface with an elevated flame temperature.
The total radiative heat loss from the surface was found to decrease with increasing fuel
injection velocity, due to the decreases in the incoming gaseous radiative heat flux and
conductive heat flux from the flame. Furthermore, the optical depth was determined to be
neither thick nor thin for all those blue flames. CO2 and H2O were found to contribute
approximately 64% and 34% of radiative interaction, respectively. The remainder
radiative interaction was due to methane.
The problem of diffusion flame extinction induced by flame radiation was also
analyzed by Sohrab et al. (1982) for a counterflow configuration. A criterion of flame
extinction limit was presented in their study, though the turning point of the extinction limit caused by radiative heat loss was not explicitly described.
42
Subsequently, Platt and T’ien (1990) and Daguse et al. (1996) suggested that the
existence of extinction caused by the radiative heat loss from the gas phase. Daguse et al.
(1996) also noted that the radiation reduces flame temperature, flame width, and production of minor species. These effects were more pronounced at low stretch rates,
where extinction was caused by the excessive radiative heat losses compared to chemical
heat release.
Chao et al. (1990) studied the structure and extinction characteristics of diffusion
flames with flame radiation by using a droplet combustion model. Similar to the
counterflow diffusion flames, they found that steady droplet burning is possible only for droplet sizes within certain range. Extinction of smaller droplets is caused by finite-rate kinetics while extinction of larger droplets is caused by excessive radiative heat loss.
Some numerical studies on stagnation point diffusion flames using non-gray narrowband model and detailed kinetics were carried out recently (e.g. Bedir, 1998; Shih et al., 1999; Frate et al., 2000; Rhatigan et al., 2002). These studies found that the diffusion flames can be unusually thick due to the low stretch rates. The effects of gas phase radiation were also evaluated in these studies. It was also suggested in these studies that the accurate narrowband gaseous radiation models are necessary for quantitative study of diffusion flames, especially at low stretch rates.
Physically, since the flame zone thickens with the decrease of the stretch rate
(Willliams, 1985), this thickening leads to more radiation heat loss and less heat release rate per unit volume of the flame zone. As a result, the ratio of radiative heat loss to the heat release increases, and flame temperature decreases with decreasing stretch rate. The
43
reduction of stretch rate therefore increases the flame thickness, and eventually results in the gas phase radiative extinction.
Furthermore, for the condensed phase fuel, as the stretch rate decreases, the dimensional flame standoff distance increases, and the fuel burning rate decreases. As a result, the combustion heat generated per unit time per unit flame area decreases and a
“low-power” flame is produced. However, the rate of radiative loss is decreased at much slower rate than that of the heat generation (especially for large activation energy reactions). Therefore, by competition, the radiative heat loss becomes significant when the stretch rate is small.
As reviewed in the previous section, since most of the earlier studies focus on high stretch diffusion flames, the present investigation of the response and dynamics of the low-stretch flames will fill the fundamental voids of our current understanding in low stretch rate regime. The study of the dynamics of the low stretch flames will complete the task started more than a decade ago and will provide fundamental insights into the science of combustion.
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1.3.2 Diffusion Flame under Micro-gravity
One major difficulty of experimental study of low stretch diffusion flame is that these flames are more susceptible to the influence of buoyancy-driven flow. The stretch rate induced by the buoyant flow around the flame could be higher than the imposed stretch rate. This seems to imply that the microgravity environment will be the vehicle for the study of low-stretch flame phenomena. One apparent obstacle, however, is associated with the size limitation of the apparatus.
Unlike premixed flames, the flame thickness of a diffusion flame increases with decreasing stretch rate and scales inversely with the square root of the stretch rate
(Williams, 1985). Furthermore, the lateral flame size has to be much larger than the flame thickness in order to preserve the quasi-one-dimensional (Quasi-1D) nature of the steady flame. We have found that a lateral size of 10 times the flame thickness is needed to ensure its one-dimensionality. Furthermore, several theoretical calculations (e.g.
Maruta et al., 1998; Frate et al., 2000) indicate that the flame thickness of a diffusion flame at a stretch rate of 2 s-1 can be as wide as 2~3 cm. This implies that the lateral flame dimension has to be at least 20 cm. Since the separation distance between two opposing jets is typically proportional to the jet dimension, this renders a fairly large- scale burner system in order to ensure the truly quasi-1D opposed-jet diffusion flames.
Such a requirement, however, is not feasible in the current drop tower and space flight facilities.
Recently, Maruta et al. (1998) tested the extinction limits of counterflow diffusion flames of air and methane (diluted with nitrogen) through drop tower experiments and
45
compared the experimental results with numerical calculation using detailed chemistry and thermodynamic/transport properties using optically-thin assumption. Radiative heat
loss from the flame zone has been taken into consideration. Even though the general trends agree with each other for experimental and numerical results, there is obvious disagreement at the low stretch extinction limits. The reason of this disagreement could be due to the flame thicknesses of the low stretch diffusion flames are so large such that they are comparable or even wider that the separation space of the two opposed jets of opposed jets in their study. Due to the space limitation of microgravity tests, the diameter of the jets used in the study of Maruta et al. (1998) is only 1.6 cm and the separation of the two jets varies from 1.5 to 2.5 cm. The narrow space between the two jets may interfere with the flame structure and enhance the conductive heat loss from the flame to the jets. In addition, the temporal limitation (about ten seconds) may also prevent the flame from reaching steady state.
1.3.3 Alternative Low-Stretch Diffusion Flame Configuration
T’ien et al. (1978) numerically studied a stagnation-point diffusion flame with a condensed fuel. In this study the surface radiation was included. But not much computation was carried out due to the limitation of computational capability.
Subsequently, Foutch and T’ien (1987) used the radiative loss as well as a densimetric
Froude number to characterize the blowoff and quenching extinction boundaries in stagnation-point diffusion flames under various convective conditions. An important conclusion of this study by Foutch and T’ien (1987) was that, the shape and location of
46
extinction boundaries, as well as a number of important flame characteristics, were
almost identical for the buoyant, forced, and mixed convective environments they
modeled. There are obvious differences in the flow field of forced and buoyant cases,
because the governing momentum equation and boundary conditions are different for
these two situations. Nevertheless, similar flame structure and extinction characteristics
were found for stretched flames in forced, mixed and buoyant flows. The study of Foutch
and T’ien (1987) also indicates that it is possible to use natural convection to induce a
very low stretch rate flow under normal gravity, and thereby suggesting that the low
stretch diffusion flames can be studied under normal gravity condition utilizing the
buoyancy-induced flow field.
Following the configuration suggested by Foutch and T’ien (1987), the first
experimental low-stretch diffusion flame was established beneath a cylindrical solid
PMMA sample of varying large radii (Olson, 1997; Olson and T’ien, 2000). The stretch
rate was as low as 2 s-1, as the ice-bath-cooled solid fuel with radius of curvature greater
than 200 cm in their studies. The results showed that the scaling of the experiments to
produce effectively low stretch flames in a normal gravity is possible. However, since
solid fuel was used in their studies, the heat transfer in solid phase was never truly steady
due to the finite thickness of the sample. Heat losses into the interior decayed with time
during the heat-up transient process, but increased at later times with surface regression.
In addition, there were many experimental complexities for solid fuel diffusion flames,
such as the influences of the bubble layer and sample swelling on the solid-phase temperature profiles, the changes in the material properties at the glass transition, etc.
47
1.3.4 Flame Instabilities of Low Stretch Diffusion Flames
Continuing the discussion of Sec. 1.2.2.2.2, up to date there are only a few studies
focusing on diffusion flame instabilities under low stretch.
Garabinski and T’ien (1994) predicted a pulsating/oscillating near the extinction limit
of the low stretch diffusion flames using the stagnation point flow model with radiation.
Cheaham and Matalon (1996a, 1996b) also examined near-limit oscillations of spherical
diffusion flames at low stretch. A critical Damköhler number where an instability
develops was introduced in their work. They also predicted that the oscillation frequency
depends on standoff distance. For 5~8 mm standoff distance, the frequency is
approximately 1 Hz. Favorable comparison was been made with recent candle flame
experiments in microgravity environment (Dietrich et al., 1994, 2000). In the experimental study of Dietrich et al. (1994, 2000), it was found that the candle flame
oscillation grew with amplitude and eventually the flame was extinguished during the
oscillation. The order of magnitude of frequency is 1 Hz.
By using buoyancy induced stagnation-point flow burner, Olson and T’ien (Olson,
1997; Olson and T’ien, 2000) observed multi-dimensional “flamelets” throughout their
tests. They noted that cellular flame structures (or “flamelets”) happen when the buoyant
stretch rate is smaller than 3 s-1 (R >100 cm, R is the radius of the cylindrical sample). At
this low stretch condition, several cellular flame structures cover the solid surface with
dark (un-reactive) channels between them and they meander around the burning surface very slowly (time scale ~ several minutes). The initial channel width is of the order of a
48
couple of centimeters, which is the same order as the flame thickness; the minimum
dimension of the flame cell is more than twice as much. Subsequently, the flame cells
shrink in size and weaken when either the stretch rate is decreased or the heat loss
(conductive or radiative) is increased. Eventually, these flame structures quench.
Flamelets are unique near-limit low-stretch flame phenomena observed for the first time in this geometry. The triggering mechanism for this type of instabilities is still not well understood, although thermo-diffusive, hydrodynamic, and Rayleigh-Taylor instabilities
may each or all be important (Olson, 1997).
Nanduri et al. (2003) numerically studied the edge of a nitrogen-diluted hydrogen
flame burning in air using a constant density, one-step reaction model in a plane two- dimensional counterflow configuration, with special emphasis on the radiative, low- stretch flame phenomena. It was shown that radiative heat loss plays an important role in the onset of low-stretch diffusion flame instabilities and becomes the dominant source of flame instability near the 1D low-stretch radiative extinction limit. Generation of transient cellular flame structures for stretch rates close to the 1D low-stretch radiative extinction limit was noted. Moreover, the existence of cellular flame structures for stretch rates below the 1D radiative extinction limit demonstrates the ability of these flames to resist quenching by radiative loss.
The present study therefore aims to verify such multi-dimensional flame structures predicted for gaseous diffusion flames. We will later demonstrate the existence of multi- dimensional flame structures in gaseous diffusion flames at very low-stretch rates even for the near-unity Lewis number mixture. This in turn will suggest that, the heat loss
49
process, especially, the radiative heat loss, also plays a significant role in triggering and enhancing the flame instability near the radiative extinction limit.
1.4 Motivations and Objectives of Study
1.4.1 Motivations
The low stretched diffusion flame has its practical interest in applications. At first it relates to the human’s activities in space. For example, in spacecraft, the atmospheric control system and local cooling fans within hardware racks, or the air flow induced by the movement of nearby objects, can create low-velocity forced flow environments around those objects. These low-velocity flows could impinge upon flammable materials and low stretch diffusion flames may happen.
Not only in microgravity environment the low stretch flame is possible, reduced gravity on other stars and planets also has the potential to generate very low stretch rate on flames due to the buoyancy-induced convection. Furthermore, the low stretch flame phenomena are of direct relevance to large buoyant fires even under normal gravity, where local low-stretch regions can exist especially in the downstream part of the fire.
The low-stretch diffusion flame response is also of importance to the study of radiation- induced flame instabilities. Therefore, to investigate the dynamics of laminar “flamelets”
(Williams, 1985) both high and low stretch rates should be included. This more complete study will extend our understanding of both laminar and turbulent combustion.
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Unfortunately, there are currently very few experimental databases available
regarding the flame structure and dynamics of gaseous diffusion flames in the low-stretch
regime. Furthermore, the measurements obtained at relatively high stretch rates normally
cannot be applied or extrapolated to the low stretch rate regime. Such a void in our
fundamental understanding is mainly due to the experimental difficulties in establishing
low-stretch counterflow diffusion flames in normal gravity.
In view of the above considerations, particularly, inspired by the benchmark works of
Olson and T’ien (Olson, 1997; Olson and T’ien, 2000), an alternate configuration is proposed to investigate the response and dynamics of low-stretch gaseous diffusion flames. In such a configuration, a diffusion flame is established by bottom burning of gaseous fuel mixture discharged from a porous Tsuji type burner in a purely buoyant flow to avoid the complexities of condensed phase fuel. With different fuel dilutions, the dilution limits of hydrocarbon fuel at very low stretch can be studied using this innovative burner configuration. In addition, the flame standoff distance can be
independently controlled by fuel injection speed at a given fuel composition and stretch
rate. Thus, the surface temperature and surface radiation can be controlled by adjusting the fuel injection speed.
1.4.2 Objectives
There are five objectives for the present experimental investigation.
At first, we would like to demonstrate the feasibility of using the proposed
configuration for the study of low-stretch gaseous diffusion flames, with detailed
51
experimental characterization. Low-stretch flame phenomena of interest in the present
experimental investigation include flame stability map, extinction and sooting limits.
Secondly, we will compare the present experimental results for diffusion flames of ~2
s-1 to those obtained by the seminal work of Tsuji and co-workers (1967, 1969, 1981,
1982) for relatively high stretch rates ranging from 12 to 103 s-1, with special emphases on the flame stability diagram and fuel dilution limit. The boundaries leading to sooting flames and flame extinction will be identified in terms of fuel mixture injection speed and fuel dilution.
The third focus of this study is the detailed structure of low-stretch flames which are resolved by advanced optical methods. Since the flame thickness of a diffusion flame increases with decreasing stretch rate and scales inversely with the square root of the stretch rate, the low-stretch flames would facilitate the experimentation in terms of flame structure mapping. The study will include thermal and species profiles, using non- intrusive laser diagnostics, in order to provide insights into the development of comprehensive models.
The fourth objective is to demonstrate the existence of flame instabilities as the diffusion flame approaches extinction at very low stretch rate. These flame instabilities could be triggered by several mechanisms as discussed in Sec. 1.2.2.2.2 and Sec. 1.3.4.
Assuming that the cellular flame phenomena are caused by the imbalance of thermal and mass transport, the theory would suggest at least one Lewis number (either the fuel or oxidizer) has to be less than unity for the cellular instability to occur. In this study we will later demonstrate the existence of multi-dimensional flame structures in gaseous diffusion flames at very low-stretch rates even for the near-unity Lewis number mixture.
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At last, recognizing the importance of an accurate radiation model for quantitative
descriptions of low-stretch flames, the simulated quasi-1D flame structure will be
compared with experimental measurements. Both gas phase and surface radiations are considered. Comparison with experimental results allows the assessment of the predictive
capabilities of kinetics mechanism and radiation models. The extinction limits are also
calculated by current numerical modeling, the simulation results can provide more physical insights of controlling mechanisms of flame extinction.
In the following, the experimental specifications and the diagnostics techniques employed will be first presented in Ch. 2 and Ch. 3, respectively. Numerical methodology is addressed in Ch. 4. Results, including the structure and response of quasi-
1D low stretch flames, the dependence of extinction limit on fuel dilution and fuel injection speed, the onset of multi-dimensional flame instabilities, the characteristics of various flame instabilities, and the numerical simulation will be reported and discussed in
Ch. 5. Finally the conclusions and the recommendation of future work are described in
Ch. 6.
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CHAPTER 2
EXPERIMENTAL SETUP
In this experimental study, the buoyancy-driven flow is the controlling mechanism that
exerts an extremely low stretch rate on the flame without forced flow. Thus, the present
study aims to utilize the normally unwanted buoyancy-induced flowfield to achieve very
low stretch rates. In the following, the buoyancy-induced stretch rate and the nominal
fuel mixture injection speed will be first defined. Next, the design of the low stretch
burner system will be the detailed. Subsequently, the operating procedures, low stretch
flame demonstration, and experimental uncertainties will be discussed.
2.1 Definitions
2.1.1 Buoyancy-Induced Stretch Rate
Following the definition of the mixed convection stretch rate in the study of Foutch and T’ien (1987), an equivalent buoyant stretch rate can be determined by setting the
Richardson number to unity:
β∆TgR3 Grν 2 β∆ TgR Ri ==222 = =1, (2-1) Re ⎛⎞VR V ⎜⎟ ⎝⎠ν
where Gr is the Grashof number, Re the Reynolds number, V the characteristic buoyant
velocity, g the gravitational acceleration, R the characteristic length dimension (e.g. the burner radius of curvature), ∆T the temperature difference between the characteristic
54
temperature and the ambient temperature, ν the viscosity, and β the expansion coefficient.
As such, V = β∆TgR .
Without an opposing air jet, Foutch and T’ien (1987) demonstrated that it is possible to use buoyancy-induced flow to produce a diverging flowfield, similar to a weak
counterflow configuration. For a given ∆T, the stretch rate induced by the buoyant force,
ab, can be defined as
dV 1 β∆Tg g = a = ∝ . (2-2) dR b 2 R R
For the purely natural convection, the buoyancy-induced stretch rate can be given by
(Foutch and T’ien, 1987):
1 ⎡⎛ ρ e − ρ * ⎞ g ⎤ 2 a = a = ⎜ ⎟ , (2-3) b ⎢⎜ e ⎟ ⎥ ⎣⎝ ρ ⎠ R ⎦
where ρ e is the free stream density and ρ * is the characteristic density.
Foutch and T’ien (1987) also defined a mixed-convection stretch rate by introducing
the densimetric Froude number. When there exists an external forced stretch rate af , for a
2 given densimetric Froude number Φ=(aabf) , the mixed-convection stretch rate is expressed as
a ≡ a f ()1+ Φ . (2-4)
Therefore, the parameters af and Φ characterize the mixed convection boundary layer.
In the study of Foutch and T’ien (1987) the characteristic density ρ * is chosen as a
constant of 0.261 kg/m3, which is about the density of air at 1400 K. Based on this
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definition, the buoyancy-induced stretch rate for our current burner with radius of curvature R being 382 cm is 1.43 s-1.
Since the choice of characteristic density is somewhat arbitrary, a simpler definition
of buoyancy-induced stretch rate is obtained by setting the density ratio in Eq. (2-4) as
unity. This simplified definition is expressed as:
g a = , (2-5) b R
-1 which yields a buoyancy-induced stretch rate of ab = 1.60 s when considering R = 382 cm. This value, therefore, provides the upper limit for the buoyancy-induced stretch rate obtained using the present configuration.
For simplicity, Eq. (2-5) is used in the present study as a measure of the flame global stretch rate in both experiments and simulations. In addition, if a proper characteristic density for current configuration could be found through numerical simulation or other means, it is straightforward to convert current definition to that of Foutch and T’ien
(1987).
2.1.2 Nominal Fuel Mixture Injection Speed
In the presence of flame the burner injection speed can be difficult to define
experimentally, since the local conditions along the burner surface cannot be readily obtained. An ‘averaged’ fuel mixture injection speed, referred to as the nominal fuel
mixture injection speed (vf), will instead be used in order to avoid confusion. This value
will herein be defined in the following manner. First, the averaged mass flux at the burner
surface (VF) is calculated using the total mass flow rate divided by the burner surface
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area. Then, vVf = Ffρ , where ρf is fuel mixture density at far upstream, i.e. at ambient
condition. This value of fuel mixture injection speed is, of course, not equal to the actual
fuel injection speed at the burner surface. For the purpose of direct comparison between
the current simulated results with the previous literatures (e.g., Tsuji, 1982), the
computed mass flux at the burner surface (VF) from the simulations will also be
converted to the nominal fuel injection speed values. From here on, any mention of “fuel
injection speed” or “fuel mixture injection speed” will refer to the nominal fuel mixture
injection speed.
2.2 Burner Facility
2.2.1 Overview
The flame to be studied is a methane/air diffusion flame formed by injecting fuel
mixture downwards at very low flow rates through current facility. Extremely low stretch
rates are achieved by using a spherically-shaped burner with a large radius of curvature
(R =382 cm). The downward orientation of the burner exit allows the study of the
forward stagnation point diffusion flame induced by the buoyant force under normal
gravity. If the optional bottom air jet in included, the forced airflow against the burner
surface can increase the stretch rate above that induced by the natural convection alone.
Figure 2.1 shows a simple schematic of the burner, while Fig. 2.2 is a picture of diagonal
view of the burner apparatus along with a steady flame.
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Gaseous Mixing R Fuel Chamber Inlet
Gaseous Dilute Inlet
Steel Wool Cooling Water Pipe 6.5” 8.0” 6.5”
Extension Plate Porous Bronze Surface Brass Screen
Figure 2.1 Schematic of present experimental setup. R is the radius of curvature of burner surface.
Figure 2.2 Diagonal view from underneath of the present burner, including a quasi- one-dimensional low-stretch diffusion flame.
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The flow of fuel (methane with 99.97% purity) and the dilution gas (nitrogen with
99.998% purity) are controlled by upstream sonic nozzles. Both gases are mixed together in the mixing chamber as shown in Fig. 2.1. The mixture is then injected horizontally into
the burner body through 50 holes which uniformly distributed around the circumference
of the top of the burner body. The burner body is filled with steel wool to adjust the mixture flow to be uniform and steady. Finally the mixture is fed through a quarter inch thick porous sintered-bronze dome into the ambient air. The size of the pores ranges from
20 to 45 microns. The porous material is shaped with a ~400 cm radius of curvature. A 1- inch thick extension plate seamlessly continues the burner surface with the same radius of curvature as the porous material. Cooling water coils contained inside the extension plate serve to cool the extension plate in a controlled fashion.
In Fig. 2.2, we can also see that the burner body is secured in a steel frame. To eliminate the effects of air current in the laboratory, the experimental apparatus is enclosed in a metal screen cage. An exhaust section above the apparatus is necessary to
remove the combustion products.
The whole facility is seated on three lab jacks. By adjusting these jacks, the relative distance between the burner surface and the optical probe (i.e. laser beam) can be read out through a micrometer. Another function of these jacks is the maintenance of leveling of the whole facility. If the burner is not carefully leveled, the lower stagnation point is shifted away from the physical center of the burner surface. Thus the axial symmetry is not guaranteed.
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2.2.2 Porous Burner
Since the equivalent buoyant stretch rate is proportional to the square root of g/R (cf.
Eq. 2-5), it would suggest zero stretch rate when using a flat plate burner. Zero stretch
rate in a stagnation-point geometry, however, can only be approached asymptotically. As
stretch rate approaches zero, the physical domain (e.g. flame thickness and burner
diameter) approaches infinity. Just by using a flat disc with a finite radius will not
achieve a zero stretch rate since the strength of buoyant convection will be governed by
the flow at the edge of the disc which depends on the disc radius. This edge driven flow
pattern will not generate a uniform flame and a boundary layer with constant thickness
(Restrepo and Glicksman, 1974). On the other hand, for the curved burners with large
scale, both previous studies (e.g., Olson, 1997) and our current setup demonstrated that a
good approximation of quasi-one-dimensional low-stretch flame can be achieved.
Because the buoyancy-induced stretch rate exclusively depends on the radius of the curvature in current configuration, the manufacturing and measurement for the spherical burner surface are essential tasks. The material for the burner surface is sintered bronze
(GKN Sinter Metals), which is produced by molding and sintering the metallic particles.
The (averaged) pore size is defined by the size of the particles. To obtain the uniform permeability, the pore size of the porous material used for current burner ranges from 20 to 45 µm. The thickness of the fixture is one-quarter inch.
It is necessary for the flame size to be large enough to ensure the quasi-one-
dimensional flame in the lateral/tangential direction. Furthermore, to capture the
“flamelets”, or multi-dimensional phenomena, the lateral length scale of flame should at
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least cover several flamelets and accompanying extinction gaps between them. When
taking the physical size limitation of facility and the complexity of setup into account, it
is found that the lateral flame size of 10 times of the flame thickness, say 2 cm at a stretch
rate of about 2 s-1 (Maruta et al., 1998; Frate et al., 2000), is sufficient for our study. As
such, the present spherical porous burner surface has a 20 cm arc-length.
Since the raw material is flat, the porous fixture needs to be shaped to a fixture with
uniformly curved surface. To avoid the damaging and blocking the pores of this fixture,
the required curvature of the fixture is made by compressing the flat material in a hard
mold instead of machining directly on the material. In addition, when the pore size is
about 20 µm, the material offers a good elasticity. Therefore, it is easier to make the
material with expected curvature by bending the flat fixture. The mold is composed by
two pieces, one has a concave surface and the other one has a convex surface. The radius
of the curvature of the inner surface of the mold is machined to the expected value. To prevent the bent fixture from bouncing back, it is held in a circular adapter ring after
bending. Later, the adapter ring along with the burner surface is installed into the burner
body during assembly.
After the fixture is made, the resulting radius of curvature is accurately measured by the Coordinates Measurement Machine (LK Metrology System, Inc.). The uncertainty of this measurement is within 1%. Several burner surfaces with different radii of curvature
(R=150 cm ~ 500 cm) have been tested for current facility. Note that this range of radius
-1 of curvature corresponds to ab = 1.4~2.5 s . Extensive tests demonstrate that the flame
responses in this low stretch rate range are qualitatively similar. Finally, the one with
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R=382 cm was chosen for further detailed investigation because this resulting porous
burner is of relatively better mechanical quality.
2.2.3 Burner Body
The burner body is made of aluminum. The overall shape of burner body is
cylindrical. The inner diameter is about 20 cm and height is 30 cm. The air-tight spacious
volume inside the burner body is completely filled with steel wool to help produce a
uniform flow at the burner exit. Fuel mixture is injected into this burner from the top of facility horizontally through 50 holes with half inch diameter. In order to minimize the edge effects for a burner arc-length of 20 cm, a 50 cm wide extension plate is used to continue the radius of curvature of the burner surface seamlessly. Active cooling water goes through the pipes imbedded inside the extension plate.
2.2.4 Experimental Operation
Because the relatively large-scale gaseous diffusion flame is studied herein, some
necessary precautions are required for initiating and stabilizing such a flame.
1. Exhaust hood
The exhaust fan has to be on before and during any test. The ceiling exhaust fan is connected with the exhaust hood with a pipe. The hood is big enough to prevent the combustion products from entering the laboratory. In addition, the air flow of the exhaust
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fan has to be carefully adjusted so that it will not disturb the buoyancy-induced flow
field. According to the study of Olson (1997), the open upper screen section would
provide an entrainment volume that is sufficient to damp out any significant induced
flows by the exhaust fan. As such, the stagnation point flow induced by buoyancy can be
preserved.
2. Cooling water
The next step before experiments is turning on the cooling water. The purposes of
cooling water are:
a. to maintain the surface temperature by controlling the cooling rate;
b. to prevent the burner body and extension plate from being overheated.
3. Nitrogen purge
For safety reasons, before turning on the fuel in the gas supply system, the purging
nitrogen must run through the whole burner for about 1 minute. Likewise, after the fuel is
shut down, the purging nitrogen continues for about 1 minute.
4. Mixing delay
When the fuel (methane) and diluent gas (nitrogen) are supplied by setting the
pressure ahead of the sonic nozzles, they are mixed with each other in the mixing
chamber and burner body. Because of the big volume of the burner body and small flow rates of gas supplies, it takes 30 seconds to 1 minute for the mixture to be well mixed
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before exiting the porous burner surface. Therefore, when the upstream gas supplies are changed there is always a time delay for the flame to respond.
5. Ignition
A regular propane gas igniter is used to initiate the combustion. In case that the soot generated from the igniter flame blocks the tiny pores in the porous burner surface, the flame should be ignited at the inner edge of the extension plate. After ignition, usually, it takes 3~5 minutes for the whole system to reach steady state.
2.2.5 Demonstration of Quasi-1D Low-stretch Diffusion Flames
To demonstrate the quality of the steady quasi-one-dimensional diffusion flames obtained using the present burner, various steady flames were examined at different conditions. Figure 2.3 shows the side-view of four sample flames with constant fuel mixture injection speed (0.8 cm/s) and varying nitrogen dilution. Since the luminosity of the flame is very dim, the chemiluminescence images are taken under dark background with large aperture size. On the other hand, the image of the burner head was taken by the same camera at same location but under different illumination and aperture setting. Thus, all of the pictures shown in Fig. 2.3 are obtained by combining of two images for better view of both burner surface and flame together.
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Figure 2.3 Side-views of steady quasi-1D flames under various nitrogen dilution levels (in terms of mole fraction). It shows the uniformity of the quasi-1D flames along the burner surface at different conditions.
It is seen from Fig. 2.3 that the flame luminosity increases from light blue to bright blue, and bright yellow and blue, as the nitrogen dilution is decreased. When the nitrogen percentage in the fuel mixture is greater than 45% (by volume), only the blue flame is visible. When the nitrogen dilution becomes less than this critical value (the sooting limit), we can observe the appearance of a separate yellow sooting layer above the blue reaction zone. The sooting layer becomes brighter and moves further away from the blue flame as the nitrogen dilution is reduced further. Thus, the limiting nitrogen dilution leading to sooting flames for this injection speed is about 45% in the case shown in Fig.
2.3.
Experimental results confirm that the current apparatus is suitable for studying very low-stretch (1~2 s-1) diffusion flames under normal gravity. In general, the quasi-1D diffusion flames have the following characteristics:
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1. Flame surface is smooth, continuous everywhere;
2. Flame surface is almost flat, even thought it is slightly curved due to the curvature
of the burner surface;
3. The color of the non-sooting flames is light blue and the corresponding
temperature could be as low as 1300 K, as measured by using Raman scattering;
4. It is very steady, and the flame can run as long as the gas supply maintains;
5. The flame is much thicker than the opposed-jet diffusion flames which are usually
established at higher stretch rate range.
It is also noted that the steadiness of the present quasi-1D flames facilitate the use of
laser diagnostics for mapping flame structure. Furthermore, we will show in due course
that with the capability of fine adjustment of fuel injection speed and fuel dilution level,
the present burner system can be used to identify various flame instabilities and extinction limits.
2.2.6 Uncertainty Analysis
2.2.6.1 Repeatability
To ensure the reproducibility over the range of the controlling parameters
investigated, most experimental results reported in this work have been gone though
multiple checks via various ways. For example, for a target condition of mixture
composition and fuel mixture injection speed, we have compared the results by either
gradually increasing/decreasing the fuel injection speeds at the fixed dilution level or
gradually increasing/decreasing the dilution level at the fixed fuel injection speeds. It is
66
shown that the reproducibility of this facility is very good. In general, the uncertainty of repeating tests is within 1.5%. The flame structures measured from multiple experiments operated under the same experimental conditions at different times are also very consistent.
2.2.6.2 Flow Rate Control
All the sonic nozzles used in this study are calibrated by a Wet Gas Meter
(Shinagawa Inc., Japan). The accuracy reported by the manufacture is within ±0.1%.
When those sonic nozzles are operated at choking condition, an explicit function of gas
flow rate versus setting pressure right before the nozzle throat (with the pressure gauge
accuracy being less than ±0.1%) is obtained by linear regression. Since the gas properties
are different for different species, calibrations are required for every species. It is also
found that the uncertainties associated with the mixture composition and fuel injection speed are estimated to be within ±0.2% and ±0.1%, respectively.
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CHAPTER 3
OPTICAL DIAGNOSTICS SYSTEMS
Optical methods are ideal for combustion application since they are usually remote and almost non-perturbing (Ecbreth, 1996). Especially, after 1960s, laser-based techniques became increasingly important in combustion research because of the emergence of a new generation of lasers and detection devices with better performance and reliability.
Optical diagnostics techniques usually provide non-intrusive detection of many physical and chemical properties, such as velocity, temperature, and major as well as minor species, involved in the combustion process. Even though there are some disadvantages of optical diagnostics, the unique advantages are very attractive as compared with conventional “probe-type” diagnostics:
• Advantages
– Non-intrusive, non-contact, in-situ methods;
– Allow fast or real-time measurements;
– Make two-dimensional information (an image) often available;
– Can be applied to harsh and hostile environments, like high temperature
and high pressure conditions;
– Minor or trace species (e.g., pollutants, active radicals) are detectable.
• Disadvantages
– Optical access (windows) may be difficult for certain cases;
– The high energy incident laser used could change the medium;
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– Quantitative analysis is more complicated and difficult than conventional
methods.
During the past decades, more and more applications of optical diagnostics in
experimental studies have been successfully achieved (Eckbreth, 1996). In particular,
spectroscopic methods are one important category of the optical techniques. They have
become fundamental tools in science and engineering for the detection, resolution, and
recording of energetic phenomena occurring in nuclei, atoms, or molecules. Usually, but
not always, the light source with a specified wavelength/frequency is required for
spectroscopic studies. Furthermore, analysis of the output light signals with respect to their composition is a major focus of these methods.
In this body of work, two standard spectroscopic methods are introduced, they are
Raman Scattering Spectroscopy and Planar Laser Induced Fluorescence (PLIF). Besides the two relatively complicated spectroscopic techniques, two other passive optical methods that do not acquire light source (excitation) for the experiments, namely Infra-
Red (IR) imaging and chemiluminescence imaging, are also employed in this study.
In this chapter, the setup and related specifications for the present diagnostics systems are addressed. The spontaneous Raman spectroscopy is used to measure temperature distribution, while the OH-PLIF is introduced as the method to map the OH concentration in the flame. IR-imaging and chemilimenescence imaging are also briefly described.
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3.1 Spontaneous Raman Spectroscopy
In the past several decades, the spontaneous Raman scattering has been successfully applied in a number of practical combustion systems (cf. Eckbreth, 1996). But its utilization is generally restricted to certain fuels, stoichiometrics, and operating conditions due to the relatively weak intensity of the Raman signals. For instance, luminous emissions from the sooting flame should be depressed or avoided. In our study, the quasi-1D steady flame can be adjusted to a soot-free blue flame. It is an ideal object of Raman spectroscopy study.
This section focuses on the application of Raman scattering in our current study. The fundamentals of Raman effects and the corresponding quantum mechanical theory are
briefly addressed in Appendix A. In the following, the experimental setup and data
analysis are highlighted.
3.1.1 Experimental Setup and Capability
A picture of the entire Raman system and burner facility is shown in Fig. 3.1. The
laser beam (green line) and the path of Raman signal collection (blue line) are also
illustrated in Fig. 3.1. The yellow circle delimits the test section. Figure 3.2 is a schematic
showing the key components in the current Raman scattering system.
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Laser beam Test section
Raman signal
Figure 3.1 Experimental setup of Raman scattering system.
Controller w/ Pulse Generator
Spectrometer Nd:YAG
Intensified CCD Camera Filter
Ls3 Ls1 Retro- collector M2
Ls2 Test Section M3 Beam Dump
PC M1 Figure 3.2 Schematic of Raman scattering setup.
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Due to the relatively weak Raman signals, the present setup aims to:
1) avoid or minimize the severity of flame luminosity and other background
noise;
2) optimize the spatial resolution in the measurement;
3) maximize the signal-to-noise ratio of the Raman signal.
With the above objectives in mind, the details and specifications of the key
components, including laser, laser optics, optical collection system, spectrometer,
controlling system, beam dump, and optical housings are discussed in the following.
A) Laser
Nd:YAG laser (Continuum, Powerlite 8010) is used to generate a high-power visible
green light at 532 nm with its maximum output energy being around 700 mJ/pulse at this wavelength. The pulse width is about 5~7 nanoseconds and the linewidth is 1 cm-1. The divergence of the laser beam is negligible (only 0.45 mrads based on full angle for 86% of energy). In order to avoid the breakdown of room dust/air within the test section, the output energy of YAG laser is adjusted to no more than 400 mJ/pulse.
B) Laser Optics
The converging lens with a 600-mm focal length (Ls1 in Fig. 3.2) focuses the 532 nm laser light into the test section. The spatial resolution is then defined by the size of the focal spot, i.e. minimum beam diameter and waist. Although the smaller the focal spot, the higher the signal intensity and better spatial resolution in general, there is a limitation
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of the energy intensity because of the air molecules could be ionized when the incident
light intensity is higher than a certain threshold value.
Previous studies (e.g. Tambay and Thareja, 1991) show that the threshold intensity
for the laser-induced breakdown of air is around 1010 W/cm2 at the current frequency. In
present study the threshold intensity is found to be only 1.6×104 W/cm2. This discrepancy could be due to the dust contamination in the room air.
Recognizing the trade-off of higher laser intensity for maximizing Raman signals and
low enough intensity for preventing air from breakdown, a focal lens and a laser energy
are chosen, namely as 600 mm focal length and 400 mJ/pulse.
A general equation that relates the spot diameter (dspot) of a convex lens to the focal
length (f), wavelength of the laser beam (λ), and the initial diameter of the laser beam (d0) is written as:
dspot = 2.44 fλ / d0.
Thus, the lens of f = 600 mm and the initial laser beam diameter of 8mm yields dspot ~
100 µm when using 532 nm light source.
During our experiments, it is also found that the breakdown threshold value of laser energy intensity is higher in the region close to the burner surface because the reactants and products on the fuel side of the flame are much “cleaner” as compared to the room air that is driven by buoyancy. As labeled in Fig. 3.3, the picture including the burner surface, laser beam, and quasi-1D flame shows relative location of this clean zone, which is between the burner surface and the flame. Note that the fuel mixture is supplied from the “dust-free” bottle gases.
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Figure 3.3 Picture showing the laser beam (green line in the middle) and a flame (bottom) along with a burner head (top) and scale. For this demonstration flame, the nitrogen dilution is 75% and the fuel mixture injection speed is 1.00 cm/s.
C) Optical Collection System
As shown in Fig. 3.2, the optical collection system contains a retro-collector, converging lenses (Ls2 and Ls3), reflecting mirrors (M1, M2, and M3), one optical filter, and ICCD camera. Figure 3.4 shows a picture of the optical collection system. The blue line in Fig. 3.4 indicates the path of the Raman signal collection.
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Figure 3.4 Picture of optical collection system.
C-1) Retro-Collector
The retro-collector is a concave mirror. It is placed on the opposite side of the
collecting lens (Ls2). It serves as a collector on the other side of the test section since the
Raman signal is emitted in all directions. To increase the collecting solid angle, the
diameter of this concave mirror is as large as 3 inches and the focus length is 30 cm. The
fine adjustment of the focal point is achieved by a two-dimensional translation stage so
that it is located at the center of the test section. By comparing the signal intensity with and without this retro-reflector, it shows that the Raman signal can be enhanced up to
80% with this retro-reflector.
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C-2) Converging Lenses
The converging lenses include two convex lenses, namely Ls2 and Ls3 in Fig. 3.2.
Ls2 is placed on an extension rail to collect the Raman signal both directly from the test
section and reflected from the retro-reflector. Similar to the retro-collector, in order to
collect as much signal as possible, the diameter of this lens (Ls2) is 3 inches and the focus length is 30 cm.
The other converging lens (Ls3) is located in front of the entrance of the spectrometer. Its focal length is 10 cm. The combination of these two converging lenses
(Ls2 and Ls3) can generate a clear image right at the slit opening of the spectrometer.
C-3) Reflecting Mirrors
Three high quality flat reflecting mirrors are employed in this optical collection
system. The biggest one is a 3 inches by 3 inches square mirror (M1), which is placed on
the extension rail to collect most of the Raman signal from the collecting lens (Ls2). The
other two mirrors, M2 and M3, are smaller, which are 2 inches in diameter round and 1
inch by 1 inch square mirrors, respectively.
These mirrors are used not only for redirecting the signal to the spectrometer, but also
for rotating the signal image by 90-degree. The original signal is horizontally polarized as
the incident laser beam, while the grating of the spectrometer is sensitive to vertical
polarization.
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C-4) Optical Filter
OG550 (Schott) is located in front of the entrance of spectrometer to eliminate the scattering and reflecting laser light at 532 nm from the test section. It cuts off the light of wavelength below 540 nm.
C-5) ICCD Camera
Since the Raman signal generally is very weak, an intensified CCD (ICCD) camera
(PI-MAX 1024 RB, Princeton Instruments) is used in this optical collecting system. It is located at the exit of the spectrometer. An adapter is required for adjusting the location of the camera to obtain the focused image on the camera detector.
In this ICCD camera, the incident photons generate photoelectrons by collision on the photocathode of an image intensifier. Then photoelectrons are accelerated in the electronic field and enter “micro-channel plate” (MCP). The single electron can go through one of the micro-channels and is multiplied by successive collisions with the channel wall. When the packet of a group of electrons exits the micro-channel, it strikes a phosphor screen. The kinetic energy of the electron packet is converted by the phosphor into photons. Finally, the image is directed to the CCD array through an optical fiber.
This allows a very faint signal to be detected by the regular CCD camera. Our current gain setting is 200 for most of the experiments.
D) Spectrometer
The Raman spectrograph is taken by a spectrometer (SPEX, 270M). This spectrometer is controlled by the software “WINSPEC32” via its SPEX232 computer interface. In the spectrometer, a 1200 grooves/mm plane holographic grating is installed.
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Spectral dispersion of the spectrometer is 3.1 nm/mm. The slit width is usually set as 0.2
mm to obtain a fine resolution, while the slit height is 10 mm. The spectral resolution
with 1200 grooves/mm grating is about ±0.1 nm within the wavelength range
investigated. Calibration of the spectrometer is done using a neon light source because
the standard neon spectrum chart provides a good reference for the wavelength range of
interest.
Furthermore, several sources of broadening, such as Doppler broadening and
instrumental broadening need to be accounted for. In this study, the most important broadening effect is the instrument broadening which is related to the finite dimension of the slit opening of spectrometer entrance. Therefore, the spectrum obtained is convolution of Raman signal and the so-called instrument or slit function. To obtain this slit function for present spectrometer system, a helium-neon (He-Ne) laser has been used as reference light source because of its very narrow linewidth at 632.8 nm.
E) Controlling System
System control, signal synchronization, and data acquisition are achieved through a
PC. The ICCD is externally triggered by the laser. The synchronization is done by a built-
in pulse/delay generator in the camera controller, namely the “programmable timing
generator (PTG) module”.
The ST-133 camera controller (Princeton Instruments) is a compact controller for the
PI-MAX ICCD camera. It provides up to 1 megapixel per second data transfer rate. The
gate width and gate delay are adjustable, which are specified by the operator.
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F) Beam Dump and Optical Housings
Beam dump is used to collect and absorb the astray laser beam and scattered laser
light. To reduce the background noise, most of the optical collection systems are covered
by colored or black housings.
3.1.2 Quantitative Temperature Measurement
In air-fed combustion studies, the temperature measurement can be performed quite
accurately using nitrogen Raman spectrum, as demonstrated by numerous investigations
(e.g. Eckbreth, 1996). In the present nitrogen-diluted methane/air diffusion flames, N2 is the preferred species of thermometry due to its abundance, pervasiveness, and well- understood Raman spectrum.
There are several methods to measure the temperature based on Raman scattering spectroscopy. Here, the temperature is determined by “curve-fitting” the measured spectrum based on the theoretical spectra library. Typically, the spectra of the Q-branch
Stokes are used for temperature measurement. The theoretical spectral distribution as a function of temperature is obtained from the quantum theory. Although the details about the theoretical aspects can be found in Long (1977) or Bradley (1990), a brief description is given in Appendix A.
The method of least squares is employed for the “best-fit”. It may be considered as a special case of the more general method of maximum likelihood (Bevington and
Robinson, 1992). For the least squares method, the objective of finding the optimal fit to the data is equivalent to minimizing the chi-squares (χ2), which is calculated based on the
sum of the squares of the residuals and is the index of the degree of “best-fit”.
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The curve-fitting of experimental data and theoretical spectra are performed by using
the software “CARSFIT” developed by the Sandia National Laboratories (Farrow et al.,
1985). Figure 3.5 shows an example, comparing the best-fit theoretical spectrum and the
experimental spectrum of nitrogen at about 1530 K. The corresponding χ2 is 0.128, and
the uncertainty (to be discussed in Section 3.1.4) associated with this curve-fitting is ±25
K.
3
2.5
Experimental data 2 Theory
1.5
1 Relative IntensityRelative
0.5
0 2200 2250 2300 2350 Raman Shift (cm-1)
Figure 3.5 Comparison of experimental and theoretical spectra for N2 at the “best-fit” temperature of 1530±25K. The experimental data are taken at 11.2 mm away from burner surface in a diffusion flame (75% nitrogen/ 25% methane burning in air), with fuel mixture injection speed of 1.10 cm/s.
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3.1.3 Qualitative Species Measurement
For the qualitative study of the major species profiles across the flame, Raman spectra over a wavelengths range of 560-660nm are acquired using the current setup. In this wavelength window, not only nitrogen Raman spectrum is included, distinct Raman signals of several other major species are also covered.
As an example, the full spectra at different locations across the flame are shown in
Fig. 3.6. All the intensity of the distinct spectra are normalized by the nitrogen peak for better illustration in Figs. 3.6 (a) and (c). The laser beam scans through the flame in the vertical/transverse direction, as indicated in Fig. 3.6 (b). At each location, the corresponding Raman spectra are shown in Fig. 3.6 (a). In these spectra, distinct Raman signal from the major species, including CO2, O2, N2, CH4, and H2O, are noted. These
Raman spectra can show the relative species concentration at different locations across
the flame. For example, there is no detectable CH4 (O2) Raman signal on the air (fuel)
side. It implies that the thin reaction zone can be located by checking the intensity change
of CH4 or O2 signal.
Figure 3.6 (c) also demonstrates the nitrogen Raman spectra across the flame. As discussed earlier, the temperature measurements are based on the shape of the nitrogen
Raman spectra. The different shapes of nitrogen spectra at different location indicate the temperature distribution across the flame.
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Figure 3.6 Raman spectra for the diluted methane/air diffusion flame. The dilution level is 75% nitrogen and the fuel mixture injection speed is 1.10 cm/s. (a) Spectra at different locations marked in (b). (c) Nitrogen spectra for this case at different locations.
3.1.4 Uncertainty Analysis for Raman Temperature Measurements
3.1.4.1 Uncertainty of Spatial Location Determination
The current Raman setup is a point measurement. In order to obtain a spatially resolved temperature profile, the relative position between the burner surface and laser probe needs to be determined. For current experimental setup, there are two major sources leading to the error for such a determination of relative location.
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3.1.4.1.1 Mechanical Translation System
Raman spectra are obtained at different locations in the transverse/vertical direction
from the burner surface. Since it is more difficult to directly shift the laser beam, which is
perpendicular to the burner symmetry axis, up and down without affecting the alignment
of the whole system, the burner facility is translated instead. The translation system for the whole burner facility includes:
a. A micrometer (Mitutoya Corp., Japan) with a high accuracy of ±0.01mm;
b. A pendulum hanging on the top frame of the burner to monitor the leveling of
the burner facility;
c. Three lab jacks to hold the whole facility and maintain the horizontal level when
changing the vertical location of the burner.
The whole facility can be moved up and down by adjusting three lab jacks. In this way, the Raman measurements can be conducted at different locations away from the burner surface. However, the position uncertainty of the mechanical translation system is somewhat large since the leveling of this relatively large scale system is not easy to be maintained. Nonetheless, the uncertainty of this translation system is estimated to be no more than 0.3 mm.
3.1.4.1.2 Steering Effect
Due to the change of the index of refraction in the hot flame zone, the position uncertainty caused by the deviation of the light beam is also important. Beam steering
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occurs whenever there is a density (basically index of refraction) gradient normal to the light beam direction. This causes the beam to “bend”. The resulting error on the beam deviation increases with increasing density gradient and with increasing path length along the test section. This beam-steering effect can be as large as hundreds of micrometers.
Most of the low-stretch diffusion flames investigated herein are relatively weak and thick, with the peak temperature being about 1300~1600 K. The estimated position uncertainty caused by this “steering effect” in the current study is about 100 µm.
Considering all the above uncertainty factors, the overall accuracy of the measurement in the transverse/vertical direction can be assessed. In this study, the major source of the position error comes from the mechanical translation system. Therefore, the overall uncertainty for the position measurement in Raman experiments is estimated to be
0.3 mm.
3.1.4.2 Uncertainty of Temperature Measurement
After obtaining the best-fit temperature through the least squares method, the uncertainty of the temperature measurement is determined based on the temperature range beyond which the theoretical spectrum appears to deviate from the experimental spectrum. This procedure is demonstrated in Fig. 3.7, where the experimentally obtained
N2 Raman spectrum is compared to several theoretical spectra at varying temperatures.
The solid line is the theoretical spectrum at the best-fit temperature of 1230 K, which agrees quite well with the experimental data. As shown in Fig. 3.7, the uncertainty of
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temperature measurement in this is estimated to be ±30 K in that there is no noticeable visual difference between experimental spectrum and theoretical spectra calculated within the temperature range of 1230±30 K.
5
Experimental data 4 Theory (best-fit, 1230 K) Theory (1200 K) Theory (1260 K) 3
2 Relative Intensity 1
0 2200 2250 2300 2350 Raman Shift (cm-1)
Figure 3.7 Comparison of experimental spectrum and theoretical Spectra at different temperatures for a diffusion flame with 40%N2 /60%CH4 burning in air. The fuel injection speed is 0.30 cm/s and the position of measurement is 6.0 mm away from the burner surface.
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3.2 OH-PLIF (Planar Laser-Induced Fluorescence)
3.2.1 Overview
There are several advantages make LIF/PLIF very unique and attractive for optical diagnostics in the high temperature reacting flow, including
• The corresponding experimental setup is relatively simple;
• Planar LIF (PLIF) is very suitable to map the flame structure;
• It provides a sensitive probe for detecting minor species in ppm level, such as the
key radicals in the reaction zone or leading to pollutant formulation.
Certainly, there are also some limitations or disadvantages for LIF/PLIF, such as:
• Tunable laser is very expensive and complex apparatus;
• Quantitative measurement is usually complicated.
To demonstrate the uniformity of quasi-1D flames and various multi-dimensional flame front instabilities, OH-PLIF is employed herein because of OH radical is a key radical in combustion. The OH radical is highly reactive and is a “chain carrier” in combustion kinetics. Thus, OH is a good marker characterizing the reaction zone and flame surface. In addition, OH is one of the most abundant active radicals in flame. The relatively larger OH concentration implies stronger LIF signals.
There exist a large number of wavelengths to excite OH radicals by laser light (Dieke and Crosswhite, 1962). Many factors affect the LIF signal quality. To obtain relatively
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strong LIF signal, the absorption coefficient of OH at the selected wavelength has to be
optimized based on the following considerations:
• Generally, a strong absorption is desirable because a large absorbed energy means
strong fluorescence emission;
• To minimize the image distortion, however, strong absorption should be avoided;
• The signal intensity should be a weak function of temperature for the current
experiment;
• At the selected excitation wavelength, other molecules (other than OH) in the
system should have very low transition probability;
In view of all the above considerations, the OH excitation scheme is chosen in the
band of A 2Σ+← X 2Π electronic transition. Owing to the high population density in the ground vibrational state, PLIF usually calls for the excitation from this state, i.e. v”= 0, while the selection of the target vibration level (v’) depends on the experimental
requirement. In the current study, the target is chosen to be v’=1. The excitation wavelength is about 283.5 nm, which corresponds to the Q1(8) rotational line. The current
UV laser system is available for such as excitation of this rotational-vibrational-electronic
transition.
The setup of the present OH-PLIF system is described in the following section. The
underlying physics and data processing can be found in Appendix B.
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3.2.2 Experimental Setup
The current facility for OH-PLIF measurement includes the following subsystems:
UV tunable dye laser, optics for laser sheet generation, collection/monitoring system,
controlling system, and beam dump. Figure 3.8 is the schematic of the present OH-PLIF system.
Controller Nd:YAG w/ Pulse Generator
Intensified DYE CCD Camera
Doubler UV Lens Iris F1 Lc F2 Ls
Beam Dump
PC Test Section
Figure 3.8 Schematic of OH-PLIF system.
A) UV Tunable Laser
The ultraviolet (UV) laser light used for OH excitation is obtained by frequency doubling the output of a tunable dye laser (Continuum, ND6000) pumped by a pulsed
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Nd:YAG laser (Continuum, Precision 8010). The input pump laser is 532 nm green light
with a repetition rate of 10 Hz.
The dye laser employed includes an optical bench, two dye circulators, and a
computer controller. The wavelength tunability is achieved through a sine drive mechanism on a mirror and a fine grating (2400 grooves/mm). The precise scanning of
wavelength via a motor is controlled by a computer. Rhodamine Chloride 590 is chosen
as the dye along with methanol as the solvent. The output of dye laser is a visible light of
a wavelength about 567 nm. Subsequently, the frequency of this 567 nm light is doubled
using a frequency doubler, thereby producing an UV light of 283.55 nm. This frequency
doubler (UVT, Continuum) uses KD*P and BBO crystals for doubling or mixing on
frequency. The resulting UV light has a pulse width of 7 ns and an intensity of 10~20
mJ/pulse. The florescence signal (~306 nm) captured by the collecting CCD is from the A
2Σ+ → X 2Π (1, 1) band of OH.
B) Optics for Laser Sheet
Figure 3.9 shows that a combination of cylindrical/spherical UV lenses are used to
generate a laser sheet. The cylindrical lens has a negative (concave) 75 mm focal length,
while the spherical convex lens has a positive (convex) 500 mm focal length. A constant
width laser sheet can be obtained through such an optical system. The resulting minimum
thickness of the laser sheet is ~0.1 mm and the width of the laser sheet at the center of the
test section is about 40 mm.
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Side view
Cylindrical Spherical UV lens UV lens
Top view
Figure 3.9 Schematic of laser sheet generation optics.
C) Collection/Monitoring System
The components of the collection system are two optical filters, one UV camera lens, and ICCD camera. The 3 mm-thick filter of WG305 (Schott) can cut off the light of wavelength less than 290 nm. As such, it can filter out the incident laser scattering of
283.5 nm. The second filter UG11 (Schott) is used to remove the visible and longer wavelength light, which only allows the band between 240 and 400 nm to pass through.
The thickness of this UG11 is 2 mm. PLIF imaging is then accomplished through a UV
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camera lens (Nikon, UV-Nikkor, 105mm, f/4.5) and an ICCD (PI-MAX 1024 RB,
Princeton Instruments).
D) Controlling System
Data acquired by the ICCD camera is routed to a computer for processing and
display. The ST-133 controller (Princeton Instruments) is a compact controller for the PI-
MAX camera. It provides the data transfer rate up to 1 Mega pixels per second and also
offers a standard video output, which makes it possible to record the evolution of the
detected OH-PLIF.
A programmable timing generator (PTG) module is installed in the controller to
provide a gated exposure for the ICCD camera. The gate width and gate delay are
specified according to the particular experimental requirements.
Figure 3.10 illustrates the data flow in the controlling system. At first, the PTG is
externally triggered by a signal from the laser system. PTG can then synchronize and
coordinate the gate operation and data transmission in the ICCD camera when the laser sheet arrives the test section.
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PTG VCR Controller Monitor Trigger from Laser
Signal/Power Serial Port
Gate Computer Control ICCD
Data Acquisition CCD Detector
MCP Command
Figure 3.10 Flow chart of controlling system for OH-PLIF measurements.
3.2.3 Data Analysis
The magnification factor of the present OH-PLIF imaging system is determined by taking an image of a ruler at the same location as the laser sheet. For the present OH-
PLIF setup, this factor is 11.1 pixels/mm obtained by this method. MatLab (version 6.5) is used to analyze the PLIF images. Listed below are some key issues related to data- processing.
1) Location of Burner Surface
To determine the location of the burner surface is essential for the flame structure measurement. Since the burner surface is always reflecting and emitting some strong
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light as the incident laser sheet passes the test section, this bright light signal in the PLIF
image can provide a good reference of the location of the burner surface. The uncertainty
of determination of the burner surface location is 1~2 pixels. Therefore, the uncertainty of
burner position for the current OH-PLIF setup is less than 0.2 mm.
2) Conversion and Normalization
After the location of the burner surface is identified, the origin of the coordinate is fixed. Once the magnification factor is known, the spatial coordinates of the image are
set. To compare different sets of data, the intensity values are normalized using the
corresponding maximal signal intensity.
3) Averaging and Plotting
To improve the signal-to-noise ratio, normally 100 frames of OH-PLIF images are averaged for the
steady quasi-1D flames. Furthermore, for processing the OH-PLIF data of quasi-1D flames, pixel-binning
is also used to minimize the random noise.
3.3 IR Imaging
The surface temperature is not only one important part in the thermal structure of the present flames, but also the controlling parameter of the surface radiation. IR imaging is used to detect the surface temperature in this study. The IR camera (ThermaCAM
SC2000) can image and measure the emitted infrared radiation from an object. The spectral range of this IR camera is 7.5 to 13 µm.
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The fact that radiation is a function of object surface temperature makes the determination of surface temperature possible. It has to be noted that the radiation measured by the IR camera depends on the temperature of the object and the surface emissivity.
3.3.1 Important Factors of IR Camera
Since IR imaging is a “line of sight” process, the absorption and emission of the medium between the target object and IR camera are coupled into the resulting image. To measure surface temperature, it is necessary to take into account the following factors:
A) Emissivity of the Object
The burner surface is made of sintered bronze. Using Fourier Transformation Infra-
Red (FTIR) technique, the emissivity of this burner surface is measured to be about 0.34 in the wavelength range of 5-12 µm.
In addition, the IR camera-deduced temperature value is compared to a thermocouple reading. This is carried out by using a sample porous plate with a thermocouple
imbedded underneath the surface. A hot plate is used to heat up the sample porous plate.
By comparing the thermocouple data with the camera reading, the emissivities over a
temperature range can be obtained, as shown in Fig. 3.11.
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0.55
0.5
0.45
0.4
0.35 Emissivity 0.3
0.25
0.2 400 450 500 550 600 650 Temperature (K)
Figure 3.11 Emissivity of the bronze porous plate calibrated by an imbedded thermocouple.
It is seen that when the temperature is less than 500 K, the emissivity is about 0.34, which agrees quite well with the FTIR-measured value. However, when the temperature is higher than 500 K, the surface of the sample material appears to be oxidized because the color of the sample surface becomes darker and darker. As a result, the emissivity increases as the temperature is increased, as shown in Fig. 3.11. After this calibration test, the black layer of copper-oxides covers the original sample completely. It has to be pointed out that such surface oxidization is greatly minimized during the flame experiments, because the fuel mixture is injected from the burner. The present non- premixed system also prevents the oxygen in the air contact with the burner surface directly.
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B) Distance between Object and Camera
This parameter is involved because that radiation is being absorbed between the object and the camera. Also, the transmittance drops as the distance increases.
C) Ambient Temperature and Relative Humidity
To consider the radiation emitted and absorbed by the atmosphere between the camera and the object, the ambient temperature has to be measured in advance.
Especially, when the surface emissivity is low and the object temperature is relatively close to the ambient, the ambient temperature is very important for the accuracy of the surface temperature measurement. The surface temperature can also be compensated by the fact that the transmittance is somewhat dependent on the relative humidity of the atmosphere. Therefore, the ambient temperature and relative humidity in the lab are monitored by a digital thermostat and relative humidity meter (HR Meter), respectively.
With all the above parameters are accounted for, the surface temperature can be outputted by the camera. To further calibrate the temperature reading from the IR camera, it has been checked by a pre-calibrated blackbody cavity radiator (with an accuracy of
1oC). The temperature range calibrated is from room temperature to 773 K.
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3.3.2 Surface Temperature Measurement
Direct IR images of the burner surface are taken by using the IR camera viewing from the bottom of the burner. The temperature values are then obtained by setting the emissivity as 0.34.
However, with the presence of a flame, the measurement of surface temperature is not straightforward due to the “contamination” of flame radiation. Figure 3.12 compares the
IR images of the burner surface with and without the flame. The top image shows the surface radiation right after the flame is extinguished by shutting off the fuel mixture supply; while the bottom image is the radiation from both flame and burner surface. As such, the temperature values shown in Fig. 3.12(b) are incorrect because the emissivity of the flame is not known.
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Figure 3.12 Direct IR images taken from the bottom of the burner. (a) IR image after the flame is extinguished. (b) IR image for the combination of flame and burner surface.
In both Figs. 3.12 (a) and (b), the temperature profiles along the centerline are shown as the white lines at the bottom. Figure 3.12 (a) shows that the temperature of the surface is fairly uniform over the center portion of the porous surface, which is represented by the area bounded by a white circle of 6 cm radius. Note that the radius of the porous burner surface is about 10 cm. In the core region of 6 cm radius, the surface temperature is quite constant at 423 K (302 F), with a standard deviation of less than 5 degrees Celsius.
Beyond this core region, the temperature seems to drop continuously along the radial
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direction to the temperature of the extension plate. Also note that the sharp peak near the burner edge is not true indication of higher temperature, which is caused by the change in the emissivity due to the presence of the sealing ring therein. These measurements indicate that the temperature of the burner surface remains very low compared to the flame temperature, and the radiation heat flux is quite uniform in a considerably larger area at the center of the burner surface.
To filter out the strong radiation from the gas phase (flame zone), the surface temperature is measured in the following manner. During the experiment, a sequence of surface radiation images are taken immediately after the flame is extinguished by shutting off the fuel supply. Since it takes 2~3 seconds for the hot gas products to flow away from the surface, the temperature reading drops dramatically at the very first couple of seconds, due to the disappearance of the flame. After the hot products drift away from the
field of view of camera, the IR camera is now aiming at the hot burner surface without
interference of the flame. We can then monitor the evolution of the surface temperature
during the burner cooling process. By extrapolating the time-varying surface temperature
plot to zero time, which represents the onset of flame extinguishment, the burner surface
temperature with the presence of the flame can be defined.
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440
420
Burner Surface Temperature 400 prior to Flame Extinction
380 Temperature (K) 360
340 0 50 100 150 200 Time (s)
Figure 3.13 Time variation of the burner surface temperature after the flame is extinguished at time=0. Symbols are the mean temperature in the core region (cf. Fig. 3.12) obtained by the IR camera. Line denotes the result using linear regression.
Figure 3.13 demonstrates how the burner surface temperature is extrapolated. Again,
extinction is achieved by shutting down the fuel supply at reference time zero.
Immediately after extinction, the surface temperature of the burner decays with time,
typically 0.1~0.5 K/s. This relatively slow decaying rate is due to the large thermal
inertial of the solid burner head. Since the IR-measured surface temperatures are fairly uniform over the core region of the burner surface, an average temperature over the 6 cm radius core region at the center of the burner is used for extrapolation. It is also seen from
Fig. 3.13 that the time variation of surface temperature is quite linear. The coefficient of
determination is typically greater than 0.98. Therefore, the burner surface temperature
prior to flame extinction is determined by linearly extrapolating to time=0. The
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uncertainty associated with the extrapolated burner surface temperature is estimated to be
0.4%.
3.4 Chemiluminescence Imaging
In the present study, most of the quasi-one-dimensional steady flames appear to be
“light blue” color. It is well-known that the excited-state CH (CH*) is the primary source of the chemiluminescence in this kind of non-sooting flames (Gaydon and Wolfhard,
1960). Other chemiluminescence species in the flame include OH*, C2*, and CO2*.
To qualitatively study the evolution of the reaction zone, the global
chemiluminecence, which is combination of the all the chemiluminescence emitted from
the reaction zone, is also very useful even without the use of narrowband filters to isolate
any specific chemiluminescence. The chemiluminescence imaging is then used to
compare with the data obtained by Raman scattering and OH-PLIF.
3.4.1 Experimental Facilities
The experimental setup for chemiluminescence imaging contains:
1) Color CCD camera (KP-D20, Hitachi Kokusai Electric Inc.) used here is a single
integration type of CCD. It is complemented by a digital signal processing system to
provide high quality images even under low light conditions. It also provides color
images via digital technology. This high density CCD camera features 380,000 effective
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picture elements. The camera is operated continuously during data acquisition. The exposure time is set to 1/60 second for each single shot.
2) A camera lens (Fujinon, HF25HA-1) collects the chemiluminecence signal from the flame. It has a short focal length (f# =1.4, focal length=25 mm) which provides a wide field of view.
For the current setup of chemiluminescence imaging, the resolution of the image is
7.37 pixels/mm. The spatial uncertainty is within one pixel. In term of the length scale,
the uncertainty level is about 0.1~0.2 mm.
3.4.2 Data Analysis
0
10
20
30 (mm)
Figure 3.14 Side chemiluminescence image across the flame. Nitrogen dilution is 75% and fuel mixture injection speed is 1.10 cm/s.
Figure 3.14 shows an example of global chemiluminescence image of a quasi-one- dimensional diffusion flame. The burner surface and the scale at the right side are appended to the original chemiluminescence image with the same pixel coordinates.
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Again, this image verifies the uniformity of the quasi-1D flame. Furthermore, the brightest luminous part, which is located at 10~11 mm away from the burner surface, indicates the rigorous reaction zone. It is also noted in Fig. 3.14 that the edge of the bright luminous zone on the air side is sharper than that on the fuel side. Additionally, the chemiluminescence is still visible over a wide range (5~10 mm away from burner surface) on the fuel side.
In Fig. 3.15, the corresponding normalized chemiluminescence intensity profile is plotted in the transverse direction at any location close to the symmetry axis, since the flame is quite uniform along the burner surface. The chemiluminescence signal intensity curve is normalized by the peak value. It is seen from Fig. 3.15 that the profile is not symmetrical. On the air side (to the right of the peak) the intensity drops from the peak dramatically. However, the curve has a long “ramp” on the fuel side (to the left of the peak). This is because the current chemiluminescence imaging is a “line-of-sight” technique. Even though the camera is focused on the center of the flame surface, the final image detected by the camera is actually the integration of chemiluminescence signal along the light path. Due to the slight curvature of the burner surface, the flame surface is similar to shape of the burner surface, which is spherical and convex. Thus, the integration along the straight light path generates the long “ramp” shape on the fuel side.
To resolve this type of problem, typically the de-convolution calculation is needed.
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1.2
1
0.8 Bright luminous zone
0.6
0.4
0.2 Normalized Chemiluminescence Signal
0 05101520
Distance away from Burner Surface (mm)
Figure 3.15 Normalized chemiluminescence distribution across the flame. Nitrogen dilution is 75% and fuel mixture injection speed is 1.10 cm/s.
In this study, only the location of the peak chemiluminescence and the bright luminous zone are of interest. This information can be obtained from the intensity profile directly without applying the mathematical de-convolution. As an example, it is seen from the intensity profile of Fig. 3.15 that there is “dent” on the fuel side. As such, the left/inner edge of the bright luminous zone can be easily defined. The location of the right/outer edge of the luminous zone is defined as the location of the maximum slope on the air side. With this definition of the bright luminous zone, the vigorous reaction zone in the flame can be identified. Comparing Fig. 3.15 with the direct image shown in Fig.
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3.14, the bright layer in the chemiluminescence image corresponds to the luminous zone defined in the intensity profile of Fig. 3.15.
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CHAPTER 4
NUMERICAL METHODOLOGY
The experimental quasi-one-dimensional flame is modeled by an axisymmetric configuration shown in Fig. 4.1. In this configuration, the origin is located at the center of the bottom burner surface. The coordinates, x and y, are the tangent (radial) and transverse (axial) coordinates, respectively. Without any forced air flow from the bottom, the stagnation point flow field is induced by the natural convection.
R Porous g Burner Surface Fuel Injection u
v
x Flame y Stagnation Point
Buoyancy-Induced Air Flow
Figure 4.1 Configuration of the present quasi-one-dimensional diffusion flame.
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4.1 Justification of Stagnation-Point Boundary Layer Model
At first, it is noticed that natural convection near a horizontal plate has been
investigated by several earlier studies (e.g. Wagner, 1956; Gill et al., 1965; Singh et al.,
1969). These studies presented the flow solutions from the center towards the edge with
the assumption that the boundary layer has a zero thickness at the edge. Clifton and
Chapman (1969) defined a critical boundary layer depth at the plate’s edge as the
characteristic length scale for this configuration. Aihara et al. (1972) carried out a systematic experimental study on the downward facing heated plates. Their work provided velocity and temperature fields that show the complex nature of the buoyant flow around the horizontal heated plate. An inversion layer was found outside the viscous boundary layer. Aihara et al. (1972) claimed that the system is very sensitive to small disturbances. Also at elevated temperatures the radiant heat transfer is significant compared with the convection, making heat transfer correlations difficult.
Contrast to the complicated flow field in the boundary layer of flat plate with finite dimension (Clifton and Chapman, 1969; Aihara et al., 1972), the boundary layer flow near the stagnation point of a cylindrical or axially symmetric blunt body can be much simpler. Ostrach (1964) systematically studied laminar flows under gravitational body force. He pointed out that the laminar boundary layer results for a horizontal cylinder should be valid when Grashof numbers are in the range of 104 to 109. In addition the
tangential velocity was shown to increase from zero at the lower stagnation point
approximately linearly up to 60o along the surface of the cylinder (Ostrach, 1964). This is
true for any transverse location across the boundary layer. Ostrach (1964) further claimed
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that the boundary layer thickness at the lower stagnation point possesses an approximately constant value over a large range of azimuthal angle, say 30o. Therefore,
in the neighborhood of the symmetry axis (x = 0), the boundary layer thickness is
constant, as the result of a stagnation point flow.
The above conclusion also implies the similarity between the stretch rates induced by
a forced flow and a free convection, although there are obvious differences in the two
resulting flow fields because of the differences in momentum equation and the associated
boundary conditions. Furthermore, with the presence of flame, similarity of flame structure and extinction characteristics between the two flow fields has been reported by
Foutch and T’ien (1987).
Ostrach (1964) also extended those results for the 2D bodies to axisymmetric bodies by reviewing several previous studies, including those of Merk and Prins (1953) and
Braun et al. (1961). It was found that the same conclusions are held for the axisymmetric
blunt bodies (Ostrach, 1964).
With an arc length of 20 cm and a radius of curvature of 382 cm in our current
configuration, the azimuthal angle of the burner surface is only about 2o. Based on the
dimension of this burner, the Grashof number is of the order 107. Therefore, according to
the study of Ostrach (1964), the stagnation-point type, laminar boundary layer theory is a good approximation of the present buoyancy-induced flow.
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4.2 Flame Radiation Model
4.2.1 Overview
Radiation contributes to the heat loss from the flame as well as the burner surface.
T’ien (1986) summarized several important studies on the low-stretch flames and
concluded that flame radiation and surface radiation are significant factors leading to
flame extinction at low-stretch conditions.
The simplest radiation model uses the gray gas assumption wherein the radiative
properties of the gas are spectrally independent. In these gray models, the radiation
intensity is attenuated from the blackbody radiation intensity by a constant absorption
coefficient. In many flame analyses, the Planck mean absorption coefficient as a
continuous function of the temperature and partial pressure of the gas, is often used.
However, the flame is actually not optically thin. The use of the Planck mean absorption coefficient introduces quantitative inaccuracy in the cases where flame radiation is important, such as the low-stretch flames.
Bedir et al. (Bedir et al., 1997; Bedir, 1998) thoroughly compared and discussed most of the radiation models currently available for combustion study in the literature.
According to their work, the statistical narrowband model is one of the most accurate
models. This model is also computationally tractable and is therefore the model of choice
for the present simulation. The line-by-line calculation is the most accurate computational
scheme but not practical in flame simulation of the type we are interested in here because
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of the computational expense. Since this model was described in detail in the study of
Bedir (1998), only some important aspects are highlighted in the following.
The statistical narrowband model is used to maintain the spectral properties of the
participating gases. Real gases absorb and emit in discrete intervals and quantities across
the radiation spectra. These irregular patterns are a result of transitions in energy states of
the gas molecules in the presence of radiative energy, or photons. Although the emissive
and absorptive properties of a gas appear as lines at discrete frequency intervals, several
phenomena contribute to the broadening of the lines into bands. If the bands are
sufficiently narrow, the blackbody radiation intensity can be treated as a constant within a
particular narrow band, and consequently be taken out of the integral. In the present
narrowband model, collision broadening is the primary broadening effect at atmospheric pressure and the temperature range of interest, although Doppler broadening is also
included in this model (Bedir et al., 1997; Bedir, 1998).
In the case of a blackbody surface, the radiative flux coming out of the surface is
simply a function of the surface temperature. We have extended the model to consider
gray surface so that the surface reflection of radiation from the gas phase is accounted
for. This gray surface model creates a coupling between the gas phase radiation and
surface radiation, complicating the calculation of the radiative boundary condition.
4.2.2 Radiation Modeling
A narrowband radiation model is employed in this work to compare with
experimental data for the thick low-stretch flames. The radiatively participating species
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considered herein are CO2, H2O, and CO. Unfortunately, no narrowband radiation data
are currently available for methane. The Curtis Godson approximation (Godson, 1953) is
applied to extend the narrowband model to the non-isothermal and non-homogeneous
combustion regimes. The transmittance of a gas mixture is the product of the individual
gas transmittance (Kim et al., 1991; Bedir, 1998).
In order to solve the energy equation, the net radiation flux (Qnet) must first be obtained at each point. The discrete ordinates method is used in order to include the directional dependence of the radiation. In this manner, the angular variation of the radiation intensity is modeled over a number of discrete intervals, or ordinates. In the
current simulation, the non-gray narrowband radiative transfer equation is solved via the
S8 discrete ordinates method, using a 20-direction Gaussian quadrates set (Bedir, 1998).
The radiative flux is determined by integrating the spectral radiation intensity over the solid angle Ω and frequency ν:
dQnet d ⎡⎤ =Ω∆∑ ⎢⎥∫ ψ Idν ν , (4-1) dy dy ∆ν ⎣⎦4π
where ψ is the direction cosine and Iν is the spectral radiation energy flux per unit solid
angle, i.e., spectral radiation intensity.
Previous simulations of radiating diffusion flames employing this statistical narrowband model (e.g. Bedir et al., 1997; Bedir, 1998; Rhatigan et al., 1998; Frate et al.,
2000) have opted for a simplified radiative boundary condition by setting the boundary as
a perfect blackbody. For the current study, a more general radiation formulation, enabling
the modeling of a gray surface boundary, employed. This improved model allows us to
study the interaction between the burner surface radiation and the gaseous flame
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radiation. The emissivity of the burner surface is experimentally measured using a FTIR
spectrometer. The results show that the burner surface is quite gray spectrally because the
measured emissivity is fairly constant in the wavelength range investigated (1.8~12 µm).
Thus, the averaged value of emissivity, 0.34, is used in the simulation for the presumed
diffusely gray burner surface.
In order to take the surface radiation into account, the radiative transfer equation has
to be modeled in the following fashion (Menart et al., 1993):
∂Ω∂→Is(), τ () s′ s ∂ νν=+Ω→I ()sIsss⎡ + ()(), τ ⎤ ∂∂ss′ bwwwννν ∂ s⎣ ⎦ ss′= (4-2) s ∂ ⎛⎞∂→τ ()ss′ + ν Isds()′′, ∫s ⎜⎟bν w ∂∂ss⎝⎠′
where s and s’ are the position variables along a path, τν (ss′ → ) is the spectrally
∂→τ (ss′ ) averaged transmittance along the path from s’ to s, ν gives the spectrally ∂s′ s′=s
averaged absorption coefficient, subscripts b and w respectively denote the blackbody
and the burner surface (y=0), and superscript “+” represents the positive y direction. The
first term on the right hand side of Eq. (4-2) represents the local emission. The second
term on the right hand side of Eq. (4-2) represents the local absorption of the surface
emission, while the last term represents emission from the participating species along the
line of sight from sw to s. This equation shows the correlation between the absorption
coefficient and the radiation intensity (Bedir, 1998).
To solve the spectral radiative intensity Iν from the equation of transfer (Eq. 4-2), the
+ corresponding spectral radiative intensity on the burner surface Iswwν (),Ω is given by
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1−ε I +−sIs,,Ω=ε +wν nIsdˆ Ω Ω Ω, (4-3) wwννν() wbww () ˆ w ν() w π ∫nw Ω<0
where εwν is the spectral emissivity of the burner surface, nˆw is the normal vector from the burner surface, and superscript “-” represents the negative y direction. The first term on the right hand side of Eq. (4-3) represents the emission from the burner surface, while the second term represents the wall radiative reflection, which indicates the interaction between the surface radiation and gas phase radiation. If a blackbody assumption is
applied on the burner surface, i.e. ε wν = 1, the second term on the right hand side of Eq.
(4-3) vanishes. For the procedure of numerical simulation, the negative directed intensity
− (incoming to the burner surface), Isν ( w ,Ω) , is computed first since the blackbody assumption is still valid for the ambient air. Then this negative directed intensity is inputted into Eq. (4-3) to solve the radiative intensity on the burner surface.
Additionally, the radiative heat fluxes in both positive and negative directions and net radiation flux (Qnet) at each point in the computational domain can be readily computed with the solved radiation intensity (e.g. Bedir et al., 1997; Bedir, 1998; Rhatigan et al.,
1998).
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4.3 Numerical Modeling
4.3.1 Formulation
4.3.1.1 Assumptions
The basic assumptions for current quasi-1D modeling are summarized as follows:
1. Axisymmetric laminar flow field;
2. Forward stagnation-point boundary layer under normal gravity (1 g);
3. The gas phase is ideal gas;
4. Fick’s law for mass diffusion;
5. Gaseous fuel mixture is uniformly discharged from the porous burner surface;
6. The temperature distribution along the burner surface is constant;
7. The temperature of the gas mixture at burner surface is the same as the
temperature of the solid burner surface;
8. Scalar variables, such as temperature and species concentration, are a function of
the axial direction (y) only.
4.3.1.2 Governing Equations
In the following governing equations, x and y are respectively tangent/radial and transverse/axial coordinates, u and v are respectively the velocity components in x and y directions, p the pressure, µ the viscosity coefficient, λ the thermal conductivity, and cp the specific heat at constant pressure, T the temperature, Ru the universal gas constant, ρ the mixture density, ρe the ambient density, and Qnet the net radiation flux. For the i-th
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species, Yi is the mass fraction, Viy the diffusion velocity in the y-direction, cpi the specific heat at constant pressure, Mi the molecular weight, hi the specific enthalpy, and ωi the molar rate of production.
A) Continuity Equation:
∂ ρuxκ ∂ ρvxκ ()+ ()= 0 , (4-4) ∂x ∂y where κ=1 for the axisymmetric flow, while κ=0 for the 2D planar flow.
B) x-Momentum Equation:
Since the natural convection is considered here, the gravity body force term is
included in this equation. Near the stagnation point, the x-component of the gravitational
vector, gx, can be written as:
x gg=− . (4-5) x R
Therefore, the x-momentum equation becomes:
∂∂∂∂∂uupux⎛⎞ ()ρρuv+=−+−() ⎜⎟ µρ g. (4-6) ∂∂∂∂∂x yxyy⎝⎠ R
Furthermore, since the pressure gradient across the boundary layer, i.e. in y-direction, is zero, the pressure gradient in the x-direction at any point in the boundary layer is equal to that outside the boundary layer. Thus the first term of the right hand side in Eq. (4-6) is:
∂p dp x ==ρρgg =− . (4-7) ∂x dxex e R
Substituting Eq. (4-7) into Eq. (4-6), we obtain the following x-momentum equation:
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∂u ∂u ∂ ⎛ ∂u ⎞ x ()ρu + ()ρv = ⎜µ ⎟ + (ρe − ρ)g . (4-8) ∂x ∂y ∂y ⎝ ∂y ⎠ R
C) Energy Equation:
II dT d⎛⎞ dT dT dQnet ()ρλρωvcpiiypiiii−+⎜⎟∑∑ YV c ++= h M 0 . (4-9) dy dy⎝⎠ dyii dy dy
D) Species Equations:
dY d ()ρv i + ()ρY V − ω M = 0 . (4-10) dy dy iy i i i
4.3.2 Transformed Governing Equations
4.3.2.1 Similarity Transformation
According to the studies of Smooke et al. (1986) and Foutch and T’ien (1987), the governing equations Eqs. (4-4) and (4-8)-(4-10), are further simplified based on the following two transformations:
1) V=ρv is the mass flow rate in the transverse direction, and is only a function of
the transverse coordinate y;
u 2) f ' = is the derivative of the modified stream function, where ab is the axb
buoyancy-induced stretch rate defined earlier.
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After transformation and setting κ=1, the equations of continuity, x-momentum, energy, and species reduce to: dV + 2abρf '= 0 , (4-11) dy
ddfdf⎛⎞′′ 2 ρρ− g e , (4-12) ⎜⎟µρ−−Vafb ()′ + =0 dy⎝⎠ dy dy ab R
dT 1 d ⎛ dT ⎞ ρ I dT 1 I 1 dQ net , (4-13) −V + ⎜λ ⎟ − ∑YiViy c pi − ∑hiωi M i− = 0 dy c p dy ⎝ dy ⎠ c p i dy c p i c p dy
dY d − V i − ()ρY V + ω M = 0, (i = 1,2,...I) . (4-14) dy dy i i i i
4.3.2.2 Boundary Conditions
The corresponding boundary conditions for the transformed governing equations Eqs.
(4-11)-(4-14), are:
(1) For y =L, i.e. oxidizer boundary:
f ′ ==0,TTeiie , YY =, , (4-15, 16, 17)
where Te is the ambient temperature, Yi,e is the ambient mass fraction of the i-th species.
Subscript “e” denotes the boundary on the air side, which is the ambience (y=L).
(2) For y = 0, i.e. on the burner surface:
VvfFFF==ρ ,'0, ⎛⎞dT , (4-18, 19, 20, 21) ⎜⎟λχρ+=QVcTTHVVYYVnet,, w F p F(), w −+ e w i F = F i ,,, F + F i F iy F ⎜⎟dy + ⎝⎠y=0
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where VF the fuel mixture mass flux rate at the burner surface, vF the fuel mixture
velocity (cm/s) at the burner surface, χi the known incoming mass flux fraction, Qnet, w the net radiation flux out of the burner surface, and Hw the burner heat loss flux
(described later in detail). Subscript “F” denotes gas phase quantities at the burner surface (y=0), and subscript “w” represents the solid phase quantities at the burner surface.
The boundary condition on the burner surface of the energy equation, Eq. (4-20), is derived based on the heat balance, which is discussed in details in the following section.
4.3.2.3 Heat Balance at Burner Surface
The current model takes into account the radiative heat transfer in the gas phase, the radiative absorption, reflection and emission at the burner surface, and the burner heat loss to the surroundings. Figure 4.2 shows the resulting energy balance at the burner surface. Performing the energy flux analysis over the burner control volume (delimited by the dashed rectangle), the energy conservation at the burner surface can be expressed as:
dT Conduction from the gas phase (λ ) dy y=0+
+ net radiation flux out of burner surface (Qnet, w )
= Heat to warm up the fuel mixture (VcFpFw, () T− T e) + Burner heat loss (Hw).
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The net radiation flux at the burner surface is expressed as the difference between the absorbed flux (Qa) and emitted flux (Qe), which is equivalent to the difference between the incoming radiative flux (Q-) and outgoing radiative flux (Q+):
QQQQQnet, w=−= a e +−()00 −( ) . (4-22)
The heat loss (Hw) contains the heat conducted to the burner assembly in the solid phase and the heat carried away by the cooling water. This value, however, cannot be readily evaluated. As a result, the overall burner heat loss (Hw) through the burner surface is estimated by assuming that it corresponds to a fraction of total heat flux into the burner surface, including the conductive heat flux from the gas phase and the net radiation flux.
Namely, Hw is modeled as
⎡⎛ ⎞ ⎤ ⎜ dT ⎟ H w = ξ ⎢ λ + Qnet,w ⎥ , (4-23) ⎜ dy + ⎟ ⎣⎢⎝ y=0 ⎠ ⎦⎥ where ξ is the heat loss fraction parameter. In our calculations, the final value of ξ is
adjusted until the computed surface temperature (Tw ) matches the measured one.
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to cooling to burner water body Fuel g Heat Mixture Te Loss Hw Burner - Surface + Tw Conduction Net radiation flux from gas to surface Qnet.w
Emitted Incident Reflected Incident radiation radiation radiation radiation y from from from from surface flame surface ambient
Figure 4.2 Schematic of energy balance at the burner surface.
4.3.3 Numerical Method
The governing equations, Eqs. (4-11)-(4-14), are discretized by finite difference.
Second order central differential method is used to discretize the diffusion term, while the upwind scheme is employed for the convection term. An existing code, which was used in the study of Rhatigan et al. (2002), is modified for the present calculations. The structure of this code is similar to that of the well-known OPPDIF code (Lutz et al., 1996) for solving the opposed-jet diffusion flames. The present code can solve the whole system of equations on an adaptive non-uniform mesh distribution.
To include the detailed chemical kinetics, and thermodynamic/transport properties, standard packages, including CHEMKIN (Kee et al., 1989) and TRAN (Kee et al., 1986),
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are employed. The detailed chemical kinetics for methane oxidization is taken from GRI-
Mech 3.0 (Smith et al.), which contains 52 species and 325 reactions.
The computational domain is finite, which covers a sufficiently wide range from the burner surface to the oxidizer boundary, where the local temperature is equal to ambient temperature and the resulting temperature gradient is zero. The grid independence test is also performed. Since the adaptive non-uniform mesh is used, more grid points are distributed in the regions with steep gradients and gradient derivatives. Recognizing that computation of narrowband model at each grid point is numerically expensive, grid points of 200~300 within a 30~45 mm physical domain are used, which are found to provide grid-independent solutions.
For mapping the flame response curve continuously and capturing the extinction turning point, the one-point temperature-controlling method developed by Nishioka et al.
(1996) is employed. An “internal condition”, chosen from the existing grid points of a convergent solution, is introduced, i.e. T=T* at y=y*. While there is no specific restriction about T* and y*, y* is typically chosen within the region of relatively steep temperature gradient. Since the internal condition is now an extra condition for the system of the governing equations, one of the original boundary conditions has to be removed. For example, when the value of ab is specified, the most natural boundary condition to remove is the fuel mixture mass flux VF at the burner surface. As a result, this removed boundary condition becomes an edge value of the solution. Starting from an existing solution, the solution of the next point along the response curve can therefore be obtained by fixing y* and varying the value of T*. This approach is found to be efficient in generating the entire flame response curve.
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CHAPTER 5
RESULTS AND DISCUSSION
The experimental results show that the current burner is suited for studying gaseous diffusion flames at extremely low stretch rates previously unattainable under normal gravity. By using a burner with a large radius of curvature (R~400 cm), the buoyancy induced stretch rate is as low as 2 s-1.
This chapter summarizes the experimental and numerical results. The uniformity of the resulting quasi-1D flames is first demonstrated (Sec. 5.1). Flame stability map of low stretch diffusion flames is shown in Sec. 5.2. Detailed structures of quasi-1D diffusion flames are demonstrated in Sec. 5.3. Section 5.4 presents various multi-dimensional flame instabilities. Finally, experimental results and numerical simulation are compared in Sec. 5.5.
5.1 Uniformity of Quasi-1D Diffusion Flames
The uniformity of the quasi-1D flames is tested by imaging the reaction zone using
OH-PLIF. A sample side-view of OH-PLIF image of a methane flame diluted by 75 %N2 is shown in Fig. 5.1(a). The burner surface is located at the upper edge of the figure.
Figure 5.1(b) compares the vertical profiles of OH-PLIF intensity at five different locations along the flame surface, as indicated by the dash lines in Fig. 5.1(a). All these profiles are shifted to a flame reference coordinate according to the location of maximum
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OH-PLIF intensity. The overall similarity in the shapes of all the profiles indicates that the OH concentration is quite uniform along the flame.
15000 (b) A B 10000 C Standoff Distance FWHM D E 5000 OH-PLIF Intensity (Counts) OH-PLIF Intensity
0 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Flame Coordinate (cm)
Figure 5.1 (a) OH-PLIF image of a steady quasi-1D flame. (b) Comparison of OH-PLIF intensity profiles at varying radial locations.
Furthermore, the sharp increase in the OH-PLIF intensity profile on the fuel side of the flame will be used as a ‘marker’ for the measurement of flame standoff distance. It is convenient to define the flame standoff distance by the distance between the burner surface and the location of this steep slope of the OH-PLIF profile. For example, in Fig.
5.1, the standoff distance is approximately 9.5 mm everywhere along the burner surface
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in this case. In addition, the reaction zone thickness of the steady quasi-one-dimensional flame can also be characterized based on the FWHM (full width at half maximum) of this
OH-PLIF intensity distribution. It is seen from Fig. 5.1 (b) that this reaction zone thickness is about 1.5 mm for the diffusion flame shown in Fig. 5.1.
Figure 5.2 plots the steady diffusion flame standoff distance and OH-FWHM, as a function of fuel mixture injection speed for two different fuel dilutions, namely 25% and
60% methane in nitrogen. The corresponding surface temperatures, measured using the
IR camera, are also reported. It is seen that the flame standoff distance increases with increasing injection speed, while the burner surface temperature decreases. The flame standoff distance is rather sensitive to the fuel injection speed: if we double the injection speed, the standoff distance increases about 70%. This is one key advantage of this burner configuration, since the standoff distance can be controlled by simply adjusting the fuel injection speed. The OH-FWHM is not very sensitive to the fuel injection speed as shown in Fig. 5.2, which keeps in the range of 1.5~2.2 mm. Furthermore, the OH-
FWHM at this low-stretch rate (1.6 s-1) is much larger than those of high-stretch rate diffusion flames reported in the literature (e.g. Smooke et al., 1986; Puri et al., 1987;
Sung et al., 1995), which is in the order of 0.2-0.6 mm.
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(a) 25% CH4/75% N2 12 500 Burner Surface Temperature (K)
10 Standoff Distance 480
8 460 6 440 4
Length Scale (mm) Scale Length 420 2 OH-FWHM
0 400 0.6 0.8 1.0 1.2 1.4 1.6
(b) 60% CH4/40% N2 12 550 Burner Surface Temperature(K)
10 Standoff Distance 540
8 530 6 520 4 Length Scale (mm) 510 2 OH-FWHM 0 500 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Fuel Mixture Injection Speed (cm/s)
Figure 5.2 Steady diffusion flame standoff distance, OH-FWHM thickness, and burner surface temperature as a function of fuel mixture injection speed: (a) 25% CH4/75% N2 and (b) 60% CH4/40% N2.
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5.2 Flammability and Instability Map of Low Stretch Diffusion Flames
The flammability and instability diagram of methane-air diffusion flames is mapped in terms of fuel mixture injection speed and nitrogen dilution level. Various flame patterns are observed by gradually varying either the dilution levels or the fuel mixture injection speed. Conditions leading to sooting flames, non-sooting steady quasi-1D flames, flame extinction, and various multi-dimensional flame patterns are identified.
Figure 5.3 shows the resulting flame stability map of the low-stretch (~1.6 s-1) diffusion flame studied in this work. Two clear major boundaries are observed in the diagram. These two boundaries divide the entire map into three regions: sooting flame, non-sooting flame, and extinction. The two boundaries, respectively, referred as the sooting limits boundary and the extinction limits boundary, are almost parallel to each other. Raman measurements show that the flame temperatures of the non-sooting blue flames are no more than 1600 K, which is below the critical temperature for soot formation (Glassman, 1996).
In Fig. 5.3, the filled area indicates the flame instabilities, which will be addressed in a later section. All the boundaries shown in Fig. 5.3 represent the best fit to many conditions examined. There is some overlapping between those neighboring regions. For example, the horizontal boundary between the Quasi-1D flames and the instability region is within 1.33±0.02 cm/s; the upper vertical branch of the “extinction limits” is within
0.86±0.005 (in term of nitrogen mole fraction). Other oblique boundaries have certain uncertainty levels in both vertical and horizontal directions to some extent. In general, the relative uncertainty levels for all the boundaries in Fig. 5.3 are less than 1.5%.
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2
Waves and 1.5 Bumps Blue Flame and Yellow Sooting Layer
1 Sooting Limits Quasi-1D Blue Flame (Non-sooting) Extinction 0.5 Limits
Extinction
Nominal Fuel Mixture Injection Speed (cm/s) 0 0 0.2 0.4 0.6 0.8 1 Nitrogen Dilution
Figure 5.3 Flammability and instability diagram for the present low-stretch methane diffusion flames. Nitrogen dilution represents the nitrogen mole fraction in fuel mixture. Shaded regions represent the flame instability conditions.
5.2.1 Sooting Flame Boundary
A luminous soot layer can be observed to separate from the blue flame only when the injection speed is greater than 0.4 cm/s and the nitrogen dilution less than 65%. Soot formation close to the extinction limit is inhibited because of the low flame temperatures.
An example of steady flame with sooting layer can be found in Fig. 2.3.
The present sooting limits are also compared to those of Tsuji and coworker (Tsuji and Yamaoka, 1969; Tsuji, 1982) for moderate to high stretch rates (12 to 103 s-1) in
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methane-air diffusion flames. In the flame-stability diagrams of Tsuji and Yamaoka,
(1969) and Tsuji (1982), the sooting critical value of non-dimensional fuel injection
1/2 speed (-fw), defined as (vf/U)(Re/2) , was plotted as a function of stretch rate (2U/R) for the cylindrical burner, where vf is the fuel mixture injection speed, U the air-stream velocity, , Re=UR/ν, R the cylinder radius and ν is the mean kinematic viscosity. For pure methane-air diffusion flames, Tsuji and Yamaoka (1969) found that, with decreasing stretch rate, the critical (-fw) leading to sooting flames decreases and tends to approach a constant value of ~0.35. Nonetheless, it would be difficult to extrapolate the previous data to a lower stretch rate, say 1~2 s-1.
Figure 5.3 shows that the sooting limit for the present low-stretch pure methane-air flame is vf= 0.4 cm/s. For the purely buoyant flow, the characteristic buoyant velocity is used to characterize U, which can be obtained by assuming unity Richardson number.
Thus the present critical (-fw) for sooting limit is ~0.28, which is lower than that of Tsuji and Yamaoka (1969).
5.2.2 Extinction Limits Boundary
Along the extinction limit curve in Fig. 5.3, two distinct extinction modes are observed using the present burner. Extinction at low injection speeds is governed by significant conductive heat loss to the burner due to the small flame standoff distance. As the fuel injection speed is increasing, the flame recedes from the burner and the heat loss to its surface is reduced. The governing extinction mechanism then becomes flame
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radiative heat loss. The controlling of heat loss at two different extinction modes will be examined by numerical simulation in Sec. 5.5.
5.2.2.1 Burner Heat Loss Extinction
Along the lower branch of the extinction boundary, the injection speed of fuel mixture is very low (e.g. 0.1~0.2 cm/s). Here the extinction is expected to be controlled by a different mechanism from the high dilution case. As the injection speed is decreased, the standoff distance is reduced and the substantial conductive heat loss to the burner surface lowers the flame temperature and increases the burner surface temperature; the flame extinguishes due to the unbalance of the heat generation and heat loss to the burner surface.
Although the overall trends observed in Fig. 5.3 agree with the results reported by
Tsuji and coworkers (Tsuji and Yamaoka, 1969, 1971; Tsuji, 1982), this is the first time that experimental data are available for such an ultra-low stretch rate. For pure methane- air flames, Tsuji and Yamaoka (1969) showed that with decreasing stretch rate, the critical fuel injection speed (-fw) leading to conduction-induced extinction decreases and approaches a limiting value of ~0.18, which is higher than the present data of 0.10
(injection speed of 0.15 cm/s) obtained at much lower stretch rate.
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5.2.2.2 Radiative Extinction
At the upper vertical branch of the extinction limit, as the nitrogen dilution is increased, the heat release per unit volume of fuel mixture decreases until stable combustion is no longer possible due to the existence of a heat loss mechanism. It is seen from Fig. 5.3 that to the right of the extinction curve, when nitrogen dilution is greater than 86%, no flame is possible. This dilution level becomes independent of fuel mixture injection speed, as indicated by the vertical slope at large injection speeds. Thus, this value corresponds to the intrinsic nitrogen dilution limit for methane at this ultra-low stretch rate. For the present methane/air diffusion flames, the dilution limit is found to be
(86.0±0.5)% nitrogen dilution. This value is slightly larger than that reported by Ishizuka and Tsuji (1981) and Tsuji (1892) at larger stretch rates, which was 83.5% nitrogen.
Another recent experimental study by Bundy et al. (2003) on methane/air diffusion flames reported that the dilution limit when using N2 as a suppressant is 84.1% at a global stretch rate of ~20 s-1.
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5.3 Detailed Structure of Quasi-1D Diffusion Flames
Since the flames currently under investigation are weak and hence more susceptible to external disturbances, non-intrusive optical measurements are necessary for the study of flame structures. The detailed structures of steady quasi-1D flames characterized herein include thermal profiles measured by the Raman spectroscopy and OH profiles measured by the OH-PLIF. Additionally, IR imaging is used to measure the burner surface temperature. As an alternative approach and a reference, the traditional thermocouple measurement is also conducted in this study. Results obtained by different approaches at the same experimental conditions are compared in this section.
5.3.1 Temperature Profiles
5.3.1.1 Thermocouple Measurement
Thermocouples are are based on the “Seebeck effect”, which occurs in electrical conductors that experience a temperature gradient along their length. Since temperature measurements can be readily made at low cost with shop-built probes and ordinary voltmeters, thermocouples have been widely used in combustion research.
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5.3.1.1.1 Radiation Correction
Quantitative interpretation of thermocouple measurements in high-temperature environments depends on many factors. These factors include the geometry and the optical properties of the thermocouple bead and wires, the local velocity and transport properties of the gases surrounding the thermocouple, and the radiation heat exchange and interaction between the thermocouple and the surroundings. Shaddix (1999) reviewed the literatures about the thermocouple corrections and compared different investigations on this topic. Particularly, several choices of Nusselt number correction have been discussed. A typical arrangement of thermocouple used in combustion is shown in Fig. 5.4. This “Y” shape thermocouple has relatively long lead wires, which are placed in a protective, ceramic support cover and also bent outward in order to provide certain tension for the wires. This arrangement can reduce the heat conduction back to the lead wires because of the long thin section between the thermocouple bead and the wires inside the support cover.
Thermocouple Wire
+ Ceramic Ceramic Support _ Rod Cover Thermocouple Bead
Figure 5.4 Schematic of the thermocouple configuration used in this study.
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For the particular geometry of the thermocouples shown in Fig. 5.4, the Nusselt number correlation model of Ranz and Marshall (1952) is commonly accepted for low-Re convection over a spherical thermocouple bead. Namely,
1/2 1/3 Nudsph, =+2.0 0.60Re d Pr ,
where Nudsph, is the Nusselt number, Red is the Renolds number based on the diameter of the bead (d) and average flow velocity, and Pr is the Prandtl number. The gas property values are evaluated at the free stream conditions for this correction. By solving the energy balance equation, the corrected temperature for the local gas temperature (Tg) is written as (Shaddix, 1999)
44 TTg =+TCεσ TC()/ T TC − TdkNu w d, sph ,
where TTC is the uncorrected thermocouple-measured temperature, εTC is the emissivity of the thermocouple, σ the Stefan-Boltzman constant, Tw the ambient temperature, and k the conductivity of the gas mixture. This method is also adapted in the current study for the correction of convection and radiation.
The selection of thermocouple is determined by the targeting temperature range and the resolution requirement of the experiments. A R-type thermocouple (Pt/13%Rh-Pt) is used to measure the transverse temperature profiles at several conditions. The bead diameter is only 0.365 mm to guarantee the fast response and minimal disturbance in the
combustion field. For temperature correction, εTC is set to be 0.22, which is the emissivity of R-type thermocouple in the vicinity of 1400K (Grosshandler et al., 1980).
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5.3.1.1.2 Temperature Distributions of Steady Flames
Even though the low stretch diffusion flame is very sensitive to any disturbance by physical probes, it is observed that thermocouple measurements can be somehow tolerated in certain cases investigated. It is expected that thermocouple measurements can at least provide the general trend of thermal profile of the low-stretch diffusion flames in the cases where the flame is relatively strong. It is found that when the nitrogen dilution is sufficiently low (<50%) and the fuel injection speed is sufficiently high for given fuel mixture, the flame is robust enough to allow the use of a thermocouple to measure local temperatures without inducing local or global extinction.
Figure 5.5 compares the thermocouple-measured temperature profiles (after radiation correction) at varying injection speed for the case with 40% nitrogen dilution. The reported values of temperature are averaged from 5 measurements at each location. The fluctuation of temperature reading is normally within 2%.
It is seen from Fig. 5.5 that the flame location (denoted by peak temperature location) recedes from the burner surface and the peak temperature increases, as the fuel injection speed increases. Specifically, when the fuel injection speed changes from 0.30 cm/s to 0.75 cm/s, the peak temperature increases from 1260 K to 1720 K, and the distance of the peak temperature from the burner surface is almost doubled. Furthermore, comparison with the results obtained using non-intrusive diagnostics shows that the locations of the maximum temperature agree well with the Raman and OH-PLIF measurements within ±1.5 mm.
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60% CH4/40% N2 1800 Nominal Fuel Injection Speed 1600 0.75 cm/s 0.55 cm/s 1400 0.40 cm/s 0.30 cm/s 1200
1000
800 Temperature (K) 600
400
0 5 10 15 20 Distance from Burner Surface (mm)
Figure 5.5 Comparison of thermocouple-measured temperature distributions at different fuel mixture injection speeds for the 60%CH4/40%N2 mixture.
In Fig. 5.5, the surface temperatures are measured by IR imaging. It is shown that the surface temperature generally decreases with increasing fuel mixture injection speed, although the difference in surface temperatures for the condition examined is relatively small.
It is also seen from Fig. 5.3 that the critical sooting limit is about 0.70 cm/s at 40% nitrogen dilution level. Thus, for the case with fuel injection speed of 0.75 cm/s, the flame appears sooting. It is shown in Fig. 5.5 that the maximum temperature of this case is more than 1700 K. For the other three cases with fuel mixture injection speed being less than 0.70 cm/s, their maximum temperatures are no more than 1600 K and the resulting flames are non-sooting.
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For the low injection speed case (0.30 cm/s), the flame is very close to the extinction limit (i.e. 0.28 cm/s for 40% N2 dilution), the flame temperature is only about 1200 K.
Certainly, the presence of the thermocouple has a relatively strong impact on such a weak flame. More fluctuations in the thermal profile are observed in this case. Hence, for the weak flames near extinction, non-intrusive optical techniques must be employed for quantitative study.
5.3.1.2 Raman Scattering Measurement
Although the thermal profiles can be measured by thermocouple for certain cases as illustrated in Fig. 5.5, the experimental uncertainty of this intrusive method is unclear. As mentioned earlier, the low stretch flame is very sensitive to any disturbance because local distortion and extinction of the flame surface have been observed when the thermocouple is placed near or into the flame zone. The disturbance is not only caused by the modification of the local aerodynamics, but also the radiation interaction between the thermocouple probe and the flame or the burner surface.
Therefore, the Raman scattering method is employed here for quantitative study of flame structure. Its application is much more complicated than the thermocouple measurement, but this non-intrusive method can provide the reliable thermal profiles for the low stretch diffusion flames. The thermocouple measurement is also compared with the Raman scattering measurement for those cases where both methods are applied.
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Table 5.1 Five representative cases for Raman measurement
Nominal Fuel Nitrogen Mixture Case Flame Description Dilution Injection Speed (cm/s) Steady bright blue flame, far from the A 0.40 0.55 extinction limit Steady light blue flame, very close to the B 0.40 0.30 lower instability zone and extinction limit Steady blue flame, close the upper instability C 0.75 1.30 region D 0.75 1.10 Steady blue flame Steady light blue flame, close to the upper E 0.75 0.75 branch of the extinction limit
Five representative quasi-1D flames are selected for Raman measurement studies.
The detailed conditions of these cases are listed in Table 5.1. As illustrated in Fig. 5.6, these five cases encompass two different nitrogen dilutions. For Cases A and B, the nitrogen dilution level is relatively low, namely 40% nitrogen in the fuel mixture. For
Cases C, D, and E, the nitrogen dilution is as high as 75%.
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2
Waves and 1.5 Bumps Blue Flame and Yellow Sooting Layer C
D 1 Sooting Limits Extinction Quasi-1D E Limits Blue Flame (Non-sooting) A 0.5 Extinction B Fuel Mixture Injection Speed (cm/s) Speed Injection Mixture Fuel
0 0 0.2 0.4 0.6 0.8 1 Nitrogen Dilution
Figure 5.6 Five selected cases for detailed Raman scattering measurement.
Raman spectra over a range of wavelengths (560~660 nm) are investigated. In this wavelength window, it covers CO2 (peaks at 571 nm and 574 nm), O2 (peaks at 580 nm),
CO (peaks at 600 nm), N2 (peaks at 607 nm), CH4 (peaks at 630 nm), and H2O (peaks at
660 nm) spectra.
Using Case A as an example, the Raman spectra at different locations across the flame are shown in Fig. 5.7. For better illustration, all the intensities of the distinct spectra are normalized by the peak nitrogen intensity at the same location. Note that this normalization does not affect the temperature measurement because temperature determination is based on the shape of N2 Raman spectrum.
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Figure 5.7 Averaged (5000 shots) Raman spectra at varying distance from the burner surface for Case A (40% nitrogen dilution and 0.55 cm/s fuel mixture injection speed).
It is also noted that the closest location to the burner surface which can be measurable by Raman scattering is about 3 mm away from the surface in the current setup, due to the reflection interference from the burner surface. Because of the weak intensity of the
Raman signal, 5000 shots are taken for every data acquisition in order to improve the signal to noise ratio.
To measure temperature, the nitrogen spectra are analyzed by using CARSFIT software. Figure 5.8 highlights the nitrogen spectra of Case A. The Raman scattering
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signals of N2 shown in Fig. 5.8 cover the wavelength range of 604-609 nm, which is wide enough to include the nitrogen Raman signals needed for temperature determination.
By curve-fitting the experimental spectrum based on the theoretical spectrum calculation, the temperature at 3.7 mm away from the burner surface is measured as 925
K. As approaching towards the flame zone, it is shown in Fig. 5.8 that the first hot band, which is to the left of the major peak, becomes more and more significant till moving outside the flame zone. The increasing intensity of the first hot band indicates that the local temperature is increasing. Furthermore, at 8.2 mm away from the burner surface, the second hot band start to emerge, and the temperature at this location is determined to be about 1450 K.
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Figure 5.8 Averaged (5000 shots) Raman spectra of nitrogen at varying distance from the burner surface for Case A (40% nitrogen dilution and 0.55 cm/s fuel mixture injection speed).
In general, the shape of the hot bands is more sensitive to the temperature change.
Thus, the accuracy of the curve-fitting method is better in the high temperature environments where the hot bands show up. Certainly, the subtle difference between the shapes of nitrogen spectra of different temperatures cannot be readily identified from the spectra shown in Fig. 5.8 without detailed analysis involving the theoretical quantum calculation.
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5.3.1.3 Comparison of Measured Temperature Profiles
The knowledge of the temperature profiles is an essential part of the flame structure investigation. The temperature distribution indicates the overall flame response. It is determined by all the chemical-physical processes in the flame zone. In a later section, the measured temperature profiles using Raman scattering are compared to the simulated results.
The temperature profiles obtained by Raman scattering and thermocouple measurement are compared in this section. All the thermocouple measurements are corrected by the method introduced in section 5.2.1.1.1. As illustrated in Fig. 5.6, five representative cases are chosen to demonstrate the flame structures of quasi-one- dimensional diffusion flames.
The error bars shown in the following temperature profiles are determined at each individual point. The horizontal error bar indicates the uncertainty of the determination of spatial location, while the vertical error bar shows the uncertainty of the temperature measurement. The uncertainty analysis of Raman measurements has been discussed in
Section 3.1.4. For the thermocouple measurements, the horizontal error bar is not shown since the spatial location is measured by a micrometer with an accuracy of ±10 µm; while the vertical error bar of all the thermocouple measurements is ±1% of the measured value according to the manufacturer.
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Case A: 40% nitrogen dilution, 0.55 cm/s fuel mixture injection speed
In Fig. 5.6, it is shown that Case A is the one close to the sooting limit boundary. The color of this flame is bright blue. The flame is sufficiently strong to withstand the external disturbance of the thermocouple probe. No local extinction is observed when the thermocouple intrudes into the flame.
1800
1600
1400
1200
1000 Temperature (K)
Thermocouple 800 Bright luminous zone Raman
600
2 4 6 8 10 12 14 16 Distance from Burner Surface (mm)
Figure 5.9 Temperature distribution across the flame for Case A. Both thermocouple- measured and Raman-measured data are included. The shaded region shows the observed bright luminous zone.
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Figure 5.9 compares the Raman-measured and thermocouple-measured data for Case
A. Using the Raman scattering measurement as the reference, the peak temperature of this flame is 1692 ±30 K. It is located at 11.2 mm away from burner surface. The region to the left of this peak is referred as fuel side, while the region to the right of this peak is referred as air side.
It is seen from Fig. 5.9 that the value of peak temperature measured by thermocouple is very close to Raman result. The difference between them is within the uncertainty range of the Raman scattering measurement. However, the location of the peak temperature differs by about 1 mm for these two measurements in this case. The location of peak temperature measured by thermocouple is to the left of that measured by Raman scattering.
The shaded section in Fig. 5.9 indicates the bright luminous zone of the flame determined by the chemilumenescence imaging. It covers the range from 9.9 mm to 11.2 mm away from the burner surface in the transverse direction. The peak temperatures measured by both methods are all lying in this region, as expected.
On the fuel side of the temperature profile, thermocouple measurement also agrees well with the Raman scattering measurement. However, larger discrepancies are seen on the air side. The thermocouple data are less than the Raman-measured temperatures by
150~200 K. It is noted in experiments that a small distorted “dent” on the flame surface is resulted form the insertion of the thermocouple on the air side. This distortion is due to the changes of the local flow field and radiation interaction between the thermocouple and the adjacent flame surface. However, when the thermocouple is inserted in the space between the flame and burner surface, it is NOT obvious to see such a change on the
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flame surface even though it is believed that similar effects by thermocouple intrusion should also exist on the fuel side.
Case B: 40% nitrogen dilution, 0.30 cm/s fuel mixture injection speed
This case is very close to the lower extinction limit, as illustrated in Fig. 5.6. The flame strength of Case B is much weaker than that of Case A which has a larger fuel injection speed. The maximum temperature measured by Raman scattering is only
1446±30 K for this case, and is located at 8.0 mm away from the burner surface.
1500
Raman Thermocouple
1000 Temperature (K)
Bright luminous zone
500
2 4 6 8 10 12 14 16 Distance from Burner Surface (mm)
Figure 5.10 Temperature distribution across the flame for Case B. Both thermocouple- measured and Raman-measured data are included. The shaded region indicates the observed bright luminous zone in the flame.
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Similarly, Fig. 5.10 compares the Raman-measured and thermocouple-measured data for Case B. The difference between the peak temperatures for both measurements in this case is more than 100 K. The peak location obtained by thermocouple measurement is about 1 mm to the left of that measured by Raman scattering. The shaded section in Fig.
5.10 covers the range from 7.3 mm to 8.5 mm in the transverse direction. The peak temperature measured by Raman scattering is within this region, although that measured by thermocouple is located outside the luminous zone.
On the fuel side of the temperature profile, thermocouple measurement is higher than the Raman scattering measurement by about 50 K. However, on the air side, the thermocouple measurement is less than the Raman-measured temperature by 200~300 K.
In this case, the local extinction is observed near the thermocouple wire when it is inserted into the flame surface. Large discrepancies of the measured temperature profiles indicate that the thermocouple measurement is not suitable for a weak flame like Case B.
Case C: 75% nitrogen dilution, 1.30 cm/s fuel mixture injection speed
As shown in Fig. 5.6, Case C has the largest fuel injection speed among all those five cases. It is very close to the upper instability region. The blue flame of this case is strong enough to withstand the external disturbance of the thermocouple probe. No local extinction is observed when the thermocouple intrudes into the flame.
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1800
1600 Raman Thermocouple
1400
1200
1000
Temperature (K) 800 Bright luminous zone
600
400 2 4 6 8 10 12 14 16 18 Distance from Burner Surface(mm)
Figure 5.11 Temperature distribution across the flame for Case C. Both thermocouple- measured and Raman-measured data are included. The shaded region shows the observed bright luminous zone.
Figure 5.11 shows both the Raman-measured and thermocouple-measured temperature profiles for Case C. The Raman measured peak temperature is 1611±35 K, which is located at 12.5 mm away from the burner surface. It is seen from Fig. 5.11 that the peak temperature measured by thermocouple is only 50 K less than that determined by Raman scattering measurement. Again, the difference between the locations of the peak temperature measured by two different methods is within 1 mm in this case. The peak location predicted by thermocouple measurement is to the left of the Raman-
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measured peak. The shaded section in Fig. 5.11 covers the range from 11.5 mm to 12.8 mm in the transverse direction. The peak temperatures measured by both methods all fall in this region.
On the fuel side of the temperature profile, thermocouple measurements are generally
50 K less than those of the Raman scattering measurements. On the air side, the discrepancies between the thermocouple data and the actual temperature could be as large as 200 K. Similar to Case A, it is also noticed that the local flame surface shows a small dent when the thermocouple is placed near the flame surface on the air side.
Case D: 75% nitrogen dilution, 1.10 cm/s fuel mixture injection speed
This case is the second one in the series of tests with high nitrogen dilution level of
75%. Since the fuel mixture injection speed is smaller than that of Case C, the Case D flame suffers more conductive heat loss to the burner surface due to the smaller stand-off distance. However, the flame of this case is still sufficiently strong to withstand the intrusion of thermocouple.
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1600
Raman (K) Thermocouple (K) 1400
1200
1000
800 Bright luminous zone Temperature (K) Temperature
600
400 2 4 6 8 10 12 14 16 18
Distance from Burner Surface (mm)
Figure 5.12 Temperature distribution across the flame for Case D. Both thermocouple- measured and Raman-measured data are included. The shaded region shows the observed bright luminous zone.
It is seen from Fig. 5.12 that the Raman-measured peak temperature is 1530±25 K.
Both the value and location of peak temperatures measured by two methods match with each other quite well. Also, the location of the measured peak temperature falls in the luminous zone determined by the chemilumenescence imaging for both measurements.
The luminous zone covers the range from 10.2 mm to 11.5 mm in the transverse direction away from the burner surface. On the fuel side of the temperature profile, thermocouple-
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measured temperature is slightly higher than the Raman-measured one by about 20~50 K.
On the air side, the thermocouple measurement is less than the Raman-measured temperature by 50~200 K.
Case E: 75% nitrogen dilution, 0.75 cm/s fuel mixture injection speed
This case is the third one in the group of highly diluted methane/air diffusion flames.
As shown in Fig. 5.6, this case is also very close to the extinction limit boundary. The maximum temperature measured by Raman scattering is 1455±45 K, which is located at
9.0 mm away from the burner surface, as shown in Fig. 5.13.
150
1600
Raman 1400 Thermocouple
1200
1000
800 Temperature (K)
Bright luminous zone 600
400 2 4 6 8 10 12 14 16 18 Distance from Burner Surface (mm)
Figure 5.13 Temperature distribution across the flame for Case E. Both thermocouple- measured and Raman-measured data are included. The shaded region shows the observed bright luminous zone.
The shaded section in Fig. 5.13 covers the range from 8.0 mm to 9.2 mm in the transverse direction away from the burner surface. The peak temperature measured by
Raman scattering is within this region.
When conducting thermocouple measurement for this case, the local flame extinction is apparent in the region next to the thermocouple wire. Larger discrepancies of maximum temperature and temperature distribution shown in Fig. 5.13 indicate that the use of thermocouple in this case is not suitable at all.
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Overall Comparison for Five Cases
In Figs. 5.14 and 5.15, the Raman-measured temperature profiles together with their corresponding OH-PLIF and chemiluminescence signal intensity profiles are compared for Cases A-B, and C-E, respectively. In both Figs. 5.14(a) and 5.15(a), as the fuel injection speed increases, the peak temperature location shifts away from burner surface.
The flame standoff distances based on the OH-PLIF profile, denoted as symbols in Figs.
5.14(b) and 5.15(b), are also shown to increase with increasing fuel mixture injection speed. In addition, the overall temperature profile (Figs. 5.14(a) and 5.15(a) ) shifts up as the fuel mixture injection speed is increased, probably due to a decrease in the burner heat loss. This decrease in burner heat loss to the surroundings is due to a decrease in the burner surface temperature, measured using IR imaging. In a later section, the numerical simulation can provide further insight into this observation by examining the heat flux at the burner surface.
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40% Nitorgen Dilution in Fuel Mixture 1800 1600 (a) 1400
1200 A
1000 B 800 600 Case A Temperature (K) 400 Case B
1 (b) B A 0.8
0.6
0.4
0.2 Normalized Intensity 0 0 5 10 15 20 Distance from Burner Surface (mm)
Figure 5.14 (a) Comparison of the Raman-measured temperature profiles for Cases A and B (40% nitrogen dilution). (b) OH-PLIF and chemiluminescence profiles for Cases A and B. Symbols denote the OH concentration profiles, while lines represent the chemiluminescence profiles.
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1800
1600 (a)
1400
1200
1000 C 800 D Case E 600 Case D E Temperature (K) 400 Case C D 1 E C (b) 0.8
0.6
0.4
0.2 Normalized Intensity Normalized 0 0 5 10 15 20 Distance from Burner Surface (mm)
Figure 5.15 (a) Comparison of the Raman-measured temperature profiles for Cases C, D and E (75% nitrogen dilution). (b) OH-PLIF and chemiluminescence profiles for Cases C, D and E. Symbols denote the OH concentration profiles, while lines represent the chemiluminescence profiles.
In general, it is seen from Figs. 5.14 and 5.15 that the locations of peak temperature,
OH-PLIF peak intensity, and maximum chemiluminescence intensity coincide quite well.
Hence, either one of these values can be used as a marker for the location of the reaction zone in the flame. As expected, the reaction zone recedes from the burner surface as the
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fuel injection speed is increased. We further note that, the chemiluminescence profiles, represented by lines, have a wide ‘ramp’ towards the burner side due to the curvature of the flame and the ‘line-of-sight’ collection of the flame luminosity. The profiles do show, however, how the OH profiles extend well beyond the CH* chemiluminescence in the air-side of the flame.
5.3.2 Qualitative Species Distributions
OH radical profiles of the steady quasi-1D low-stretch flames and various multi- dimensional flames are characterized with OH-PLIF technique in this study. The OH-
PLIF results also demonstrate the uniformity of the resulting quasi-1D flames, as discussed in Section 5.1.
Besides the OH-PLIF measurement, the Raman spectra can be used to measure the concentrations of the major species in combustion system, such as CO2, O2, CH4, H2O, etc. Since the spectral window investigated in this study is wide enough to cover the
Raman signals of most the major species in methane/air flames, the qualitative trend of species variation can be readily obtained. With the knowledge of the Raman cross-section for each species and collection efficiency of the optical system, which are in general determined by experiments, the species concentration profiles can be quantitatively determined.
For each case in Fig. 5.6, Raman spectra between 560 nm to 660 nm are recorded at different locations. Figure 5.7 shows that distinct Raman spectra of several major species can be detected. From left (short wavelength) to right (long wavelength), they are CO2,
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O2, N2, CH4, and H2O. In this section, qualitative variations of the major species across the flame are shown for different cases, which provide further insight into understanding the detailed flame structure.
Again, the five cases in Fig. 5.6 are studied and compared. Raman spectra of Case A-
E are shown in Figs. 5.16-5.20, respectively. For each case, five representative locations are chosen to illustrate the species variations. These five locations include two on the fuel side (top two panels), one at the location of the peak temperature (middle panel), and two on the air side (bottom two panels).
We first noted that since the intensity of Raman spectra of each species vary with temperature and species concentration, the spectra shown in Figs. 5.16-5.20 are normalized by the corresponding peak N2 intensity at each location. As expected for a typical diffusion flame structure, methane Raman spectra appear on the fuel side, while on the air side, oxygen Raman spectra are observed. At the location of peak temperature both the Raman spectra of methane and oxygen are not detectable. Due to the diffusion of combustion products, Raman spectra of CO2 and H2O are seen at all five locations studied. For all cases, Raman signals from CO at 600 nm are not apparent because of its weak intensity.
In addition, the laser-induced C2 fluorescence signals due to 532 nm excitation (cf.
Barlow and Miles, 2000) are noted on the fuel side of the flames. In contrast to Raman scattering, laser-induced fluorescence (LIF) is a resonant absorption/emission process and is characterized by typical cross-sections roughly ten orders of magnitude larger than those of molecular scattering processes. Therefore, it is not surprising to see that the C2 fluorescence signals are strong in some circumstances.
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Comparing the signals of laser-induced C2 fluorescence for Cases A and B (Figs. 5.16 and 5.17), it is seen that more C2 species are generated under the near-sooting condition
(Case A). It is also noted that in Figs. 5.18-5.20, the laser-induced C2 fluorescence comes into sight at the location close to the peak temperature on the fuel side of the flame.
Future careful calibration is needed in order for quantitative determination of these major species profiles.
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Figure 5.16 Raman spectra of Case A (40% nitrogen dilution, 0.55 cm/s fuel mixture injection speed) at five different locations away from the burner surface: 3.7 mm, 7.1 mm, 11.2 mm, 12.1 mm, and 14.5 mm.
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Figure 5.17 Raman spectra of Case B (40% nitrogen dilution, 0.30 cm/s fuel mixture injection speed) at five different locations away from the burner surface: 3.0 mm, 5.2 mm, 8.0 mm, 10.9 mm, and 12.5 mm.
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Figure 5.18 Raman spectra of Case C (75% nitrogen dilution, 1.30 cm/s fuel mixture injection speed) at five different locations away from the burner surface: 3.0 mm, 9.6 mm, 12.5 mm, 14.4 mm, and 16.3 mm.
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Figure 5.19 Raman spectra of Case D (75% nitrogen dilution, 1.10 cm/s fuel mixture injection speed) at five different locations away from the burner surface: 3.1 mm, 8.9 mm, 11.2 mm, 13.3 mm, and 16.0 mm.
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Figure 5.20 Raman spectra of Case E (75% nitrogen dilution, 0.75 cm/s fuel mixture injection speed) at five different locations away from the burner surface: 3.3 mm, 7.1 mm, 9.0 mm, 11.1 mm, and 14.7 mm. Note that only the spectra in the wavelength range of 560 nm-610 nm are shown in this figure.
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5.4 Multi-Dimensional Flame Instabilities
The current burner system also allows us to experimentally investigate multi- dimensional low-stretch flame structures. Different instability patterns are recorded by the direct chemiluminescence imaging and OH-PLIF techniques. Experimental observations of multi-dimensional flame behavior are described first, followed by the discussion of the possible mechanisms accounting for such flame instabilities.
5.4.1 Instability Patterns
Several multi-dimensional flame phenomena are observed near the extinction boundary. The multi-dimensional flame structures seem to help the flame to survive prior to complete extinction, and hence would extend the flammability limit beyond that predicted by the quasi-1D model (Nanduri et al., 2003).
For certain nominal fuel injection speeds and fuel dilutions, particularly near the extinction limits, different multi-dimensional flame patterns begin to emerge, as delineated in Fig. 5.21. They are: moving waves/bumps, moving single/multiple stripes, moving single/multiple holes, mixed moving stripes and holes, and periodic holes.
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2
Stripes Waves /Holes Waves/Bumps and 1.5 Bumps Blue Flame and Yellow Sooting Layer
1 Sooting Limits Quasi-1D Blue Flame (Non-sooting) Extinction 0.5 Limits Fuel Mixture Injection Speed (cm/s) Periodic Holes Extinction 0 0 0.2 0.4 0.6 0.8 1 Nitrogen Dilution
Figure 5.21 Diagram of flammability and instabilities. Nitrogen dilution represents the mole fraction of nitrogen in the fuel mixture.
Those flame patterns labeled/colored in Fig. 5.21 are found by gradually varying either the dilution level or the fuel mixture injection speed. These flame instabilities tend to be created as either the nitrogen dilution level approaches the dilution limit or the fuel injection speed is sufficiently low. These multi-dimensional structures become larger and/or more frequent until, eventually, the flame is extinguished.
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Figure 5.22 Summary of multi-dimensional flame patterns observed in the present study. Direct images show the view from underneath the burner.
Chemiluminescence images of the multi-dimensional flame structures currently identified are shown in Fig. 5.22. These can be separated into five different categories: moving waves/bumps, moving single/multiple stripes, moving single/multiple holes, mixed moving stripes and holes, and periodic holes.
(1) Moving Waves/Bumps
Traveling waves and bumps start to form in the flame surface for large nominal fuel injection speeds (greater than 1.35 cm/s), as shown in Fig. 5.21. These structures are
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originated from the wrinkling of the quasi-one-dimensional flame surface. If the wrinkling occurs only in one particular direction, spanning the entire flame surface, it is called a ‘wave’. If the wrinkling is localized and occurs only inside a limited circular area within the flame surface, it is called a ‘bump’. The frequency of formation of moving waves/bumps increases with increasing inert dilution, while the amplitude of the waves/bumps increases with fuel injection speed.
Since the flame surface is continuous for waves and bumps, the bottom view of chemilumenescence of this pattern is hard to be identified. Although this pattern is not shown in Fig. 5.22, it can be seen from the “snap shots” of OH-PLIF images shown in
Figs. 5.23 and 5.24.
(2) Moving Single/Multiple Stripes
If the wave standoff distance becomes large enough, it causes the local extinction of the flame surface. Single or multiple stripes show up near the center region as the moving waves break up. Once formed, these stripes cut through the entire flame surface area. These extinction regions form rapidly and move towards the burner edge, keeping a fairly constant width. In the case of multiple stripes, the stripes form with a thin flame strip, i.e. flamelet, between them as they travel together with identical speed. The increased chemiluminescence at the flame edges indicates that there is a local increase in the reaction rate after the formation of the stripe. As the nitrogen dilution is increased, the number and the frequency of the generation of stripes become larger.
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(3) Moving Single/Multiple Holes
In some cases, we can also observe holes which open up near the center of the flame.
Generally, the holes originate from the moving bumps on the flame surface that rapidly expand to 1.5-4.0 cm diameter size and are then convected towards the burner edge. As they move away from the center, the holes slowly increase in size. The edge of the hole is brighter than the rest of the flame, indicating an increased reaction rate therein.
(4) Mixed Moving Stripes and Holes
Stripes and holes can be observed together from time to time. In some cases, neighboring holes can join as they grow, creating a stripe.
Furthermore, our experimental observations show that the moving waves/stripes/holes do not have a particular orientation or moving direction. However, we have noticed that the directions of moving waves/stripes/holes are very sensitive to the horizontal level of the burner assembly. If the burner is not carefully leveled, those moving instabilities do have a preferred moving direction and orientation. During our experiments, from time to time, we also observe the waves/stripes moving in various directions alternatively. In some other cases, the multiple waves/stripes are not parallel with each other on the flame surface either. Therefore, there is no preferred direction or orientation for the moving waves, holes, and stripes.
The OH-PLIF imaging can provide further insight into the structure of this phenomenon. The cross section of the flame surface can be shown by using OH-PLIF. In
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addition, the unambiguous bright signal in the two-dimensional image indicates the location of reaction zone. Both Figs. 5.23 and 5.24 show the side-views of the evolution of some typical transient multi-dimensional flame structures. The images clearly illustrate the presence of local quenching of the flame surface, indicated by the lack of
OH-PLIF signal. The flame edges are very distinguishable from the ‘dark’ region in between. This observation is consistent with the direct visualization shown in Fig. 5.22.
Figures 5.23 and 5.24 also show how the formation of stripes or holes is normally preceded by local flame wrinkling, i.e. waves/bumps.
Figure 5.23 OH-PLIF sequences showing the evolution of a single stripe or hole.
Figure 5.23 illustrates the temporal evolution of a moving stripe or hole. At the reference time t=0, the flame surface wrinkles and a small moving wave or bump is created. The moving wave/bump then quickly breaks, forming a single stripe or hole.
The brighter edges of the stripe/hole are always bent toward the air side because the stoichoimetric mixture fraction (Williams, 1985) changes locally near the extinction
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region. Subsequently, the size of the black stripe/hole grows until it reaches its maximum size. One of the flame edges (left side) then changes to an ignition front, advancing into the fuel-air mixture. This edge flame (e.g. at t=2.0 sec) clearly shows an increase in OH concentration.
Figure 5.24 OH-PLIF sequences showing the evolution of multiple stripes.
Figure 5.24 also demonstrates the creation of multiple stripes. Similar to the process in Fig. 5.23, starting from a moving wave at first, two stripes are simultaneously formed.
The stripes expand but do not join together, leaving a thin flame strip in the middle. This thin cellular structure is maintained for at least 0.8 sec. After this, it is either extinguished due to heat loss or moves outside of the laser sheet. It is noted that this thin flame strip remains stationary with a width comparable to the flame thickness for at least
0.4 sec. Such stationary cells for low-stretch diffusion flames have been numerically predicted (e.g. Nanduri et al., 2003).
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(5) Periodic Holes
When the fuel injection speed is sufficiently slow that it is close to the extinction limit induced by burner heat loss, large holes are created near the center of the burner. These holes grow and then rapidly close in a periodic fashion. The frequency of the periodic patterns is roughly 1 Hz, although it changes with the hole size. The hole size increases with increasing nitrogen dilution or decreasing fuel injection speed, which can be as small as 2 cm or reach the size of the burner diameter. Figure 5.25 shows a sample periodic hole during the opening and closing periods. Note the increased luminosity of the rapidly closing flame, indicating an enhanced reaction rate. The process from hole formation to closing takes approximately 600 ms.
Figure 5.25 Evolution of a periodic hole.
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5.4.2 Mechanisms of Instability of Low-stretch Diffusion Flames
In general, the stability of the combustion system is determined by a variety of physicochemical conditions of the experiments and properties of the fuel and oxidizer.
Some well-known flame instabilities that may be relevant to the instabilities observed in the present experiment are discussed herein, considering that the scales of the observed instability are comparable with the flame thickness.
First, the Rayleigh-Taylor instability has been observed previously in the combustion of flat condensed phase fuel (e.g., Orloff and deRis, 1971). Secondly, the thermal- diffusive instability can also contribute to the cellular flame structure. Furthermore the heat loss, including radiative and/or conductive heat loss, can be an important factor for triggering and promoting the flame instability.
5.4.2.1 Rayleigh-Taylor Instability
This instability is unique to the gravitational environments. The original concept of this type of instability was first proposed by Rayleigh (1916). It has been proved that there exists a critical Rayleigh number, above which the cellular convection pattern shows thus in turn enhances the heat flux in the horizontal layers (Ostrach, 1964; Bejan,
1984). For example, If the top fluid surface is free and the bottom surface is rigid, this critical Rayleigh number based on the thickness of horizontal layer is 1108.
This type of instability was also observed in combustion fields (Orloff and deRis,
1971; Vantelon et al. 1987) of solid fuel. Olson (1997) compared with these earlier results, and found that the critical value of Rayleigh number of 460 agrees well with the
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experiment data for the onset of flame instability over cylindrical or flat solid fuel. Thus, the “Bénard cells” (cf. Sec. 1.2.2.2.2) should not exist if the critical Rayleigh number is less than 460 for the configuration of bottom burning under normal gravity. Furthermore,
Olson (1997) also showed that it is possible to observe the “flamelets” when the critical
Rayleigh number is about 200, if considering the decrease of the actual flame standoff distance when the flame instabilities occur.
In current study, the Rayleigh number is estimated to be about 100~200 near the extinction limits, based on the typical flame temperature and flame standoff distance from the burner surface. Similar to the observation of Olson (1997), we note that the internal circulation, which is one basic characteristic of Bénard cells, is not observed. The multi-dimensional flame structures always move along the flame surface towards the edge of the burner.
In summary, it appears that some type of Rayleigh-Taylor instability may play a role in the onset of flame intabilities for current burner configuration. However, the resulting instability behavior is very different from the original concept of Bénard cells.
5.4.2.2 Thermal-Diffusive Instability
As introduced in Sec. 1.2.2.2.2, the thermal-diffusive instability is due to non-unity
Lewis number. In this study, Lewis number of fuel mixture (methane diluted with nitrogen) is very close to unity. Therefore, it is not likely thermal-diffusive effects are the controlling effects in current study. Nevertheless, the local Lewis number is not always close to unity because of the variations of the composition and temperature across the
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flame zone. When the flame is very weak and near extinction, it is possible that the flame could break into instability patterns due to the thermal-diffusive effects.
5.4.2.3 Instability Related to Heat Loss
Besides the diffusional-thermal effects, the heat loss process can also play a very important role in flame instabilities. An early study by Kirkby and Schmitz (1966) first reported that oscillatory behavior of flame temperature leads to extinction when a substantial heat loss exists. Some recent studies (e.g. Cheatham and Matalon, 1996) further showed that a thermal-diffusive instability can be enhanced in the presence of heat loss in the system. Numerical studies (e.g., Sohn et al., 2000; Nanduri et al., 2003) also predicted that the heat loss, specifically, the radiative heat loss, can induce flame instability near the extinction limits.
Experimentally, it appears that the low-stretch instabilities tend to happen near the extinction limits, caused by excessive radiative or/and conductive heat loss. As a self- sustain strategy, the near limit flame tends to break into separate flamelets to survive the complete extinction.
In closing this section, the controlling mechanisms of these instabilities of low stretch diffusion flames are still unclear. It could be any type of the above instabilities or any combination of them. However, it is expected that heat loss plays an important role in triggering and promoting the instabilities in the near-limit low stretch diffusion flames.
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5.5 Computational Results
The experimental quasi-one-dimensional flames are also investigated numerically using a steady-state laminar ‘boundary layer’ type model, employing complex chemical kinetics, thermodynamic/transport properties, non-gray gas phase radiation model and gray surface radiation treatment. As introduced in the Chapter 4, three controlling parameters have to be specified in the calculations in order to compare with experimental results.
5.5.1 Effects of Three Controlling Parameters
Three controlling parameters can be independently varied in the current numerical model: buoyancy-induced stretch rate (ab), nominal fuel mixture injection speed (vf), and burner heat loss fraction (ξ). These parameters do have a fixed value, but must be optimized to achieve the best possible fit with the available experimental data.
Varying the global stretch rate (ab) is analogous to varying the burner curvature.
The data of Fig. 5.26 illustrate how the stretch rate affects the thermal profile by keeping the same flame location. Here the fuel mixture is composed of 25% methane and 75% nitrogen (by volume). For the purpose of comparison, the burner heat loss parameter (ξ) has been set to zero for all the cases shown in Fig. 5.26. In order to fix the location of the peak temperature, the fuel injection speed for each case has been adjusted accordingly, hence the variation in burner surface temperatures. From Fig. 5.26, it is noted that the flame thickness increases while the peak temperature decreases slightly, as the stretch rate decreases. The stretch rate value thus mostly affects the flame thermal thickness. In
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this study, the optimal stretch rate (obtained from the best fit to the experimental data) differs from the nominal stretch rate calculated by using the measured geometry of the burner surface, together with Eq. (2-5). After extensive calculations, a best-fit value (for the current geometry) of 2.25 s-1 is found to be a generally acceptable stretch rate for all the experimental conditions investigated in this study. This value is fixed for the remainder of the numerical solutions.
1800
1600 -1 a (s ) 1400 b 2.25 1200 1.50 1.23 1000
800
Temperature (K) Temperature 600
400
0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.26 Comparison of computed temperature profiles for different stretch rates with ξ =0.
The effect of nominal fuel injection speed (vf) is examined by varying this single parameter. A comparison of results, with fixed stretch rate (2.25 s-1), burner heat loss
(ξ =0), and nitrogen dilution level (75% by volume), is shown in Fig. 5.27 as a function of vf. The results clearly show how the flame retreats from the burner surface as the fuel injection speed increases. As a result, the surface temperature decreases as the fuel
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injection speed increases. It is also noticed that the maximum temperature does not change much as the fuel injection speed varies in this case. The proper value of injection speed, for comparison with the experimental data, is therefore chosen so as to provide a standoff distance similar to that of the experimental value.
1600 vf (cm/s) 0.95 1400 1.07 1200 1.17
1000
800
Temperature (K) 600
400
0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.27 Comparison of computed temperature profiles for different nominal fuel -1 injection speeds with ab=2.25 s and ξ =0.
In the present simulations, a change in the heat loss fraction (ξ) is shown to modify the burner surface temperature. In Fig. 5.28, the stretch rate is fixed as constant (2.25 s-1) and the nominal fuel injection speed (vf) is set to 0.55 cm/s (Case A), while the burner heat loss parameter, ξ, is varied. The nitrogen dilution level (by volume) for the comparison is prescribed as 40%. In Fig. 5.28, as ξ is increased from 0 to 0.75, the burner surface temperature decreases by more than 150 K. The surface temperature
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decreases as the burner heat loss is increased because of the energy balance restriction
(Eq. 4-20) at the burner surface. The peak flame temperature slightly decreases with increasing heat loss. Since the burner heat loss regulates the temperature gradient and local temperature at the burner surface, the proper value of ξ for the current calculations is chosen in order to match the experimentally obtained burner surface temperature.
1800 ξ 1600 Case A 1400 0 1200 0.25 0.50 1000 0.75 800
Temperature (K) 600
400
0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.28 Comparison of computed temperature profiles at various burner heat loss levels for fixed stretch rate and nominal fuel injection speed. Nitrogen dilution level is equal to that of Case A.
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5.5.2 Comparison of Experimental and Computational Temperature Profiles
Through the use of the Raman scattering and the IR imaging techniques, it is possible to utilize the experimental thermal profiles to evaluate the accuracy of the current numerical modeling. In order to properly compare the results, the optimal stretch rate for the numerical simulations is fixed at 2.25 s-1 (as described in earlier section). In the following results, the numerical temperature distribution is obtained by varying the nominal fuel mixture injection speed (vf), and the burner heat loss parameter (ξ) to match:
(a) the experimentally obtained flame standoff distance, and
(b) the surface temperature value obtained by IR imaging.
Such an adjustment of boundary conditions in order to achieve better comparison with experiments is simply due to the uncertainties in the determination of boundary conditions. This technique is, however, common practice in combustion modeling (e.g.
Mueller et al., 1995; Massot et al., 1998; Seiser et al., 1998; Smooke et al., 2000). For the studies involving Tsuji type burner in particular, Dixon-Lewis et al. (1984) noted a discrepancy between the computed and experimental values of fuel injection speed and stretch rate. By comparing the simulated flame structure with the experimental results of
Tsuji and Yamaoka (1967) and Tsuji (1982), they found that it is necessary to increase the numerical stretch rate and reduce the fuel injection speed in order to obtain a good comparison between numerical results and experimental data. In a similar fashion, it is observed in the present work that the numerical stretch rate has to be increased (from 1.6 to 2.25 s-1) and the fuel injection speed has to be decreased (see Table 5.2) from their original values, in order to match the experimental data. The discrepancy between the
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computed and experimental fuel injection rates could be attributed to the small pressure gradient along the burner surface caused by the buoyancy-induced stagnation point flow.
It further leads to the larger fuel injection rate near the edge than the center of the burner because the fuel injection rate is proportional to the local pressure drop across the porous burner surface. This multi-dimensional fuel injection rate distribution along the burner surface cannot be accounted for by the current quasi-1D modeling.
40% Nitrogen Dilution in Fuel Mixture 1800
1600 (a) Case A 1400
1200 1000 800 Experimental 600
Temperature (K) Numerical 400
1600
1400 (b) Case B
1200
1000
800
600 Temperature (K) 400 0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.29 Comparison of experimental and computational temperature profiles for (a) Case A and (b) Case B.
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75% Nitrogen Dilution in Fuel Mixture 1800 1600 (a) Case C 1400 1200 1000 800 600 Experimental Temperature (K) Numerical 400
1600 (b) Case D 1400
1200
1000
800
600 Temperature (K) Temperature 400
1600
1400 (c) Case E
1200
1000
800
600 Temperature (K) Temperature 400 0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.30 Comparison of experimental and computational temperature profiles for (a) Case C, (b) Case D, and (c) Case E.
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In Figs. 5.29 and 5.30, the experimental temperature profiles for all five cases (A-E) investigated are compared to the numerical simulations. The vertical error bars shown in
Figs. 5.29 and 5.30 are calculated for each individual Raman measurement. It is seen that, except for Case B (which is close to lower branch of extinction limit), all the other cases show good agreement of the temperature distribution profiles between experimental data and numerical results. The computed temperature distribution in these cases is within the uncertainty interval of Raman measurement. As for the discrepancies in Case B, we will later show how the current model breaks down in the region of low fuel mixture injection speeds, near the extinction limit induced by burner heat loss.
Table 5.2 further shows that, for the same level of nitrogen dilution, the resulting relative burner heat loss percentage (ξ) decreases with increasing fuel mixture injection speed. Since the total heat loss flux decreases dramatically with the increase of the fuel injection speed and flame standoff distance, the decrease in the absolute value of burner heat loss (Hw) is even more pronounced as the fuel injection speed increases. This result implies that the heat loss through the burner surface becomes less dominant and the radiative heat loss from the flame becomes more important as the fuel injection speed increases.
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Table 5.2 Comparison of experimental data and simulated results for all five cases Experimental Computational N2 Condition Condition Case Dilution Heat Loss ab,exp vf,exp ab,comp vf,comp Heat Loss (%) -1 -1 Hw (s ) (cm/s) (s ) (cm/s) 2 Parameter ξ (W/cm ) A 40 1.60 0.55 2.25 0.40 0.5764 0.82 B 40 1.60 0.30 2.25 0.25 0.7480 0.91
C 75 1.60 1.30 2.25 0.95 0.1777 0.57 D 75 1.60 1.10 2.25 0.76 0.3241 0.71 E 75 1.60 0.75 2.25 0.58 0.3759 0.73
5.5.3 Extinction Limits
The experimental flammability map shown in Fig. 5.6 shows the observed extinction limits for the current configuration. Along the extinction limit curve, two controlling mechanisms are expected. Extinction at low fuel injection speeds (the lower branch of the extinction curve) is governed by the significant burner heat loss (Hw), due to increased burner surface temperature at such small flame standoff distances. For large fuel injection speeds, the flame recedes from the burner and the heat transfer at its surface is greatly reduced. Extinction at large injection rates can still be reached by increasing the fuel dilution (upper branch of the extinction curve). The governing extinction mechanism then becomes flame radiative heat loss. This will be studied in detail in this section using numerical simulation.
In order to numerically verify the experimental observations of the existence of two distinct flame extinction modes at very low stretch rate (2.25 s-1), the flammability limits are obtained using the current numerical model. This is done by plotting the maximum
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flame temperature (Tmax) versus either the nitrogen dilution level (Fig. 5.31), or the injection velocity (Fig. 5.32). It is noted that multiple solutions are obtained in both Figs.
5.31 and 5.32 due to the non-linearity of the governing equations. The lower branch is the
“unstable” solution, while the upper branch is the actual “stable” burning flame solution.
The turning point of the convergence of the lower branch and the upper branch defines the extinction limit (cf. Sec. 1.1). In order to capture the extinction turning point, the flame controlling method is employed, as discussed in Sec. 4.3.3.
1700
1600
1500
1400
1300 vf (cm/s) 1200 1.15
Peak Temperature(K) 1100 0.95
1000 0.7 0.75 0.8 0.85 0.9 Nitrogen Dilution (in Mole Fraction)
Figure 5.31 Calculations performed near the upper extinction limit for a given stretch rate 2.25 s-1. The maximum flame temperature is plotted for the case with ξ =0.57, at two different nominal fuel injection speeds: 0.95 cm/s and 1.15 cm/s.
Figure 5.31 shows the limiting behavior for two cases with relatively high fuel injection speeds (near upper limit) at a fixed stretch rate of 2.25 s-1. One is the same as
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Case C in Fig. 5.6 (vf=0.95 cm/s), while the other has an even larger injection rate (1.15 cm/s). In Fig. 5.6, it was shown that the experimentally-obtained upper dilution extinction limit becomes independent of the fuel injection speed, as long as this value is sufficiently large (> 0.95 cm/s). Indeed, both cases shown in Fig. 5.31 exhibit almost the same response for different injection speeds. At the turning point, the maximum temperature is about 1300 K and nitrogen dilution level is 87.3% and 87.9% for vf=0.95 cm/s and 1.15 cm/s cases, respectively. These computed extinction limits in term of nitrogen dilution compare well with the experimental result of 86.0±0.5%. This indicates that current simulations with narrowband radiation model can accurately predict the extinction limit when flame is sufficiently far away from the burner surface.
1600 10 T Location of Peak Temperature max 9 from Burner Surface (mm) 1400 8 1200 7
1000 6
5 800
Temperature (K) 4 Tw 600 3
400 2 0.12 0.16 0.2 0.24 Nominal Fuel Injection Speed (cm/s)
Figure 5.32 Calculations performed near the lower extinction limit for a given stretch rate 2.25 s-1 and ξ =0.91. The flame peak temperature and surface temperature, as well as the flame location based on the location of peak temperature, are plotted as a function of nominal fuel injection speed.
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Figure 5.32 demonstrates the limiting behavior near the lower branch of the extinction limit curve (40% fixed nitrogen dilution). The relative burner heat loss is fixed at 91% for all solutions (i.e. ξ =0.91), as found from the results of Case B (near lower extinction curve). It is shown in Fig. 5.32 that the computed maximum and surface temperatures, and the location of peak temperature are all dependent on the nominal fuel mixture injection speed. As the fuel injection speed is decreased and the flame approaches the burner surface, the maximum flame temperature decreases, while the burner surface temperature increases. The resulting extinction limit, in terms of fuel injection speed (shown as the dashed line), is 0.157 cm/s at the given 40% nitrogen dilution level. This result is considerably low, when compared to the experimental value
(at the same nitrogen dilution) of 0.28 cm/s (cf. Fig. 5.6).
Since the presence of solid surface can play a role as sinks for radicals, it is necessary to investigate the possible effects of surface-induced radical recombination on low-stretch diffusion flame response. The surface quenching of radicals have been examined by a number of studies (e.g., Vlachos et al., 1994; Aghalayam et al., 1998;
Fernandes et al., 1999). It was found that the ignition and extinction temperatures can be altered significantly by surface reactions. Particularly, for methane/air premixed flames, the H radical quenching plays the largest role in increasing extinction temperature, while surface losses of other radicals, such as CH3, O, and OH also contribute to the increased extinction temperature (Vlachos et al., 1994). In this study, the surface quenching effects are evaluated by a simple ‘radical sink’ approach as conducted by Rhatigan (2001). This method assumes an infinitely fast radical absorption mechanism at the surface without
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considering the detailed surface reaction mechanism. It can be treated as an extreme case for surface quenching that the concentrations of all the important radicals, such as, H,
CH3, O, and OH, are set to zero at the burner surface. The computed results using this
‘radical sink’ method show that the surface quenching for those radicals does NOT noticeably affect the flame structure and flame extinction. The reason for the negligible surface quenching effects may be due to the very small concentrations of those radicals at the burner surface for the present flame conditions. For example, at the lower extinction limit (cf. Fig. 5.32), without considering the surface quenching, the mole fraction of H is
-10 -7 -12 only 1.85×10 , while the mole fractions of CH3, O, and OH are 1.88×10 , 2.70×10 , and 1.07×10-10, respectively. Therefore, there is no obvious change in flame response if these radical concentrations are set to zero at the burner surface.
If the difference between the numerical and experimental results on lower extinction limits is not because of the surface quenching effects, it may be explained in part by the current assumption of constant heat loss percentage. It is expected that the true heat loss percentage (ξ) will increase as the fuel injection speed decreases further till the extinction limit is reached, resulting in extinction of the flame at larger injection rates.
The difference between the experimental and computed results at low injection speeds may also be due to the limitations of quasi-one-dimensional modeling itself. For the lower fuel injection speeds, the flame standoff distance becomes relatively small, consequently the multi-dimensional heat conduction, which is caused by the temperature gradient in the radial/tangential direction (x) near and at the surface, would play a more important rule in effecting flame extinction.
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To further investigate the radiation effects on extinction, the radiation heat fluxes obtained using the current narrowband and surface radiation models are examined for flames near the upper (large flow rate) and lower (low flow rate) extinction limits in Figs.
5.33 and 5.34, respectively. The corresponding temperature and heat release profiles are included in Figs. 5.33(a) and 5.34(a) as a spatial reference. It is clear that the peak location of heat release rate is always consistent with the peak location of temperature.
The figures show how the flame standoff distance from the lower extinction limit flame
(Fig. 5.34) is much smaller than that for the upper extinction limit flame (Fig. 5.33).
Figures 5.33(b) and 5.34(b) show the relative importance of the radiative fluxes originating from the gas phase and the burner surface. The fluxes are labeled as follows:
1) Q+ is the radiation flux in the positive y direction (away from the burner surface);
2) Q- is the radiative flux in the negative y direction (toward the burner surface).
At the surface, Q+ is representative of the total radiative heat flux of surface emission and reflection. The component of this surface flux (Qemiss) corresponding purely to emission is marked in Figs. 5.33(b) and 5.34(b) with a triangle. At the oxidizer boundary (y=L), Q+ is representative of the net radiation loss of the system to the surroundings. At the burner surface, Q- represents the net incident radiation from the gas phase. At the oxidizer edge of domain (y=L), the value of Q- is the background blackbody radiation originating from the ambient.
The resulting Qnet is the total radiative heat flux, i.e. Qnet = Q+ − Q− . A positive value for Qnet is defined as a net heat flux towards the ambience, i.e. in the positive y
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direction. For comparison the burner heat loss (Hw) is also marked in both Figs. 5.33(b) and 5.34(b).
Nitrogen Dilution: 87.9%, Nominal Fuel Injection Speed: 1.15 cm/s Heat Release Rate (W/cm 1400 20
1200 (a) 15 1000
800 10
600 5
Temperature (K) 400 3 200 0 ) 0.3 (b)
) 0.25 2 0.2 Q - 0.15 Q net 0.1 H w Q + Q 0.05 emiss
Heat Flux (W/cm Heat Flux 0
-0.05 0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.33 (a) Profiles of temperature and heat release rate for a flame near the upper extinction limit with 87.9% nitrogen dilution and 1.15 cm/s nominal fuel injection speed. (b) Profiles of radiative heat fluxes for this case.
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Nitrogen Dilution: 40%, Nominal Fuel Injection Speed: 0.157 cm/s Heat Release Rate (W/cm 1400 30
1200 (a) 25
1000 20
800 15
600 10
Temperature (K) 400 5 3 200 0 ) 0.7
) (b) 2 0.6 Q 0.5 - Q 0.4 net Q 0.3 + Q emiss 0.2 H w Heat Flux (W/cm FluxHeat 0.1
0 0 5 10 15 20 25 30 Distance from Burner Surface (mm)
Figure 5.34 (a) Profiles of temperature and heat release rate for a flame near the lower extinction limit with 40% nitrogen dilution and 0.157 cm/s nominal fuel injection speed. (b) Profiles of radiative heat fluxes for this case.
Figures 5.33(b) and 5.34(b) show how the radiative heat fluxes change continuously along the y direction. Several features of the radiative fluxes are similar for both the low and high injection rate cases, and therefore innate to this flame geometry. At the surface, the radiative flux Q+ has a finite value due to both emission and reflection components.
Moving away from the burner surface, the value of Q+ increases as the temperature and
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concentrations of the radiatively participating gases increase. The subsequent slight
decrease in Q+ is due to absorption in the gas phase. In the same manner, moving from
the oxidizer boundary (y=L) towards the flame, the value of Q- increases due to emission
from the radiatively participating species near the flame region, the subsequent slight
decrease in Q- is due to the absorption in the gas phase near the burner surface. As a
result, the net radiative heat flux (Qnet) profile (from left to right) first decreases slightly
starting from the burner surface, then increases significantly close to and in the reaction
zone, after the reaction zone, the Qnet slightly decreases and is approaching to a constant
heat loss to the ambient at the edge of domain (y=L).
Table 5.3 Heat flux analysis at two extinction limits
Heat Extinction Tw Tmax Q+(0) Q-(0) Qnet(0) Hw Qcond(0) Qnet(L) Release Condition (K) (K) (W/cm2) (W/cm2) (W/cm2) (W/cm2) (W/cm2) (W/cm2) Flux (W/cm2)
87.9% N2, vf=1.15 335.25 1294.7 0.1386 0.1729 -0.0343 0.0660 0.0814 0.2047 2.008 cm/s 40% N2, vf=0.157 632.35 1372.1 0.4867 0.2690 0.2177 0.5786 0.8536 0.6192 2.486 cm/s
Table 5.3 further compares some key values of the heat fluxes both at the burner
surface (y=0) and the other edge of the domain (y=L) shown in Figs. 5.33(b) and 5.34(b).
The total heat release flux is calculated by integrating the volumetric heat release rate
with respect to distance y in Figs. 5.33(a) and 5.34(a). The comparison between these two
cases illustrates a remarkable difference of the heat flux distributions depending on the
extinction mode. For the lower extinction limit, the outgoing radiative heat flux at the
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burner surface Q+(0) is about two times higher than that of upper extinction limit, mainly due to the stronger emission on the burner surface, caused by the larger surface temperature (Tw). The large value of Qnet(0) at the surface for the lower-limit flame, indicates a large net radiative heat loss from the surface to the ambient. Very little of this heat flux is reabsorbed by the gas phase, and therefore most of this energy is lost to the ambience. At the same time, an even greater heat loss is attributed to the burner heat loss
(Hw). The large value of Hw is attributed to the large magnitude of heat conduction at the surface (Qcond(0)), which is ten times that of the upper-limit flame. Extinction at the lower limit boundary is therefore reached through both contributions from Hw and Qnet(L). For the upper extinction limit, on the other hand, the total radiative heat flux at the surface
(Qnet(0)) is negative. This indicates a net heat gain from the gas phase to the burner surface. At the same time, the burner heat loss (Hw) remains comparatively low. For the upper limit extinction, therefore, most of the heat loss for the system comes from the radiative heat transfer from the gas phase to the ambience, contributing a large part to the final net loss: Qnet(L).
When comparing the relative importance of Qnet(L) and Hw, it is clear that the radiative heat loss to the ambient surroundings (Qnet(L)) dominates the heat loss process of the upper extinction limit, while the burner surface heat loss (Hw), including heat conduction at the surface and surface radiation, accounts for the lower extinction limit.
This conclusion verifies our previous argument regarding the existence of two distinct types of extinction mechanisms for low-stretch extinction limits at various fuel injection speeds.
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CHAPTER 6
SUMMARY AND RECOMMENDATION FOR FUTURE WORKS
6.1 Summary
In present work, we experimentally and computationally investigated the structure, dynamics, and extinction behavior of radiative gaseous diffusion flames at one fixed low- stretch rate. The experimental results show that the current burner is suitable to study gaseous diffusion flames at extremely low stretch rates previously unattainable under normal gravity. By using a burner with a large radius of curvature (R~400 cm), the buoyancy induced stretch rate ( gR) is as low as ~1.6 s-1. The flame stability diagram of methane-air flames is mapped in terms of fuel mixture injection speed and nitrogen dilution. Conditions leading to sooting flames, flame extinction, and various multi- dimensional flame patterns are identified.
Two distinct extinction modes are observed using the present burner. Extinction at low injection speeds is governed by the increase in conductive heat loss to the burner due to the small flame standoff distance and elevated surface radiative heat loss. As the fuel injection speed is increased, the flame recedes from the burner and the heat loss to the burner surface is reduced. The governing extinction mechanism is then dominated by flame radiative heat loss. For the present nitrogen-diluted methane/air diffusion flames, the dilution limit, beyond which no combustion is possible, is found to be 86% nitrogen in fuel, which is independent of the fuel mixture injection speed. This value is slightly
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larger than that reported by Tsuji and coworkers (Tsuji and Yamaoka, 1967, 1969, 1971;
Tsuji, 1982) at larger stretch rates.
A variety of multi-dimensional flame phenomena are observed near the extinction boundary. They are: moving waves/bumps, moving single/multiple stripes, moving single/multiple holes, mixed moving stripes and holes, and periodic holes. The multi- dimensional flame structures are expected to help the flame to survive close to extinction condition, and hence would extend the flammability limit beyond that predicted by the quasi-1D model. The heat loss, either conductive or radiative, plays an important role in triggering and promoting the instabilities in the present low-stretch diffusion flame with near-unity Lewis number.
Since the flames currently under investigation are weak and hence more susceptible to external disturbances, non-intrusive optical measurements are needed. Several advanced, non-intrusive, optical diagnostics techniques are used to study the flame structure, under various nitrogen dilution levels and fuel mixture injection speeds. Gas- phase temperatures are measured (within 30-50 K) by Raman scattering, while the burner surface temperatures are measured by infra-red imaging. OH-PLIF and chemiluminescence imaging techniques are used to help characterize the reaction zone of the flames. The OH-PLIF and chemilumenescence results demonstrate the uniformity of the resulting quasi-1D flames and are in agreement with the Raman measurements.
The measured temperature profiles of low-stretch diffusion flames are also compared with numerical simulations. The current numerical scheme, together with the narrowband radiation model and gray surface radiation, are shown to adequately predict the flame structure and flame response for quasi-1D flames, except for the cases of small standoff
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distances. Even though the simulated values of stretch rate and fuel mixture injection speed need to be adjusted at the boundary, in order to match the experimental data, the differences are fairly consistent for all the cases investigated. The numerical simulation is also shown to be capable of predicting the two extinction modes. The gas radiative extinction (upper limit) is well reproduced using this model. This extinction mode is shown to be fairly independent of the injection speed and standoff distance, and therefore a fundamental property of the mixture. The burner heat loss extinction (lower limit) found using simulations is, however, lower than that found experimentally. This last observation implies that the quenching at the low fuel injection speed may have to be modeled by a more complex multi-dimensional formulation. Furthermore, through detailed analysis of the radiative heat fluxes for near-limit flames, it is confirmed that the upper extinction limit, for large injection speeds, is mainly caused by gas phase radiative heat loss to the ambience, while the conductive heat loss to burner and the radiative heat transfer (surface and gas phase) are responsible for the appearance of a lower extinction limit, for low fuel injection speeds.
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6.2 Future Works
In the future study, we shall continue our efforts to investigate low-stretch flames over a wider range of conditions, in order to create a truly comprehensive database of diffusion flame instability and extinction boundaries, as well as of their flame structures and fundamental flammability limits. In order to obtain a wider range of stretch rates, a low-speed, opposed, forced convective flow will need to be added to the present setup.
This will allow experimental mapping of the flame response, including the instability and extinction boundaries, as functions of the stretch rate and fuel (or oxidizer) dilution at varying fuel mixture injection speeds. Different diluents can be tested as fire suppressants, including N2, CO2, and Ar. Note that CO2 is a radiatively participating species, while Ar and N2 are not. The possible reversal of suppression effectiveness
(Frate et al., 2000) at low stretch rates can then be explored experimentally. A range of gaseous hydrocarbon fuels are also of particular interest.
Because the flame thickness of a diffusion flame increases with decreasing stretch rate, we have demonstrated herein that the present quasi-1D low-stretch flames can facilitate the experimental mapping of the diffusion flame structure. Besides the temperature profiles measured by Raman scattering, the quantitative measurement of species concentration is useful for further scrutinizing the numerical models. Raman spectra obtained in this work can also be used to determine the concentrations of the major species in flames, such as hydrocarbons, CO2, O2, H2O, CO, H2, etc., with appropriate calibrations. The OH concentration distribution can be obtained by OH-PLIF after careful calibration and the determination of related quantum-mechanical parameters.
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Chemiluminesence of excited species can also be used for quantitative flame structure analysis. Certain narrowband filter will have to be employed to pick up the chemiluminescence signals from the selected excited species, such as CH* and OH*. It is noted that the mathematical de-convolution is required for the quantitative chemiluminesence imaging study since it is a path-averaged measurement.
Along with the experiments, a parallel computational study is also needed. A multi- dimensional simulation, utilizing simplified chemistry and radiation models, can also be employed to explore the mechanisms of flame responses, including extinction and instabilities.
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APPENDIX A
FUNDAMENTALS OF RAMAN SCATTERING
A-I. Stokes and anti-Stokes
The Raman process is an inelastic process of light in matter, and is independent of the frequency of the incident photon. If a photon is scattering inelastically by a molecule, it may gain energy and be scattered at a frequency higher than the incident frequency, or it may lose energy and be scattered at a frequency lower than the incident one. Thus, spectral bands appear above and below the incident frequency; these bands are called anti-Stokes or Stokes bands, respectively. The energy difference between incoming and scattered light usually corresponds to a rotational or a vibrational energy difference in the molecule. The basic concepts of Rayleigh and Raman effects are introduced in the following.
As illustrated in Fig. A.1, only the first two vibrational energy levels of a molecule are considered in this simple model, v=0 and v=1, which are respectively the ground state and the first excited vibrational state. When an energetic photon of incident laser light, hνL, with a frequency νL, interacts with a molecule in the ground state v=0, it can excite the ground state molecule to a so called “virtual state” with higher energy level. If the molecule decays back to the ground state, the light with the incident frequency νL is scattered and this elastic scattering process is called Rayleigh scattering.
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Vibrational Rayleigh Raman Virtual State ) L ν
es k Sto Laser (h Anti-Stokes
v=1 ) ) L L ν ν
1 ν h Laser (h Laser (h
v=0
Figure A.1 Energy diagram of Raman scattering by molecules. v is the vibrational quantum number. The solid lines denote the different rotational energy levels. h is the Plank constant, ν is frequency.
As shown in Fig. A.1, if the molecule decays back to v=1 instead of the ground state after excitation by an incident laser ligher hνL, the scattered frequency becomes (νL- ν1), where ν1 is the fundamental vibrational frequency. Note that this line energy differs from the original incident energy, hνL, by hν1, as marked in Fig. A.1. Now suppose that a photon energy of laser light, hνL, interacts with a molecule in the state v=1 and excites it to a virtual state. If the molecule decays back to v=0, the scattered energy is h(νL+ν1) and the scattered frequency (νL+ν1) differs from the exciting frequency νL by ν1. Therefore, the vibrational Raman anti-Stokes line has the frequency of (νL+ν1), while the vibrational
Raman Stokes line has the frequency of (νL-ν1), as illustrated in Fig. A.1. Furthermore, the relative intensities of the Stokes and Anti-Stokes lines are determined by the molecular population distribution among the allowed energy states. At a given
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temperature T, with the assumption of Boltzmann distribution, the equilibrium distribution can be written as
−Ei kTB nNeit= , (A-1) where Nt is the total number of molecules present, ni the number of molecules at the i-th energy state Ei, and kB the Boltzmann’s constant.
Since the ground state is more populated according to Eq. (A-1), the Stokes line is typically more intense than the anti-Stokes lines. This is one reason why the Stokes lines are usually chosen when applying Raman scattering measurement.
In general, the Raman shift can be written as:
hEJEJ()ννLS−=()v, ff −( v, ii) , (A-2) where νL is the frequency of incident laser light, νS is the frequency of Stokes light, v is the vibration quantum number, J is the rotational quantum number. The subscript f and i denote the final state and initial state, respectively.
In the above equation, if v is fixed (only J varies), the change of energy levels is defined as “pure rotational Raman scattering”. If we only consider the change of v as illustrated in Fig. A.1, it yields the so-called “pure vibrational Raman scattering”. If both v and J are varying, it yields the “vibration-rotational Raman scattering”. In particular, those lines with fixed J (i.e., ∆J=0) are referred as Q-branch in the series of vibrational- rotational lines.
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A-II. Temperature Measurements
Since the shape of Raman spectrum depends on the distribution of the sample molecules at different vibrational-rotational energy levels, which in turn depends on the temperature according to the Boltzmann’s equation (Eq. A-1), the temperature information for the investigated gaseous system can be translated out from the overall shape of the Raman spectrum of the molecule of interest.
We take the Q-branch of N2 Raman spectrum as an example. The intensity of Raman scattering in the direction perpendicular to the incident light (I) can be expressed as
(Boiarski, 1978):
4 NEJkTexp{−−() v, / }(ννLR) I ()ν ∝ , (A-3) R T
where, T is the temperature, N is the total number density of nitrogen molecules, νR is the frequency of Raman scattering.
The fact that the Raman spectra are a function of the temperature makes temperature measurement possible. For N2 Q-branch in particular, the transition of the first excited state (so-called “hot band”) emerges when the temperature of the system exceeds 1100 K.
When the temperature increases further, the “hot band” becomes stronger and other transitions of higher excited states emerge.
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APPENDIX B
FUNDAMENTALS OF LIF/PLIF
Laser induced fluorescence, LIF, is a well-established, sensitive technique for detecting concentration of specific atoms and molecules. Generally, fluorescence denotes the radiation emitted by a molecule or atom when it decays by spontaneous emission of a photon in an “allowed” transition from a higher to lower energy state.
In a laser induced fluorescence measurement, the upper states are populated by a laser source with an excitation frequency tuned to a resonance between the excited state and a lower state. Typically, the lower state is in the ground electronic level, as the higher electronic levels may be negligibly populated at normal combustion temperatures. After excitation, the laser-populated upper state may undergo a number of subsequent processes, such as:
1. The molecule can return to its original quantum state by (laser-induced) stimulated emission;
2. Absorption of an additional photon can excite the molecule to higher energy states, including the ionized levels.
3. The internal energy of the system can be altered via inelastic collisions with other molecules, producing rotational and vibrational energy transfer, as well as electronic energy transfer; the latter is often referred to as electronic quenching.
4. Interactions between the separated atoms of the molecule, known as “internal” or
“half” collisions, produce internal energy transfer and dissociation of the molecules.
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When the dissociation is produced by a change from a stable to a repulsive electronic arrangement in the molecule, it is called predissociation.
Besides those above processes, the fluorescence is another process characterized by spontaneous emission from the excited states. This particular radiative decay process competes with other processes.
The basic physics of fluorescence can be illustrated in Fig. B.1 using a simple two energy level diagram. Here, we only consider the situation when the predissociation and photoionization are negligible.
Level 2
b12 b21 A21 Q21
Level 1
Figure B.1 Energy level diagram for a simple two-level LIF case.
In Fig. B.1, b12 and b21 are respectively the rate constants (coefficients) for absorption and stimulated emission. They are related to the Einstein coefficient for the stimulated emission, B, through the relation:
BI b = b = ν , (B-1) 12 21 c
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where Iν is the incident laser irradiance per unit frequency interval (spectral
2 irradiance in units of W/cm -s) and c, the speed of light. Also, A21 is the Einstein coefficient, indicating spontaneous emission from Level 2 to Level 1. Q21 is the collisional quenching rate. Note that in this simple model shown in Fig. B.1, the collisional excitation Q12 can be omitted in normal combustion environment, since these two energy levels are widely separated (typically a few electron volts).
Writing the rate equations for the temporal derivatives of the energy level population, denotes by Nj at level j, we have:
dN j ()t = ∑ Ni ()t Rij − ∑ N j ()t R ji , (B-2) dt i≠ j i≠ j where Rij (Rji) is the rate coefficient for all events transferring molecules from level i (j) to j (i) (s-1).
For example, in this two-level model shown in Fig. B.1, the rate equation for the upper energy level (Level 2) becomes:
dN 2 =−Nb N() b ++ A Q . (B-3) dt 1 12 2 21 21 21
The population conservation equation may be written as
0 NNN112=+, (B-4) where the superscript “0” indicates the level population prior to the laser excitation. For electronic transitions in the visible and ultraviolet spectral regions, there is generally negligible population in the upper electronic state prior to the laser excitation, i.e.
0 N 2 = 0 .
Then, the solution to Eq. (B-3) is:
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− t Nt=− bN0τ 1 eτ , (B-5) 2121() ( ) where the time constant τ (in unit of second) is given by
−1 τ =+++[bbAQ12 21 21 21 ] .
When the laser pulse is long enough as compared to the time constant τ, i.e. t p >> 1, the steady state (denoted by the subscript “ss”) assumption is valid. τ
Then we can write the steady state solution as:
0 NbN2,ss = 12 1τ . (B-6)
It is more convenient to rearrange this equation as:
B 1 NN= 0 12 , (B-7) 2,ss 1 BB+ I sat 12 21 1+ ν Iν
sat where the saturation spectral intensity Iν is defined as
sat ()AQc21+ 21 Iν = . (B-8) BB12+ 21
3 Finally, the fluorescence rate RF (number of photons/cm /s) at steady state is
BA RANssAbNN===() 00τ 12 21 . (B-9) F 21 2 21 12 1 1 BB+ I sat 12 21 1+ ν Iν
0 We can see that the fluorescence rate is proportional to the initial total population ( N1 )
0 of a given species at particular energy level (Level 1). Furthermore, N1 is proportional to the species concentration.
Equation (B-9) can be further simplified for two limiting cases:
sat (1) At low laser excitation intensities, i.e. Iν < Iν ,
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0 A21 RNBIF ≈ 112ν . (B-10) AQ21+ 21
This is so-called linear fluorescence equation, as the fluorescence is linearly
proportional to incident laser intensity, but dependent on the quenching rate.
sat (2) At high laser excitation intensities, i.e. Iν >> Iν ,
0 B12 RNAF ≈ 121 . (B-11) B12+ B 21
This result approaches the saturation limit. The fluorescence signal is now
independent of both the laser intensity and the quenching rate.
Finally, the fluorescence signal power, F, is proportional to the fluorescence rate RF through
Ω F = hν A lR , (B-12) 4π f F where hν is the photon energy of the emitted fluorescence, Ω the collection solid angle,
Af the focal area of the laser beam, and l the axial length along the beam from which the fluorescence is observed.
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APPENDIX C
MODELING FOR SPECTRAL AND DIRECTIONAL RADIATIVE
HEAT TRANSFER
The thermal radiation in a “radiatively participating” medium has to be considered in many studies of combustion, since the i inherent radiative heat transfer process is one essential part of the energy conservation in the system.
Along a line of sight, radiation can experience both attenuation and augmentation.
When a photon (for an electromagnetic wave) interacts with a gas molecule, it may be either absorbed or scattered. At the same time, a gas molecule may spontaneously emit an appropriate photon. Since the size of the gas molecule is very small comparing to the wavelength involved in those processes, the scattering process of photons by molecules is always negligible for heat transfer applications (Modest, 2002).
Due to the nature of the thermal radiation, i.e. electromagnetic waves or photons, the radiative intensity is a function of the frequency and the propagation direction of the waves/photons. The modeling of spectral and directional dependence of radiative heat transfer is highlighted in the following sections.
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C-I. Narrowband Models
The radiative properties of a molecular gas usually vary strongly and rapidly across the spectrum, so that a “gray” gas assumption is always never a good one (Edwards,
1976). Due to the variation of the spectral lines at distinct spectral locations, there may be tens of thousands of spectral lines are needed to be accounted for in the study of radiative heat transfer. It makes this calculation extremely difficult to carry out. Consequently, a number of approximation spectral models have been developed. Particularly, the narrowband model enables one to calculate spectrally averaged emissivity and absorption coefficients with reasonable accuracy within a small frequency range (narrowband).
Certainly the computational task of narrowband spectral modeling is not as onerous as the actual spectral line calculation. Therefore, it is numerically affordable choice for practical modeling when the spectral dependence is considered.
To find spectrally averaged values of absorption coefficient and the emissivity in a finite spectral narrowband, some information must be available on the spacing of individual lines within this band and on their relative strengths. A number of models have been developed over decades to this purpose (Modest, 2002). Among them, two extreme cases are the Elsasser model, in which equally spaced lines of equal intensity are assumed; and the statistical models, in which the spectral lines are assumed to have random spacing and/or intensity.
Nevertheless, all the narrowband models require a database containing both the information of line spacing parameter and the mean absorption coefficient of each narrowband over the entire spectrum at different temperature. The narrowband data used
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here for CO, CO2, and H2O are generated by Soufiani and Taine (1997) from their line- by-line calculations along with the HITRAN’92 database (Rothman et al., 1992). The temperature and spectral range of the current database are respectively 300-2900 K and
150-9300 cm-1.
Recently, Daguse et al. (1996) showed that simulation with a statistical narrowband model can provide a good agreement between numerical and experimental results in a
H2/N2/O2 stagnation-point diffusion flame system. It is also demonstrated (e.g. Bedir et al, 1997; Shih et al., 1999; Frate et al., 2000; Rhatigan et al., 2002) that the statistical narrowband model with an exponential tailed inverse line strength distribution (Malkmus,
1967) can be successfully applied to diffusion flame systems with various types of fuels.
Following these previous studies, the statistical narrowband (e.g. Bedir, 1998) is chosen to calculate the non-gray radiative heat transfer in current simulation.
In this model, the averaged transmittance of an isothermal and homogeneous gaseous medium over a path length (s’→s) of a molar fraction Xi and a total pressure p is written as (Bedir, 1998):
⎡⎤βπκ⎛⎞2 u τ ()ss′ →=exp⎢⎥ −νν⎜⎟ 1 + − 1 , (C-1) ν πβ⎜⎟ ⎣⎦⎢⎥⎝⎠ν
where κν is the mean absorption coefficient, βν = 2πγνν δ the mean line width to
spacing ratio, γν the line half-width, and δν the mean line spacing parameter, and
uXpss=→i ′ the pressure path length. The subscript ν represents the property inside the spectral range (narrowband), ∆ν.
This narrowband model is further extended to the non-isothermal and non- homogeneous systems by using the Curtis-Godson approximation (Godson, 1953). With
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this approximation, the transmittance of a non-isothermal and non-homogeneous gas medium is given by Eq. (C-1) with the following equivalent mean absorption coefficient
κν ,e and equivalent mean line width to spacing ratio βν ,e . Here the subscript e refers to the equivalent band parameter.
s us()′′′→= s pXds (C-2) ∫s′ i
1 s κκ,ei()s′′′→= s pX ds (C-3) ννu ∫s′
1 s βκβ()s′′′→= s pX ds (C-4) ννν,ei∫s′ uκν ,e
Eventually, the transmittance of a gas mixture of is obtained from multiplication of the transmittance of individual gases.
C-II. Discrete Ordinates Method
In the radiative heat transfer analysis, not only the spectral dependence can complicate the problem, but also the directional dependence of radiative heat transfer since the radiative intensity field is a strong function of angular directions. In general, an integro-differential equation of radiative transfer has to be solved in both spatial coordinates and direction coordinates. Among those solution methods of this complex problem, the discrete ordinates method or S-N method may be implemented to arbitrary order and accuracy (Modest, 2002). This method has been used by many investigators
(e.g. Yang and Lloyd, 1985; Zhang et al., 1989; Kim et al., 1991; Bedir et al., 1997) in the radiative heat transfer using the radiative intensity as the primary variable.
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The discrete ordinates method is a finite differencing approximation of the directional dependence of the equation of transfer. It is based on a discrete representation of the directional variation of the radiative intensity. A solution is found by solving the equation of transfer for a set of discrete directions spanning the total solid angle range of 4π.
Integrals over solid angle are approximated by numerical quadrature. The choice of quadrature scheme is arbitrary, though it is desirable to choose sets of directions and weights that are completely symmetric (Modest, 2002). The name “S-N” indicates that N different direction cosines are used for each principle coordinate.
When the ordinate directions are determined, the associated angular weights must be considered. Determination of the angular weights is more difficult than finding the ordinates. The most commonly used restrictions on the angular weights are the even moment conditions (Modest, 2002).
The type of quadrature widely used is either Gaussian, which does not include the direction cosine ψ= 0, -1, and 1, or Lobatto, which includes these directions. For the M-th order S-N discrete ordinates method, the total number of ordinate directions in one- dimensional quadrature is M (Kim, 1990). The radiative heat transfer with a narrowband model in the current study is solved by a S8 discrete ordinates method, using a 20- direction Guassian quadrature set (cf. Bedir, 1998).
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