OH-PLIF MEASUREMENTS AND ACCURACY INVESTIGATION IN …

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OH-PLIF MEASUREMENTS AND ACCURACY INVESTIGATION IN HIGH PRESSURE GH2/GO2 COMBUSTION

By

ARAVIND VAIDYANATHAN

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008

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© 2008 Aravind Vaidyanathan

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To my Guru ‘Sainath of Shirdi’

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ACKNOWLEDGMENTS

I express my sincere gratitude to my advisor, Dr. Corin Segal, for giving me the

opportunity to do research under his valuable guidance and providing me with moral support and

encouragement during the ups and downs of my graduate studies. I am also grateful to all the

members of the PhD advisory committee for their critical evaluation and valuable suggestions on

my research work. I am indebted to Dr. Jonas Gustavsson for his continued patience and

guidance like an elder brother.

I thank all my colleagues in the Combustion and Propulsion Laboratory; moreover

working with people of diverse cultural background is a memorable experience. I am grateful to

all my friends and relatives for their continued support and encouragement. I also express my

sincere gratitude to my Master of Science advisor Prof. Job Kurian of IIT Madras, India and all

my teachers who have helped me push the limits of my thinking and imagination. Finally I am

extremely thankful to my parents for their endless support to me in pursuing higher education.

This work has been performed with the support from NASA Grant NCC3-994 with

Claudia Meyer as the Program Manager.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF TABLES...........................................................................................................................7

LIST OF FIGURES .........................................................................................................................8

NOMENCLATURE ......................................................................................................................12

ABSTRACT...................................................................................................................................16

CHAPTER

1 INTRODUCTION ..................................................................................................................17

Hydroxyl Radical (OH) in Non-premixed Flames .................................................................25 Motivation for the Current Work............................................................................................28

2 OH PLANAR LASER INDUCED FLUORESCENCE - THEORY AND REVIEW ...........29

Fluorescence Modeling...........................................................................................................29 Fluorescence and Interference Signals ............................................................................37 Laser ................................................................................................................................38 Absorption and Excitation, Line Shape and Fluorescence Efficiency ............................38 Experimental Constants...................................................................................................38

Review of OH PLIF Diagnostic Studies.................................................................................39 Fluorescence Strategy and Interference Signals..............................................................64 Laser ................................................................................................................................64 Absorption & Excitation, Line Shape and Fluorescence Efficiency...............................65 Experimental Constants...................................................................................................66

3 EXPERIMENTAL FACILITY AND DIAGNOSTICS METHODS.....................................68

Experimental Test Facility and Operating Conditions ...........................................................68 OH-PLIF Diagnostics .............................................................................................................72 Wall Boundary Conditions .....................................................................................................75

4 OH-PLIF IMAGE PROCESSING AND QUANTITATIVE ANALYSIS ............................77

Fluorescence and Interference Signals ...................................................................................77 Laser .......................................................................................................................................82 Absorption and Excitation, Line Shape, and Fluorescence Efficiency ..................................84 Experimental Constants ..........................................................................................................86

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5 RESULTS AND UNCERTAINTY ANALYSIS ...................................................................89

Chamber Pressure Measurements...........................................................................................89 OH-PLIF Measurements.........................................................................................................92 Quantification of OH Concentration and Uncertainty at 10, 27, 37 and 53 bar ...................100

6 CONCLUSIONS ..................................................................................................................121

7 FUTURE WORK..................................................................................................................123

APPENDIX

A MATLAB® SCRIPTS USED FOR DATA PROCESSING.................................................125

B PROPOSED NEW METHODOLOGY FOR PHOTON CALIBRATION..........................154

C OH ABSORPTION PROFILES...........................................................................................160

OH Absorption Profiles at 10 bar and 2500–3500 K Temperature Range...........................160 OH Absorption Profiles at 27 bar and 2500–3500 K Temperature Range...........................163 OH Absorption Profiles at 37 bar and 2500–3500 K Temperature Range...........................166 OH Absorption Profiles at 53 bar and 2500–3500 K Temperature Range...........................169

D OH NUMBER DENSITY CONTOURS..............................................................................172

Thirteen Instantaneous OH Number Density Contours at 10 bar.........................................172 Thirteen instantaneous OH Number Density Contours at 27 bar .........................................176 Thirteen Instantaneous OH Number Density Contours at 37 bar.........................................180 Thirteen Instantaneous OH Number Density Contours at 53 bar.........................................185

E TEMPERTURE MEASUREMENTS AND BOUNDARY CONDITIONS........................190

LIST OF REFERENCES.............................................................................................................196

BIOGRAPHICAL SKETCH .......................................................................................................203

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LIST OF TABLES

Table page 1-1 Previous Experimental Studies on Rocket Injectors..........................................................21

2-1 Review of OH-PLIF Diagnostics.......................................................................................40

3-1 Experimental Operating Conditions ..................................................................................72

4-1 Colliding Species Cross Section for Collisional Quenching .............................................86

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LIST OF FIGURES

Figure page 1-1 Chamber wall cracks due to local heating. Blanching indicates regions of insufficient

wall cooling........................................................................................................................17

1-2 Comparison of CFD predicted wall heat flux measurements with experimental results .................................................................................................................................18

2-1 Two-State Quasi-Steady Two-Step Modeling of Fluorescence.........................................29

2-2 Physical significance of the terms in OH number density expression...............................37

2-3 Pressure range in the reviewed studies ..............................................................................67

3-1 Combustion Chamber Cross Section .................................................................................68

3-2 Injector Details...................................................................................................................69

3-4 Laser spectral profile measured using Burleigh Wavemeter before doubling to 283 nm ......................................................................................................................................73

3-5 OH-PLIF Experimental Set-up ..........................................................................................74

4-1 Average of 13 instantaneous images obtained at near steady state for chamber pressure of 10 bar...............................................................................................................78




4-5 Normalized laser sheet intensity profile variation obtained from acetone fluorescence images ................................................................................................................................83

4-6 Camera calibration corresponding to the detection strategy employed in the OH-PLIF measurements and region of interest ........................................................................87

5-1 Chamber pressure versus time for GH2/GO2 combustion for 10 bar and O/F mass flow of 3.7..........................................................................................................................90


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5-5 Instantaneous image-processed OH-PLIF images at near steady state chamber pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar.................................................................93

5-6 Average of thirteen instantaneous image-processed OH-PLIF images at near steady state chamber pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar..........................................94

5-7 Average of thirteen instantaneous image-processed OH-PLIF images at near steady state chamber pressure of (a) 35, (b) 36, and (c) 37 bar indicating the repeatability and reliability of OH-PLIF measurements for determination of OH concentration..........95

5-8 Mean position of reaction zone determined from the average OH-PLIF images at (a) 10, (b) 27, (c) 37 and (d) 53 bar.........................................................................................97

5-9 Temperature and specie mole fraction variation based on equilibrium calculations with equivalence ratios of 0.5–3 at (a) 10, (b) 27, (c) 37 and (d) 53 bar .........................102

5-10 Absorption coefficient (12

9'

1

BBf∑ ) variation with equivalence ratio and temperature

(2500–3500 K) at (a) 10, (b) 27, (c) 37 and (d) 53 bar showing that the variation with respect to mean is 12.4, 14.6, 14.5 and 15.1% respectively ............................................104

5-11 Absorption profile of OH at (a) 3017 K and 10 bar, (b) 3085 K and 27 bar, (c) 3103 K and 37 bar, and (d) 3125 K and 53 bar simulated using LIFBASE showing a complete overlap with the laser spectral profile at all pressures .....................................106

5-12 Overlap integral laser abs dνΦ Φ∫ variation at (a) 10, (b) 27, (c) 37 and (d) 53 bar with temperature corresponding to equivalence ratio of 0.5–3, indicating that the variation with respect to mean is 1.3, 1, 0.8 and 0.5% respectively and can be assumed negligible..........................................................................................................................109

5-13 Collisional quench rate Q21 variation at (a) 10, (b) 27, (c) 37 and (d) 53 bar with temperature and colliding species mole fraction corresponding to equivalence ratio of 0.5–3 indicating that the variation with respect to mean is 4.1, 3.9, 3.8 and 3.7 % respectively ......................................................................................................................112

5-14 Instantaneous OH number density contours at near steady state chamber pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar .................................................................................113

5-15 Average of thirteen instantaneous OH number density contours at near steady state chamber pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar. ...............................................114

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5-16 OH-PLIF measurement uncertainties at (a) 10, (b) 27, (c) 37 and (d) 53 bar .................117

B-1 Calibration set-up for photon calibration.........................................................................154

B-2 A series of 900 images of 32x32 pixel size was obtained at each exposure....................156

B-3 A series of 900 images of 32x32 pixel size was obtained each exposure........................157

B-4 Counts vs exposure time at 532 nm .................................................................................158

B-5 Photons vs counts at 310 nm............................................................................................158

C-1 Absorption profile of OH simulated using LIFBASE at equivalence ratio of (a) 0.5, (b) 1, (c) 1.5, (d) 2, (e) 2.5 and (f) 3 corresponding to temperatures of 2500–3500 K for gaseous H2-O2 flame at 10 bar. ..................................................................................162


C-3 Absorption profile of OH simulated using LIFBASE at equivalence ratio of (a) 0.5, (b) 1, (c) 1.5, (d) 2, (e) 2.5 and (f) 3 corresponding to temperatures of 2500–3500 K for gaseous H2-O2 flame at 37 bar. ........................................................................................168


D-1 Thirteen instantaneous OH number density contours at near steady state chamber pressure of 10 bar.............................................................................................................176




E-1 Chamber wall temperatures vs time at inner locations of 37, 47, 58, 70, 89 and 102 mm from the injector face................................................................................................190

E-2 Chamber wall temperatures vs time at middle locations of 37, 47, 58, 70, 89 and 102 mm from the injector face................................................................................................190

E-3 Chamber wall temperatures at inner and middle locations along the chamber wall at end of the 8 s ....................................................................................................................191

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E-4 Exponential function assumed for heat flux evolution with time ....................................191

E-5 Experimental and computational temperatures at 37 mm axial location.........................192





E-10 Experimental and computational temperatures at 102 mm axial location.......................194

E-11 Chamber wall heat fluxes calculated based on 3D computations and linear + unsteady assumption at 37 bar .........................................................................................195

E-12 Computational and Experimental Temperatures for 37 bar at the end of 8s. ..................195

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NOMENCLATURE

A Electronic Excited State

Alaser Cross sectional area of the laser beam or sheet (cm2)

Pixel ProjectionA Pixel projection area (cm2)

21A Spontaneous emission rate (s-1)

12B Einstein B coefficient for absorption (cm3J-1s-2)

21B Einstein B coefficient for emission (cm3J-1s-2)

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'B 212B c (cm J-1)

c Speed of light (cms-1)

C Heat capacity (J kg-1 K-1)

E Laser energy per pulse (J)

E( )v Laser spectral energy per pulse (Jcm)

1g Degeneracy in the ground electronic state

2g Degeneracy in the upper excited electronic state

GO2 Gaseous oxygen

GH2 Gaseous hydrogen

h Planck’s constant (Js)

I( )v Laser spectral fluence (Wcm-2 cm)

J Jet momentum flux ratio

k Thermal conductivity (W m-1 K-1)

Bk Boltzmann constant (J K-1)

l Laser sheet thickness (cm)

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LOx Liquid Oxygen

M Molecular weight (g)

n Total population density (cm-3)

1n Population density in the ground state (cm-3)

2n Population density in the excited state (cm-3)

on Total number density (cm-3)

pN Number of photons

OH-PLIF Hydroxyl Planar Laser-Induced Fluorescence

O/F Oxidizer / Fuel

P Pressure (bar)

qA Heat flux per unit area (W m-2)

21Q Collisional quench rate (s-1)

ReD Reynolds number based on diameter

RET Rotational energy transfer

T Temperature (K, oC)

Tinner Temperature at 3.2 mm from inner wall (K, oC)

Tmiddle Temperature at 9.5 mm from inner wall (K, oC)

U velocity (m/s)

V Volume probed by the laser (cm3)

VET Vibrational energy transfer

12W Stimulated absorption rate (s-1)

21W Stimulated emission rate (s-1)

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X Electronic ground state

ΔT Temperature difference (K, oC)

Δt Time difference (s)

Δx Distance between temperature measurement locations

cvΔ Collisional width (cm-1)

DvΔ Doppler width (cm-1)

shiftCvΔ Collision induced shift (cm-1)

D shiftvΔ Doppler induced shift (cm-1)

ν Wavenumber (cm-1)

im Reduced mass of OH and the colliding species

is Colliding species cross section

4πΩ Fraction of solid angle

lτ Laser pulse duration (ns)

Bf Boltzmann factor

( )c vf Normalized collisional line shape function (cm)

( )D vf Normalized Doppler line shape function (cm)

( )abs vΦ Absorption line shape function (cm)

( )laser vΦ Laser spectral profile (cm)

F ( )( )

2 2

2 2

O H actual

O H stoichiometric

m mm m , equivalence ratio

F Fluorescence yield

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ρ Density (kg m-3)

ic Colliding species mole fraction

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

OH-PLIF MEASUREMENTS AND ACCURACY INVESTIGATION IN HIGH PRESSURE

GH2/GO2 COMBUSTION

By

Aravind Vaidyanathan

August 2008 Chair: Corin Segal Major: Aerospace Engineering

In-flow species concentration measurements in reacting flows at high pressures are needed

both to improve the current understanding of the physical processes taking place and to validate

predictive tools that are under development, for application to the design and optimization of a

range of power plants from diesel to rocket engines. To date, non intrusive measurements have

been based on calibrations determined from assumptions that were not sufficiently quantified to

provide a clear understanding of the range of uncertainty associated with these measurements.

The purpose of this work is to quantify the uncertainties associated with OH measurement

in a oxygen-hydrogen system produced by a shear, coaxial injector typical of those used in

rocket engines. Planar OH distributions are obtained providing instantaneous and averaged

distribution that are required for both LES and RANS codes currently under development. This

study has evaluated the uncertainties associated with OH measurement at 10, 27, 37 and 53 bar

respectively. The total rms error for OH-PLIF measurements from eighteen different parameters

was quantified and found as 21.9, 22.8, 22.5, and 22.9 % at 10, 27, 37 and 53 bar respectively.

These results are used by collaborators at Georgia Institute of Technology (LES), Pennsylvania

State University (LES), University of Michigan (RANS) and NASA Marshall (RANS).

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CHAPTER 1 INTRODUCTION

Over the past several decades, considerable effort has been dedicated for the development

of rocket engine technology including the space shuttle main engine (SSME) which operates at

pressures of 350 bar and a range of upper stage engines which operate with pressure ranges from

several bars to fewer than 100 bar. Yet, considerable difficulties remain to develop a design tool

that will adequately describe the physical processes occurring in the rocket engines. These

predictive tools require validation through accurate experiments.

An example of a current area of concern is illustrated by the photograph of the SSME

injector face shown in Figure1-1 The cracks and blanching in the chamber wall near the outer

row of the injectors is due to local uneven heating and must be corrected in future design.

Figure 1-1. Chamber wall cracks due to local heating. Blanching indicates regions of insufficient wall cooling [Courtesy: Mr.Kevin Tucker, NASA Marshall Space Flight Center, Huntsville, AL]

The consequences can be viewed as increased flight risk and maintenance costs and

indicates that that there is still a need to better understand the combustion chamber dynamics.

The most reliable method to accomplish this task is by the experimental study of the full scale

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engines; however despite their reliability and robustness these experiments are costly. Hence,

Computational Fluid Dynamics (CFD) is continuously being developed for future designs.

The capabilities and limitations of CFD as a rocket injector design tool were addressed by

Tucker et al. [1]. The major challenges currently faced in CFD are due to lack of adequate date

base for the CFD validation. The expected performance of the CFD is such that the physical

description of the problem will develop from a small scale simulation to near full prototype with

continuously increased complexity and confidence [1, 2].

An example of the current status of the predictive capability is shown in Figure 1-2.

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300

X (mm)

q" (M

W/m

^2)

Wall Heat Flux MeasurementsTeam 1Team 2; Calculation 1Team 2; Calculation 2Team 3Team 4Team 5Team 6

CFD Comparison to Wall Heat Flux Measurements

Figure 1-2. Comparison of CFD predicted wall heat flux measurements with experimental results

[Source: 3rd International Workshop on Rocket Combustion and Modeling, Paris, March 2006]. The CFD predicted results of the six different groups are inconsistent with each other and quite inaccurate when compared to experiment.

The plots in Figure 1-2 show the comparison of wall heat fluxes results obtained from

various CFD groups with the experiments. The CFD predicted results of the six different groups

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are inconsistent with each other and quite inaccurate when compared to experiments. This shows

that considerable improvements need to be made in the predictive capabilities of the CFD tool.

Tucker et al. [1] indicated the necessity to obtain experimental database for a single

element gas-gas injector for code validation and optimization of the injector performance.

According to the authors [1] the single element design, referred to as the baseline design, can be

used to model performance and environmental indicators as function of the geometric variables

like orifice sizes, post tip thickness and cup details of the injector. Moreover the simplicity to run

a CFD code for a single element injector for code validation and subsequent improvement in the

code before validating more complex configurations were also addressed in detail.

In the study conducted by Calhoon et al. [3] a systematic approach to investigate and

characterize high performance injectors are explained in detail. The importance of single element

injector small scale testing, which gradually paved ways to multi element full scale testing of

rocket engines was also emphasized.

The importance and relevance of gas-gas injector for the development of gas-liquid

injector technology was further discussed by Schley et al. [4] who indicated that the accurate

prediction of gas-gas system using the CFD codes is necessary before applying the CFD codes to

predict gas-liquid system. Clearly, the accurate prediction of the gas-gas system is not a

sufficient condition to predict gas-liquid system but is a necessary preliminary step before the

inclusion of additional complexities like accurate treatment of atomization and spray

combustion.

The gas-gas single element dataset consists of

• inflow measurements of species concentration, temperature and velocity; • temperature boundary conditions at inlet and exit of the combustion chamber; • wall heat transfer boundary conditions;

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A brief review of the existing experimental data focused on the inflow species

measurements for coaxial injector studies is tabulated in Table 1-1 and covers rocket injector

studies in the past 10–15 years. The reviews clearly indicate the lack of adequate inflow

quantitative species measurement with a thorough uncertainty analysis. Furthermore, when

evaluated, the uncertainties shown in Table 1-1 indicate that considerable work remains to be

done to improve the existing accuracy so that the database may be useful to support code

validation.

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Table 1-1. Previous Experimental Studies on Rocket Injectors Uncertainty Ref. Injector type Chamber

Pressure (bar)

Parameters Experimental Method

Species Quantification Source

(% error) Rms error (%)

Foust et al. [5]

Single element shear (GH2/GO2)

13 Inflow velocity and species concentration (H2O, H2, O2)

LDV for velocity and Raman spectroscopy for species

Mole fraction of H2O,H2 and O2

(i) Non-linear temperature dependence of Stoke band factor (40)

40

Foust et al. [6]

Single element shear, swirl (GH2/GO2)

13–69 Inflow species concentration (H2O, H2, O2)

Raman spectroscopy

Mole fraction of H2O,H2 and O2

(i) Laser pulse energy fluctuation(5), (ii) Non-linear temperature dependence of Stoke band factor (45)

45

Brumm-und et al. [7]

Single element shear (LOx/GH2)

20 Inflow species visualization (OH)

Planar Laser Induced Pre-dissociation Fluorescence (PLIPF)

Signal intensity (qualitative)

- -

Mayer et al. [8]


15–100 Jet and flame visualization

Shadowgraph, Flame emissions


- -

Yeralan et al. [9]

Single element swirl (LOx/GH2)

28 Inflow species concentration (H2O, H2, O2) and temperature

Raman spectroscopy

Mole fraction of H2O, H2 and O2.

(i)Calibration measurements (40), (ii)Shot noise

40

Wehrm-eyer et al. [10]


60 Inflow species visualization (H2O, H2, O2)

Raman spectroscopy


- -

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Table 1-1. Continued. Uncertainty Ref. Injector type Chamber

Pressure (bar)




Herding et al. [11]


1–10 Inflow species visualization (OH)

OH emissions


- -

Candel et al. [12]


10 Inflow species visualization (OH, O2) Temperature

#PLIF for OH and O2. CARS for temperature


- -

Ivancic et al. [13]


60 Inflow species visualization (OH), Temperature

OH emissions CARS for temperature


- -

Juniper et al. [14]


70 Inflow species visualization (OH)

OH emissions


- -

Mayer et al. [15]


20–60 Jet and flame visualization

Shadowgraph, Flame emissions


- -

Yeralan et al. [16]


28 Inflow species concentration (H2O, H2, O2) and temperature

Raman spectroscopy

Mole fraction of H2O, H2 and O2.

(i)Calibration measurements (19), (ii)Shot noise(10)

22

23


Pressure (bar)




Mayer et al. [17]


63 Jet and flame visualization

Shadowgraph, OH emissions


- -

Kalitan et al. [18]

Single element swirl (LOx/CH4)

41 Inflow species (OH, CO2) and jet visualization

OH visualization by PLIF and emission images, CO2 by emission images and jet visualization by shadowgraph and laser light scattering


- -

Singla et al. [19]

Single element shear (LOx/CH4)

1–70 Inflow species visualization (OH, CH)

OH and CH emissions


- -

Singla et al. [20]


63 Inflow species concentration (OH) and visualization (OH)

PLIF for OH concentration and OH emissions for flame visualization

Signal intensity ( semi quantitative)*

(i) Boltzmann fraction variation in 2000–2500 K temperature range (10), (ii) laser beam absorption by OH(10–30) and (iii)Variation in quench rate due to species and temperature variation

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Pressure (bar)




Singla et al. [21]

Single element shear (LOx/CH4)

25–30 Inflow species visualization (OH)

PLIF for OH visualization


(i) UV PAH fluorescence and OH fluorescence are of same intensity at 25–30 bar

-

Smith et al. [22]


40–60 Inflow species (OH) and jet visualization

Shadowgraph, OH emissions


- -

Vaidyan-athan et al. [23]

Single element shear (GO2/GH2)

10–37 Inflow species concentration (OH)

PLIF for OH concentration

Mole fraction of OH

(i) Boltzmann fraction variation in 2500–3000 K temperature range (15), (ii) laser beam absorption by OH over a distance of 3 mm(8)

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#PLIF – Planar Laser Induced Fluorescence *Singla et al. [20] provided semi-quantitative OH distribution in signal intensities without converting them to the actual number densities. Additional error sources which typically originate from photon calibration, shot noise, spatial variation of camera sensitivity and spatial variation in laser sheet intensity profiles were not addressed. One of the main objectives of the study carried out by Singla et al. was to provide OH distribution for CFD validation.

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From the previous experimental studies tabulated in Table 1-1, it can be seen that only one

third of them addressed the uncertainties associated with the measurements and only a limited

number of factors have been included. A comprehensive and thorough investigation of the

uncertainties associated with the inflow measurements is clearly needed. This is the primary

motivation of the present work.

Before discussing the motivation of the current work, the importance of hydroxyl radical

measurement in non premixed flames is reviewed.

Hydroxyl Radical (OH) in Non-premixed Flames

In the injector vicinity of a non-premixed flame the OH radical is present in the reaction

zone of the fuel-oxidizer shear layer jets and is, therefore, a good flame marker [24–32].

Seitzman et al. [25] characterized OH structures in turbulent non-premixed hydrogen

flames and found that the OH was confined to the flame as a thin structure at the base of the

flame and was also found in the diffuse regions near the tip of the flame where the hot product

gases existed.

According to Barlow et al. [27] OH concentration peaks near the stoichiometric condition

in hydrogen flames. In this study [27] the equivalence ratio in the shear layer of supersonic and

subsonic jets varied between 0.8–1. The authors opined that since the stoichiometric contour is

often separated from the centre of the shear layer in turbulent diffusion flames, the OH

fluorescence can be a good reaction zone marker. In this study [27] the growth and relative

widths of shear layer for both compressible and incompressible flow were determined based on

the OH measurements.

Clemens and Paul [28] also discussed the use of OH as reaction zone marker. According to

the authors [28] the OH can also appear as a product in lower temperature regions due to its

relatively slow three-body recombination reaction, H+OH+M → H2O + M, M being the third

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body. However, these regions appear as distributed and diffused OH zones when compared to the

thin laminar like filament structures in the primary reaction zone. Thus the appearance of OH in

the shear reaction zones represents the flame front and could be used to mark the reaction zones

in the GH2/GO2 combustion carried out in the current study. Similarly Ivancic et al. [13] in the

study of time and length scales in LOx/GH2 rocket combustors found out that the OH emissions

present on the symmetry line in the near injector regions come from the OH radicals produced

within the reaction zone.

Donbar et al. [30] identified the reaction zone structures in a turbulent non-premixed

methane jet flames based on CH-OH PLIF images. According to the authors [30] if the wrinkling

in the flame is not severe, the fuel rich boundary of the OH zone can be identified and used as

the stoichiometric contour. The stoichiometric contour in this study was identified as existing in

a thin zone in the gap between CH and OH regions. The stoichiometric contours were used to

determine the flame surface density and degree of flame wrinkling.

The visualization of reaction zone from OH-PLIF images is mentioned in the work done

by Pickett et al. [31]. According to these authors in non-premixed flames OH is consumed in the

fuel rich region and hence the OH zone is confined to the flame whereas in the case of premixed

flames, OH continues to exist in high temperature product regions. Singla et al. [21, 22] cites the

importance of OH radical in high pressure cryogenic flames as representing the characteristics of

combustion reactions, presence in high temperature stoichiometric regions and flame-front

marker.

Experimental investigation of the effects of heat release in a subsonic turbulent planer H2

jet was done by Theron et al. [32]. In this study H2 was injected through the central rectangular

slot whereas air was supplied from the upper and lower channels above and below the slot

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respectively. The OH radical was tracked by fluorescence technique and the mean position of the

reaction zone was identified as the position of maximum OH fluorescence signal intensity from

the centre line along the test section height. The axial evolution of the mean position of the

reaction zone was represented as the stoichiometric contour of maximum temperature.

These studies clearly identified the usefulness of tracking OH in non-premixed flames as a

marker of the flame zone that is close to stoichiometric region; hence the continuous use of OH

measurement for combustion applications.

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Motivation for the Current Work

Based on the existing information the present work is focused on providing OH

measurement with a detailed uncertainty analysis. The flow field is generated by a shear coaxial

H2/O2 flame.

This study was aimed at obtaining quantitative OH concentration at chamber pressures of

10–50 bar range and oxygen/fuel (O/F) mass flow ratio of four using OH-PLIF diagnostic. The

uncertainty sources and their respective contributions to the OH concentration measurements

will be addressed and discussed in detail in Chapters 4 and 5.

The data obtained here includes OH-PLIF measurements at pressures of 10, 27, 37 and 53

bar. Temperature measurements for boundary conditions are also included to compliment the

information provided to the CFD modelers. The data corresponding to chamber pressure of 10,

27, 37 and 53 bar were post-processed in this work and the uncertainties associated with the OH

measurements were identified and evaluated.

Thus, the rest of the document includes the following discussions:

• theory and review of OH planar laser induced fluorescence • experimental facility and diagnostic methods employed • OH-PLIF image processing and quantitative analysis • results and uncertainty analysis • conclusions • future work

Equation Section 2

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CHAPTER 2 OH PLANAR LASER INDUCED FLUORESCENCE - THEORY AND REVIEW

A brief discussion of laser induced fluorescence (LIF) application to obtain the number

density of the species being probed, in this case, OH is given below followed by a review of

existing studies.

Fluorescence Modeling

Fluorescence modeling is based on a two level excitation / detection strategy within the

linear regime. Detailed explanations are given in Eckberth [33] and others [34–39].

λ = 283 nm

λ = 306-320 nm

ν’’

ν’ ν’

ν’’

Laser Excitation

01

23

01

23

01

23

01

23

A A

X X

Fluorescence Emission

Ground State

Excited State

Step 1 Step 2Vibrational level

Rotational level

λ = 283 nm

λ = 306-320 nm

ν’’

ν’ ν’

ν’’

Laser Excitation

01

23

01

23

01

23

01

23

A A

X X


Ground State

Excited State

Step 1 Step 2λ = 283 nm

λ = 306-320 nm

ν’’

ν’ ν’

ν’’

Laser Excitation

01

23

01

23

01

23

01

23

A A

X X

Fluorescence Emissionλ = 283 nm

λ = 306-320 nm

ν’’

ν’ ν’

ν’’

Laser Excitation

01

23

01

23

01

23

01

23

A A

X X


Ground State

Excited State

Step 1 Step 2Vibrational level

Rotational level

Figure 2-1. Two-State Quasi-Steady Two-Step Modeling of Fluorescence

The laser induced fluorescence process is illustrated in Figure 2-1. It consists of a two step

process: the first step is the excitation of the molecule/radical from the ground state (X) to the

upper excited state (A) by laser absorption; the second step is the spontaneous emissions of

photons when the molecule relaxes from the upper excited state to their ground states. Given the

certain energy loss associated with the process, emission is at longer wavelength than the

excitation. Emission occurs very close after absorption and is of the order of less than 10 ns in

the case of OH in an atmospheric flame [38]. The quantification of the number of photons

collected in this process can be used to determine the number density of the molecule/radical in

30

the region of interest provided all the processes involved in the fluorescence are properly

accounted for and modeled.

The processes involved in fluorescence can be more specifically termed as stimulated

absorption-W12, stimulated emission-W21, spontaneous emission-A21 and collisional quenching-

Q21. These four processes of energy transfer take place between the electronic states, in this case,

the ground state (X) and the upper excited state (A). In the upper excited state the two processes

of interest are the rotational energy transfer -RET and the vibrational energy transfer -VET.

The excitation is provided by a monochromatic source from a pulse laser with short

duration of less than 10 ns. This permits fluorescence detection time of less than 500 ns which

helps in avoiding the interference from other background emissions during diagnostics.

The rate of absorption by the molecule/radical is given by

1212 2

BW I( )

cv⎛ ⎞= ⎜ ⎟

⎝ ⎠ (2-1)

Here 12W (s-1) is the stimulated absorption rate, 12B is the Einstein B coefficient for

absorption (cm3J-1s-2), c is the speed of light (cms-1), I( )v is the laser spectral fluence (Wcm-2 cm)

given bylaser

E( )A l

vτ

, where E( )v is the laser spectral energy per pulse (Jcm), Alaser (cm2) is the cross

sectional area of the laser beam or sheet and lτ (s) is the laser pulse duration. Since the

absorption process involves laser/molecule interaction it is called stimulated absorption rate.

The molecule/radical will relax from the upper state to the ground state by the following

three processes as described below.

The first path constitutes of stimulated emission, in which the molecule/radical interacts

with the laser and returns to the ground state. The stimulated emission rate, W21 (s-1) is given by

31

2121 2

BW I( )

cv⎛ ⎞= ⎜ ⎟

⎝ ⎠ (2-2)

where 21B is the Einstein B coefficient for emission (cm3J-1s-2). The absorption and emission

rates are related by

1 12 2 21g W =g W (2-3)

Here 1g and 2g are the degeneracies of the ground and the upper electronic states respectively.

The second path constitutes of the spontaneous emission in which the molecules relax from

the upper excited state to the ground state by emitting fluorescence. This is the main mechanism

for LIF signal production. The spontaneous emission rate is dictated by Einstein coefficient for

spontaneous emission 21A (s-1). The spontaneous emission rate and the stimulated absorption

rate are related by

321

12

A8

Bhπ ν= (2-4)

where h (J.s) is the Planck’s constant and ν is the wave number of the particular individual

transition (cm-1).

In the third process, the molecules in the upper excited electronic state can relax to the

ground state by collisions with other molecules called collisional quenching. The quenching rate

is modeled as,

12

218

Q Bi i

iB i

k TPk T π

⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

∑c sm

(2-5)

where P is the pressure, Bk is the Boltzman constant, T is the temperature, ic represents the

colliding species mole fraction, is , the colliding species cross section and im is the reduced

mass of excited molecule/radical ,in this case, OH and the colliding species. Quenching

32

represents the rate of non-radiative decay of the excited state molecule to the ground state. It can

be noticed from Equation 2-5 that quenching linearly increases with pressure and hence at high

pressures the fluorescence signal intensity due to spontaneous emission can be significantly

reduced due to quenching. This is one of the major challenges in applying LIF techniques at high

pressures.

In RET the molecules in the upper excited rovibrational state can move to neighboring

rotational levels in the same excited electronic state due to collisions with other molecules.

Similarly in VET the molecules migrate to neighboring vibrational levels of the same upper

excited state. The collisional quench model in Equation 2-5 needs to be modified to take into

account the effect due to RET and VET. The modified model for collisional quench rate of OH

which also takes into account the effect of RET and VET is discussed in Chapter 4 in detail.

Other mechanisms involved in the energy transfer processes are predissociation and

photoionization [33]. Predissociation is the process in which the excited molecule dissociates

prior to the emission of the photon. In photoionization, the excited molecule gets ionized prior to

the emission of the photon.

Based on the two state two step model as shown in Figure 2-1 a mathematical formulation

of all the processes involved in fluorescence is made to infer target species number density. The

population density in the ground state, n1 (cm-3) and in the excited state n2 (cm-3) constitute the

total population density of n = n1 + n2 (cm-3) for the specific robvibrational transition being

excited. The rate of change of molecules in the upper excited state (A) per unit volume is then

given by

( )21 12 2 21 21 21W W Q A

dnn n

dt= − + + (2-6)

33

In the current study fluorescence in the linear regime is considered, thus the fluorescence

signal is linearly proportional to the input laser irradiance. In other words, the number of

fluorescence signal photons collected is linearly proportional to the number of input laser

photons supplied during the duration of the pulse. In contrast to linear regime, fluorescence

signal photons become independent of both laser irradiance and collisional quenching in the case

of saturation regime. The laser irradiance used in the current study which is 0.445 x 106 W/cm2 is

nearly four-five orders of magnitude less than the laser irradiance employed for saturation LIF

studies by Carter et al. [40]. Hence for the current study the pumping is weak and the

fluorescence can be considered to be in the linear regime.

At steady state, 2dndt

is zero and in the linear regime, as 12W is negligible [33], n2 is

expressed as

1 122

21 21

W(Q A )

nn =

+ (2-7)

The fluorescence signal or the number of photons, pN can then be expressed as

p 2 21N A V4 ln τπΩ

= (2-8)

where, V (cm3) is the volume probed by the laser and4πΩ is the fraction of the solid angle

detected.

Substituting the expression of n2 from Equation 2-7 and rearranging Equation 2-8

( )

21p 1 12

21 21

AN W V

Q A 4 ln τπΩ

=+

(2-9)

For weak pumping, n2<< n1 and total population density n ~ n1. The population density n1

(cm-3) in the ground state rovibrational energy level is related to the total number density of the

34

molecule/ radical by n1 = noBf . Here no is the total number density and Bf is the Boltzmann

fraction of the specific rovibrational energy level in the ground state. Thus, pN in Equation 2-9

can be rewritten as

( )

21p 12

21 21

AN W V

Q A 4o

B ln f τπΩ

=+

(2-10)

Substituting the expression of 12W from Equation 2-1 into Equation 2-10

( )

12 21p 2

21 21

B AN I( ) V

Q A 4co

B ln f v τπΩ⎛ ⎞= ⎜ ⎟ +⎝ ⎠

(2-11)

Emitted and absorbed light has a finite bandwidth which is called the line broadening [33,

35]. This means that in reality, the energy of a dipole transition which is well defined by the

energy difference between two quantum states is not monochromatic and has a certain spectral

width and shape. The line broadening in a typical combustion environment is due to three main

reasons, namely natural broadening, collisional/pressure broadening and Doppler broadening.

Each is briefly discussed below.

Natural broadening is due to the finite lifetime of the molecule/radicals in the excited

state. If the molecule were to radiate energy for an infinite period, the line shape is a delta

function. Since the lifetime is finite it represents a Lorentzian function [35]. In general the effect

of natural broadening is much smaller compared to collisional and Doppler broadening; hence, it

is often neglected [33]. Similarly in the case of collisional broadening, the lifetime of the

molecule in radiating the energy is reduced if it collides with other molecules. The Doppler

broadening occurs due to the Doppler shift caused by the relative motion of the molecule and the

laser beam propagation.

The collisional broadening represented by a Lorentzian function [35] is

35

2

1(2

( )2

) c

co

cv

vv v

vπ

Δ

Δ⎛ ⎞− + ⎜ ⎟⎝ ⎠

=f (2-12)

where ( )c vf is the normalized line shape function, cvΔ is the spectral width associated with

collisional broadening, ov is the central frequency of the transition involved. For OH the

collisional width could be calculated from the empirical model provided by Davidson et al [41]

based on spectroscopic measurements carried out in a shock tube at conditions of 60 bar and

1735 K.

0.75

-13000.140 cmCo

PvP T

⎛ ⎞⎛ ⎞ ⎡ ⎤Δ = ⎜ ⎟⎜ ⎟ ⎣ ⎦⎝ ⎠⎝ ⎠ (2-13)

Similarly the Doppler broadening represented by Gaussian profile [35] is

20.52 ln 2( exp 4ln 2) o

DD D

v vv v

vπ

⎡ ⎤⎛ ⎞−⎛ ⎞ ⎢ ⎥− ⎜ ⎟⎜ ⎟Δ Δ⎝ ⎠ ⎢ ⎥⎝ ⎠⎣ ⎦=f (2-14)

where ( )D vf is the normalized line shape function, DvΔ is the spectral width associated with

collisional broadening and ov is the central frequency of the transition involved. The Doppler

width [35] is

2

-7 -12

8 ln (2)7.16 x 10 cmB o

D ok Tv Tv v

Mmc⎡ ⎤Δ = = ⎣ ⎦ (2-15)

where T is the temperature, kB, the Boltzmann factor, m, the mass of the molecule/radical and M

is the molecular weight of the molecule/radical which is OH in the current study.

The spectral distribution due to the line broadening is expressed as a normalized line shape

function, ( )abs vΦ and is defined as ( ) 1abs v dv+∞

−∞

=Φ∫ . The absorbing species line shape function,

36

( )abs vΦ is obtained as the convolution of collisional and Doppler line shape functions which is

generally referred to as the Voigt profile [33, 35].

Moreover, the central frequency of the absorption profile gets shifted due to the collision

with neighboring molecules and/or due to the Doppler effect [20, 37, 41]. The collision induced

shift for OH is given [20, 41] by

0.45 0.08

-1 shift

3000.0305 cmCo

PvP T

±⎛ ⎞⎛ ⎞ ⎡ ⎤Δ = − ⎜ ⎟⎜ ⎟ ⎣ ⎦⎝ ⎠⎝ ⎠ (2-16)

and the Doppler shift [37] is given by

-1D shift

v cmcov v ⎛ ⎞ ⎡ ⎤Δ = − ⎜ ⎟ ⎣ ⎦⎝ ⎠

(2-17)

Here shiftCvΔ and D shiftvΔ represent the collisional and Doppler shifts respectively, ov is the

central frequency of the specific rovibrational transition, v, the velocity of the molecules and c, is

the speed of light.

In the current study, the absorption profile for OH is simulated using the commercially

available software LIFBASE [37]. The laser profile used in this study is assumed to be well

represented by the Gaussian profile. The laser line profiles and the absorption line profiles

relevant to the current study will be discussed later in Chapters 3 to 5.

Thus, to account for the spectral distribution of the laser profile and the absorption profile

of the target species, the fluorescence signal in Equation 2-11 is modified as

( )

12 21p 2

21 21

B AN I( ) ( ) V

Q A 4c abs lo

B v v dvn f τπΩ⎛ ⎞= Φ⎜ ⎟ +⎝ ⎠∫ (2-18)

Substituting for laser l

E( )I( )A

vvτ

= and E( ) E ( )laserv v= Φ where E is the laser energy per pulse and

( )laser vΦ is the laser line shape, into Equation 2-18 and rearranging,

37

( )

12 21p 2

21 21

B AEN VA Q A 4c laser abs

o B dvfn

πΩ⎛ ⎞⎛ ⎞= Φ Φ⎜ ⎟⎜ ⎟ +⎝ ⎠⎝ ⎠∫ (2-19)

(I) 1) Fluorescence (i) Detection Electronics(ii) Excitation / Detection

Strategy

(iii) Detection Environment

2) Interference Signals

(iv) Laser internal scattering

(ii) Background emission(iii) Mie / Rayleigh

Scattering

(III) 1) Absorption and Excitation

(i) Boltzmann factor (Temperature)

(ii) Absorption Coefficient (Spectroscopy)

2) Line Shape(iii) Overlap integral (line shape & laser

center line shift)(iv) Model (Collisional & Doppler width/shift)

3) Fluorescence Efficiency(v) Quench rate

(Collider species cross section/ mole fraction,Pressure, Temperature )

(vi) Model for quantum yield

(II) 1) Laser

(i) Shot to shot power fluctuation

(ii) Laser sheet / beam profile variation

(iii) Laser absorption (OH & other molecules)

(IV) 1) Experimental

Constants(i) Probe volume

(ii) Solid angle detected(iii) Transmission efficiency of filters

(iv) Photon detection efficiency of camera

( )p

OH

12 212

21 21

N

B AE VA c A Q 4

o

laser absBf d

nν

π

=⎡ ⎤⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

∫W

OH-PLIF Measurement


Strategy





Scattering









(II) 1) Laser








( )p

OH

12 212

21 21

N

B AE VA c A Q 4

o

laser absBf d

nν

π

=⎡ ⎤⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

∫W

OH-PLIF Measurement


Strategy





Scattering









(II) 1) Laser








( )p

OH

12 212

21 21

N

B AE VA c A Q 4

o

laser absBf d

nν

π

=⎡ ⎤⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

∫W


Strategy





Scattering









(II) 1) Laser








( )p

OH

12 212

21 21

N

B AE VA c A Q 4

o

laser absBf d

nν

π

=⎡ ⎤⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

∫W

OH-PLIF Measurement

Figure 2-2. Physical significance of the terms in OH number density expression

Equation 2-19 can be rearranged in terms of OH number density. The physical significance

of the terms from the experimental, modeling and quantifying point of view are shown in Figure

2-2. The four categories of OH-PLIF measurement mentioned in Figure 2-2 are discussed here.

Fluorescence and Interference Signals

The excitation and detection strategy of OH consists of A-X (0, 0), A-X (1,0), A-X (3,0)

transitions of which A-X(1,0) is employed in the current study. The detection electronics

employed to collect fluorescence could be an ICCD camera, photodiode or spectrograph. The

detection environment of OH is typically a combustion zone. The interference signals refer to the

38

potential interferences from other species in the combustion environment, elastic scattering and

the background emissions.

Laser

The laser pulse energy employed in PLIF measurements and the shot to shot power

fluctuation needs to be monitored. The laser beam/sheet profile is non-uniform in space and

needs to be corrected for quantitative measurements. The laser is absorbed by OH and other

species in the combustion environment resulting in attenuation of the beam as it traverses

through the flame. All these factors contribute to the measurement uncertainties.

Absorption and Excitation, Line Shape and Fluorescence Efficiency

The Boltzmann fraction, Bf in the initial state population, noBf varies with temperature

and hence a careful selection of rovibrational transitions with minimum temperature dependence

is recommended for PLIF diagnostics. The dependence of absΦ with temperature and pressure is

to be accounted for species quantification. The determination of fluorescence yield from

Equation 2-5 also requires the knowledge of colliding species mole fraction in addition to

temperature and pressure fields.

Experimental Constants

The strength of the fluorescence signal detected depends on the intersection volume of

laser beam/sheet with the flame known as the probe volume and the fraction of solid angle

collected. To avoid the interference signals and elastic scattering, optical filters are employed

while collecting fluorescence; however most of the optical filters have transmission efficiency of

less than 60 % at 310 nm where the OH fluorescence is detected. In addition to this the photon

detection efficiency at 310 nm for an ICCD camera is less than 25 %. All these reduce the

strength of the detected fluorescence signal.

39

Review of OH PLIF Diagnostic Studies

LIF techniques can be used for temperature, pressure, velocity, density or mole fraction

measurements in wide range of environments [33, 35, 38, 42, 43]. Equation 2-19 helps determine

the number density directly from the fluorescence signal. Moreover PLIF provides species

measurements in various fluids including combustion environments. Hanson [42] provided a

detailed review of the application of planar imaging of fluorescence, giving examples of PLIF

application to obtain species concentration, 2D temperature fields, velocity and pressure

imaging. In the following discussions, studies related to OH fluorescence and its planar imaging

in combustion zones will be presented.

A brief review of the OH-PLIF diagnostics is tabulated in Table 2-1. The table is set up to

identify the four categories as (I) Fluorescence and interference signals, (II) Laser energy

fluctuation, spatial profile non-uniformity and attenuation, (III) Absorption coefficient variation

with temperature, overlap integral modeling and dependence on temperature and pressure, and

fluorescence yield modeling and dependence on temperature and pressure and (IV) Experimental

constants corresponding to Figure 2-2. The last column in the table indicates the main results

from each study.

40

Table 2-1. Review of OH-PLIF Diagnostics Authors Target Species (I)

Fluorescence strategy and interference signals

(II) Laser energy, spatial profile and attenuation

(III) Absorption &excitation line shape and fluorescence efficiency

(IV) Experimental constants- transmission & photon detection

Observations

Dieke & Crosswhite [44]

OH emissions in atmospheric flame

- - - - fundamental study which provided ultraviolet bands of OH in 280–355 nm

Allen & Hanson [24]

Imaging OH in atmospheric heptane-air flame

Excitation Q1(6), A-X(1,0) Detection (1,1) at 310 nm camera Interference elastic scattering from droplets

10 mJ per pulse

The Q1(6) transition at 283 nm was devoid of temperature dependence across the field of view

Interference filter with ε=15% at 310 nm was used to collect fluorescence. Signal collected at 90o to laser

OH fluorescence was used to comprehend the hydrodynamic flame structure and the combustion zones

Jeffries et al. [45]

OH,NH, CH, CN & NCO fluorescence spectrum in atmospheric CH4/N2O flame

Excitation(OH) 312.22 nm, A-X(0,0) Detection(OH) 350 nm, A-X(0,1) Monochromator, photomultiplier

0.2 mJ per pulse

- - Excitation specific to OH produced weak fluorescence emissions from NH and CN due to electronic energy transfer between molecules/ radicals

41

Table 2-1. Continued. Authors Target Species (I)





Observations

Smith & Crosley [46]

(i) Quenching rate constants of OH with H2, N2O & ten hydrocarbons at 1200 K (ii) OH is produced by thermal decompositi-on of H2O2

Excitation(OH) 310.65 nm, A-X(0,0) Detection(OH) 309 nm, A-X(0,1) Monochromator, photomultiplier

2 mJ per pulse (i) Measured time decay of the fluorescence with pressure was used to obtain quenching rate constants. (ii) The measured cross sections had 15% accuracy

- Attractive forces between the molecules need to be properly taken into account in the case of quenching models for accurate prediction of quenching cross sections.

Garland & Crosley [47]

- - - Temperature and species dependent quenching cross section of OH was predicted using a model based on attractive forces

- The predicted quenching cross sections of NH3, H2, NO, O2, H2O, N2O,CH4, CO and CO2 agreed within +30 % of the experimental values

42






Observations

Edwards et al. [48]

OH-LIF in solid propellant flames at 35 bar

Excitation(OH) 306.42 nm, A-X(0,0) Detection(OH) 310 nm, A-X(0,1) Monochromator, Photomultiplier Interference elastic scattering from particulates

(i) 6 mJ per pulse (ii) significant laser attenuation (iii) increase in optical thickness with pressure

(i)Quenching decreased the LIF signal with increasing pressure. (ii) Saturation LIF to avoid effects of quenching.

Fluorescence collected at 90o to laser propagation

(i) Lack of availability of high pressure kinetic and spectroscopic data were addressed as the major challenges in LIF at high pressures

43






Observations

Schefer et al. [26]

OH concentration in turbulent CH4-jet flame

Excitation P2(7), A-X(1,0) Detection 312 nm vidicon camera

(i) Laser attenuation was negligible. (ii) radiative trapping was < 5%

+5 % variation in initial state population in 1000–2000 K temperature range

10 nm bandwidth filter centered at 312 nm

(i)OH concentration was obtained from flat flame calibration. (ii) +10 % error from calibration measurements, 7% due to photon statistics (iii) OH concentration was five times higher than equilibrium values in reaction zones

Seitzman et al. [14]

OH-PLIF in a turbulent non-premixed H2/air jet atmospheric flame

Excitation Q1(3), A-X(0,0) Detection A-X(0,0),(1,1) CCD camera

(i) 50–120 mJ per pulse (ii) laser absorption is 3–20 %

+40 % variation in initial state population in 1000–2000 K temperature range

- Spatial autocorrelation was used to determine flame angle and correlation lengths

44






Observations

Kohse-Hoinghaus et al. [49]

Line shape, temperature and estimated OH concentration from a CH4/air flat flame at 1–10 bar

Excitation 283nm ,A-X(1,0) Detection A-X(0,0),(1,1) Photomultiplier

1.5 mJ per pulse

(i) There was loss of fluorescence signal due to quenching and absorption line shape broadening with increasing pressure and the estimated signal reduction was of the order of 100 in the 10–100 bar range.

Interference filter centered at 315 nm with FWHM of 38 nm

(i) The simulated Voigt profile matched well with the measured one (ii) OH concentration from absorption measurements with 30% accuracy agreed well with numerical predictions (ii) Feasibility of applying numerical modeling to obtain effect of quenching and line broadening on fluorescence efficiency was mentioned

45






Observations

Seitzmann & Hanson [50]

Comparison of A-X (1,0), (0,0) and (3,0) schemes for quantitative fluorescence imaging . The A-X(1,0) scheme is highlighted here

- (i) 10 mJ/cm2

(4 mJ for 80x0.5 mm sheet) is considered to ensure fluorescence in linear regime within + 5% down to zero energy (ii) Need to apply corrections for spatial laser profile variation

(i) Need to choose rotational transition with low temperature dependence (ii) Overlap integral variation in a non-isobaric flow(1–5 bar) is 30–40% for lasers with line width of 0.2–0.5cm-1 (iii) Overlap integral variation with temperature (1000–2500K) is less then + 5% for line widths less than 0.5 cm-1 (iv) quench rates vary only by <10% in regions of OH concentration

(i) Assumption: Fluorescence is emitted equally into 4πSr (ii) Random noise in the detector(ICCD) is contributed by shot noise, quantum efficiency, electron gain, dark, readout and digitization noise (iii) Pulse to pulse variation in laser bandwidth contributes to error in OH concentration measurement.

(i) Actual laser induced excitation and emission can deviate from the two state, two step quasi steady model leading to systematic errors (ii) Nonlinear responses to change in laser energy, population fraction and depletion are well within the range of A-X(1,0) excitation scheme.

46






Observations

Locke et al. [51]

Merits and demerits of PLIF applied to reactive flows

Obstacles include stray light interferences, quenching contributions and RET

- - - Merits include 2D imaging, multi species probing, identifying primary reaction zones, temperature field imaging and semi-quantification

Carter & Barlow [52]

OH & NO-PLIF in a turbulent non-premixed H2/air jet atmospheric flame

Excitation(OH) O12(8), A-X(1,0) Detection(OH) A-X(0,0),(1,1) photomultiplier tube photocathode

- (i) The need for spectroscopic data for quenching correction was mentioned (ii) Colliding species and temperature field data was obtained from equilibrium calculations

- (i) To obtain OH concentration an initial calibration was carried out in a lean H2/air flame in a Hencken burner

47






Observations

Paul [53] Temperature dependent collisional model for OH in 250–2500 K range

- - - - (i) A function for predicting temperature dependent cross section for collisional quenching of OH by various molecules is provided (ii) A model for fluorescence yield in A-X(1,0) excitation scheme by incorporating effect of VET in the excited electronic state(A)

48






Observations

Allen et al. [54]

Imaging OH in 1–10 bar heptane, methanol and ethanol-air flame

Excitation(OH) 283 nm, A-X(1,0) Detection(OH) 316-371 nm ICCD camera Interference 100 ns gate time to avoid background luminosity and chemiluminescent gas emissions.

(i)3 mJ per pulse. (ii) laser attenuation was estimated as ~30% due to absorption by hydrocarbons

(i) Effect of pressure on fluorescence signal intensity in linear regime was analyzed based on steady state and multi level transient approach

A combination of filters transmitted fluorescence from 316–371 nm

(i) As long as fluorescence was in linear regime, quasi steady state model used in deriving fluorescence yield was valid for the experimental conditions investigated.

49






Observations

Battles and Hanson [55]

LIF measurements of OH and NO in 1–10 bar methane flames: Fluorescence modeling and experimental validation

Excitation(OH) P1(8),285.685 nm, A-X(1,0) Detection(OH) A-X(0,0) Photomultiplier tube(PMT) Interference No significant interference near 285 nm

(i)100 μJ per pulse to ensure fluorescence in linear regime (ii) Judicious selection of absorption transition to avoid significant laser attenuation

(i) Fluorescence signal was modeled as two state two step steady process in linear regime (ii) Use of laser with large bandwidths to minimize effect of pressure on overlap integral. (iii) Laser with large bandwidths provided more flexibility in tuning the centre line of the absorption profile

- (i) The single point OH equilibrium concentration from LIF measurements agreed well with the calculated equilibrium values of OH. (ii) This implied that the effect due to overlap integral, absorption line strength variation due to temperature and fluorescence yield were well accounted by the model used to predict them

50






Observations

Locke et al. [56, 57]

OH-PLIF imaging to lean burning JP-5 combustor at 10–14 bar

Excitation(OH) One among R1(1), R1(10), Q1(1) at A-X(1,0) Detection(OH) A-X(0,0) ICCD camera

(i) 10 mJ per pulse (ii) laser beam spatial non-uniformity was corrected by fluorescence imaging of R590 dye solution

- Interference filter centered at 315 nm with FWHM of 10.6 nm

The practical importance of applying PLIF to high pressure combustor was highlighted

Paul et al. [58]

Collisional quenching of OH at high temperature measured in a shock tube in 1900–2300 K temperature range

Excitation(OH) Q1(2)/Q1(5), A-X(1,0) Detection(OH) 310 nm,A-X(0,0) Photomultiplier tube(PMT)

- (i) Rate coefficients from fluorescence life time was converted into quenching cross sections by dividing with average collisional velocity of the species pair (ii) Quenching model formulated by Paul53 could predict the temperature dependent behavior observed from experiments

Bandpass filterer, 310+5 nm

At 2300 K, the ratio of the measured quenching cross section to quenching model [53] predicted values for H2O and O2 are 1.12 and 0.537 respectively

51






Observations

Nandula et al. [59]

(i) Single point LIF measurement in turbulent lean premixed methane flame. (ii)Temperature & species (H2,H2O,O2) from Raman/ Rayleigh measurements

Excitation(OH) O12(8), A-X(1,0) Detection(OH) 310 nm,A-X(0,0) ,(1,1) Photomultiplier tube(PMT)

- (i) The species concentration and temperature obtained from STANJAN was used to calibrate the measurement from a H2-air and CH4flame. (ii) The fluorescence signal was corrected for the variation in Boltzmann fraction and collisional quench rate.

- (i) Uncertainties in measurement were identified as 10.5% due to shot noise and 5% due to wavelength drift. (ii) Location and growth of shear layer were determined from the OH distribution. (iii) The super equilibrium OH concentration were nearly four times higher than the equilibrium counter parts

52






Observations

Ngyuen et al. [60]

OH concentration from LIF measurements in a methane-air Bunsen flame. Rayleigh /Raman measurements

Excitation(OH) O12(8), A-X(1,0) Detection(OH) 295–340 nm, A-X(0,0) ,(1,1) Photomultiplier tube(PMT)

(i)40 μJ per pulse to ensure fluorescence in linear regime (ii) O12(8) transition was chosen to avoid significant laser attenuation

(i) For electronic quenching corrections, the temperature and colliding species concentration data were obtained from Raman/Rayleigh measurements. (ii) The OH number density was calibrated against the equilibrium OH composition corresponding to the measured Rayleigh temperature in a lean CH4-air flame

Combination of color glass filters (WG-295 & Hoya U-340)

(i) In the study, it was observed that the temperature and OH concentrations at the inner flame zones could be well predicted using a one dimensional premixed laminar flame model incorporating finite rate chemistry.

53






Observations

Arnold et al. [61]

Quantitative measurements of OH by PLIF from a laminar premixed methane / air flat flame at pressures of 1, 5 and 20 bar

Excitation(OH) P1(8), A-X(1,0) Detection(OH) A-X(0,0) ,(1,1) ICCD Interference (i) 120 ns gating to suppress flame emissions.

(i)1 mJ per pulse (ii) Back-ground subtraction to avoid light reflections (iii) laser spatial variation was corrected

(i) Boltzmann fraction variation was 10 % in the range of 1300–3200K (ii) Absorption line shape was measured by careful scanning of P1(8) line. (iii) Temperature data was obtained from CARS and numerical simulation

(i) WG295 filter was used to suppress the elastic scattering (ii) Spatial variation (pixel to pixel) of camera sensitivity was corrected

(i) Absolute concentration was obtained from 1D absorption measurements

Atkan et al. [62]

OH LIF, 2D and spectroscopic measurements at 5–36 bar in a laminar premixed methane/air flames

Excitation(OH) 280–287nm, A-X(1,0) Detection(OH) 310 nm, A-X(0,0) ,(1,1) CCD camera Interference No interference from other molecule

(i) 14 mJ per pulse (ii) Estimated laser absorption was less than 10 %

(i) Scanned excitation spectra and simulated excitation spectra matched very well and signified that there are no interferences from other molecules in the A-X(1,0) 280–287 nm range (O2 interference for A-X(3-0) scheme)

Bandpass filter(WG305 and UG11) centered at 310 nm, FWHM-16 nm and peak transmission efficiency of 5.5%

(i) The advantages of the A-X(1,0) LIF detection scheme were identified as devoid of fluorescence trapping (A-X(0,0))

54






Observations

Hicks et al. [63]

Fluorescence imaging of combustion species in gas turbines up to 20 bar and associated complexities

Excitation(OH) 283nm, A-X(1,0) Detection(OH) 310-320 nm, A-X(0,0) ,(1,1) ICCD camera Interference Interferences from PAH as they are broadband absorbers and emitters in the emission spectrum of OH, flame emissions, laser light scattering & wall luminescence

(i) 16 mJ per pulse (ii) laser sheet non-uniformity was corrected by obtaining the quartz reflected images of the laser sheet (iii) Back-ground subtraction of the non-resonant images

(i) Pressure induced line broadening and quenching effects which tend to decrease the fluorescence signal. (ii) Selection of line transitions with weak absorption coefficients to avoid considerable laser absorption and attenuation

(i) Combination of WG-305 & UG 11 filters (transmission efficiency ~56% in the 310–320 nm range). (ii) Weak signals require pixel binning in the camera (iii) Determination of camera magnification and its accurate alignment.

Complexities in OH imaging (i) Test rig and optical system vibration and displacement (ii) Optical window cleanliness(soot formation on the windows), cooling and structural integrity (iii) laser wavelength drift (iv) Optical thickness of the medium (v) Noisy spikes in the collected signal due to abrupt rise in laser intensity

55






Observations

Tamura et al. [64]

Collisional quenching of OH measured in a premixed laminar methane flames at < 1 bar

Excitation(OH) R2(6), A-X(0,0) Detection(OH) A-X(0,0) PMT

<0.5 μJ per pulse

(i) Flame temperatures were measured from the excitation scans. (ii) For quenching rate determination, equilibrium compositions of the colliding species concentration were calculated. (iii) Quenching contributions from individual colliding species was calculated based on temperature dependent rate expression

- (i) The measured quench rate and the calculated quench rate based on temperature and species dependent quench rate model agreed very well. (ii) The excellent agreement between the calculations and the experiments showed that collisional quench rate could be well predicted from knowledge of gas temperature and colliding species concentration

56






Observations

Candel et al. [12]

OH-PLIF to investigate shear coaxial cryogenic jet flames

Excitation(OH) Q1(6), 283.92 nm A-X(1,0) Detection(OH) A-X(0,0) ICCD Interference Raman signal at 296 nm from the liquid phase

30 mJ per pulse

(i) The Q1(6) transition was selected to minimize the temperature dependence

UG-5 and WG-305 fliter

(i) LOx jets scattered and dispersed the laser sheet thereby affecting OH fluorescence

Meier et al. [65]

Species and temperature measurements from piston engine(10 bar) and aero engine test rig(6 bar)

Excitation(OH) 282-286 nm A-X(1,0) Detection(OH) 315 nm, A-X(0,0) ICCD camera Interference Interference from fuel fluorescence

(i) 5–10 mJ per pulse. (ii) Laser sheet spatial variation was corrected by normalized acetone fluorescence images on an average basis (iii) laser shot to shot energy fluctuation was monitored using a fast photodiode

(i) Transition was selected to minimize the variation of state population in 1000–3000 K temperature range

(i) Interference filters centered around 315 nm with FWHM 30 nm

(i) Areas of OH concentration were used to identify zones of homogenous combustion and high heat realse.

57






Observations

Frank et al. [66]

OH-PLIF in heptane and Jet-A spray flames at 5, 7 and 11 bar

Excitation(OH) 283nm A-X(1,0) Detection(OH) 315 nm, A-X (0,0),(1,1) ICCD camera Interference Scattering from fuel droplets

(i)3 mJ per pulse (ii) Laser attenuation across the flame at higher pressures was attributed to increased OH number density and hydrocarbons

(i) At high pressures there was considerable decrease in fluorescence signal due to quenching and line broadening.

Interference filters

(i)The OH distribution was used to analyze the turbulent spray structure

Hicks et al. [67]

OH-PLIF applied to combustors burning Jet-A fuel at pressures of 9 and 18 bar

Excitation(OH) 282nm A-X(1,0) Detection(OH) 316 nm, A-X (0,0),(1,1) ICCD camera Interference Scattering from fuel droplets

25–30 mJ per pulse

- Interference filters centered at 316 nm with FWHM 2.6 nm and peak transmission of 16%

(i) OH-PLIF images were used to mark flame and recirculation zones. (ii) The use of OH-PLIF images in fuel injector design and kinetic modeling was highlighted.

58






Observations

Stocker et al. [68]

Identification of rotational lines of OH in H2/O2 and methane/air flame

Excitation lines at A-X(0, 0), (1,0), (2,0) and (3,0) were recorded using spectrograph

5 mJ per pulse - - (i) The entire rovibrational transitions in the 240–325 nm range were excited, detected, identified and tabulated

Thiele et al. [69]

OH-PLIF in spark ignited combustion of H2/air mixtures

Excitation(OH) 283nm A-X(1,0) Detection(OH) 310 nm, ICCD camera

0.2 mJ per pulse

- - (i) The raw gray scale images were filtered using a 2-D Gaussian filter to reduce noise. (ii) The flame front position was identified as the region of steepest gradient in the flame/OH image. (iii) Temporal evolution of the flame kernel was identified from the OH images.

59






Observations

Schulz et al. [70]

Laser absorption by H2O at shock heated temperatures of 900–3000 K in 200–300 nm range and pressures of 1–70 bar

Detection CCD camera Spectrograph

Light from deuterium lamp

- - (i)Laser absorption by H2O at 283 nm was negligible for pressures of 1–70 bar and 900–3000 K temperature range

Santhanam et al. [71]

OH-PLIF visualization in actively forced swirl-stabilized spray combustor

Excitation(OH) 283.4 nm A-X(1,0) Detection(OH) 315 nm, ICCD camera

(i)6 mJ per pulse (ii) Neglected the variation of laser sheet intensity

(i) For OH calibration, the effect due to variation in quenching cross section across the flame was neglected

10 nm narrow band pass interference filter at 315 nm

(i) To calibrate OH, water vapor in atmospheric pressure at high temperatures was used as the calibration source

60






Observations

Grisch et al. [72]

OH-PLIF measurements in H2/air diffusion flame

Excitation(OH) Q1(5) A-X(1,0) Detection(OH) A-X (0,0),(1,1) ICCD camera

(i)<10 μJ per pulse (ii) Laser shot to shot power fluctuation was monitored

(i) For calculation of collisional quench rate, the colliding species concentration and temperature were obtained from adiabatic equilibrium conditions

UG5 and WG 295 filters

(i) OH calibration was carried out in a H2/air flame of equivalence ratio 0.9. (ii) Fluorescence intensity of OH along the height was compared with the simulated OH profiles. (iii) The estimated uncertainty in absolute OH concentration was 20%

61






Observations

Meyer et al. [73]

OH-PLIF in swirl-stabilized spray flames


(i) 24 mJ per pulse (ii) shot to shot power fluctuations was estimated as + 5%

(i) Boltzmann fraction variation was + 12.5 % in the range of 1100–2400K (ii) The collisional quenching rate variation with species concentration and temperatures corresponding to equivalence ratios of 0.5 to 3 was estimated to be + 30 % in that range

WG 295 and UG 11

(i) Laser energy absorption due to OH and droplet scattering accounted to + 10 % uncertainty.

Kalitan et al. [18]

OH-PLIF in LOx/methane flames at 41 bar


(i) Signal attenuation due to laser absorption by OH. (ii) Light scattering as it traversed through spray

- UG11 and WG305 filter

(i) OH images were used as indicators of combustion zones of high temperatures

62






Observations

Singla et al. [20]

OH-PLIF in LOx/GH2 jet flames up to 63 bar

Excitation(OH) Q11(9.5) A-X(1,0) Detection(OH) 306-320 nm, A-X (0,0),(1,1) ICCD camera, Spectrometer Interference Raman scattering from LOx jet

(i) 42 mJ per pulse (ii) laser beam absorption by OH was estimated to be 10–30 % (iii) Laser beam is absorbed and scattered by LOX core in the centre

(i) The variation of Boltzmann fraction accounted to 10% in the range of 2000–2500 K and was considered insignificant (ii) The collider species concentration and temperature field for quench rate at 63 bar was calculated based on the collider species mole fraction and temperature field of a counter flow LOx/GH2 flame at 1 bar

Bandpass filter (i) A detailed description of fluorescence modeling was provided. (ii)Quenching did not strongly perturb the spatial fluorescence (iii) The collected fluorescence spectra matched well with the simulated spectra from LIFBASE (iv) The mean position of the flame, flame stabilization, corrugation and unsteadiness of the jet were observed from OH images

63






Observations

Singla et al. [21]

Feasibility of OH-PLIF in LOx/methane jet flames upto 30 bar

Excitation(OH) Q11(9.5) A-X(1,0) Detection(OH) 306-320 nm, A-X (0,0),(1,1) ICCD camera, Spectrometer Interference PAH fluorescence

42 mJ per pulse

- (i) Filter scheme 1: 56% transmission at 310–320 nm (ii) Filter scheme 2: 25% at 308 nm with FWHM of 15 nm

(i) The limiting factor for OH-PLIF in oxygen/methane flame above 25 bar was PAH fluorescence interference when compared to laser absorption in hydrogen/oxygen flames (ii) The LOx/methane flame was less stabilized compared to LOx/H2 flame

64

Based on these studies certain observations are useful as follows

Fluorescence Strategy and Interference Signals

The choice of excitation at A-X(1,0) and detection at A-X(0,0), (1,1) in the 306–320 nm

range has the advantage that the elastic and laser internal scattering can be effectively blocked.

Moreover there are no interferences from molecules like H2O and O2 in the combustion

environment. The radiative trapping which is predominant in the A-X(0,0) scheme is negligible

[62]. To suppress the flame emissions and to collect all the fluorescence, gate width of the order

of ~150 ns for the detection system, in this case ICCD camera can be employed. The background

emissions need to be corrected depending on the signal strength.

Laser

The laser pulse energy / area of 10 mJ/cm2 could ensure fluorescence in the linear regime

within + 5% [50]. Hence laser energy typically of 2–3 mJ with a sheet cross section of 40 mm x

0.5 mm could be effectively used to ensure fluorescence in the linear regime. The laser

attenuation across flame/ combustion environment depends on the strength of the absorption

transition excited, the number density of the molecule, unwanted absorption by molecules like

hydrocarbons and the path length traversed by the laser. The laser absorption and attenuation can

vary from less than 5 % to 100 % across the flame depending on the flame conditions. In a

GH2/LOx flame the absorption of laser by other combustion species like H2O was found

negligible at 283 nm [20, 70].

The use of a strong transition with a laser of large line widths and low energy to ensure

fluorescence in the linear regime can be viewed as a potential method to obtain fluorescence of

good signal strength. The use of lasers with relatively larger line widths can lead to excitation of

rovibrational lines neighboring the strong transitions. Hence the excitation of these lines needs to

be taken into account in the fluorescence modeling. The laser shot to shot power fluctuation

65

could be monitored and corrected or the mean value of the laser energy can be used provided the

uncertainty from energy fluctuation is accounted in quantitative measurements. To correct for the

laser sheet profile variation in space, acetone fluorescence images [65] from the same excitation

wavelength, 283 nm in this case could be used.

Absorption & Excitation, Line Shape and Fluorescence Efficiency

In quantitative measurement, one of the major uncertainties is due to the initial state

population variation with temperature and is normally 10–15% in the 1500–2500 K range. This

problem could be approached in the following ways. The transition could be selected such that

the variation of the state population in the temperature range of interest is negligible so that it

does not contribute to the uncertainty in the measurements. The second approach is to obtain the

temperature field information in the region of interest either from calculations based on

equilibrium conditions, detailed numerical simulation of the combustion field /reference flame or

by calibration measurements via thermocouple measurements, Raman / Rayleigh measurements

in actual combustion environment/ reference flame. However, each of these approaches has

themselves a degree of uncertainty. The third approach is to determine the uncertainties in the

measurements due to state population variation in the temperature region of interest and account

for the uncertainties in the quantitative measurements [73].

The line broadening and shifting at higher pressures reduce the overlap integral and hence

the fluorescence signal. The variation in the overlap integral needs to be, therefore taken into

account in quantitative measurements. The reduction in fluorescence signal due to decrease in

the overlap integral can be overcome by employing lasers with larger line widths [55].

The effect of collisional quenching in reducing the fluorescence efficiency can lead to

signal reduction of the order of a factor of 100 in the 10–100 bar range [49]. Most of the works

which utilize OH-PLIF for applied spectroscopy uses collisional quench model given by

66

Equation 2-5 for calculation of collisional quench rate. This requires the knowledge of the

pressure, temperature, mole fraction and temperature dependent cross section of the colliding

species. The expression for temperature dependent cross section from a complex collision model

and the measured temperature dependent cross sections of the colliding species such as H2, H2O,

and O2 are available in the literatures [53, 58, 64]. The knowledge of temperature and mole

fraction of the colliding species can be obtained in the same way as the temperature field data is

obtained to account for initial state population variation. The quenching rate variation across the

combustion field is not significant [20] and could normally account for less than 10% variation

[50].


The fluorescence process is considered such that it is emitted equally in all directions and

that the photons are Poisson distributed [35]. There is, thus an uncertainty in the exact number of

photons detected and this uncertainty is called shot noise. The uncertainties in detection system

also arise due to the quantum efficiency of the photocathode, the thermal current in the CCD

chip known as dark current, readout noise in the A/D conversion and the digitization noise [35,

50]. The spatial variation of camera sensitivity across the chip also adds to the uncertainties. For

weak fluorescence signal detection pixel binning at the cost of resolution is also recommended.

Thus the challenges involved in applying OH-PLIF at high pressures and temperatures in

the linear regime could be recognized as 1) rotational level population dependence on

temperature, 2) reduced fluorescence efficiency due to absorption line shape broadening and

collisional quenching, 3) laser beam attenuation, absorption and steering, 4) scattering

interference from other molecules and 5) insufficient spectroscopic data.

The thirty nine OH fluorescence studies described above were largely done in low pressure

as shown in Figure 2-3.

67

Sample of 39 OH Fluorescence Studies

0

5

10

15

20

25

1-10 bar 10-20 bar 20-30 bar 30-40 bar 40-50 bar 50-60 bar

Num

ber o

f Stu

dies

Pressure

Figure 2-3. Pressure range in the reviewed studies

Of the studies conducted at 20 bar or higher, only four were directed towards OH-PLIF in

cryogenic flames from a coaxial injector. No previous work other than the recent study done by

Vaidyanathan et al. [23] involved OH-PLIF in gaseous shear injector studies at high pressures.

Accurate measurement in gaseous environments is an important precursor to cryogenic studies to

establish robust computational methods [1, 4].

In the current work, the temperature range will be selected to account for the variations in

Boltzmann fraction and the OH concentration will be bracketed within the temperature range.

The uncertainty sources and their contribution to the species concentration measurement is thus

the major goal of this work.

Furthermore the OH-PLIF measurements obtained as a part of this work, will compliment

the very few existing data sets at high pressures.

Equation Section (Next)

68

CHAPTER 3 EXPERIMENTAL FACILITY AND DIAGNOSTICS METHODS

The experimental test facility, operating conditions and diagnostic methods are described

below.

Experimental Test Facility and Operating Conditions

The experimental test facility consists of the combustion chamber, the injector and the

propellant/purge feed system with valves and regulators. The schematic of the cross section of

the combustion chamber with the injector assembly, windows for optical access and exhaust

nozzle is shown in Figure 3-1.

Injector AssemblyExit Nozzle

Quartz Windows (Uncooled)Segmented Chamber Wall

Injector AssemblyExit Nozzle

Quartz Windows (Uncooled)Segmented Chamber Wall

Figure 3-1. Combustion Chamber Cross Section

The combustion chamber is made of oxygen free Copper. A detailed description along

with the transient thermal analysis of the chamber could be found in Reference 74 and 76. The

combustion chamber geometry cross section has an inner dimension of 25 mm x 25 mm and an

outer dimension of 63.5 mm x 63.5 mm. The inner cross section has radius corners of 3 mm. The

combustion chamber was equipped with UV grade fused silica windows for optical access. The

windows are flush with the inner chamber wall and are not cooled.

69

The injector assembly houses a single element coaxial shear injector. The details of the

injector assembly are shown in Figure 3-2 [74, 76].

0.106 (2.69)D3, in(mm)

0.087 (2.2)D2, in(mm)

0.047 (1.2)D1, in(mm)

0.106 (2.69)D3, in(mm)

0.087 (2.2)D2, in(mm)

0.047 (1.2)D1, in(mm)

OxidizerTube Fuel

Post

Spacer

Figure 3-2. Injector Details

The injector and the fuel annulus were made of oxygen free copper and the injector

housing was made of stainless steel. The oxidizer is injected straight into the chamber through

the center tube while the fuel is injected through the annular region surrounding it. The injector

is supported by a spacer to ensure that the oxidizer nozzle stays in the centre of the injector/fuel

annulus assembly during the operation. The spacer also acts as a baffle to provide uniform

distribution of fuel flow upstream to the chamber entrance.

Other features in the combustion chamber including the exhaust nozzle assembly,

segmented chamber extensions and igniter are described in detail in Reference 74. The exhaust

nozzle is replaced with different areas to ensure the desired chamber pressure. The segmented

chamber extensions are used to vary the chamber lengths and adjust the window locations

relative to the injector. The combustion inside the chamber was initiated by spark ignition

housed in one of the chamber extensions. The leads of the igniter were connected to a high

voltage transformer capable of providing 10, 000 volts.

70

The propellant/purge system supplies the fuel and oxidizer for the experiments and

nitrogen for purge. Both the propellants and the nitrogen are pressure fed from high pressure gas

bottles through tubing that incorporate regulators and valves at their respective locations and are

described in detail in Reference 74. The control of the propellant pressure and the mass flow

rates for different test conditions and the opening and closing of the propellant lines at the

beginning and end of the combustion tests are achieved using pressure regulators, regulating

needle valves, solenoid valves and check valves.

The DAQ/control system comprises of the power supply unit, DAQ/control hardware,

DAQ/control software and the DAQ sensors. A detailed description of the DAQ system is given

in Reference 74.

Several temperatures are measured to provide boundary conditions for each measurement.

Thermocouples are placed in chamber, injector face, exhaust nozzle and the heat flux

thermocouples are housed in chamber walls. The chamber thermocouple is housed in the

segmented chamber extension located immediately upstream of the exhaust nozzle and protrudes

into the chamber and hence into the flame. An Omega K-type thermocouple is used as the

chamber thermocouple with an inconel sheath of diameter 1.59 mm with an exposed tip and a

response time of 15 ms. The chamber thermocouple is used to monitor the temperature rise

during the runs which indicates the initiation and sustenance of combustion.

The injector face thermocouples consist of two thermocouples housed in the injector face

of the fuel annulus. An additional thermocouple is located behind the injector housing to detect

possible backflow. The location of the injector face thermocouples are at 2.1 mm and 4.2 mm

radially outwards from the center of the injector and a detailed schematic showing the

thermocouple locations are given in Reference 74. The temperature measurements from the

71

injector face thermocouples are used to infer the temperature of the recirculation region formed

at the injector face. The exhaust nozzle thermocouple measures outflow boundary conditions.

The heat flux thermocouples are embedded in the side chamber walls. At each axial

location there are two thermocouples. Depth location of the two heat flux thermocouples in side

chamber walls at any chamber cross section is shown in Figure 3-3. Their axial location is given

in detail in Reference 74 along with an analysis of wall heat fluxes.

25 63.5

31.753.17

9.535

Heatflux thermocouplelocations

Figure 3-3. Location of Heat Flux Thermocouples, dimensions in mm

The calculation of heat fluxes based on the temperature measurements from these two locations

will be explained later in the section “Wall Boundary Conditions” section.

The GH2/GO2 experimental conditions investigated in the current study are tabulated and

presented in Table 3-1. The nominal pressures were selected to cover the range from 10–50 bars.

The values indicated in the table are the actual measured values.

72

Table 3-1. Experimental Operating Conditions P bar

O/F Massflow

O/F Velocity

F Hydrogen massflow g/s

Hydrogen velocity m/s

Exit nozzle ID mm

Chamber Length mm

10 3.77 0.39 2.12 0.197 130 1.70 169.3 27 3.72 0.39 2.15 0.395 96.5 1.70 169.3 37 3.79 0.40 2.11 0.58 103.5 1.70 169.3 53 3.85 0.40 2.08 0.75 93.4 1.70 169.3

The GH2/GO2 combustion experiments lasted for 9.75 s following ignition for 10 bar case

where as for all the other test cases the combustion run time was limited to 7.75 seconds

following ignition.

OH-PLIF Diagnostics

For the PLIF experiments third harmonic output at 355 nm from a Nd-YAG (Continuum

Surelite II) pulsed laser was used to pump the OPO (Continuum Panther). The FWHM spectral

width of output beam measured using a Burliegh WA-4500 wavemeter was ~5 cm-1 and the

centerline of the laser before doubling corresponded to 563.03 as shown in the Figure 3-4. The

measured spectral width was in agreement with the manufacturer’s specification. The output

from the OPO was frequency-doubled to obtain a UV beam at 283 nm.

73

Figure 3-4. Laser spectral profile measured using Burleigh Wavemeter before doubling to 283 nm

The UV beam had a measured pulse energy of 0.89 mJ and was used to excite the OH A-X

(1,0) rotational transitions. The laser beam at 283 nm was formed into a sheet of 4 cm x 0.05 cm

cross section using a series of fused silica lenses. The sheet was made 4 cm in height; however

the central portion of 2 cm of the light sheet passed through the chamber to ensure that the wings

of the Gaussian beam are not used for PLIF diagnostics.

The schematic of the OH-PLIF diagnostic setup is shown in Figure 3-5. Fluorescence

images were collected perpendicular to the direction of laser beam propagation using an ICCD

camera (DiCam-Pro Cooke Corp.) equipped with 105mm/4 telephoto UV lens. The laser and the

camera were synchronized using a pulse generator (DG 535 Stanford Research Systems) and

were operating at 10 Hz. The camera was used in double shutter mode such that it collected

fluorescence for 100ns in synchronization with the laser in the first image. The second image

was collected 500ns after the first image for the same duration of 100ns to capture flame

74

emissions. The effective resolution of the camera was 66 micrometer/pixel in 4 x 4 binning

mode. A combination of 3mm WG 305 Schott and 3 mm UG 11 filters were used to collect

fluorescence from 306–320 nm while effectively blocking elastic scattering. The combined

transmission efficiency of the filters was about 55% between 306 and 320 nm.

Figure 3-5. OH-PLIF Experimental Set-up

OH-PLIF images were acquired for the entire run time at the rate of 10 Hz with 100 ns

exposure time. Out of the instantaneous OH-PLIF images recorded, thirteen of the instantaneous

images recorded at the near steady state at the end of the experiments were averaged and

represented as averaged OH-PLIF image. Correspondingly, thirteen background emission images

recorded by operating the camera in the double shutter mode were averaged. The instantaneous

and averaged background emission images were then subtracted from the instantaneous and

averaged OH-PLIF image respectively.

75

Wall Boundary Conditions

The wall boundary conditions consist of wall heat fluxes determined from temperature

measurements in the combustion chamber. Conley et al. [76] calculated the heat fluxes from the

temperature measurements. In this and in the previous study [75, 76] the heat fluxes were

calculated by solving the steady state one dimensional heat conduction equation and adding a

correction term to compensate the heat absorption by the chamber as shown below

( ) ,2 ,1A ,2 ,2q

2o o

i o

T TC xk T Tx t

−⎛ ⎞Δ= − + ⎜ ⎟Δ Δ⎝ ⎠

r (3-1)

where Aq , is the heat flux, Δx is the distance between the thermocouple pairs, the subscripts ‘i’

is assigned for thermocouple close to the inner chamber wall, ‘o’ represents the one farthest and

1 and 2 represents the initial and final times respectively.

The very nature of heat transfer in the combustion chamber is three dimensional. Thus

calculation of heat fluxes based on 1D assumption can introduce errors. Thus in the current work

the heat flux was calculated by numerically solving the unsteady 3D heat conduction equation.

The method will be discussed in detail in the following section.

The chamber extensions shown in Figure 3-3 incorporate thermocouple pairs placed next

to each other and separated by 7 mm in the transverse direction. For each thermocouple pair, the

temperatures are measured at 3.2 and 9.5 mm from the inner chamber walls respectively. The

temperature at location 3.2 mm from the inner wall is denoted as Tinner and that measured at 9.5

mm is denoted as Tmiddle.

A 3D model of the central portion of the chamber from 37 to 102 mm from the injector

face was chosen as the computational domain. The central portion of the chamber was selected

since the temperature measured outside of this domain did not indicate an axial temperature

76

gradient. The outer wall was assumed to be insulated such that the heat released during the

experiment was assumed to be accumulated in the chamber. The validity of the insulated wall

assumption was checked by imposing forced convection at the outer walls, assuming outer wall

temperature to be at 100oC and ambient air temperature set at 27oC. Forced convection was

calculated by assuming an air velocity of 10 m/s. These conditions are considerably more

dissipative than experienced during the experiments. The heat transfer for the case of a laminar

forced convection past a flat plate with the prescribed values was calculated. The heat transfer

thus determined was 0.1% of heat flux values in the chamber walls due to combustion and thus

all the heat released during the transient process was assumed to accumulate in the walls.

The computational temperatures which evolved over the period of 7.75 seconds were

matched with the actual temperatures obtained from the experimental run at the inner and middle

locations which are at 3.2 and 9.5 mm from the inner chamber walls, respectively. The imposed

heat flux at the inner chamber wall was changed for different sets of computation so that the

temperatures Tinner and Tmiddle obtained from the computations, matched the experimental results

within 4 to5 oC. The discretized 3D heat conduction equation [77] is

( )( )

( )( )

( )( )

( )( )

1, , , , , , 1, , , , 1, , , , , , 1, ,2 2

, , 1, , , , , , 1, , ,, ,2 2

2 2

2 =

i j l t i j l t i j l t i j l t i j l t i j l t

i j l t i j l t i j l t i j ti j t

k kT T T T T Tx y

Ck T T T T Tz

+ − + −

+ − +

− + + − +

+ − + −dt

d dr

d dt

(3-2)

Here, the density, r , and heat capacity, C , for Copper 110 are 8700 kg/m3 and 385 J/(kg K),

respectively The computational domain consisted of a 51 x 51 x 51 grid and the time step was

0.0001 seconds. The heat flux obtained through this procedure is used to accompany the in-flow

species concentration measurement in the process of code validation. The Matlab scripts used for

data processing are detailed in Appendix A.Equation Section (Next)

77

CHAPTER 4 OH-PLIF IMAGE PROCESSING AND QUANTITATIVE ANALYSIS

The OH-PLIF image processing, the methodology for determining the OH concentration

and the uncertainties in the measurement analyses are discussed below.

Fluorescence and Interference Signals

The background emission was subtracted from the fluorescence + background images. The

images for the four different test cases are shown in Figure 4-1 to 4-4. Figure 4-1(a) to 4-4(a)

show the raw image which has been corrected by subtracting the background shown in Figure 4-

1(b) to 4-4(b). The intensity levels of the background subtracted OH-PLIF images are shown in

Figure 4-1(c) to 4-4(c).

78

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

10 20 30 40 50 (a)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

10 20 30 40 50 (b)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

10 20 30 40 (c)

Figure 4-1. Average of 13 instantaneous images obtained at near steady state for chamber

pressure of 10 bar; (a) OH-PLIF + background emission image, (b) background emission image and (c) OH-PLIF image

79

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

10 20 30 40 50 60 70 (a)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

10 20 30 40 50 60 70 (b)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

5 10 15 20 25 30 (c)



80

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

20 40 60 80 (a)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

20 40 60 80 (b)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

5 10 15 20 25 (c)


pressure of 37 bar; (a) OH-PLIF + background emission image, (b) background emission image and (c) OH-PLIF image.

81

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

20 40 60 80 100 120 140 (a)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

20 40 60 80 100 120 140 (b)

Height (mm)

Wid

th (m

m)

O2→H2→

H2→

0 5 10 15

-2

0

2

5 10 15 20 25 (c)



82

From Figure 4-1 to 4-4, it is evident that at higher pressures of 37 and 53 bar, the

background emissions are stronger than at 10 bar. This shows that collection of fluorescence

with a gate-width narrowed to 100 ns was not sufficient to suppress the flame emissions. The

sources of the background emissions are recognized as typical flame emissions from OH and

water molecules in a H2/O2 flame [8]. The spectra of background emissions from a LOx/GH2

flame in the range of 300 to1100 nm at 60 bar was measured by Mayer et al. [15] and found that

the contributions from the OH and O2 flame emissions lied in the 300 to 400 nm range, the

predominant spectra being OH A-X (0,0) branch at 310 nm. The contributions from H2O could

be found spanning the 400 to1000 nm range. It is noteworthy to note the transmission of UV

filters used in this study to block the elastic scattering and transmitted light in the range of 300 to

400 nm and above 650 nm. The UV filters WG 305 & UG 11 served as the best combination

considering the low laser energy of 0.89 mJ /pulse and the large laser line width of 5cm-1 used

here, which both tend to decrease the fluorescence signal strength. Thus considering the

emissions from H2/O2 flame and the transmission range of UV filters, the background emissions

observed in the current study were identified as due to OH, O2 and H2O.

Laser

The laser shot to shot power fluctuation was monitored for 290 pulses. The average of the

290 laser pulse energies accounted to 0.89 mJ/ pulse with a standard deviation of 0.10 mJ/ pulse.

The fluctuation in the laser energy accounted for an uncertainty of 11 %.

The laser sheet profile variation in space was corrected from calibration using acetone

fluorescence. The laser sheet at 283 nm was passed through the chamber filled with acetone

vapor and the 2D fluorescence was collected by effectively blocking the elastic scattering using

the UV filters and ICCD camera. Ninety acetone fluorescence images were averaged and

normalized with the maximum intensity/counts along the width to obtain the spatial variation of

83

the laser sheet in the region of interest. The normalized laser sheet profile variation in a

percentage intensity scale is shown in Figure 4-5. The laser sheet had maximum intensity of

above 90% at heights of 11 to 15 mm while it gradually decreased to 25% at heights of 1 and 19

mm on either side.

Figure 4-5. Normalized laser sheet intensity profile variation obtained from acetone fluorescence images. The intensity is provided in percentage scales. The intensity is above 90 % at heights of 11 to 15 mm and gradually decreases to 25% at heights of 1 and 19 mm

Based on the normalized acetone fluorescence images shown in Figure 4-5, the laser sheet

intensity variation in space was corrected for all the OH-PLIF images acquired in the current

study and the resultant uncertainty calculated as the ratio of the standard deviation to the average

values of the 90 normalized fluorescence images was 5.9 %.

The absorption of the laser sheet by OH and other molecules that interact with the laser

beam as it passed through the combustion chamber need to be further discussed. In GH2/GO2

combustion one of the main combustion products is water vapor. The absorption cross section of

H2O between 190 and 320 nm at 900-3000 K temperature ranges and pressures up to 70 bar

increases as a function of temperature [70]. However the effect of absorption is small enough for

wavelengths above 280 nm such that the absorption by H2O can be neglected. The laser beam

absorption, as it traversed through the region of interest was insignificant as seen in Figure 4-1 to

84

4-4. The laser beam absorption by OH will be estimated based on the Beer-Lambert’s law, once

the OH number density is determined.

Absorption and Excitation, Line Shape, and Fluorescence Efficiency

The fluorescence signal in Equation 2-19 is rearranged and the number density of OH,

OHon is expressed as

( )p

OH12 21

221 21

N

B AE VA A Q 4c

o

laser absB

nf

dνπ

=⎡ ⎤⎛ ⎞ Ω⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ +⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦

∫ (4-1)

The term ( )122

Bc laser abs

Bf dν⎛ ⎞ Φ Φ⎜ ⎟⎝ ⎠ ∫

represents the overlap between the laser spectral profile

and the specific rovibrational absorption profile of the molecule under consideration. This is

valid when the laser spectral width is small enough that it does not excite other rovibrational

branches existing nearby. In the experiment carried out here, the OPO spectral width of 5 cm-1

was large enough to excite a series of nine rovibrational lines around 283 nm. In this case, the

collected signal, pN expressed in Equation 4-1 needs to be modified so that the excitations of all

the rovibrational transitions lying within the spectral bandwidth of the OPO are properly taken

into account. Thus Equation 4-1 is modified to include the contributions of a series of rotational

lines resulting in

( )

pOH 9

121 21

221 21

N

BAE V

A A Q 4c

o

laser abs

B

nf

dνπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞ Ω⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ Φ Φ ⎜ ⎟⎜ ⎟ ⎜ ⎟+⎢ ⎥⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

(4-2)

Before the interpretation of the concentration from Equation 4-2 the parameters in the

expression need to be examined in detail. The nine rotational transitions of OH A-X (1-0) lying

85

within the spectral width of the laser having a Gaussian profile centered at 35334.2 cm-1 with

FWHM 5 cm-1 as shown in Figure 3-5 were identified as

21 2 12 1 2 12 2 12 2(6) (3) (3) (6) (1) (1) (2) (2) (14) [37]P Q R Q Q R Q R R+ + + + + + + +

The term

9

121

2

B

c

Bf⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

∑ denoted as

12

9'

1

BBf∑ (cmJ-1), where 12

' 122

BB =

c is temperature

dependent due to Bf . The line shape absΦ in ( )laser abs dνΦ Φ∫ is both temperature and pressure

dependent and the quench rate 21Q determined from Equation 2-5 also requires the knowledge of

temperature field and colliding species mole fraction as discussed in Chapter 2.

The different approaches to circumvent this problem were identified from the review of

OH-PLIF diagnostic studies as calibration measurements via Rayleigh/Raman measurements of

temperature & species and calculations / numerical simulation based on equilibrium conditions.

The other approach is to obtain the variation in12

9'

1

BBf∑ , laser abs dνΦ Φ∫ and 21Q with

temperature and colliding species mole fraction corresponding to a broad range of equivalence

ratio. The approach used in this study is to use the average values of 12

9'

1

BBf∑ , laser abs dνΦ Φ∫

and 21Q for the calculations, and determining the uncertainty in the OH concentration due to the

variation over a broad range of equivalence ratio. The resultant variation and corresponding

uncertainties will be presented and discussed in chapter 5.

The term 21

21 21

AA Q

⎛ ⎞⎜ ⎟+⎝ ⎠

in Equation 4-2 known as the fluorescence yield needs to be further

analyzed. The effect of quenching becomes predominant at high pressures when A21<< Q21. In

86

GO2/GH2 combustion the colliding species are mainly H2O, O2 and H2 molecules. The

corresponding colliding cross sections [53] are given in Table 4-1.

Table 4-1. Colliding Species Cross Section for Collisional Quenching Species H2O O2 H2

Colliding species cross section (Å2) 25 7 5

The fluorescence yield based on the Equation 2-5 is well represented for A-X (0-0)

transitions. For transitions also involving A-X (1-1) the expression for the fluorescence yield

needs to be modified [20, 53] to

1

21(0,0) 21(1,1) 0 10 10

21 21(0,0) 1 1 1

A A1

Q A

−⎛ ⎞⎛ ⎞= + +⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

s s sFs s s

(4-3)

where 21(0,0)A and 21(0,0)A represent the spontaneous emission rates from A-X(0,0) and A-X(1,1),

respectively. 0s and 1s represent the total effective cross sections for quenching from vibration

levels 'u = 0 and 'u = 1 respectively. The vibrational energy transfer from 'u =1 to 0 is

represented by 10s . The approximate value [53] for 21(1,1)

21(0,0)

AA

, 0

1

ss

, 10

1

ss

are 0.575, 1and 0.58

respectively.


The OH-PLIF diagnostic in this study is associated with 2D imaging of the fluorescence on

a CCD chip. Thus the volume V (cm3) in Equation 4-2 corresponding to the collected

fluorescence signal intensity in each pixel in the camera is equal to the product of the pixel

projection area Pixel ProjectionA (cm2) and the laser sheet thickness l (cm).

The uncertainty associated with the volume probed is due to the accurate determination of

the pixel resolution. The pixel resolution was obtained by calibrating it against the accurately

87

known dimensions of a wire with constant diameter and length. The resultant uncertainty due to

the variation in pixel resolution accounted to 2.8 % uncertainty in the probe volume.

To obtain absolute OH concentration in number density, the arbitrary selected unit, counts

of the camera, are to be converted to photometric units. This was done by calibration of the

camera against a light source of known irradiance. The light source used in this study was a

thousand watt, quartz halogen, tungsten filament lamp with designation of 7-1121 from Oriel

Instruments. The uncertainty in the irradiance levels near the 310 nm wavelength was 2.3 % as

mentioned in the lamp specifications. The camera calibration corresponding to the detection

strategy employed in the OH-PLIF measurements and region of interest is shown in Figure 4-6.

0 100 200 300 400 500 6000

100

200

300

400

500

600

700

800

900

Counts

Num

ber o

f Pho

tons

(Np) Np = 1.59 *Counts

Data PhotonsLinear fit

Figure 4-6. Camera calibration corresponding to the detection strategy employed in the OH-PLIF measurements and region of interest. The uncertainty in the calibration due to non linearity associated with the fit of 1.8 % together with the uncertainty in the lamp irradiance of 2.3 % amounted to a net uncertainty of 2.9 % in photon calibration.

The uncertainty in the photon calibration due to the non-linearity associated with the fit is

calculated and is 1.8 %. The net uncertainty in the photon calibration due to lamp irradiance

uncertainty of 2.3 % and uncertainty of 1.8% due to non linearity in calibration fit accounted to

88

2.9%. A proposed new methodology to calibrate the camera as part of the thesis study is

explained in Appendix B. The calibration obtained from the new method is compared with the

conventional calibration shown in Figure 4-6.

As the photons are Poisson distributed [35], there is uncertainty in the exact number of

photons detected; this is called shot noise. The uncertainty contribution from shot noise due to

the Poisson distributed photon number was calculated as the ratio of the standard deviation to the

average photon arrival from the OH-PLIF images at 10, 27, 37 and 53 bar. The uncertainty

contribution due to shot noise at 10, 27, 37 and 53 bar accounted to 6.9, 7.05, 6.8 and 6.7%

respectively.

The camera has spatial variation of pixel intensities. The systematic and random spatial

variation is eliminated by linear filtering in which the value of an output pixel in the image is

computed as a weighted average of neighboring pixels [11, 78]. In the current study, each pixel

value was computed as a weighted average of the neighboring 5 x 5 matrix of pixels with equal

weights.

The uncertainty due to systematic and random spatial variation of pixel intensities,

minimized by linear filtering [11, 78] in which the value of an output pixel in the image is

computed as a weighted average of neighboring pixels, was calculated as the ratio of the

difference in pixel intensities before and after filtering to their corresponding averaged values.

The uncertainty contribution due to pixel smoothening of the OH-PLIF images at 10, 27, 37 and

53 bar accounted to 7, 7, 6.3 and 6 % respectively.

The Matlab scripts used for data processing are detailed in Appendix A.

89

CHAPTER 5 RESULTS AND UNCERTAINTY ANALYSIS

Experiments at high pressure GH2/GO2 combustion covered Oxygen to Fuel (O/F) mass

flow ratio of 3.77 corresponding toF =2.15 and pressures of 10, 27, 37 and 53 bar. The results

presented here include (i) Experimental Conditions and Chamber pressure measurements and (ii)

Image processed OH-PLIF measurements. The uncertainty analysis includes determination of

uncertainties for the OH-PLIF measurements at 37 bar.

Chamber Pressure Measurements

In the GH2/GO2 experiments the chamber pressure was increased by increasing the

propellant mass flow rates while keeping the O/F mass flow and velocity ratios constant for a

constant exhaust nozzle area. The chamber pressure rise in time for the four experimental

conditions of GH2/GO2 combustion is shown in Figure 5-1 to 5-4. The sequence included

nitrogen pressurization followed by fuel injection and ignition. It should be noted that ignition is

identified in the figures by the high oscillation induced in the sensor recording. The pressure

increases in time and for higher pressures, which are of interest here, attains a near steady state at

7–8 sec following ignition. To attain steady-state at lower pressures longer experimental time

would have been required.

90

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

time(s)

Pres

sure

(bar

)

Chamber Pressure

Nitrogen pre-pressurization

Ignition

Combustionshut-off

OH-PLIF images range

Figure 5-1. Chamber pressure versus time for GH2/GO2 combustion for 10 bar and O/F mass flow of 3.7. The experiment continued for 10 sec following ignition.

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

time(s)

Pres

sure

(bar

)

Chamber Pressure


Ignition

Combustionshut-off

OH-PLIF images range

Figure 5-2. Chamber pressure versus time for GH2/GO2 combustion for 27 bar and O/F mass flow of 3.7 The experiment continued for 8 s following ignition.

91

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40

45

50

time(s)

Pres

sure

(bar

)

Chamber Pressure

Nitrogenpre-pressurization

Ignition

Combustionshut-off

OH-PLIF imagesat near steady state

Figure 5-3. Chamber pressure versus time for GH2/GO2 combustion for 37 bar and O/F mass flow of 3.7. The pressure attains a near steady state at the end of 8 s following ignition.

0 2 4 6 8 10 12 140

10

20

30

40

50

60

70

time(s)

Pres

sure

(bar

)

Chamber Pressure


Ignition

Combustionshut-off

OH-PLIF images at near steady state

Figure 5-4. Chamber pressure versus time for GH2/GO2 combustion for 53 bar and O/F mass flow of 3.7. The pressure attains a near steady state at the end of 8 s following ignition.

92

OH-PLIF Measurements

The OH-PLIF images acquired for the experiments include thirteen instantaneous images.

At each pressure the instantaneous images were averaged. The instantaneous images, acquired

over a period of 100 ns each are needed for validation of LES codes while the average is used for

validation of RANS codes. The OH-PLIF images shown in Figure 5-5 to 5-6 were image

processed to

• eliminate background emissions; • correct for spatial variation in laser intensity; • smoothen the images and minimize the spatial variation of pixel intensities;

Figure 5-5 to 5-6 show an example of an instantaneous image and average image for each

pressure case.

93

(a)

(b)

(c)

(d)

Figure 5-5. Instantaneous image-processed OH-PLIF images at near steady state chamber

pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar

94

(a)

(b)

(c)

(d)

Figure 5-6. Average of thirteen instantaneous image-processed OH-PLIF images at near steady

state chamber pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar.

95

To ascertain the repeatability of the OH-PLIF measurements the average of image-

processed OH-PLIF images acquired at 35, 36 and 37 bar pressure cases for similar experimental

conditions were compared and are shown in Figure 5-7 (a–c). The average OH-PLIF images in

Figure 5-7 (a–c) shows that the OH-PLIF measurements were repeatable and can be used for

determination of OH concentration with confidence.

(a)

(b)

(c)

Figure 5-7. Average of thirteen instantaneous image-processed OH-PLIF images at near steady

state chamber pressure of (a) 35, (b) 36, and (c) 37 bar indicating the repeatability and reliability of OH-PLIF measurements for determination of OH concentration.

96

The intensity levels of the image processed OH-PLIF images shown in Figure 5-5 to 5-6

are related to the number density of OH by Equation 4-2. Theses image need to be processed as

described in Chapter 4 and thus the OH number density is determined. The OH-PLIF images in

Figure 5-5 to 5-6 show certain interesting features that are noteworthy. From the OH-PLIF image

at 10 bar, it can be observed that the flame is smooth and less corrugated as seen from OH

images at higher pressures. For the four experimental conditions, O/F velocity and density ratios

governing the development of shear layer remain the same. The difference in the four

experiments is the turbulence and the heat release. In addition to these there can be also Soret

and Dufour cross diffusion effects arising from concentration and temperature gradients. These

secondary effects need to be evaluated in complimentary CFD efforts.

As noted, the OH radical in a non premixed flame is considered to be a good marker of the

reaction zone. Similar to the study described in Reference 32, the stoichiometric contour was

traced from the axial evolution of the location of maximum OH intensity in the flame, as

indicative of the mean position of the reaction zone [32]. Thus from all four average OH PLIF

images, shown in Figure 5-6(a–d), the mean position of the reaction zone was quantitatively

determined and is shown in Figure 5-8(a–d).

97

(a)

(b)

(c)

(d)

Figure 5-8. Mean position of reaction zone determined from the average OH-PLIF images at (a)

10, (b) 27, (c) 37 and (d) 53 bar. The OH-PLIF signal at 27 and 37 bar would indicate a lifted flame, however this is an effect of strong background correction.

98

The mean position of the reaction zone at 10 bar shows that the flame is anchored at the lip

of the oxidizer post and is typical of the coaxial shear flames [20]. For test cases at higher

pressures of 27 and 37 bar the OH-PLIF signal would indicate a lifted flame, however this is an

effect of strong background correction. In all cases the flame is anchored at the lip. The shear

layers merge at 16–17 mm from the injector face at pressures of 27, 37 and 53 bar. The location

of the maximum OH concentration is similar for all cases, explaining the similar effect of same

density and velocity ratio on shear layer development regardless of the difference in turbulence

and heat release rates.

To analyze the effect of turbulence the Reynolds number of GO2 and GH2 were calculated

as 1UDρμ

and ( )3 2U D D−ρμ

whereρ is the density, U, the velocity andμ the dynamic

viscosity of the gas, and D1, D2 and D3 are the dimensions of injector as shown in Figure 3-2

respectively. The Reynolds number, ReD for GO2 was 38100, 75380, 112767 and 148637 and for

GH2, ReD was 5752, 11534, 16936 and 21900 at 10, 27, 37 and 53 bar respectively. The ReD of

GH2 and GO2 clearly indicates that flow regime is turbulent. The momentum flux ratio was

defined as J =( )( )

2

2

2

2

U

UGO

GH

ρ

ρ. For all the pressure cases the momentum flux ratio that governs the

growth of the shear layer remained the same and was 2.7.

In the study by Seitzman et al. [25] the OH structures in turbulent non-premixed hydrogen

flame were characterized at ReD of 2300, 8600, 25000 and 49500. It was found that, as the flow

transits from laminar to turbulent regime, there is significant change in the OH structures from

low strain rate, thick filament zones to high strain rate, thin filament, more diffuse regions.

Another notable observation was that at higher Reynolds number the OH structures became

increasingly convoluted and similar behavior was observed in the current study also.

99

The studies which focused on shear coaxial cryogenic flames [11, 12, 13, 19, 20, 21]

identified the wrinkling, corrugation and flapping of the flame to be caused by the combined

effects of turbulence and instabilities in the flow field. Singla et al. [20, 21] proposed stability

criteria based on the ratio of oxidizer lip thickness to the flame thickness and for the flame to be

stable the ratio needed to be greater than one. As the flame anchors on the oxidizer lip, the size

and dynamics of the recirculation region in the lip wake influences the flame stability.

Thus, in the current study the wrinkling and corrugation of the flame, at higher pressures

with higher Reynolds number, is attributed to the increased turbulence where as the flapping of

the flame which is evident from the instantaneous OH distribution in Appendix D is attributed to

the instability dictated by two factors: (i) the size of the recirculation zone in the wake of

oxidizer lip and, (ii) the large scale flow fluctuation in the recirculation region formed on the

injection face around the jet injectors .

100

Quantification of OH Concentration and Uncertainty at 10, 27, 37 and 53 bar

To determine the number density from the image-processed OH-PLIF images in Figure 5-5

to 5-6, the values of 12

9'

1

BBf∑ , laser abs dνΦ Φ∫ and 21Q in Equation 4-2 are calculated as follows.

A broad range of equivalence ratio for GH2/GO2 combustion was considered and covered

0.5–3 range [73]. The OH radical probed in the shear reaction zone of the GH2/GO2 combustion

is known to exist mostly around the region of stoichiometry. Hence, the equivalence ratio of 0.5–

3 could be considered a very broad range of conditions in the flame. Therefore this assumption is

quite conservative and is expected to yield a larger uncertainty than actually encountered in the

experiment. However given the lack of data it was adopted here to bracket with confidence the

possible experimental uncertainty.

In a first approximation equilibrium conditions are assumed. The equilibrium conditions

for the chemical reactions pertaining to the GH2/GO2 experiments carried out at 10, 27, 37, and

53 bar was calculated using STANJAN [79]. The variation of temperature and mole fraction of

species, H2O, H2, and O2 with equivalence ratio of 0.5–3.0 is shown in Figure 5-9(a–d). It was

found that, the temperature varied between 2500 and 3500 K, with the maximum at

stoichiometry.

101

0.5 1 1.5 2 2.5 30

0.5

1

Mol

e fra

ctio

n

Equivalence ratio (φ)2000

2500

3000

3500

4000

Tem

pera

ture

(o C)

Mole fraction H2O 10bar Mole fraction H2 10 bar Mole fraction O2 10 barTemperature 10 bar

(a)

0.5 1 1.5 2 2.5 30

0.5

1

Mol

e fra

ctio

n

Equivalence ratio (φ)2000

2500

3000

3500

4000

Tem

pera

ture

(o C)

Mole fraction H2O 27 bar Mole fraction H2 27 bar Mole fraction O2 27 barTemperature 27 bar

(b)

102

0.5 1 1.5 2 2.5 30

0.5

1

Mol

e fra

ctio

n

Equivalence ratio (φ)0.5 1 1.5 2 2.5 3

2000

2500

3000

3500

4000

Tem

pera

ture

(o C)


(c)

0.5 1 1.5 2 2.5 30

0.5

1

Mol

e fra

ctio

n

Equivalence ratio (φ)0.5 1 1.5 2 2.5 32000

2500

3000

3500

4000

Tem

pera

ture

(o C)


(d)

Figure 5-9. Temperature and specie mole fraction variation based on equilibrium calculations

with equivalence ratios of 0.5–3 at (a) 10, (b) 27, (c) 37 and (d) 53 bar. The temperature has a maximum value of 3500 K at stoichiometry and decreases to a minimum of 2500 K at equivalence ratio of 3.

103

The variation of 12

9'

1

BBf∑ (cmJ-1) with temperature which in turn varies with the

equivalence ratio is shown in Figure 5-10(a–d).

0 1 2 3 4 524

25

26

27

28

29

30

31

32

33

34

Equivalence ratio (φ)

Abs

orpt

ion

Coe

ffici

ent (

cmJ-1

)

Absorption Coefficient 10 barMean Absorption Coefficient 10 bar

(a)

0 1 2 3 4 522

24

26

28

30

32

34


Abso

rptio

n C

oeffi

cien

t (cm

J-1)


(b)

104

0 1 2 3 4 522

24

26

28

30

32

34


Abso

rptio

n C

oeffi

cien

t (cm

J-1)


(c)

0 1 2 3 4 522

24

26

28

30

32

34


Abs

orpt

ion

Coe

ffici

ent (

cmJ-1

)


(d)

Figure 5-10. Absorption coefficient (12

9'

1

BBf∑ ) variation with equivalence ratio and temperature

(2500–3500 K) at (a) 10, (b) 27, (c) 37 and (d) 53 bar showing that the variation with respect to mean is 12.4, 14.6, 14.5 and 15.1% respectively.

The mean value of 12

9'

1

BBf∑ is used for the calculation. The uncertainty due to the

variation with temperature/equivalence ratio with respect to mean at 10, 27, 37 and 53 bar is

12.4, 14.6, 14.5 and 15.1 % respectively.

105

The absorption profiles of OH at 10, 27, 37 and 53 bar were simulated using LIFBASE

[37]. To simulate the absorption profile absΦ , the collisional and Doppler widths were obtained

from Equation 2-13 and Equation 2-15 respectively. The absorption profiles at 3017 K and 10

bar, 3085 K and 27 bar, 3100 K and 37 bar, and 3125 K and 53 bar for an equivalence ratio of 2

along with the laser spectral profile are shown in Figure 5-11(a–d).

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)

Laser ProfileOH Absorption Profile at T =3017 and 10 bar

(a)

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)


(b)

106

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)


(c)

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)


(d)

Figure 5-11. Absorption profile of OH at (a) 3017 K and 10 bar, (b) 3085 K and 27 bar, (c) 3103

K and 37 bar, and (d) 3125 K and 53 bar simulated using LIFBASE showing a complete overlap with the laser spectral profile at all pressures.

The OH absorption profiles at 10, 27, 37 and 53 bar were simulated for a broad

temperature range of 2500–3500 K corresponding to the equivalence ratio of 0.5–3 and are

107

provided in the Appendix C. The OH absorption profile broadens and the centre line of the OH

absorption profile shifts with pressure and temperature.

The overlap integral of the absorption profile of OH at 10, 27, 37 and 53 bar, and the

Gaussian spectral laser profile, laserΦ is calculated by laser abs dνΦ Φ∫ . As a result of the variation

of the absorption profile with temperature, the determined overlap integral also varies for each

pressure case over the broad range of temperature in the flame. To find out the variation the

overlap integral is calculated for a temperature range of 2500–3500 K corresponding to an

equivalence ratio of 0.5–3 at 10, 27, 37 and 53 bar. The results are shown in Figure 5-12(a–d).

0 1 2 3 4 50.133

0.134

0.135

0.136

0.137

0.138

0.139

0.14

φ

Ove

rlap(

cm)

Overlap Integral 10 barMean Overlap Integral 10 bar

(a)

108

0 1 2 3 4 50.128

0.1285

0.129

0.1295

0.13

0.1305

0.131

0.1315

0.132

0.1325

0.133

φ

Ove

rlap(

cm)


(b)

0 1 2 3 4 50.126

0.1265

0.127

0.1275

0.128

0.1285

0.129

0.1295

0.13

φ

Ove

rlap(

cm)


(c)

109

0 1 2 3 4 50.122

0.1222

0.1224

0.1226

0.1228

0.123

0.1232

0.1234

0.1236

0.1238

0.124

φ

Ove

rlap(

cm)


(d)

Figure 5-12. Overlap integral laser abs dνΦ Φ∫ variation at (a) 10, (b) 27, (c) 37 and (d) 53 bar with

temperature corresponding to equivalence ratio of 0.5–3, indicating that the variation with respect to mean is 1.3, 1, 0.8 and 0.5% respectively and can be assumed negligible.

The uncertainty due to the variation in the overlap integral at 10, 27, 37 and 53 bar is

determined as 1.3, 1, 0.8 and 0.5 % respectively over the broad temperature range of 2500–3500

K and is therefore assumed negligible. The overlap integral could also vary due to the centre line

shift of the laser profile. The center line of the laser profile was measured as 283.015 from the

Burleigh Wavemeter. The uncertainty in the overlap integral variation at 10, 27, 37 and 53 bar

due to the laser center line shift accounts to 2.8, 1.6, 1 and 0.2 % respectively.

The absorption profile broadens and gets shifted as pressure increases. Hence in most of

the studies carried out using lasers with small spectral widths of less than 1 cm-1, the centre line

wavelength of the laser needs to be shifted in order to overlap with the center line wavelength of

the OH absorption profile. The most important area of concern is the pressure broadening. The

overlap between the laser spectral profile and the pressure broadened absorption profile

110

decreases leading to a decrease in the strength of the collected fluorescence signal as the pressure

increases. The spectral width of the laser employed in this study was larger than the spectral

width of the broadened absorption profile even at elevated pressures such as 37 and 53 bars. This

can be considered as an advantage since it was ensured that the laser profile overlapped with the

absorption profile at all pressures thereby ensuring fluorescence with good signal strengths.

The variation of quench rate, 21Q at 10, 27, 37 and 53 bar with temperature and the species

mole fraction corresponding to equivalence ratio of 0.5–3 is shown in Figure 5-13(a–d).

0 1 2 3 4 51.08

1.1

1.12

1.14

1.16

1.18

1.2

1.22x 1010


Col

lisio

nal Q

uenc

h R

ate(

s-1)

Collisional Quench rate 10 barMean Collisional Quench rate 10 bar

(a)

111

0 1 2 3 4 52.95

3

3.05

3.1

3.15

3.2

3.25

3.3x 1010


Col

lisio

nal Q

uenc

h R

ate(

s-1)


(b)

0 1 2 3 4 53.9

3.95

4

4.05

4.1

4.15

4.2

4.25

4.3

4.35

4.4x 1010


Col

lisio

nal Q

uenc

h R

ate(

s-1)


(c)

112

0 1 2 3 4 55.8

5.9

6

6.1

6.2

6.3

6.4

6.5x 1010


Col

lisio

nal Q

uenc

h R

ate(

s-1)


(d)

Figure 5-13. Collisional quench rate Q21 variation at (a) 10, (b) 27, (c) 37 and (d) 53 bar with

temperature and colliding species mole fraction corresponding to equivalence ratio of 0.5–3 indicating that the variation with respect to mean is 4.1, 3.9, 3.8 and 3.7 % respectively.

The mean value of 21Q is used to calculate F in Equation 4-3. The uncertainty due to the

variation of 21Q at 10, 27, 37 and 53 bar with temperature and colliding species mole fraction

corresponding to equivalence ratio of 0.5-3 with respect to mean is 4.1, 3.9, 3.8 and 3.7 %,

respectively.

All the parameters in Equation 4-2 required for determination of OH number density was

calculated and the image-processed OH-PLIF images in Figure 5-6 and 5-7 were converted into

absolute concentration. Figure 5-14(a–d) and 5-15(a–d) represents instantaneous and averaged

OH concentration at 10, 27, 37 and 53 bar respectively. Appendix D includes complete set of

instantaneous OH number density contours for all the pressure cases.

113

(a)

(b)

(c)

(d)

Figure 5-14. Instantaneous OH number density contours at near steady state chamber pressure of

(a) 10, (b) 27, (c) 37 and (d) 53 bar

114

(a)

(b)

(c)

(d)

Figure 5-15. Average of thirteen instantaneous OH number density contours at near steady state

chamber pressure of (a) 10, (b) 27, (c) 37 and (d) 53 bar.

115

The uncertainty due to laser absorption by OH creating a horizontal incident photon flux

gradient, estimated from average OH number density using Beer-Lambert’s law [35],

( )9

121

OH2o

BI exp -h

I co

laser abs

Bfd znν ν

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟= Φ Φ⎜ ⎟⎜ ⎟

⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

∑∫ , for z= 1mm path length of the laser at 10, 27,

37 and 53 bar was 2, 3.3, 3.8 and 4.7 % respectively.

In summary, the uncertainties associated with OH quantitative measurement based on the

conservative assumptions made here were quantified for 10, 27, 37 and 53 bar cases as shown in

Figure 5-16(a–d).

–

1.3%

2.8%–

4.1%–

CameraCamera Calibration – 2.9%Shot noise – 6.9%Pixel Smoothening – 7%

Other SignalsLaser scattering - blockedBackground emission - correctedFluorescence trapping -negligible for A-X(1,0)

AbsorptionBoltzmann factor (Temperature)

Absorption Coefficient (Spectroscopy)

Line ShapeOverlap integral (line shape)Overlap integral (laser center line shift)Model (Collisional & Doppler width/shift)

Fluorescence EfficiencyQuench rate (Collider species cross section/ mole fraction,Pressure, Temperature )Model for quantum yield

Laser Shot to shot power fluctuation - 11%

Laser sheet spatial variation- 5.9%

Laser absorption (OH) – 2%

Laser absorption(H2O) - negligible

VolumePixel area – 2.8%

( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

12.4%

Total uncertainties (rms error) = 21.4 %

–

1.3%

2.8%–

4.1%–









Laser absorption (OH) – 2%



( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

12.4%


(a)

116

–

1%

1.6%–

3.9%–

CameraCamera Calibration – 2.9%Shot noise – 7%Pixel Smoothening – 7%








Laser absorption (OH) – 3.3%



( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

14.6%


–

1%

1.6%–

3.9%–

CameraCamera Calibration – 2.9%Shot noise – 7%Pixel Smoothening – 7%











( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

14.6%


(b)

–

0.8%

1%–

3.8%–

CameraCamera Calibration – 2.9%Shot noise – 6.8%Pixel Smoothening – 6.3%











( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

14.5%


–

0.8%

1%–

3.8%–

CameraCamera Calibration – 2.9%Shot noise – 6.8%Pixel Smoothening – 6.3%











( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

14.5%


(c)

117

–

0.5%

0.2%–

3.7%–












( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

15.1%


–

0.5%

0.2%–

3.7%–












( )

pOH 9

121 21

221 21

N

B AE VA c A Q 4

o

laser abs

Bfd

n

νπ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟ ⎛ ⎞⎛ ⎞ ⎛ ⎞Φ Φ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+⎝ ⎠ ⎝ ⎠⎝ ⎠⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑∫

W

15.1%


(d)

Figure 5-16. OH-PLIF measurement uncertainties at (a) 10, (b) 27, (c) 37 and (d) 53 bar. The rms error include the contributions from (i) camera calibration (ii) shot noise, (iii) pixel smoothening, (iv) laser power variation, (v) laser spatial variation, (vi) laser absorption by OH, (vii) absorption coefficient, (viii) overlap integral, (ix) quench rate variation and (x) pixel area accuracy and accounted to total rms error of 21.4, 22.8, 22.5 and 22.9 % at 10, 27, 37 and 53 bar respectively.

The rms error includes the contributions from:

i. Camera calibration ii. Shot noise

iii. Pixel smoothening iv. Laser power variation v. Laser spatial variation

vi. Laser absorption by OH vii. Absorption coefficient

viii. Overlap integral ix. Quench rate variation x. Pixel area accuracy

118

The uncertainty due to camera calibration of 2.9%, laser shot to shot power fluctuation of

11%, laser sheet spatial variation of 5.9 % and pixel area of 2.8 % remain the same for all the

pressure cases. The uncertainties due to the laser shot-to-shot power fluctuation could be

eliminated by monitoring the laser energy variation during the experiments. The uncertainty in

laser sheet spatial variation in could be eliminated by monitoring the spatial profile during

experiments from a separate test cell, uniformly filled with a fluorescing substance like acetone.

The shot noise accounted to 6–7 % in all the pressure cases. The average number of

photons collected in all the pressure cases was in the 200–225 range. As the pressure increases

the decrease in the OH signal strength is expected due to collisional quenching. But in the

current study the increase in the pressure was achieved by increasing the propellant mass flow

rate resulting in increased OH production at higher pressures. Thus as the pressure increased the

strength of the OH signal collected primarily depended on the collisonal quenching and

increased OH production. The uncertainty due to pixel smoothening used to minimize the

contribution of camera sensor randomness was also 6–7% for all the pressure cases.

The uncertainty due to the laser absorption by OH was estimated to increase from 2 to 4.7

% in the 10–53 bar range. From the OH-PLIF images in Fig. 5 it could be recognized that the

effect of laser absorption is negligible for all the pressure cases and as indicated by the

uncertainty estimation too.

Of all the uncertainties the variation of the absorption coefficient with temperature was the

highest and was 12 to 15 % in the 10 to 53 bar range. The uncertainty due to this can be reduced,

provided the 2D temperature field is available through measurements or calculations. For flames

with wrinkling, corrugation and large fluctuations the use of temperature field data from

119

numerical simulation or a reference flame could lead to additional errors as the instantaneous

temperature field of the actual flame and simulated/reference flame cannot be precisely matched.

The uncertainty due to the variation of overlap integral due to line shape broadening

decreased from 1.3 to 0.5 at 10–53 bar pressure range. Similarly the uncertainty in the overlap

integral due to the shift in the center line of the laser decreased from 2.8 to 0.2 % in the 10 to 53

bar range. The relatively low variations in the overlap integral is attributed to the use of large

laser line width of 5cm-1 thereby obtaining a complete overlap between laser spectral and OH

absorption profile at all pressures. Moreover the mean value of the overlap integral was reduced

by only 10 % from 10 to 53 bar in the current study compared to the 30–40% reduction of

overlap integral in other studies [50] due to the use of lasers with small line widths of the order

of 0.5–1cm-1. The uncertainty due to variation in collisional quenching was nearly 4 % in all the

pressure cases and is less significant compared to the absorption coefficient variation of 12–15%

with temperature.

The uncertainty contributions from spectroscopic constants and uncertainty in the

mathematical model describing the fluorescence process, collisional/Doppler widths and shifts,

and quench rate are identified as negligible in this study. Thus the total rms uncertainty in the

OH number density measurements for a GH2/GO2 flame determined from a broad range of

uncertainty sources accounted to of 21.4, 22.8, 22.5 and 22.9 % at 10, 27, 37 and 53 bar

respectively.

The improvements identified in the study includes elimination of uncertainties from laser

shot to shot power fluctuation, laser spatial sheet variation, and minimizing the uncertainty due

to temperature variation from simultaneous temperature measurements. The incorporation of the

improvements suggested in the study could potentially reduce the uncertainty from the present

120

uncertainty of 21–23 % to nearly 11 % for all the pressure cases thereby improving the quality of

the data for CFD code validation.

The boundary conditions included temperature measurements and evaluation of wall heat

fluxes. These data are collected simultaneously with the OH concentration and are used in the

computational studies that parallel this work. These results are included in Appendix E.

121

CHAPTER 6 CONCLUSIONS

The purpose of this work was to provide a database of in-flow planar species concentration

and to quantify the uncertainty associated with these measurements. The experimental conditions

investigated used O/F mass flow ratio fixed at 3.77 and chamber pressures of 10, 27, 37 and 53

bar. Nine rovibrational lines at A-X(1,0) transition of OH excited at 283 nm was employed to

obtain OH distribution in the shear reaction zone near the coaxial injector. The following are the

conclusions:

• Benchmark inflow OH concentration data was generated in the same experimental facility with the same propellant system and instrumentation method for a range of pressures from 10–53 bar. The instantaneous OH concentration and the averaged concentration in number densities which were inexistent in previous single injector studies over the 10–53 bar range can be used to validate of LES and RANS CFD codes respectively. This is the first contribution of the current study.

• The wrinkling, corrugation and flapping of the flame at higher pressures of 27–53 bar is

due to the combined effects of turbulence due to increased Reynolds number and jet instability caused by size and dynamics of the recirculation region in the wake of oxidizer post lip.

• The quality of the benchmark inflow data was improved by a thorough and

comprehensive uncertainty analysis and assessment, and this is the second contribution of the study.

• The systematic uncertainties, which remained the same irrespective of the experimental

conditions, were evaluated at all pressures; uncertainty due to camera calibration, laser shot to shot power fluctuation, laser sheet spatial variation and pixel area accuracy was 2.9, 11, 5.9 and 2.3 % respectively. The uncertainties due to laser shot to shot power fluctuation and laser sheet spatial variation could be potentially minimized in future studies.

• The uncertainty due to shot noise and pixel smoothening were, each 6–7% for all the

pressures cases. • The laser elastic scattering was effectively blocked and contributions from the

background flame emissions were eliminated for accurate quantitative measurements. • The uncertainty due to absorption of laser across the flame by H2O was negligible and by

OH was 2–5 % in 10–50 bar range.

122

• The uncertainty in absorption coefficient variation with temperature was 12–15 % in 10–50 bar range and was the maximum among all the uncertainties. The uncertainty could be potentially minimized provided there is availability of temperature field data from experiments/ computations.

• The uncertainty in overlap integral with temperature variation was 1.3–0.5 % and 2.8–

0.2% with laser centerline shift and the mean value of overlap integral was reduced by 10% in the 10–50 bar range. The use of lasers with larger line widths is recommended for OH-PLIF measurements at high pressures for minimizing the uncertainty due to overlap integral.

• The uncertainty in collisional quench rate variation with temperature and colliding

species mole fraction was nearly 4% at all pressures and is insignificant compared to the 12–15% variation of absorption coefficient with temperature.

• The uncertainty in the spectroscopic constants, mathematical model used to describe

fluorescence process, collisional and Doppler widths, and collisional quenching are negligible.

• The total rms uncertainty contributions in OH number density analyzed and determined

from 18 sources at 10, 27, 37 and 53 bar was 21.9, 22.8, 22.5 and 22.9 % respectively. The quality of the inflow data was improved from uncertainty assessment of two sources in previous studies to 18 sources; by quantifying 12, eliminating 2 and identifying as negligible the rest 4.The information is valuable for CFD validation as it brackets the reliability of the experimental data base. To reduce the uncertainty to nearly 11 % from the current 23%, potential areas for future improvements include elimination of the uncertainties due to laser power and spatial variation, and absorption coefficient variation with temperature.

123

CHAPTER 7 FUTURE WORK

The future work should be directed towards improving the accuracy of the OH

concentration in areas highlighted in the current study. The uncertainty in OH concentration

measured today reaches nearly 23% for all the pressure cases. Some of the major uncertainties

that were significant and that can be minimized include:

i. 12–15 % from temperature dependence of absorption coefficient ii. 11% from laser shot to shot power fluctuations

iii. 6 % from laser sheet spatial variation in intensity

The uncertainty in the absorption coefficient of 12–15 % can be minimized, if there is

availability of the temperature field data either from simultaneous temperature measurements or

from CFD simulations. This remains problematic for a number of reasons. Planar temperature

measurements in a high pressure reacting flow has not been attempted today, given the difficulty

to adapt the point wise absorption technique to the current flow field. CFD simulation either in

time averaged or time accurate formulations have uncertainties that far exceed the 12–15%

evaluated in this study. Hence while several CFD-experimental combined studies may improve

this item the future work will require considerable effort. An experimental technique that may be

attempted is a two-line OH thermometry. The advantage of using simultaneous temperature

measurements is that both the OH and temperature field data can be spatially matched. The

disadvantages results from the considerable complexity of the experimental setup and additional

contributions to overall uncertainty from the temperature measurement errors.

Thus the following procedure need to be adopted to revise both the experimental and CFD

data;

124

Step 1: the OH number density data simulated from RANS simulations should be validated

against the experimental data and the CFD code should be improved till it predicts the measured

OH concentration within the current uncertainty limits.

Step 2: the temperature field data from the improved CFD code can be used to refine the

calculation of OH concentration from experimental measurements.

The procedures in Step 1 and Step 2 should be followed iteratively till the uncertainty

contribution due to unknown temperature field attains a minimum value.

The second major uncertainty source is the laser shot to shot power fluctuation. To

eliminate it, a fixed percentage of the total laser power could be monitored through out the

experiments. Additional equipment would require a laser power meter than can be synchronized

with OH-PLIF shot to shot images.

Similarly the uncertainty from the averaged laser sheet spatial intensity could be reduced

by monitoring the spatial profile throughout the experiments. This could be done by tracking the

spatial intensity profile of the laser from a separate test cell, uniformly filled with a fluorescing

substance like acetone and synchronized with the shot to shot OH-PLIF images. Additional

experimental challenges include separate optical setup and detection electronics, and extraction

of a part of total laser power at 283 nm for acetone fluorescence.

It is estimated that incorporation of the improvements suggested here in future works

would minimize the uncertainty in the OH concentration measurements from 23 % to nearly 11

% and this is the third contribution of the study.

125

APPENDIX A MATLAB® SCRIPTS USED FOR DATA PROCESSING

The Matlab scripts used for data processing are provided here:

i. 3D heat flux processing -37 bar ii. Elimination of background emissions- 37 bar

iii. Laser sheet spatial profile uncertainty iv. Conventional photon calibration v. Poisson photon calibration - photon count 300 ns

vi. Poisson photon calibration - camera calibration vii. OH number density contours-37 bar

viii. Mean reaction zone-37 bar

126

3D heat flux processing

clear all; close all; warning off; d=0;c=0;dt=0.0001;k=1;i=0;Ar=0;s=100; t=7.75;h=0.001;e=t/(dt*s); %number of grids g=51;gz=51; %centre point cp=(g-1)/2 +1 ; dx=63.5/(g-1); Ar=(dx)^2; L=1;L1=roundn(9.3/dx,0);L2=roundn(20.3/dx,0);L3=roundn(32.3/dx,0);L4=roundn(51.4/dx,0);L5=g; %inner wall a=roundn(12.7/dx,0); %a=int32(12.7/dx); hi=roundn(0.8/dx,0); %hi=int32(0.8/dx); %ho=int16(2.4/dx); ho=3*hi; in=roundn(15.8/dx,0);m=roundn(22.2/dx,0);o=roundn(28.5/dx,0); %in=int16(15.8/dx);m=int16(22.2/dx);o=int16(28.5/dx); q=0.4*ones(g,g,g); qi=0.4*zeros(g,g,g); Temp=300*ones(g,g,m);Temp1=300*ones(g,g,m);Temp2=300*ones(g,g,m);Temp3=300*ones(g,g,m);Temp4=300*ones(g,g,m);Temp5=300*ones(g,g,m); T=300*ones(g,g,g); c=388/(8700*385)*(dx*1e-3)^-2; d=dx*1e-3*1*1e6/388; %qi=1.58; LT=300; P1=29; P2=30; %e=0.01/ %m1=1.92; n1=1; %m1(1:g)=(1.19e-6*(0:dx:63.5).^4 - 0.000167*(0:dx:63.5).^3 + 0.0063997*(0:dx:63.5).^2 - 0.034187*(0:dx:63.5) + 1.2128); m1(1:L3)=(0.0022046*(0:dx:(L3-1)*dx).^2 - 0.021241*(0:dx:(L3-1)*dx) + 1.3714); m1(L3:g)=(0.0022133*((L3-1)*dx:dx:63.5).^2 - 0.25017*((L3-1)*dx:dx:63.5) + 8.7715); for i=dt:dt:t %qi= m1*i+ n1; for j=cp-a:cp+a qi(j,cp-a,1:g)=m1'*(1-exp(-i/n1));

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qi(j,cp+a,1:g)=m1*(1-exp(-i/n1)); qi(cp-a,j,1:g)=m1*(1-exp(-i/n1)); qi(cp+a,j,1:g)=m1*(1-exp(-i/n1)); end %T(2:g-1,2:g-1)=T(2:g-1,2:g-1) + %c*dt*(T(3:g,2:g-1)-2*T(2:g-1,2:g-1)+T(1:g-2,2:g-1)+ %T(2:g-1,3:g)-2*T(2:g-1,2:g-1)+T(2:g-1,1:g-2)) ; 2D unsteady T(2:g-1,2:g-1,2:g-1)=T(2:g-1,2:g-1,2:g-1) + c*dt*(T(3:g,2:g-1,2:g-1)-2*T(2:g-1,2:g-1,2:g-1)+T(1:g-2,2:g-1,2:g-1)+ T(2:g-1,3:g,2:g-1)-2*T(2:g-1,2:g-1,2:g-1)+T(2:g-1,1:g-2,2:g-1) + T(2:g-1,2:g-1,3:g)-2*T(2:g-1,2:g-1,2:g-1)+T(2:g-1,2:g-1,1:g-2)) ; %bottom surface boundary condition T(2:g-1,2:g-1,1)=T(2:g-1,2:g-1,1) + c*dt*(T(3:g,2:g-1,1)-2*T(2:g-1,2:g-1,1)+T(1:g-2,2:g-1,1)+ T(2:g-1,3:g,1)-2*T(2:g-1,2:g-1,1)+T(2:g-1,1:g-2,1)); %Top surface boundary condition T(2:g-1,2:g-1,g)=T(2:g-1,2:g-1,g) + c*dt*(T(3:g,2:g-1,g)-2*T(2:g-1,2:g-1,g)+T(1:g-2,2:g-1,g)+ T(2:g-1,3:g,g)-2*T(2:g-1,2:g-1,g)+T(2:g-1,1:g-2,g)) ; %outer wall bc T(:,1,1:g) = T(:,2,1:g)- q(:,1,1:g)*dx*1e-3/388; T(:,g,1:g)= T(:,g-1,1:g)-q(:,g,1:g)*dx*1e-3/388; T(1,:,1:g)=T(2,:,1:g)-q(1,:,1:g)*dx*1e-3/388; T(g,:,1:g)=T(g-1,:,1:g)-q(g,:,1:g)*dx*1e-3/388; q(:,1,1:g)=388*(T(:,2,1:g)-T(:,1,1:g))/(dx*1e-3); q(:,g,1:g)=388*(T(:,g-1,1:g)-T(:,g,1:g))/(dx*1e-3); q(1,:,1:g)=388*(T(2,:,1:g)-T(1,:,1:g))/(dx*1e-3); q(g,:,1:g)=388*(T(g-1,:,1:g)-T(g,:,1:g))/(dx*1e-3); %inner wall bc T(cp-a:cp+a,cp-a,1:g)= T(cp-a:cp+a,cp-a-1,1:g)+d*qi(cp-a:cp+a,cp-a,1:g); T(cp-a:cp+a,cp+a,1:g)=T(cp-a:cp+a,cp+a+1,1:g) +d*qi(cp-a:cp+a,cp+a,1:g); T(cp-a,cp-a:cp+a,1:g)=T(cp-a-1,cp-a:cp+a,1:g)+ d*qi(cp-a,cp-a:cp+a,1:g); T(cp+a,cp-a:cp+a,1:g)=T(cp+a+1,cp-a:cp+a,1:g)+d*qi(cp+a,cp-a:cp+a,1:g); if roundn(i/dt,0)==k*s Temp(:,:,k)=T(:,:,L)-273; Temp1(:,:,k)=T(:,:,L1)-273; Temp2(:,:,k)=T(:,:,L2)-273; Temp3(:,:,k)=T(:,:,L3)-273; Temp4(:,:,k)=T(:,:,L4)-273; Temp5(:,:,k)=T(:,:,L5)-273; k=k+1; end; end; figure(1) plot(squeeze(Temp(cp-hi,cp-in,1:end)),'r'); hold on plot(squeeze(Temp(cp+hi,cp-m,1:end)),'b'); xlabel('time(ms)','FontSize',18);

128

ylabel('Temperature(^oC)','FontSize',18); grid on; title('Computaional Temperatures Inner & Middle 83 mm','FontSize',15); axis([1 e 20 LT]); set(gca,'Fontsize',15) legend('Inner','Middle',2); %Temp=T-273; figure(2) [c,h]=contourf(Temp(:,:,end)); colorbar; %line([cp-a cp-a cp+a cp+a cp-a],[cp-a cp+a cp+a cp-a cp-a],'color','w','linewidth',2); rectangle('Position',[cp-a,cp-a,2*a,2*a],'Facecolor','w') line([1 cp-in],[cp-hi cp-hi],'color',[1 1 1],'linewidth',2.5); line([1 cp-m],[cp+hi cp+hi],'color',[1 1 1],'linewidth',2.5); %line([1 cp-o],[cp+ho cp+ho],'color',[1 1 1],'linewidth',1.5); title('Computational Temperatures 2D at t=7.75s and x=83 mm','FontSize',18); set(gca,'XTick',[20 40 60 80 100 120 140 160 180 200]) set(gca,'YTick',[20 40 60 80 100 120 140 160 180 200]) set(gca,'XTickLabel',{'0.25';'0.5';'0.75';'1.00';'1.25';'1.50';'1.75';'2.00';'2.25';'2.50'}); set(gca,'YTickLabel',{'0.25';'0.5';'0.75';'1.00';'1.25';'1.50';'1.75';'2.00';'2.25';'2.50'}); xlabel('Length (inch)','FontSize',18); ylabel('Breadth (inch)','FontSize',18); %input file [filename, pathname] = uigetfile('*.*', 'Select test data file.'); if isequal(filename,0) | isequal(pathname,0) disp('User pressed cancel') %a = 0; else disp(['User selected ', fullfile(pathname, filename)]) data = load([pathname filename]); %a = 1; end %data put into different matrix b=231; c=457; t1=data(:,1); CT=data(:,2); cP=data(:,3); oP=data(:,4); fP=data(:,5); oMFR=data(:,6); fMFR=data(:,7); ofMR=data(:,8); ER=data(:,9); ITL=data(:,10); ITS=data(:,11);

129

BIT=data(:,12); WT1 = zeros(c-b+1,2); t2=(t1(b:c)-5250)/1000; %Data processing for heat flux %loop Len=[L L1 L2 L3 L4 L5];it=0; axial=[37.7 47 58 70 89.1 102.2];%Tem=[Temp Temp1 Temp2 Temp3 Temp4 Temp5]; qcomp=zeros(1,6);qlinear=zeros(1,6);Texpi=zeros(1,6);Texpm=zeros(1,6);Tcompi=zeros(1,6);Tcompm=zeros(1,6); for P1=23:2:33 P2=0; P2=P1+1; it=it+1; WT1 = zeros(c-b+1,2); t2=zeros(c-b+1,1); t2=(t1(b:c)-5250)/1000; WT1(:,1)=data(b:c,P1); WT1(:,2)=data(b:c,P2); T2=zeros(1,2);T1=zeros(1,2); T2=polyfit(t2,WT1(:,2),1);T1=polyfit(t2,WT1(:,1),1); WT(1:e,1:2)=0; t=dt:7.75/e:7.75; t=t'; WT(1:e,1)=polyval(T1,t); WT(1:e,2)=polyval(T2,t); x = [3.175 9.525]; Texp=[WT(e,1) WT(e,2)]; T2a= T(cp+hi,cp-m,Len(it))-273;T1a=T(cp-hi,cp-in,Len(it))-273; Tcomp=[T1a T2a]; Texpi(it)=Texp(1);Texpm(it)=Texp(2); Tcompi(it)=Tcomp(1);Tcompm(it)=Tcomp(2); figure(it+2) plot(x,Texp,'or',x,Tcomp,'ob'); grid on xlabel('Distance from inner wall (mm)','FontSize',18); ylabel('Temperature (^oC)','FontSize',18); axis([0 11 0 LT]); text(x(1),Texp(1)+5,num2str(roundn(Texp(1),0)),'FontSize',15,'color','r'); text(x(2),Texp(2)-5,num2str(roundn(Texp(2),0)),'FontSize',15,'color','r'); text(x(1),Tcomp(1)-5,num2str(roundn(Tcomp(1),0)),'FontSize',15,'color','b'); text(x(2),Tcomp(2)+5,num2str(roundn(Tcomp(2),0)),'FontSize',15,'color','b'); text(8,Texp(1)+20,strcat('q=',num2str(qi(cp-a,cp-a,Len(it))),'MW/m^2'),'FontSize',15,'color','k'); title(strcat('Experimental and Computational Temperature Comparisons at ',num2str(axial(it)),' mm'),'FontSize',18); set(gca,'Fontsize',15); legend('Experiment','Computation',2); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+2),'.emf'));

130

saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+2),'.fig')); if it ==1 Te=Temp; end if it==2 Te=Temp1; end; if it ==3 Te=Temp2; end if it==4 Te=Temp3; end; if it ==5 Te=Temp4; end if it==6 Te=Temp5; end; compT(1:e,1:2)=0; compT(:,1)=squeeze(Te(cp-hi,cp-in,1:end)); compT(:,2)=squeeze(Te(cp+hi,cp-m,1:end)); figure(it+8) plot(t,compT(:,1),'r',t,WT(:,1),'--r',t,compT(:,2),'b',t,WT(:,2),'--b'); title(strcat('Linear fit for temperatures at ',num2str(axial(it)),' mm'),'FontSize',18); xlabel('time(s)','FontSize',18); ylabel('Temperature(^oC)','FontSize',18); %axis([2.75 7.75 20 LT]); axis([0 7.75 20 LT]); %axis tight; grid on; set(gca,'Fontsize',15); legend('Computation inner','Experiment inner','Computation Middle','Experiment Middle',2); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+8),'.emf')); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+8),'.fig')); slope88(1,1)= T1(1,1); slope88(1,2)=T2(1,1); slope88*1e3; qcomp(it)=qi(cp-a,cp-a,Len(it)); %Linear Assumption HF881=zeros(length(WT(:,1)),1);HF88unsteady1=zeros(length(WT(:,1)),1); HF881=(388/0.00635)*(WT(:,1)-WT(:,2))/1000000; HF88unsteady1=HF881 + 1e-6*(8700*385*0.00635*T2(1,1));

131

figure(it+14) plot(t,[HF881 HF88unsteady1],'Linewidth',1); Title(strcat('Heat Flux Linear Assumption at ',num2str(axial(it)),' mm'),'Fontsize',18); ylabel('Heat Flux (MW/m^2)','Fontsize',18); xlabel('time(ms)','Fontsize',18); set(gca,'Fontsize',15); legend('HF881','HF88unsteady1',2); axis([min(t) max(t) 0 2]); grid on; saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+14),'.emf')); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+14),'.fig')); p1=polyfit(t,HF88unsteady1,1) %disp(num2str(p1(1)),'*t',num2str(p1(2))) HF881(end); qlinear(it)= HF88unsteady1(end); figure(it+20) plot(t,WT(:,1),'--r',t,WT(:,2),'--b'); title(strcat('Linear fit for temperatures at',num2str(axial(it)),' mm'),'FontSize',18); xlabel('time(s)','FontSize',18); ylabel('Temperature(^oC)','FontSize',18); %axis([2.75 7.75 20 LT]); axis([0 7.75 20 LT]); grid on; set(gca,'Fontsize',15); legend('Experiment inner','Experiment Middle',2); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+20),'.emf')); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(it+20),'.fig')); end; axial1=[0 9.3 20.3 32.3 51.4 64.5]; qcomp2D=[1.35 1.54 1.65 1.85 1.83 1.83]; axial=[37.7 47 58 70 89.1 102.2]; figure(30) plot(axial,qcomp,'-dr',axial,qlinear,'-sb',axial,qcomp2D,'-*g'); grid on; xlabel('Distance from Injector Face (mm)','FontSize',18); ylabel('Heat Flux (MW/m^2)','FontSize',18); set(gca,'FontSize',15); axis([0 130 0 4]); legend('Heat Flux Computational 51x51x51 grid','Heat Flux Linear','Heat Flux 2D',1); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(30),'.emf'));

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saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(30),'.fig')); figure(31) plot(axial,Texpi,'-or',axial,Tcompi,'--db'); grid on; xlabel('Distance from Injector Face (mm)','FontSize',18); ylabel('Temperature (^oC)','FontSize',18); set(gca,'FontSize',15); axis([20 150 80 220 ]); legend('T_i_n_n_e_r Exp','T_i_n_n_e_r Comp',1); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(31),'.emf')); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(31),'.fig')); figure(32) plot(axial,Texpm,'-or',axial,Tcompm,'--db'); grid on; xlabel('Distance from Injector Face (mm)','FontSize',18); ylabel('Temperature (^oC)','FontSize',18); set(gca,'FontSize',15); axis([20 150 80 220 ]); legend('T_m_i_d_d_l_e Exp','T_m_i_d_d_l_e Comp',1); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(32),'.emf')); saveas(gcf,strcat('E:\aravind7\combustiontests\Heatflux Processing\37bar\37bar\',num2str(32),'.fig'));

133

Elimination of background emissions

clear all close all x= [];y=[];S=[];sum1=0;z=0;sumlaser=0;sumnolaser=0;avglaser=0;avgnolaser=0;lasersubback=0;Inj=[];sumInj=0;avgInj=0;z1=0;z2=0;R=[];RB=[];sumR=0;sumRB=0;avgR=0;avgRB=0;RC=0;No=0;a=0;a1=0;a2=0; c=63; b=75; d=b-c+1; for i=c:b x{i}= imread(strcat('E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\091807OUF1IP3CA3SAT06\35barlasertunedon283nm_00',num2str(i),'A','.tif')); x{i}=double(x{i}); sumlaser=sumlaser +x{i}; y{i}= imread(strcat('E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\091807OUF1IP3CA3SAT06\35barlasertunedon283nm_00',num2str(i),'B','.tif')); y{i}=double(y{i}); sumnolaser=sumnolaser +y{i}; S{i}=x{i}-y{i}; sum1=sum1+S{i}; end %avg image avglaser=sumlaser/d; avgnolaser=sumnolaser/d; z=avglaser-avgnolaser; z(find(z<0))=0; %Reference Picture information gives 1mm = 14.09 pixels %Set Injector location pixel. ILX = 25; ILY = 101; %Create X and Y axis from reference picture information. PS = 1/15.05; XL = 0-ILX; XH = 319-ILX; YL = 0-ILY; YH = 175-ILY; Y=PS*YL:PS:PS*(YH-1); X=PS*XL:PS:PS*(XH-1); cmap=(0:20)'/20*[1 1 1]; k=7;l=95;m=25; X1=X(25:319); Y2=Y(56:148);

134

figure(1) avglaser=avglaser(56:148,25:319); image(X1,Y2,squeeze(avglaser/k)); set(gca,'Fontsize',18) axis([-1.5 max(X1) -3 3]); cmap1=(0:l)'/l*[1 1 1]; colormap(cmap1); h=colorbar('horiz'); set(h,'Fontsize',18); set(gca,'yaxislocation','right'); %rectangle rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); axis equal axis manual set(gcf,'paperposition',[0.4 4 7 3.5]) ; set(gcf, 'color', 'white'); saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\AvgOHimages06\AvgOH35bar1','emf'); figure(2) avgnolaser=avgnolaser(56:148,25:319); image(X1,Y2,squeeze(avgnolaser/k)); set(gca,'Fontsize',18) cmap1=(0:l)'/l*[1 1 1]; colormap(cmap1); h=colorbar('horiz'); set(h,'Fontsize',18); set(gca,'yaxislocation','right'); %rectangle rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); axis([-1.5 max(X1) min(Y2) max(Y2)]);

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axis equal axis manual set(gcf,'paperposition',[0.4 4 7 3.5]) ; set(gcf, 'color', 'white'); saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\AvgOHimages06\AvgOH35bar2','emf'); figure(3) z1=z(56:148,25:319); image(X1,Y2,squeeze(z1/k)); set(gca,'Fontsize',18) cmap1=(0:m)'/m*[1 1 1]; colormap(cmap1); h=colorbar('horiz'); set(h,'Fontsize',18); set(gca,'yaxislocation','right'); %rectangle rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); axis([-1.5 max(X1) -3 3]); axis equal axis manual set(gcf,'paperposition',[0.4 4 7 3.5]) ; set(gcf, 'color', 'white'); saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\AvgOHimages06\AvgOH35bar3','emf');

136

Laser sheet spatial profile uncertainty

Ulaserfluc=0; for m=140:232 for n=25:319 laser= [];lasersum=0;laseravg=0;laseravgnorm=0;fluc=0; c1=10;b1=99; d=b1-c1; for o=10:99 laser=0; laser= imread(strcat('E:\aravind7\OHPLIF\AfterProposal\092407laserprofile\laserprofile1acetone283nm\laserprofile1acetone283nm_00',num2str(o),'.tif')); laser=double(laser); fluc(o)=laser(m,n)/max(max(laser(m,:))); % lasersum=lasersum +laser; end fluc=fluc(10:99); fluc=reshape(fluc,1,prod(size(fluc))); Ulaserfluc(m-139,n-24)=100*std(fluc)/mean(fluc); end; end; mean(mean(Ulaserfluc)) %Uncertainty in laser fluctuation is 5.8664

137

Conventional phtoton calibration

close all clear all Count=[0 59.34 107.22 163.21 220.74 280.74 339.87 401.32 521.66 645.76 770.26 896.98 1026.9 1150.6 1279.3 1542.6 1884.6 2210.5 2548.1 2896.1]; Ex = [0 11000 20000 30000 40000 50000 60000 70000 90000 110000 130000 150000 170000 190000 210000 250000 300000 350000 400000 450000]; %2) 310 nm filter with FWHM 10 nm xi=0;yi=0;lamda=0;Trans=0; lamda=[279 288 305 310 315 325 331]; Trans=[0.015 0.15 7.5 15 7.5 0.15 0.015]; lnTrans =log(Trans); xi=279:1:334; yi=exp(interp1(lamda,lnTrans,xi,'spline')); figure(1) plot(lamda,Trans,'*k', xi,yi,'--k'); grid on set(gca, 'Fontsize',18); xlabel('\lambda(nm)'); ylabel('Transmission(%)'); axis([270 340 0 16]); legend('Data Transmission','Linear fit',2); saveas(gcf,'FilterTransmission310nm','emf'); %3) Lamp Irradiance pixelarea = 718.24*1e-12; %in m^2 h=6.626*1e-34; %Js f=9.67*1e14; %frequency(s^-1) Irrad=0; %(mW/m^2 nm) Energy=0;Np=0; Cou=zeros(1,20);Np1=zeros(1,20);Calib=0; A= 4.45712*1e1; B= -4.63923*1e3; C=9.09372*1e-1; D=4.13307; E= 2.07519*1e5; F=-1.47164*1e8; G=3.87410*1e10; H=-3.80406*1e12; Irrad = (xi).^-5 .* exp(A+B*(xi).^-1).*(C +D*(xi.^-1) + E*(xi.^-2) + F*(xi.^-3) + G*(xi.^-4) + H*(xi.^-5)); %Irrad = (lamda).^-5 .* exp(A+B*(lamda).^-1).*(C +D*(lamda.^-1) + E*(lamda.^-2) + F*(lamda.^-3) + G*(lamda.^-4) + H*(lamda.^-5)); Energy = sum(Irrad*1e-3.*yi*0.01)*Ex*1e-9 * pixelarea/0.55 ; Np= Energy/(h*f); Np1=Np; Cou=Count; %Cou(1)=0; %Np1(2:20)=Np(1:19); %Np(1)=0; Cou1=0:20:2900; Calib=interp1(Cou,Np1,Cou1,'spline'); %Calibconst = mean(Np(2:9)./Cou(2:9))

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Calibconst = sum((Np(2:9)./Cou(2:9)).*Cou(2:9))/sum(Cou(2:9)); figure(2) plot(Cou,Np1,'*k',Cou1,Calib,'--k') grid on set(gca, 'Fontsize',18); xlabel('Counts'); ylabel('Number of Photons(N_p)'); legend('Data Photons','Linear fit',2); saveas(gcf,'PhotonCalibration310nmFull','emf'); figure(3) plot(Cou(1:9),Np1(1:9),'*k') grid on set(gca, 'Fontsize',18); xlabel('Counts'); ylabel('Number of Photons(N_p)'); legend('Data Photons',2); saveas(gcf,'PhotonCalibration310nm','emf'); figure(4) plot(Cou(1:9),Np1(1:9),'*k',Cou(1:9), Calibconst*Cou(1:9),'--k'); grid on set(gca, 'Fontsize',18); xlabel('Counts'); ylabel('Number of Photons(N_p)'); text(100,650,['N_p = ', num2str(Calibconst,3), ' *Counts '],'FontSize',18) legend('Data Photons','Linear fit',2); saveas(gcf,'PhotonCalibration310nmEQN','emf'); Stdesti=0; errslope=0; yesti=(Calibconst*Cou(2:9)); Stdesti= (sum((Np(2:9)-yesti).^2)/(length(yesti)-2))^0.5 errslope = sqrt(sum((Cou(2:9)- mean(Cou(2:9))).^2)^-1)*Stdesti % no 95% confidence interval UPhotonCalib = (0.0286/1.59)*100

139

Poisson photon calibration – photon count 300ns

clear all close all mint=[]; x= [];y=[];z=0;PC=[];sum1=0;sumlasersq=0;sumlaser=0;sumnolaser=0;avglaser=0;avgnolaser=0;lasersubback=0;Inj=[];sumInj=0;avgInj=0;z1=0;z2=0;R=[];RB=[];sumR=0;sumRB=0;avgR=0;avgRB=0;RC=0;No=0;a=0;a1=0;a2=0; c=100; b=999; d=b-c+1; x=zeros(88,320,b-c+1); for i=c:b %i=77;j=43;k=35; x=[];y=[]; x= double(imread(strcat('E:\aravind7\OHPLIF\AfterProposal\100207PhotonCalibration\300ns\300ns_0',num2str(i),'A','.tif'))); y= double(imread(strcat('E:\aravind7\OHPLIF\AfterProposal\100207PhotonCalibration\B300\B300_0',num2str(i),'A','.tif'))); z=x-y; z(find(z<=0))=0; sumlaser=sumlaser +z; sumlasersq=sumlasersq + z.^2; sumnolaser=sumnolaser+y; poiss(i-99)=z(15,15); mint=[mint; mean2(z)]; end; %PC=x-y; %avg image avg=0; V=0;S=0;KI=0; avg=sumlaser/d; V=(sumlasersq-avg.^2*d)/(d-1); S=V./avg; KI=avg./V; %S2=S(42:50,63:216); S2=KI; avg2=avg; %avg2=avg(42:50,63:216); S3=reshape(S2,prod(size(S2)),1); avg3=reshape(avg2,prod(size(S2)),1); figure(1) set(gca,'fontsize',15); hist(S3,0:0.01:0.5) xlabel('Calibration Constant');

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ylabel('N'); text(0.35,240,['Mean = ' num2str(mean(S3))],'FontSize',12); text(0.35,190,['\sigma = ' num2str(std(S3))],'FontSize',12); title('Exposure time = 300 ns'); grid on saveas(gcf,'300ns','emf'); %mean(S3) %std(S3) figure(2) hist(avg3) mean(avg3) std(avg3) avgnolaser=sumnolaser/d; avgnolaser=reshape(avgnolaser,prod(size(S2)),1); mean(avgnolaser) std(avgnolaser) goodp=find(abs(poiss-mean(poiss)<(mean(poiss)+std(poiss)))); k=mean(poiss(goodp))/var(poiss(goodp)); poiss1=poiss*k; figure(3) set(gca,'fontsize',15); title('Exposure time = 300 ns'); hist(poiss1,(min(poiss1(goodp)): 1: max(poiss1(goodp)))) text(191,31,['Mean = ' num2str(mean(poiss1(goodp)))],'FontSize',15); text(191,21,['\sigma^2 = ' num2str(var(poiss1(goodp)))],'FontSize',15); xlabel('Photons'); ylabel('N'); grid on hold on %figure(4) set(gca,'fontsize',15); %x1=min(poiss1(goodp)):1:max(poiss1(goodp)); %x1=x1+0.05; x1=134:1:233; y2=poisspdf(x1,175); y1=length(poiss1(goodp))*y2; plot(x1,y1,'+-r') xlabel('Photons'); ylabel('N'); grid on legend('Poisson Fit','Data'); %saveas(gcf,'poiss300a','emf'); %axis([600 1400 0 250]) mean(poiss); std(poiss); k

141

Poisson photon calibration – camera calibration

%clear all close all %Counts Counts=[ 65 380 510 889 963 1124 1460 1568 ]; StdCount=[1.96 13.7421 11.11 21.9157 20.8562 22.43 31 31.52]; Counts1=Counts+StdCount; Counts2=Counts-StdCount; Calconst= [0.222 0.15831 0.12356 0.13173 0.12374 0.11648 0.12342 0.11757]; %Calibration Constant StdCal=[0.022 0.017119 0.013163 0.01182 0.011178 0.010062 0.010153 0.009]; Calconst1=Calconst+StdCal; Calconst2=Calconst-StdCal; %Calconst= [0.222 0.15831 0.12356 0.13173 0.12374 0.11648 0.12342 0.11757]*(0.7/0.55)*(0.5/0.12); Calconstavg= (sum(Counts.*Calconst))/sum(Counts); Photon=Counts.*Calconst; Photon1=Counts.*mean(Calconstavg); %Photon1=Counts.*Calconst1; Photon2=Counts.*Calconst2; Ph=Photon*(.7/.55)*(.5/.12); Ph1=Photon1*(.7/.55)*(.5/.12); Ph2=Photon2*(.7/.55)*(.5/.12); figure(1) set(gca, 'fontsize', 15); plot(Counts, Photon,'o'); xlabel('Counts'); ylabel('Photons') title('Camera Calibration at 532 nm') grid on figure(2) set(gca, 'fontsize', 15); plot(Counts, Photon*(.7/.55)*(.5/.12),'o'); xlabel('Counts'); ylabel('Photons') title('Camera Calibration at 310 nm') grid on figure(3) set(gca, 'fontsize', 15); p = polyfit(Counts,Photon1*(.7/.55)*(.5/.12),1) ; %plot(Counts,Ph,'ob',Counts,Ph1,'o--k',Counts,Ph2,'og', Counts, polyval(p,Counts),'r'); plot(Counts,Ph,'ob',Counts, polyval(p,Counts),'r'); xlabel('Counts'); ylabel('Photons') %title('Camera Calibration at 310 nm')

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text(300,900,['y = ', num2str(p(1)), ' *x '],'FontSize',15) legend('Data Photons','Linear fit'); axis([0 2000 0 1800]); grid on %saveas(gcf,'PhotonCalibration310nm','emf'); f=polyval(p,Counts); mean(abs(f-Ph)./Ph) mean(Ph) exposure=[20 60 100 140 180 220 260 300]; p1 = polyfit(exposure, Counts,1) ; figure(4) set(gca, 'fontsize', 15); plot(exposure, Counts,'o',exposure,Counts1,'ok', exposure,Counts2,'og', exposure, polyval(p1,exposure),'r'); xlabel('exposure(ns)'); ylabel('Counts') %title('Counts vs exposure at 532 nm') %text(51,1400,['y = ', num2str(p1(1)), ' *x + ', num2str(p1(2))],'FontSize',15); legend('Mean Count','Mean Count + Std','Mean Count - Std', 'Linear fit'); axis([0 350 0 2500]); grid on %saveas(gcf,'CameraCalibration','emf'); %error in estimate yesti=(Calconstavg*Counts*(.7/.55)*(.5/.12)); Stdesti= (sum((Ph-yesti).^2)/(length(Ph)-2))^0.5 %uncertainty in slope errslope=0; % errslope = sqrt(sum((Counts- mean(Counts)).^2)^-1)*Stdesti*2.447; errslope = sqrt(sum((Counts- mean(Counts)).^2)^-1)*Stdesti % no 95% confidence interval %uncertainty in intercept errintercept=0; %errintercept = 2.447*Stdesti*sqrt(0.125 + mean(Counts)^2/sum((Counts- mean(Counts)).^2)); errintercept = Stdesti*sqrt(0.125 + mean(Counts)^2/sum((Counts- mean(Counts)).^2));%no 95% confidence interval %uncertainty in photons errphotons = errslope*Counts+ errintercept;

143

OH number density contours-37 bar

clear all close all T=0;phi=0;fb=zeros(length(phi),9);Qo=0;FYield=zeros(1,length(phi)); phi=[0.5 1 1.50 2.0 2.50 3]; RH2=2*phi;%mole of hydrogen RO2=ones(1,length(phi));%mole of Oxygen PH2Omf=[0.56287 0.65876 0.5877 0.4819 0.39584 0.33237 ];% product mole fraction of H2O computed from Stanjan PH2mf=[0.018347 0.13171 0.32116 0.48396 0.5926 0.66394 ];%product mole fraction of H2 compued from Stanjan PO2mf=[0.29170 0.03997 0.0024 0.000111 0.49e-5 0.23e-6 ];%product mole fraction of O2 computed from Stanjan PHmf=[0.0076419 0.043142 0.046 0.024 0.0096 0.33e-2 ];%product mole fraction of H computed from Stanjan POmf=[0.023812 0.020238 0.00331 0.00027 0.18e-4 0.11e-5 ];%product mole fraction of O computed from Stanjan POHmf=[0.095636 0.10617 0.0385 0.0089 0.00178 0.000345];%product mole fraction of OH computed from Stanjan T=[3272 3587 3427 3103 2777 2496];%Temperature corresponding to equivalnec ratio %fb(1,:)=[0.0438 0.025287 0.025287 0.0438 0.0092877 0.0092877 0.0178930 0.0178930 0.0134081];% Boltzmann factor associated with excitation lines fb(1,:)=[0.0316 0.0167 0.0167 0.0316 0.0059896 0.0059896 0.0116 0.0116 0.0163]; fb(2,:)=[0.02838 0.0147 0.0147 0.02838 0.00524 0.00524 0.01023 0.01023 0.0165]; fb(3,:)=[0.0299 0.0157 0.0157 0.0299 0.0056 0.0056 0.0109 0.0109 0.0164]; fb(4,:)=[0.0335 0.0179 0.0179 0.0335 0.0064 0.0064 0.01254 0.01254 0.0161303]; fb(5,:)=[0.0376501 0.02069 0.02069 0.0376501 0.0075032 0.0075032 0.014538 0.014538 0.0153234]; fb(6,:)=[0.04167 0.02355 0.02355 0.04167 0.0086 0.0086 0.0166 0.0166 0.014177]; %fb(8,:)=[0.04539 0.026408 0.026408 0.04539 0.00976 0.00976 0.018776 0.018776 0.0128349]; %fb(9,:)=[0.04865 0.0291 0.0291 0.04865 0.01087 0.01087 0.0208405 0.0208405 0.0114495]; %Absorption coefficient of the individual lines (cmJ^-1) B12=[0.756 7.97 1.815 9.514 7.011 3.506 7.229 2.469 5.273]*1e12/3e10; %Lines [P21(6)_6.5 Q2(3)_2.5 R12(3)_2.5 Q1(6)_6.5 Q2(1)_0.5 R12(1)_0.5 %Q2(2)_1.5 R12(2)_1.5 R2(14)_13.5]; %Lines[35333 35333.2 35334 35334.4 35334.9 35334.21 35338.0 35338.6 %35340.31] % Pressure and collisional cross section of H2O, H2 and O2; P=36.1; sigmaH2O=22; sigmaH2=5; sigmaO2=10; %quenching Qo= 1.229e5*P*1e5*((PH2Omf*sigmaH2O/2.96) + (PH2mf*sigmaH2/1.337)+(PO2mf*sigmaO2/3.33))./(T.^0.5); %FYield FYield=1.08e6./Qo;

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%Absorption for i=1:6 fbB12(i,:)= fb(i,:).*B12; sumfbB12(1,i)=sum(fbB12(i,:)); end; figure(1) set(gca,'Fontsize',15) ; plot(phi,Qo,'--k',phi,mean(Qo)*ones(1,length(phi)),'k') legend('Collisional Quench rate 37 bar','Mean Collisional Quench rate 37 bar'); xlabel('Equivalence ratio (\phi)','fontsize',20); ylabel('Collisional Quench Rate(s^-^1)','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); ax=0; grid on saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\QuenchrateVariation','emf'); figure(2) set(gca,'Fontsize',15) ; plot(phi,FYield,'--k',phi,mean(FYield)*ones(1,length(phi)),'k') legend('Fluorescence Yield 37 bar','Mean Fluorescence Yield 37 bar'); xlabel('Equivalence ratio (\phi)','fontsize',20); ylabel('Fluorescence Yield','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); ax=0; grid on saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\FluoryieldVariation','emf'); figure(3) set(gca,'Fontsize',15) ; plot(phi,sumfbB12,'--k',phi,mean(sumfbB12)*ones(1,length(phi)),'k') legend('Absorption Coefficient 37 bar','Mean Absorption Coefficient 37 bar'); xlabel('Equivalence ratio (\phi)','fontsize',20); ylabel('Absorption Coefficient (cmJ^-^1)','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); grid on saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\AbsorCoeffVariation','emf'); j=3 L=0;x1=0;x=0;y=0;y1=0;yd=0; Ove=0; %k=[2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 2930 3000 3100 3200 3300 3400]; for i=1:6 L= dlmread(strcat('lif',num2str(T(i)),'K',num2str(i+1),'.mod'),','); x=L(:,1);

145

y1= L(:,2)/max(L(:,2)); %y=0.188*exp(-(x-35333.8).^2/9.016); y=0.188*exp(-(x-35334.2).^2/9.016); y2=y/max(y); figure(i+j) set(gca,'Fontsize',15) ; plot(x,y2,'--k',x,y1,'k'); legend('Laser Profile',strcat('OH Absorption Profile at T = ',num2str(T(i)),' and 37 bar')); xlabel('\nu (cm^-^1)','fontsize',20); ylabel('(a.u)','fontsize',20); axis([35328 35342 0 1]); grid on saveas(gcf,strcat('E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\ProfilePhi',num2str(phi(i)),'.emf')); dv=0; dx(1:79)=x(2:80)-x(1:79); %figure(3+i) %plot(dx) mean(dx); %data analysis/overlap ylaser=y/sum(y); yabs=L(:,2)/sum(L(:,2)); yabs1=yabs/mean(dx); Overlap=sum(y.*yabs1*mean(dx)); Ove(i)=Overlap; end figure(i+j+1) set(gca,'Fontsize',15) ; plot(phi,Ove,'--k',phi,mean(Ove)*ones(1,length(phi)),'k'); legend('Overlap Integral 37 bar','Mean Overlap Integral 37 bar'); xlabel('\phi','fontsize',20); ylabel('Overlap(cm)','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); grid on saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\OverlapVariation','emf'); Tempfactor= (sumfbB12.*Ove.*FYield).^-1; figure(i+j+2) set(gca,'Fontsize',15) ; plot(phi,Tempfactor,'--k',phi,mean(Tempfactor)*ones(1,length(phi)),'k'); legend('Temperature Dependent Factors','Mean'); xlabel('Equivalence ratio (\phi)','fontsize',20); ylabel('Tempfactor(cm^2J^-^1)','fontsize',20); ax=axis; axis([0 5 ax(3:4)]);

146

grid on mfTempfactor=Tempfactor.*T; figure(i+j+3) set(gca,'Fontsize',15) ; plot(phi,mfTempfactor,'--k',phi,mean(mfTempfactor)*ones(1,length(phi)),'k'); legend('Temperature Dependent Factor mole fraction','Mean'); xlabel('Equivalence ratio (\phi)','fontsize',20); ylabel('Tempfactor(cm^2J^-^1K)','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); grid on NormTempfactor=Tempfactor/mean(Tempfactor); Variation=std(NormTempfactor); Percentagevariation=100*(Variation/mean(NormTempfactor)) figure(i+j+4) set(gca,'Fontsize',15) ; plot(phi,NormTempfactor,'--k',phi,mean(NormTempfactor)*ones(1,length(phi)),'k'); legend('Normalized Tempfactor','Mean'); xlabel('\phi','fontsize',20); ylabel('NormTempfactor','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); grid on NormmfTempfactor=mfTempfactor/mean(mfTempfactor); Variationmf=std(NormmfTempfactor); Percentagevariationmf=100*(Variationmf/mean(NormmfTempfactor)) figure(i+j+5) set(gca,'Fontsize',15) ; plot(phi,NormmfTempfactor,'--k',phi,mean(NormmfTempfactor)*ones(1,length(phi)),'k'); legend('Normalized Tempfactor','Mean'); xlabel('\phi','fontsize',20); ylabel('NormmfTempfactor','fontsize',20); ax=axis; axis([0 5 ax(3:4)]); grid on figure(i+j+6) set(gca,'Fontsize',18) ; [AX,H1,H2] = plotyy(phi,[PH2Omf' PH2mf' PO2mf'],phi,T,'plot'); set(get(AX(1),'Ylabel'),'String','Mole fraction') set(get(AX(2),'Ylabel'),'String','Temperature(^oC)') %plotyy(phi,[PH2Omf PH2mf PO2mf],phi,T); xlabel('Equivalence ratio (\phi)','Fontsize',20); set(H1(1),'LineStyle','-','color','b') set(H1(2),'LineStyle','-','color','g') set(H1(3),'LineStyle','-','color','k') %set(H1(4),'LineStyle','-','color','c')

147

set(H2,'LineStyle','-','color','r') legend(' Mole fraction H_2O 37 bar', ' Mole fraction H_2 37 bar',' Mole fraction O_2 37 bar','Temperature 37 bar'); grid on Factor=0; Factormf=0; Bk= 1.38065e-23;%Boltzmann constant E=0.89*1e-3% energy of laser J/pulse; A=2.058%cm^2 V=3.46e-5 %cm^3 eta=0.12*11.5; % (Photon detection efficiency * Factor associated with Gain) epsilon=0.55; saf=5.4e-4% Solid angle fraction; MTempfactor=mean(Tempfactor) MTempfactormf=mean(mfTempfactor) Factor= MTempfactor*((E/A)*V*saf)^-1; %botlzmann fraction, overlap integral and quenching %Factor= MTempfactor Factormf= ((P*1e5/Bk)*1e-6)^-1*MTempfactormf*((E/A)*eta*epsilon*V*saf)^-1; AvgTemp=MTempfactormf/MTempfactor %Image Processing % 1) Laser Sheet Profile Variation and Subsequent Correction laser= [];lasersum=0;laseravg=0;laseravgnorm=0; c1=10;b1=99; d=b1-c1; %centre Position ILX1 = 25; ILY1=186; %Create X and Y axis from reference picture information. PS = 1/15.05; XL1 = 0-ILX1; XH1 = 319-ILX1; YL1 = 0-ILY1; YH1 = 256-ILY1; Y1a=PS*YL1:PS:PS*(YH1-1); X1a=PS*XL1:PS:PS*(XH1-1); for o=10:99 laser=0; laser= imread(strcat('E:\aravind7\OHPLIF\AfterProposal\092407laserprofile\laserprofile1acetone283nm\laserprofile1acetone283nm_00',num2str(o),'.tif')); laser=double(laser); lasersum=lasersum +laser; end laseravg=(lasersum/90)-104; %k=2;d=b1-c1; h = ones(5,5) / 25;

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laseravg = imfilter(laseravg,h,'conv'); %h = fspecial('gaussian',[5 5]); %laseravg = imfilter(laseravg,h); %z2=z; figure(i+j+7) laseravg=laseravg(140:232,25:319); laseravgnorm=laseravg/mean(mean(laseravg)); for i=1:93 laseravgnorm(i,1:295)=laseravg(i,1:295)/max(max(laseravg(i,1:295))); end X11=X1a(25:319); Y21=Y1a(140:232); %image(X11,Y21,squeeze(45*laseravgnorm)); image(X11,Y21,squeeze(100*laseravgnorm)); %[c,h]=contourf(X11,Y21,laseravgnorm,[0.3 0.4 0.5 0.6 0.7 0.8 1 1.1 1.2 1.3 1.4]); % l=1; cmap1=(0:100)'/100*[1 1 1]; colormap(cmap1); %colormap(jet); h=colorbar('horiz'); set(h,'Fontsize',18); %colorbar; %clabel(c,'manual'); hold on; rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); set(gca,'Fontsize',18) ; set(gca,'yaxislocation','right'); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); %axis square axis equal axis manual axis([-1.5 max(X11) -3 3]); grid on set(gcf,'paperposition',[0.4 4 7 3.5]) ; grid on set(gcf, 'color', 'white'); saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\LaserSheetVariation','tif'); % 2) OH-PLIF image Processing

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x= [];y=[];S=[];sum1=0;z=0;sumlaser=0;sumnolaser=0;avglaser=0;avgnolaser=0;lasersubback=0;Inj=[];sumInj=0;avgInj=0;z1=0;z2=0;R=[];RB=[];sumR=0;sumRB=0;avgR=0;avgRB=0;RC=0;No=0;a=0;a1=0;a2=0;a3=0;a4=0; c1=63;b1=75; d=b1-c1+1; c2=100;b2=100; %centre Position ILX = 25; ILY=101; %Create X and Y axis from reference picture information. PS = 1/15.05; XL = 0-ILX; XH = 319-ILX; YL = 0-ILY; YH = 175-ILY; Y=PS*YL:PS:PS*(YH-1); X=PS*XL:PS:PS*(XH-1); for i=c1:b1 x=0;y=0;z=0;z2=0;sumR=0;sumRB=0;avgR=0;avgRB=0;RC=0;No=0;a=0;a1=0;a2=0;%091807OUF1IP3CA3SAT07% x= imread(strcat('E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\091807OUF1IP3CA3SAT06\35barlasertunedon283nm_00',num2str(i),'A','.tif')); x=double(x); sumlaser=sumlaser +x; y= imread(strcat('E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\091807OUF1IP3CA3SAT06\35barlasertunedon283nm_00',num2str(i),'B','.tif')); y=double(y); sumnolaser=sumnolaser +y; %S=x{i}-y{i}; %sum1=sum1+S{i}; z=x-y; z(find(z<0))=0; figure(i) h = ones(5,5) / 25; z2 = imfilter(z,h,'conv'); %h = fspecial('gaussian'); %z2 = imfilter(z,h); z2=z2(56:148,25:319); z2=z2./laseravgnorm; %laser sheet profile variation corrected, spatial variation in intensifier is also corrected here z3=z2; a3=(1.59*z2)*Factor*1e-15; X1=X(25:319);

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Y2=Y(56:148); [c,h]=contour(X1,Y2,a3,[180 240 300 360 430 520 600]); axis([-1.5 max(X1) min(Y2) max(Y2)]); %colormap(gray); colormap(jet); h=colorbar('horiz'); set(h,'Fontsize',18); %colorbar; %clabel(c,'manual'); hold on; rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); set(gca,'Fontsize',18) ; set(gca,'yaxislocation','right'); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); title('Number Density of OH (10^1^5 molecules/cm^3)'); axis equal axis manual %axes('Position',[-1.5,-4,22.5078,8]) %axis tight %colormap gray set(gcf,'paperposition',[0.4 4 7 3.5]) ; grid on set(gcf, 'color', 'white'); %set(gcf,'Position',[200 200 800 300]); %M(i)=getframe(gcf); %saveas(gcf,'MolefractionOH7bar1','tif'); %saveas(gcf,'MolefractionOH7bar1','fig'); %figure(i+1) saveas(gcf,strcat('E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\InstOH35bar',num2str(i),'.tif')); end z=0;avglaser=0;avgnolaser=0;a4=0; avglaser=sumlaser/d; avgnolaser=sumnolaser/d; z=avglaser-avgnolaser; %z=sum1/d; z(find(z<0))=0; figure(i+1) h = ones(5,5) / 25;

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z2 = imfilter(z,h,'conv'); %h = fspecial('gaussian',[0 0]); %z2 = imfilter(z,h); z2=z2(56:148,25:319); z2=z2./laseravgnorm;%laser sheet profile variation corrected, spatial variation in intensifier is also corrected here %z2=z2./laseravgwnorm; %a4=z2*Factormf; a4=(1.59*z2)*Factor*1e-15; %a4=(z2)*Factor*1e-15; X1=X(25:319); Y2=Y(56:148); %Y1=Y(34:143); [c,h]=contour(X1,Y2,a4,[180 240 300 360 430 520 600]); %[c,h]=contour(X1,Y2,a4,[0.0001 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 ]); axis([-1.5 max(X1) min(Y2) max(Y2)]); %colormap(gray); colormap(jet); h=colorbar('horiz'); set(h,'Fontsize',18); %colorbar %clabel(c,'manual'); hold on; rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); set(gca,'Fontsize',18) ; set(gca,'yaxislocation','right'); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); title('Number Density of OH (10^1^5 molecules/cm^3)'); axis equal axis manual set(gcf,'paperposition',[0.4 4 7 3.5]) ; grid on set(gcf, 'color', 'white'); saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\36bar\Absolutedensity36bar\AvgOH35bar','tif'); %OH absorption a4re=0; a4re=reshape(a4,1,prod(size(a4))); levels=min(roundn(a4re,0)):1:max(roundn(a4re,0)); N=hist(a4re, levels);

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avgdensity = sum(levels(20:length(N)).* N(20:length(N)))/sum(N(20:length(N))) figure(199) plot(levels,N,'o') grid on %(I/Io)=exp(-h*nu* B12*N*dy) OHabsorppercent = exp(-6.636e-34*1.06e15*mean(sumfbB12)*mean(Ove)*avgdensity*1e15*0.1) % shotnoise a4r=z3; %a4r=x-y; %a4r=a4r(56:148,25:319); a4r(find(a4r<0))=0; a4r=a4r./laseravgnorm; %a4r=a4r./laseravgwnorm; a4r=(1.59*a4r ); a4r=reshape(a4r,1,prod(size(a4r))); levels1=min(roundn(a4r,0)):1:max(roundn(a4r,0)); N1=hist(a4r, levels1); avgphoton=sum(levels1(50:length(N1)).* N1(50:length(N1)))/sum(N1(50:length(N1))) figure(200) plot(levels1,N1,'o'); grid on %Uncertanities %shot noise Ushotnoise = (sqrt(avgphoton)/avgphoton)*100 %Photon Calibration UPhotonCalib = 2.9 %(0.0286/1.59)*100=1.8, irradiance= 2.3 %Shot to shot power %fluctuation(E:\aravind7\OHPLIF\AfterProposal\092407laserprofile\laserenergy) UPowerfluc = (0.10/0.89)*100 %Laser absorption Ulaserabs=(1-OHabsorppercent)*100 %Absorption Coefficient Uabsorp= (std(sumfbB12)/mean(sumfbB12))*100 %Overalp Uoverlap = (std(Ove)/mean(Ove))*100 %Ovelap line shift Uoverlapshift =100*(mean(Ove)-0.1265)/mean(Ove) %Collisonalquench rate UQo= (std(Qo)/mean(Qo))*100 %Pixel Area Upixarea= 2.8 UFilter=6.3 %Laser spatial homogenity all the points = 5.8664 ULaSpatial=5.9

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UTotalrms = sqrt(Ushotnoise^2 + UPhotonCalib^2+ UPowerfluc^2 + Ulaserabs^2 + Uabsorp^2 + Uoverlap^2 + Uoverlapshift^2 + UQo^2 +Upixarea^2 +UFilter^2 +ULaSpatial^2)

Mean position of reaction zone – 37 bar

for r=1:295 for c=1:47 if a3(c,r)== max(a3(1:47,r)) width(r)= Y2(c); end; end; end; for r=1:295 for c=47:93 if a3(c,r)== max(a3(47:93,r)) width1(r)= Y2(c); end; end; end; r=1:300; figure(12) plot(X1(12:295),width(12:295),'--k',X1(12:295),width1(12:295),'k'); hold on; rectangle('Position',[-1.5,-0.6,1.5,1.2],'Facecolor',[0.5 0.5 0.5]); rectangle('Position',[-1.5,-1.3435,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); rectangle('Position',[-1.5,1.1,1.5,0.2435],'Facecolor',[0.8 0.8 0.8]); %text text(-1.5,0,'O_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,-1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); text(-1.5,1.22175,'H_2\rightarrow','HorizontalAlignment','right','FontSize',18); set(gca,'Fontsize',18) ; set(gca,'yaxislocation','right'); xlabel('Height (mm)','fontsize',18); ylabel('Width (mm)','fontsize',18); legend('Mean reaction zone lower', 'Mean reaction zone upper'); axis([-1.5 max(X1) min(Y2) max(Y2)]); axis equal axis manual set(gcf,'paperposition',[0.4 4 7 3.5]) ; grid on set(gcf, 'color', 'white'); saveas(gcf,'E:\aravind7\OHPLIF\AfterProposal\091807OUF1IP3CA3SAT\InstOH35barmf06\LOS37bar','tif'); Equation Section 2

154

APPENDIX B PROPOSED NEW METHODOLOGY FOR PHOTON CALIBRATION

As explained in the OH-PLIF diagnostics in Chapter 4, the photons from fluorescing OH

are captured by ICCD camera which has a photon detection efficiency of 12 % at 310 nm. The

ICCD camera provides the detected photons in counts which is an arbitrary unit.

The arrival of photons on an average is Poisson distributed when a light source emits

photons at a constant rate. In this case a 10 W dc Tungsten-halogen lamp was chosen for

calibration. The calibration setup is shown in Figure B-1. A filter with transmission efficiency of

70% at 532 and FWHM of 10+2 nm was used to block all other radiations. The camera has

photon detection efficiency of 50 % at 532 nm when compared to the photon detection efficiency

of 12% at 310 nm.

NP

10 W dc light source

532 nm filterε = 70 %

lens

Photon detection(532nm)ε = 50 %

NP = Number of photons Photocathode

Micro Channel Plate (MCP)

Phosphor

NC

CCD chip

Camera

NC = CountsNP

10 W dc light source

532 nm filterε = 70 %

lens

Photon detection(532nm)ε = 50 %

NP = Number of photons Photocathode

Micro Channel Plate (MCP)

Phosphor

NC

CCD chip

Camera

NC = Counts

Figure B-1. Calibration set-up for photon calibration

The photocathode detects the photons and emits photoelectrons. The photoelectrons are

accelerated and amplified in the micro channel plate (MCP), a process referred to as gain. The

amplified photoelectrons bombard the phosphor emitting photons. In turn, theses photons are

155

detected by the CCD chip and are read out in arbitrary units called counts. The purpose of the

photon/camera calibration is to obtain the number of photons that originally arrived at the

photocathode from the arbitrary unit counts. At 532 nm, the number of photons, pN is related to

the number of counts cN by

p transmission(532) photon detection(532) (MCP,Phosphor, CCD) cN x 0.7 x 0.5 x k N= (B-1)

where (MCP,Phosphor, CCD)k represent the constant which is unknown. The expression in Equation B-1

can be rearranged in terms of CN as

( )

cp

transmission photon detection (MCP,Phosphor, CCD)

NN

0.7 x 0.5 x k= (B-2)

Also pN can be expressed as

p 532 cN K N= (B-3)

where 532K is the calibration constant at 532 nm given by

( )532transmission photon detection (MCP,Phosphor, CCD)

1K0.7 x 0.5 x k

=

Since p 532 cN K N= ,

532 CP2

P 532 C

K x Mean (N )Mean(N ) =

Variance(N ) K x Variance (N ) (B-4)

For Poisson distribution, the mean and the variance are equal. Since the photons are Poisson

distributed, P PMean(N ) = Variance(N ) .

Hence from Equation B-4 the expression for 532K can be derived and expressed as

C532

C

Mean (N )K

Variance (N )= (B-5)

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Once 532K is known, the calibration constant at 310 nm is calculated as

310 5320.7 x 0.5K = K

0.55 x 0.12 (B-6)

A 32x32 pixel area in the camera sensor was selected for the calibration. A set of 900

images were taken at exposure times of 20, 60, 100, 140, 180, 220, 260 and 300 ns. The 10 W dc

lamp source emits photons at a constant rate. In order to calibrate the camera over a range of

counts the exposure time of the camera was varied from 20–300 ns thereby detecting more

photons and hence higher counts.

1

2

3

900

32

32

1

2

3

900

32

32

Figure B-2. A series of 900 images of 32x32 pixel size was obtained at each exposure

For a fixed exposure time corresponding to a value of fixed count, Nc the calibration

constant 532K was calculated out of the 900 images at each pixel location. One out of the 32x32

pixels (centre one), has been highlighted. The calibration constant is similarly obtained for all

other pixel locations and the average of the 532K obtained for a particular exposure time

/particular counts from the 32x32 pixel matrix is represented as the corresponding average value.

157

Thus the average calibration constant 532K for the series of 20-300 ns exposure time (series of

counts) were obtained.

The distribution of the number of photons at the central pixel location highlighted in

Figure B-2 for 900 images at exposure time of 300 ns is calculated from exp osure300p 532 CN =K N

ns and

is shown in Figure B-3

120 140 160 180 200 220 2400

5

10

15

20

25

30

35

40

Mean = 175

σ2 = 175

Photons

N

Poisson FitData

Figure B-3. A series of 900 images of 32x32 pixel size was obtained each exposure

The photons that arrived over a set of 900 acquisitions are shown in Figure B-3. The mean

and the variance of the 900 acquisitions are 175. The Poisson fit with a mean and variance of 175

is also shown in the plot. For each exposure time the average of the counts of 900 images and 32

x 32 pixels was calculated and is plotted against the corresponding exposure time (ns) as shown

in Figure B-4.

158

0 50 100 150 200 250 300 3500

500

1000

1500

2000

2500

exposure(ns)

Cou

nts

Counts vs exposure at 532 nm

Mean CountMean Count + StdMean Count - StdLinear fit

Figure B-4. Counts vs exposure time at 532 nm

From the average 532K for the series of counts, the corresponding average 310K was found

out. The corresponding number of photons at 310 nm were calculated and plotted against the

number of counts and is shown in Figure B-5.

0 500 1000 1500 20000

200

400

600

800

1000

1200

1400

1600

1800

Counts

Phot

ons

Camera Calibration at 310 nm

y = 0.66247 *x

Data PhotonsLinear fit

Figure B-5. Photons vs counts at 310 nm

159

The photon calibration obtained from the proposed new methodology is Np= 0.663*Nc.

The uncertainty in the photon calibration which is due to the non-linearity associated with the fit

and accounted to 5%.

The photon calibration obtained from conventional calibration shown in Figure 4-6 was Np

= 1.59 * Nc and is higher by a factor of 2.4 when compared to the calibration obtained from the

proposed new methodology. The relatively low value predicted by the new method is attributed

to the systematic and random variation of pixel intensities from the camera sensor that could

have potentially affected the mean and variance of the Poisson distribution leading to errors. But

compared to the conventional method of photon calibration, the proposed new methodology does

not require costlier equipment like a light source of known irradiance.

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APPENDIX C OH ABSORPTION PROFILES

OH Absorption Profiles at 10 bar and 2500–3500 K Temperature Range

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Figure C-1. Absorption profile of OH simulated using LIFBASE at equivalence ratio of (a) 0.5, (b) 1, (c) 1.5, (d) 2, (e) 2.5 and (f) 3 corresponding to temperatures of 2500–3500 K for gaseous H2-O2 flame at 10 bar.

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Figure C-3 Absorption profile of OH simulated using LIFBASE at equivalence ratio of (a) 0.5,

(b) 1, (c) 1.5, (d) 2, (e) 2.5 and (f) 3 corresponding to temperatures of 2500–3500 K for gaseous H2-O2 flame at 37 bar.

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0.9

1

ν (cm-1)

(a.u

)


(c)

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 10

4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)


(d)

171

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 10

4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)


(e)

3.5328 3.533 3.5332 3.5334 3.5336 3.5338 3.534 3.5342x 10

4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ν (cm-1)

(a.u

)


(f)


172

APPENDIX D OH NUMBER DENSITY CONTOURS

Thirteen Instantaneous OH Number Density Contours at 10 bar

(a)

(b)

(c)

173

(d)

(e)

(f)

174

(g)

(h)

(i)

175

(j)

(k)

(l)

176

(m)

Figure D-1. Thirteen instantaneous OH number density contours at near steady state chamber

pressure of 10 bar; (a)-(m).


(a)

(b)

177

(c)

(d)

(e)

178

(f)

(g)

(h)

179

(i)

(j)

(k)

180

(l)

(m)



Thirteen Instantaneous OH number Density Contours at 37 bar

(a)

181

(b)

(c)

(d)

182

(e)

(f)

(g)

183

(h)

(i)

(j)

184

(k)

(l)

(m)



185


(a)

(b)

(c)

186

(d)

(e)

(f)

187

(g)

(h)

(i)

188

(j)

(k)

(l)

189

(m)



190

APPENDIX E TEMPERTURE MEASUREMENTS AND BOUNDARY CONDITIONS

The wall heat flux boundary conditions for 37 bar were calculated from temperature

measurements along the chamber wall. The chamber wall temperatures at inner and middle

locations defined in Figure 3-3 are shown in Figure E-1 and E-2.

0 2 4 6 8 10 12 1420

40

60

80

100

120

140

160

180

200

220

time(s)

Tem

pera

ture

(o C)

Tinner 37Tinner 47Tinner 58Tinner 70Tinner 89Tinner 102

Figure E-1. Chamber wall temperatures vs time at inner locations of 37, 47, 58, 70, 89 and 102 mm from the injector face

0 2 4 6 8 10 12 1420

40

60

80

100

120

140

160

180

200

220

time(s)

Tem

pera

ture

(o C)

Tmiddle 37Tmiddle 47Tmiddle 58Tmiddle 70Tmiddle 89Tmiddle 102

Figure E-2. Chamber wall temperatures vs time at middle locations of 37, 47, 58, 70, 89 and 102 mm from the injector face

191

The axial temperatures recorded at the end of 8 s for both the inner and middle locations

along the chamber wall are plotted in Figure E-3 indicating that negligible axial gradient exists in

the upstream of 37 mm and downstream of 102 mm locations, thus justifying the selection of the

37 to 102 mm domain for analysis.

20 40 60 80 100 120 14080

100

120

140

160

180

200

220

Distance from Injector Face (mm)

Tem

pera

ture

(o C

)

Tinner ExpTmiddle Exp

3D Heat Flux Calculation

Figure E-3. Chamber wall temperatures at inner and middle locations along the chamber wall at end of the 8 s

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time(s)

Nor

mal

ized

uni

t

Figure E-4. Exponential function assumed for heat flux evolution with time

192

The evolution of heat flux with time was assumed to be an exponential function as shown

in Figure E-4 to match the experimental temperatures as well as the slopes of the temperatures

rises for the 37 bar case.

The heat flux was subjected to iteration until the experimental and computational

temperatures matched within 5–6 oC as shown in Figure E-5 to E-10. and indicate the computed

and experimental values at each axial location as time dependent functions.

0 1 2 3 4 5 6 7

50

100

150

200

250

300

time(s)

Tem

pera

ture

(o C)

Computation innerExperiment innerComputation MiddleExperiment Middle

Figure E-5. Experimental and computational temperatures at 37 mm axial location

0 1 2 3 4 5 6 7

50

100

150

200

250

300

time(s)

Tem

pera

ture

(o C)



193

0 1 2 3 4 5 6 7

50

100

150

200

250

300

time(s)

Tem

pera

ture

(o C)



0 1 2 3 4 5 6 7

50

100

150

200

250

300

time(s)

Tem

pera

ture

(o C)



194

0 1 2 3 4 5 6 7

50

100

150

200

250

300

time(s)

Tem

pera

ture

(o C)



0 1 2 3 4 5 6 7

50

100

150

200

250

300

time(s)

Tem

pera

ture

(o C)



The heat fluxes thus determined in the axial direction are shown in Figure C-11 along

with the heat flux calculated from the linear+ unsteady term assumption in Equation 3-1. The

recent heat transfer studies conducted by Marshall et al [75] and Conley et al [76] used the linear

+ unsteady calculation for determining heat fluxes. It can be seen from Figure E-11 that both

calculations based on 3D computations and linear assumption showed the same trend, the heat

fluxes determined from the latter being relatively low compared to that from the former.

195

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4


Hea

t Flu

x (M

W/m

2 )

Heatflux Computational 3DHeatflux Linear

Figure E-11. Chamber wall heat fluxes calculated based on 3D computations and linear + unsteady assumption at 37 bar

The heat flux has a peak value at 70 mm indicating the location of shear layer re-

attachment. The matching of experimental and computational temperatures at the end of 8 s for

37 bar are also shown in Figure E-12.

20 40 60 80 100 120 14080

100

120

140

160

180

200

220


Tem

pera

ture

(o C

)

Tinner ExpTinner CompTmiddle ExpTmiddle Comp

Figure E-12. Computational and Experimental Temperatures for 37 bar at the end of 8s.

196

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BIOGRAPHICAL SKETCH

Aravind Vaidyanathan hails from Thiruvananthapuram, the lush green capital city of the

southern state Kerala in India. He received his bachelor’s degree in mechanical engineering from

University of Kerala, India in 2003. In 2005, he received his master’s degree in aerospace

engineering from Indian Institute of Technology–Madras, India, specializing in mixing studies in

supersonic flow. In the same year, he joined University of Florida to pursue a PhD in aerospace

engineering, specializing in OH-PLIF measurements in high pressure combustion. His research

interests include high speed gas dynamics, high pressure combustion, and laser-based flow

diagnostics.

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