Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Saca, Leslie
Master of Applied Science - MASc
University of British Columbia
This thesis is concerned with the characterization of an industrial injector, whose modus operandi is turbulent stratified premixed combustion. For this mode of operation, the fuel and air are premixed at molecular level; however, the fuel-air equivalence ratio varies locally at larger scales. A burner was designed and manufactured to house a gaseous fuel/air injector, which was provided by the industrial partner. Both fully and stratified premixed flames of methane and air were tested for a range of mean bulk flow velocities varying between 5 and 50 m/s. The (global) fuel-air equivalence ratio of the (stratified) premixed flames was set to unity. The cross-wire anemometry technique was used to characterize the background turbulent flow; and, the laser Rayleigh scattering technique was employed to investigate both the fuel and air mixedness fields as well as the turbulent flames characteristics. Near the center of the injector lobes, a hydrodynamic instability exists and is accentuated as the mean bulk flow velocity is increased. Analysis of mixedness fields suggests that the amount of the injected fuel is similar for both lobes up to 25 m/s; however, the lobe on the left-hand-side injects more fuel compared to that on the right-hand-side for mean bulk flow velocities larger than or equal to 25 m/s. Traditionally, studying the flame structure for fully and stratified premixed flames requires information regarding the mixture composition across the flame, whose acquisition is challenging. To overcome this challenge, a new parameter, referred to as the reduced temperature was introduced and quantified. It was shown that the probability density function of this parameter is similar for all tested conditions, and was used to develop a method for quantifying the burning area of the tested flames. Assuming that the flame stretch is not significant, it is obtained that stratification can slightly increase the normalized flame burning area. This is in agreement with the results presented in [1]; however, those presented here extends the findings of [1] to conditions that are more industrially relevant.
A new framework for analysis offully-premixed and stratified turbulentflames generated by an industrialinjectorbyLeslie SacaB.Sc., The University of British Columbia, 2020A thesis submitted in partial fulfillment ofthe requirements for the degree ofMASTER OF APPLIED SCIENCEinThe College of Graduate Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)May 2022© Leslie Saca, 2022The following individuals certify that they have read, and recommend to the College ofGraduate Studies for acceptance, a thesis/dissertation entitled:A new framework for analysis of fully-premixed and stratified turbulent flames generated byan industrial injectorsubmitted by Leslie Saca in partial fulfillment of the requirements of the degree ofMaster of Applied ScienceDr. Sina Kheirkhah, UBC, School of EngineeringSupervisorDr. Sunny Li, UBC, School of EngineeringSupervisory Committee MemberDr. Joshua Brinkerhoff, UBC, School of EngineeringSupervisory Committee MemberDr. Zheng Liu, UBC, School of EngineeringUniversity ExamineriiAbstractThis thesis is concerned with the characterization of an industrial injector, whose modusoperandi is turbulent stratified premixed combustion. For this mode of operation, the fuel andair are premixed at molecular level; however, the fuel-air equivalence ratio varies locally atlarger scales. A burner was designed and manufactured to house a gaseous fuel/air injector,which was provided by the industrial partner. Both fully and stratified premixed flames ofmethane and air were tested for a range of mean bulk flow velocities varying between 5 and50 m/s. The (global) fuel-air equivalence ratio of the (stratified) premixed flames was set tounity. The cross-wire anemometry technique was used to characterize the background turbulentflow; and, the laser Rayleigh scattering technique was employed to investigate both the fueland air mixedness fields as well as the turbulent flames characteristics. Near the center ofthe injector lobes, a hydrodynamic instability exists and is accentuated as the mean bulk flowvelocity is increased. Analysis of mixedness fields suggests that the amount of the injected fuelis similar for both lobes up to 25 m/s; however, the lobe on the left-hand-side injects morefuel compared to that on the right-hand-side for mean bulk flow velocities larger than or equalto 25 m/s. Traditionally, studying the flame structure for fully and stratified premixed flamesrequires information regarding the mixture composition across the flame, whose acquisition ischallenging. To overcome this challenge, a new parameter, referred to as the reduced temperaturewas introduced and quantified. It was shown that the probability density function of thisiiiparameter is similar for all tested conditions, and was used to develop a method for quantifyingthe burning area of the tested flames. Assuming that the flame stretch is not significant, it isobtained that stratification can slightly increase the normalized flame burning area. This is inagreement with the results presented in [1]; however, those presented here extends the findingsof [1] to conditions that are more industrially relevant.ivLay SummaryThe present thesis contributes to both, the development of an industrial injector that is usedin large-scale power generation gas turbine engines as well as producing knowledge for combus-tion science. As for the former, aerodynamic, mixing, and combustion characteristics of theinjector are investigated. As for the latter, a method is developed and tested that allows forstudying the burning area of both premixed an stratified flames. This is of significant impor-tance, as the developed method does not utilize a model/prior detailed combustion chemistryinformation for understanding the flame structure.vPrefaceThe research presented in this thesis was conducted by the author under the supervisionof Professor Sina Kheirkhah in the Combustion for Propolusion and Power Laboratory at TheUniversity of British Columbia, Okanagan campus. The injector of the experimental apparatuswas provided by Siemens Energy Canada Ltd. Parts of this thesis were presented in the AIAAconference in January 2022 [2].viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Laminar premixed flames . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Turbulent premixed flames structure . . . . . . . . . . . . . . . . . . . . . 4viiTABLE OF CONTENTS1.2.3 Turbulent burning velocity of premixed flames . . . . . . . . . . . . . . . 81.2.4 Stratified flames structure and burning rate . . . . . . . . . . . . . . . . . 121.3 Thesis objectives and organization of the chapters . . . . . . . . . . . . . . . . . 17Chapter 2: Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1 Burner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3 Tested conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Chapter 3: Non-reacting turbulent flow characteristics . . . . . . . . . . . . . . 38Chapter 4: Non-reacting flow mixedness characteristics . . . . . . . . . . . . . 44Chapter 5: Reacting flow characteristics . . . . . . . . . . . . . . . . . . . . . . . 50Chapter 6: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.1 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Appendix A: Technical drawings of the burner . . . . . . . . . . . . . . . . . . . 83Appendix B: The relation between the fuel-air equivalence ratio and the mea-sured Rayleigh scattering signal . . . . . . . . . . . . . . . . . . . . . 89Appendix C: Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 92viiiList of TablesTable 2.1 Calculated polynomial coefficients for curves shown in Fig. 2.5. . . . . . . 25Table 2.2 The reacting flow tested conditions. For all tested conditions, the globalfuel-air equivalence ratio is 1. U , SL0, u′, and v′ are in m/s, and Lu, lT, andηK are in mm. For all tested conditions, SL0 = 0.37 m/s and δL = 0.17 mm. 36ixList of FiguresFigure 1.1 The normalized variations of combustion species and true heat releaserate of a freely propagating and fully-premixed laminar stoichiometricmethane-air flame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 The regime diagram proposed in [3]. . . . . . . . . . . . . . . . . . . . . . 7Figure 2.1 Section view of the utilized burner. . . . . . . . . . . . . . . . . . . . . . 20Figure 2.2 Schematic diagram of the injector is reproduced with permission of Springer:Flow, Turbulence and Combustion, Effect of Fuel Stratification on OHand CH2O PLIF Multiplication of Turbulent Hydrogen-Enriched Flames,Mohammadnejad et al., pp. 263–301, 2021. The direction of the salientflow coincides with the y-axis of the coordinate system, also presented inFig. 2.1. The green arrows show the directions of fuel injection into thelobes and the black arrows schematically present the swirling motion ofthe flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.3 The hot-wire anemometry system presents (1) cross-wire and probe, (2)probe holder, (3 and 4) two translational stages (5) camera, and (6) amacro lens. Items (5 and 6) were used to acquire the position of thecross-wire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23xLIST OF FIGURESFigure 2.4 (a) is a picture of the probe touching the burner exit plane. (c) is a pictureof the hot wire probe and its holder. (b) and (d) are the insets of (a) and(c), respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 2.5 (a) and (b) are the calibration curves for wire 1 and wire 2, respectively. 26Figure 2.6 The Rayleigh scattering diagnostics hardware. Items (1), (2–4), (5), (6),and (7) are the laser, the optics, the camera, the lens, and a bandpassfilter, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 2.7 The percentile fluctuations of the laser energy over 50 s. . . . . . . . . . . 29Figure 2.8 (a) is an image of a burnt paper for the laser operating at it maximumpower after 30 mins of operation and at the location of measurements.(b) and (c) are the variations of the number of counts for the image in(a) for normal to and along the laser sheet directions, respectively. . . . . 30Figure 2.9 (a), (b), and (c) are the time-averaged variations of I, IN, and ICL, re-spectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 2.10 (a) is a sample of 2D variation of T ∗ and (b) is (a) after median basedfiltering. (c) is (a) with IS = 0. . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 2.11 The stability map for (a) premixed and (b) stratified flames. The cellswith the green and red colors pertain to tested conditions that lead tostable flames and blown-out flames, respectively. The cells with yellowcolor pertain to test conditions for which the flames are initially stableafter ignition, but they blow-out after a few seconds. . . . . . . . . . . . 35Figure 2.12 The tested experimental conditions overlaid on the Borghi-Peters diagram[3] for fully-premixed flames. . . . . . . . . . . . . . . . . . . . . . . . . . 37xiLIST OF FIGURESFigure 3.1 (a) and (b) are the mean of the axial and transverse components of thevelocity, respectively. (c) and (d) are the RMS of the axial and transversecomponents of the velocity, respectively. The square, circular, triangular,and diamond shaped data symbols pertain to U = 5, 20, 35, and 50 m/s,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 3.2 Effect of the mean bulk flow velocity on the dominant frequencies of theaxial and transverse velocity data collected at x = 8 mm. The verticalaxis is a logarithmic (with a base of 10) scale. . . . . . . . . . . . . . . . 41Figure 3.3 The spectral content of the (a) axial and (b) transverse velocity compo-nents for U = 50 m/s. The vertical axis is a logarithmic (with a base of10) scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 3.4 Integral (a) time and (b) length scales versus the tested mean bulk flowvelocity. The circle and square data points pertain to the axial and trans-verse components of the velocity, respectively. . . . . . . . . . . . . . . . 43Figure 4.1 The time-averaged Rayleigh scattering signals for the premixed conditionIR(x, y)P. (a–f) pertain to the helium flow-rates equal to that used formethane flow-rate with mean bulk flow velocities of 5, 15, 25, 35, 45, and50 m/s, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 4.2 The time-averaged Rayleigh scattering signals for the stratified conditionIR(x, y)S. (a–f) pertain to the helium flow-rates equal to that used formethane flow-rate with mean bulk flow velocities of 5, 15, 25, 35, 45, and50 m/s, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47xiiLIST OF FIGURESFigure 4.3 The spatial variation of R, evaluated from the LHS of Eq. (4.4). (a–f)pertain to helium flow-rates equal to that used for methane flow-rate withmean bulk flow velocities of 5, 15, 25, 35, 45, and 50 m/s, respectively. . 48Figure 4.4 Variations of RL1 and RL3 versus the mean bulk flow velocity of thecorresponding tested helium flow-rates. . . . . . . . . . . . . . . . . . . . 49Figure 5.1 (a, c, e, g, and i) are the reduced temperature fields pertaining to meanbulk flow velocities of 5, 15, 25, 35, and 45 m/s, respectively. (b, d, f, h,and k) are the binarized flame regions for mean bulk flow velocities of5, 15, 25, 35, and 45 m/s, respectively. The results are for fully-premixedflames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 5.2 (a, c, e, g, and i) are the reduced temperature fields pertaining to meanbulk flow velocities of 5, 15, 25, 35, and 45 m/s, respectively. (b, d, f, h,and k) are the binarized flame regions for mean bulk flow velocities of5, 15, 25, 35, and 45 m/s, respectively. The results are for stratified flames. 53Figure 5.3 The probability density function of the normalized flame temperature.The solid and dashed curves pertain to fully-premixed and stratified con-ditions, respectively. The results are stepped for clarity. T ∗AD is shown bythe dotted-dashed line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 5.4 Variation of the normalized burnt gas temperature versus the tested meanbulk flow velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 5.5 The normalized temperatures of the flame region. The PDF pertains tothe tested fully-premixed flames with U = 45 m/s. . . . . . . . . . . . . . 58Figure 5.6 Variations of T ∗1 and T ∗2 for all tested conditions. . . . . . . . . . . . . . . 59xiiiLIST OF FIGURESFigure 5.7 Variation of the normalized flame burning area versus the mean bulk flowvelocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 5.8 The 3D schematics of the flame structures for U = 5 and 45 m/s areshown (a) and (b), respectively. Overlaid on the figure are the speculatedtrajectories of the injected fuel/air from the neighboring lobes (L2 and L4)shown by the pink and red circular and cross data symbols, respectively. 62Figure 5.9 Normalized burning area versus the normalized turbulence intensity. Thesolid lines are the predictions of [4]. . . . . . . . . . . . . . . . . . . . . . 63Figure A.1 SolidWorks drawing of the bottom of the burner where the fuel tube isattached. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure A.2 SolidWorks drawing of the expansion section. . . . . . . . . . . . . . . . . 85Figure A.3 SolidWorks drawing of the settling chamber. . . . . . . . . . . . . . . . . 86Figure A.4 SolidWorks drawing of the retaining rings that hold the mesh screens inthe settling chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure A.5 SolidWorks drawing of the plenum. . . . . . . . . . . . . . . . . . . . . . 88Figure B.1 Variation of ϕ(x, y) versus IR(x, y)S/IR(x, y)P. . . . . . . . . . . . . . . . 91Figure C.1 The variation of PDF∗ at U = 45 m/s for values of IS = 16, 17 and18. The results in (a) and (b) are for the fully-premixed and stratifiedconditions, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93xivAcknowledgementsI would like to extend my deepest gratitude to my supervisor, Professor Sina Kheirkhah,for his constant support, encouragement, and guidance to help achieve my goals during thecompletion of this thesis. His patience in teaching and pushing me to be a better engineer hasallowed me to overcome the several challenges of our research. Research such as this would nothave been possible without his unwavering dedication and mentorship.I would like to thank my colleagues from the Combustion for Propulsion and Power Labora-tory, at the University of British Columbia, for their support. I would especially wish to expressmy sincerest gratitude to Sajjad Mohammadnejad. He always provided help and support to getme through the challenges of conducting the experiments and processing the data. Also, I wouldlike to thank Raymond Seida, School of Engineering machinist, for his great help in the designand manufacturing of the burner used for this study. He was tremendously helpful in determin-ing the best solution for any design challenges and provided me with countless opportunities forhands-on experience in the machine shop.I would like to extend further thanks to the Canada Foundation for Innovation (John EvansLeaders Fund), Siemens Energy Canada Ltd., and the MITACS Accelerate program for providingme with equipment and financial support that allowed me to focus on my research and reachmy goals. Specifically, I would like to thank Dr. Gilles Bourque and Dr. Phillippe Versailles(Siemens Energy Canada Ltd.), and Dr. Patrizio Vena (NRC) for their insightful discussionsxvand professional advice regarding my research.To my friends who have supported me through this journey, thank you for always being there.My family, for their unconditional love and encouragement. Despite the distance, I always feltyou close to my heart. Thank you, God, for the countless blessings and opportunities.xviDedicationTo my dad, for your endless love and for always believing in me.xviiNomenclatureSymbolsa1−6 Polynomial coefficients for calibration of wire 1c Mean progress variableAF Area of c surfaceAL Laminar flame surface areaAL Laminar flame burning areaAT Turbulent flame surface areaAT Turbulent flame burning areab1−6 Polynomial coefficients for calibration of wire 2Bi Bias errorc Temperature-based progress variableCH2O Formaldehyde moleculeCH2OPLIF Formaldehyde molecule PLIF signalCopt Collection optics efficiencycp Specific heatcp0 Specific heat of reactants at 1500 Kd DiameterDa Damko¨hler numberxviiiNOMENCLATUREE Laser energyEuu Power Spectrum Density of the axial velocityEvv Power Spectrum Density of the transverse velocityf Focal lengthf1−3 Dominant frequenciesh Vertical distance along y-axis for calculation of Luh∗ Smallest vertical distance along y-axis where Ruu becomes zeroI0 Bray-Cant stretch factorICL Rayleigh scattering intensity due to flame chemiluminescenceIi Rayleigh scattering intensity due to incident laserIi,Ref Rayleigh scattering intensity for the Reference conditionIN Rayleigh scattering intensity due to the electric noiseIR Rayleigh scattering signalIR(x, y)P Measured Rayleigh scattering signal for premixed conditionIR(x, y)S Measured Rayleigh scattering signal for stratified conditionIR,air Rayleigh scattering intensity from airIR,He Rayleigh scattering intensity from heliumIR,ref Rayleigh scattering intensity for the reference conditionIS Background Rayleigh scatteringk Boltzmann constantk1 Calibration coefficient for wire 1K1 Parameter used in Eqs. (4.3 and B.3–B.5)k2 Calibration coefficient for wire 2xixNOMENCLATUREK2 Parameter used in Eqs. (B.3–B.5)Ka Karlovitz numberL1, L3 LHS and RHS lobes, respectively∆L Averaged length of the flame frontLe Lewis numberlT Taylor length scaleLu Integral length scale evaluated from the axial velocityLv Integral length scale evaluated from the transverse velocityL Markstein lengthm˙R Mass flow-rate of reactantsnLE Vector normal to the direction of the leading edgenfft The number of points for the Fast Fourier Transform calculationOH Hydroxyl radicalOHPLIF Hydroxyl radical PLIF signalP Pressureq′ The Root Mean Square of velocities in a 3D fieldR(x, y) Mixedness parameterrc Local radius of the flame frontRL1 R spatially averaged for the left-hand-side lobeRL3 R spatially averaged for the right-hand-side lobeReT Turbulent Reynolds numberS Stratification ratioSe Precision errorxxNOMENCLATURESL Stretched laminar flame speedSL0 Unstretched laminar flame speedST,GC Global consumption speedST,LC Local consumption speedST,LD Displacement speed∆S Averaged area of the flame sheett Timeth Threshold parameterT TemperatureTref Reference temperatureTAD Adiabatic flame temperatureT ∗ Normalized temperatureT ∗1 Lower bound normalized temperatureT ∗2 Upper bound normalized temperatureT ∗AD Normalized adiabatic flame temperatureT ∗B Normalized temperature of the burnt gasT ∗M Normalized temperature at which the PDF attains a local minimum valueT ∗R Normalized temperature of the reactantsu Instantaneous gas velocity in the vertical directionu′ Root Mean Square of uU Mean bulk flow velocityU1 Flow velocity in wire 1 frame of referenceU0.95 Total uncertainty with a 95% confidence levelxxiNOMENCLATUREU2 Flow velocity in wire 2 frame of referenceU ′1 Flow velocity U1 corrected for the effect of orientation of wire 1U ′2 Flow velocity U2 corrected for the effect of orientation of wire 2v Instantaneous gas velocity in the transverse directionv′ Root Mean Square of vV1 Calibration mean voltage of the first wireV2 Calibration mean voltage of the second wireVFLAME Flame velocity vectorVGAS Gas velocity vectorw′ Root Mean Square of velocity fluctuations in z directionx Axis normal to streamwise direction∆x Side lengthy Axis normal to the streamwise directionZ Position across a freely propagating laminar flameGreek symbolsα0 Thermal diffusivity of reactants at 1500 KδL Laminar flame thicknessδPHZ Preheat zone thickness of a laminar flameδRZ Reaction zone thickness of a laminar flameη The curvilinear axisηK Kolmogorov length scaleλ0 Thermal conductivity of reactants at 1500 KρR Density of the reactants at room temperaturexxiiNOMENCLATUREρu Auto-correlation of the streamwise velocityρv Auto-correlation of the transverse velocityσair Rayleigh scattering cross section of airσF Rayleigh scattering cross section of the fuelσHe Rayleigh scattering cross section of heliumσN2 Rayleigh scattering cross section of nitrogenσO2 Rayleigh scattering cross section of oxygenσmix Mixture Rayleigh scattering cross sectionσmix,ref Mixture Rayleigh scattering cross section for the reference conditionΣ Flame surface densityτu Integral time scale estimated from axial velocityτv Integral time scale estimated from transverse velocityϕ Fuel-air equivalence ratioχair Mole fraction of airχO2 Mole fraction of oxygenχN2 Mole fraction of nitrogenχF Mole fraction of the fuelχF,P Mole fraction of the fuel for premixed conditionχF,S Mole fraction of the fuel for stratified conditionAbbreviationsDNS Direct Numerical SimulationFFT Fast Fourier TransformFOV Field Of ViewxxiiiNOMENCLATUREFWHM Full Width at Half MaximumHWA Hot-Wire AnemometryHRR Heat Release RateLHS Left-Hand-SideLE Leading Edgemini-CTA Mini-Constant Temperature AnemometerNd:YAG Neodymium, Yttrium, Aluminum, and GarnetPIV Particle Image VelocimetryPDF Probability Density FunctionPLIF Planar Laser-Induced FluorescencePSD Power Spectrum DensityRHS Right-Hand-SideRMS Root-Mean-SquaresCMOS scientific Complementary Metal–Oxide–SemiconductorSLPM Standard Litre Per MinuteSNR Signal to Noise RatioxxivChapter 1Introduction1.1 MotivationGas turbine engine combustors used for land-based power generation usually operate underthe mode of partially premixed combustion [5]. This mode of operation offers two advantages.First, partial premixing of fuel and air can feature improved combustion instabilities charac-teristics (which are mostly pronounced for fully-premixed flames [6]). Second, compared tonon-premixed flames, partial premixing of fuel and air helps reduce the burnt gas temperature,and as a result, the pollutants formation and emission [7]. Although characteristics of partiallypremixed flames have been a matter of research over the past decades and several review papershave been published (see for example [5, 8]), the understanding related to the effect of strat-ification (i.e., the spatial variation of the fuel-air equivalence ratio) on the internal structureof flames is limited and requires further investigations. Developing such understanding is ofsignificant importance since the flame internal structure can influence its burning rate, which isan important parameter for design and development of gas turbine engine combustors.The present thesis is concerned with premixed flames and a category of partially-premixedflames, referred to as stratified flames. Similar to premixed flames, stratified flames featurefuel and air mixing at molecular levels. However, compared to premixed flames that feature aspatially uniform fuel-air equivalence ratio (ϕ), this parameter can vary spatially for stratified11.2. BACKGROUNDflames at large scales. In the following, the background related to both premixed and stratifiedflames is reviewed. The literature related to both laminar and turbulent premixed flames, aswell as laminar and turbulent stratified premixed flames is discussed.1.2 BackgroundThis section has been divided into four subsections. The details related to laminar premixedflames, turbulent premixed flames, turbulent burning velocity and stratified flames structureand burning rate is discussed in subsections 1.2.1, 1.2.2, 1.2.3 and 1.2.4, respectively.1.2.1 Laminar premixed flamesLaminar premixed flames characteristics serve as a benchmark for comparisons with tur-bulent counterparts, and as a result, the laminar premixed flames are extensively used andcharacterized in the literature. For example, the temperature and several species mole fractionsof atmospheric methane-air flames (relevant to this thesis) can be accurately estimated using theCantera package [9]. Using the GRI Mech. 3.0, the temperature and heat release rate variationsnormalized by the corresponding maximum values across (along Z direction) a stoichiometricfully-premixed atmospheric methane-air flame are presented in Fig. 1.1 using dark blue andpink colors, respectively. In addition to temperature and heat release rate variations, those offormaldehyde molecule (CH2O) and hydroxyl (OH) radical are important, as they relate to theflame structure [10–13]. Specifically, the preheat (δPHZ) and reaction (δRZ) zones thicknessesand/or the relations between the chemical species and temperature are used for understandingthe flame structure [13, 14]. The former is of relevance to this thesis. Several diagnostics, e.g.the Planar Laser-Induced Fluorescence (PLIF) of hydroxyl radical and formaldehyde molecule21.2. BACKGROUND[11, 15, 16] as well as the Rayleigh scattering [11, 17], are used in the literature to measure thefully-premixed flames preheat and reaction zones thicknesses. The mole fraction and tempera-ture obtained from the laminar flames simulations can be used to generate synthetic PLIF ofOH, referred to as OHPLIF and PLIF of CH2O, referred to as CH2OPLIF using the formulationsprovided in [18]. The variations of CH2OPLIF (dark green color) as well as OHPLIF × CH2OPLIF(cyan color) are used for measuring the preheat and reaction zones thicknesses in the literature,with the corresponding variations obtained for an atmospheric stoichiometric freely propagatingfully-premixed laminar methane-air flame presented in Fig. 1.1. In past investigations [19, 20],δRZ is defined as the Full-Width at Half Maximum (FWHM) of OHPLIF × CH2OPLIF, whichis highlighted in Fig. 1.1. The leading edge of the preheat zone is obtained using 35% of themaximum CH2O PLIF signal (closer to the reactants) and the trailing edge of this zone is set tothe leading edge of the reaction zone, see for example [20–22]. The distance between the leadingand trailing edge of the preheat zone is the preheat zone thickness and is highlighted in Fig. 1.1.9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.400.20.40.60.81Fig. 1.1. The normalized variations of combustion species and true heat release rate of a freelypropagating and fully-premixed laminar stoichiometric methane-air flame.31.2. BACKGROUNDCompared to the PLIF technique, other laser-based diagnostics, such as the Rayleigh scat-tering, are also used [21, 23, 24] for estimation of the preheat and reaction zones thicknesses. Inorder to do this, a temperature-based combustion progress variable (c) is used, which is givenbyc =T − TRTAD − TR , (1.1)where TR and TAD are the fresh reactants and the adiabatic flame temperatures, respectively.Using the results presented in Fig. 1.1, the progress variable at the borders of the preheat andreaction zones can be extracted and used for estimation of δPHZ and δRZ. For example, for anatmospheric and stoichiometric freely propagating laminar premixed flame of methane and air,c = 0.15, 0.56, and 0.79 correspond to the leading edge of the preheat zone, trailing edge of thepreheat zone (also the leading edge of the reaction zone), and the trailing edge of the reactionzone, respectively. A similar procedure is followed in for example [24] for atmospheric premixedflames of methane and air with ϕ = 1. In [24], the leading edge of the preheat zone, the trailingedge of this zone, and the trailing edge of the reaction zone are selected as c = 0.1, 0.6, and0.85, respectively.1.2.2 Turbulent premixed flames structureThe present thesis is concerned with the thickness of the turbulent premixed flames aswell as how fast the reactants are converted to combustion products, which is referred to asthe burning rate/turbulent burning velocity in the literature. Both the flame thickness and theburning velocity are influenced by the turbulent flow characteristics. Traditionally, the turbulentpremixed flames regime diagram [10, 25] is used to study the effect of the normalized backgroundturbulent flow characteristics on the flame structure and burning rate. In the following, first, a41.2. BACKGROUNDbrief review of the regime diagram is presented. Then, the background related to the turbulentpreheat (δPHZ) and reaction (δRZ) zones thicknesses, as well as the burning rate/turbulentburning velocity are discussed.Originally, Borghi [26] developed the premixed flames diagram, and it was later modifiedby Peters [3]. Over the past decades, the diagram by Peters [3] has been modified throughthe investigations of several research groups, see for example [14, 27]. Although the studies of[14, 27] are of significant importance, the modifications proposed in [14, 27] are rather new andfurther data is required to assess the modifications proposed in [14, 27].Figure 1.2 presents the regime diagram proposed in Peters [3]. Different regimes can bedefined using the integral length scale (Lu) normalized by the laminar flame thickness (δL)and the root-mean-square (RMS) axial velocity fluctuations (u′) normalized by the unstretchedlaminar flame speed (SL0), which is obtained from Cantera [9] simulations. Please note that thework by Borghi [26, 28] indicated that the vertical axis of the regime diagram should be q′/SL0,where q′ =√u′2+v′2+w′23 . In this thesis, the conventional representation of the Borghi-Petersdiagram considering only the RMS axial velocity fluctuations u′, is used. The integral lengthscale is given byLu(x, y) =∫ h∗0Ruu(x, y, h)dh, (1.2)where x and y are the horizontal and vertical locations of the point at which the integral lengthscale is calculated. h is an integration variable and corresponds to the vertical distance. InEq. (1.2), Ruu is the auto-correlation of the velocity data [29] and is given by51.2. BACKGROUNDRuu(x, y, h) =[u(x, y)− u(x, y)] [u(x, y + h)− u(x, y + h)][u(x, y)− u(x, y)]2 , (1.3)where h∗ is the smallest vertical distance at which Ruu becomes zero. In Fig. 1.2, the laminarflame thickness is given by [10, 30, 31]δL =α0SL0, (1.4)where α0 is the thermal diffusivity and is given byα0 =λ0/cp0ρR, (1.5)with λ0 being the gas thermal conductivity and cp0 being the specific heat calculated at 1500 K.Similarly, ρR is the reactant density at 300 K [4].Of relevance to the present study and many practical applications is the thin reaction zonesregime in the diagram, see Fig. 1.2. This regime is defined using the Karlovitz number (Ka),which is given byKa =(u′SL0) 32(LuδL)− 12. (1.6)Peters [10] argued, for 1 < Ka < 100, turbulent eddies may penetrate into the preheat zone;however, the reaction zone remains intact and similar to that of a laminar flame, hence thethin reaction zones terminology. The border highlighting the upper bound of the thin reactionzones regime (Ka = 100) was obtained using scaling analysis. That is neither experimental nornumerical investigations were performed to obtain the border of Ka = 100 as the upper boundof the thin reaction zones, and there exist controversial observations in the literature regarding61.2. BACKGROUND10-1 100 101 102 10310-1100101102103data1data2data4100 101 102 103Fig. 1.2. The regime diagram proposed in [3].the upper bound of this regime.In order to assess if the turbulent premixed flames with 1 < Ka < 100, indeed, feature “thinreaction/preheat zones” many experimental investigations have been performed in the past.Since these zones geometries can be substantially different from those of a laminar flame, thepreheat and reaction zones thicknesses for turbulent flames are defined using the formulation in[22]. Specifically, Mohammadnejad et al. [22] used the ratio of the area of a given zone to half ofits perimeter to estimate a characteristic thickness. Effects of several turbulent flow parameterson the preheat and reaction zones thicknesses have been investigated in the past [13, 32–34]. Forturbulent flames with relatively small Karlovitz numbers, results of past studies [4, 13, 25, 32]71.2. BACKGROUNDshow that the preheat and reaction zones thicknesses are relatively small and similar to thosemeasured from the laminar flames. However, for relatively large Karlovitz numbers (for exampleKa ≈ 76.0), Mohammadnejad et al. [22] showed that both the preheat and reaction zonesthicknesses can increase up to 6.3 and 4.9 times the laminar flame counterparts, respectively.The reason for the values of the preheat zone thickness being large (compared to the laminarflame counterpart) is shown to be linked to the penetration of turbulent eddies into this zone [22].It is likely that the large values of the reaction zone thickness at large Karlovitz numbers is alsodue to the penetration of the eddies into this zone [22, 25, 35]. Similarly, as reported in [16, 36–40], the reaction layer can become broadened/distributed, and its thickness can increase up toseveral times that of the laminar flame. Compared to the studies of [16, 36–40], the DirectNumerical Simulations (DNS) of [41, 42] show that the penetration of eddies into the reactionzone only takes place for Ka ≈ 1200. Similar to the conclusions of [41, 42], experimentalinvestigations of [11, 13, 19] show that the reaction layer remains relatively thin for Karlovitznumbers up to 550. The reasons for the above discrepancy is a matter of discussions in theliterature. Mohmmadnejad et al. [22] measured the turbulent kinetic energy of the eddies in thefresh reactants and preheat zones and suggested that the controversial observations reported inthe literature may be due to the different turbulence generators used in past studies and thedistribution of energy between different eddy sizes.1.2.3 Turbulent burning velocity of premixed flamesThree definitions are provided in the literature for the turbulent burning velocity, see forexample the review paper by [32]. These definitions correspond to three terminologies for theturbulent burning velocity, which are the local displacement speed (ST,LD), the global consump-tion speed (ST,GC), and the local consumption speed (ST,LC). ST,LD is given by [32]:81.2. BACKGROUNDST,LD = (VFLAME −VGAS)LE · nLE, (1.7)where VFLAME is the velocity vector corresponding to a point at the flame front relative to thelab coordinate system. In Eq. (1.7), VGAS is the reactants velocity vector with respect to thelab coordinate system [32]. Both of the above velocity vectors are measured at the flame front,which is also referred to as the leading edge, hence the acronym “LE” in Eq. (1.7) [30, 32]. nLEis a unit vector normal to the leading edge and points towards the reactants.ST,GC is the rate at which the reactants are consumed and converted into products [10, 43],which is given byST,GC =m˙RρRAF, (1.8)where m˙R is the mass flow-rate of reactants, ρR is the density of the reactants evaluated at thereactants temperature and pressure, and AF is the flame surface area. AF is usually consideredto be the area corresponding to the mean progress variable of c = 0.5, however, this parametercan also be estimated at other mean progress variables, such as c = 0.2 [23].ST,LC allows to estimate the speed at which the reactants are converted to products locally.The local consumption speed is given by [44]ST,LC = SL0I0∫ ∞−∞Σdη, (1.9)where I0 is the Bray-Cant [45] stretch factor, Σ is the flame surface density, and η is a curvilinearaxis that is normal to the local c contour. The stretch factor is defined byI0 =SLSL0, (1.10)91.2. BACKGROUNDwhere SL is the speed of stretched laminar flame. It is shown in the literature [46, 47] that thestretch factor can be estimated from I0 = 1− Lrc , with L and rc being the Markstein length [48]and the local radius of the flame front, respectively.In Eq. (1.9), the flame surface density is given byΣ = lim∆x→0∆S(∆x)3, (1.11)where ∆S is the averaged area of the flame sheet that is present within a cube with a side lengthof ∆x. Since the estimation of the flame surface density using the above formulation requires3D measurement of the flames and this is experimentally challenging, an alternative definitionfor the flame surface density is used in the literature, which is given byΣ = lim∆x→0∆L(∆x)2, (1.12)where ∆L is the averaged length of the flame front inside an interrogation window, with a sidelength of ∆x. Bell et al. [49] performed DNS of a turbulent laboratory scale premixed flameand evaluated the flame surface density using Eqs. (1.11) and (1.12). They [49] showed thatthe predictions of the formulation that accounts for the 3D nature of the flames is 15–30%larger than the 2D counterpart. In addition to the above, it is shown that changing the imagingresolution for estimation of the flame surface density (obtained from the 2D measurements) canvary the flame surface density. For example, Wang et al. [50] and Skiba et al. [51] showed thatimproving the imaging resolution from 42 to 24 µm and from 330 to 54 µm increases the 2Dflame surface density by about 10 and 33%, respectively. Mohammadnejad et al. [4] argued thatconsidering the above factors may lead to an increase of about 140% in the estimated values of101.2. BACKGROUNDthe local consumption speed.From the above definitions provided for the turbulent burning velocity, the local and globalconsumption speeds are most relevant to this thesis. Review of the literature suggests [4, 14, 22,32, 52, 53] that, generally, u′, Lu, and ϕ can substantially influence both the local and globalconsumption speeds. To study the effect of these parameters, the majority of past investiga-tions [52, 54–58] presented variations of the global and and local consumption speeds versusu′/SL0. Several studies [59, 60] additionally considered the effect of Lu/δL0 on ST,GC/SL0 andST,LC/SL0. Recently, Kheirkhah and Gu¨lder [14] reviewed the effect of u′/SL0 on the normalizedlocal and global consumption speeds. Three remarks are reviewed from the study of [14]. First,they [14] showed that at a given turbulence intensity, the Bunsen flames feature a larger nor-malized local consumption speed compared to V-shaped flames. The reason for this differencemay be due to the reactants escaping for V-shaped flames compared to Bunsen flames [14].Second, the results compiled in [14] show that increasing the turbulence intensity from about0 to 45 increases ST,GC/SL0 from about 1 to 16; however, the normalized local consumption speedincreases from about 1 to 5. The difference between the normalized local consumption speedand the global consumption speed increases to about 5–6 folds at larger turbulence intensities(u′/SL0 ≈ 160). The reason for this discrepancy has been a matter of debate for the past8 decades. Gu¨lder [52] assumed that the reason for the above discrepancy is the penetrationof eddies close to the Taylor length scale into the flame region. Using the above assumption,a mathematical formulation was developed, where the enhancement of the local consumptionspeed due to such penetration was estimated, and the above discrepancy was addressed. Later,Nivarti et al. [53] performed similar analysis except they assumed that eddies smaller than thelaminar flame thickness can penetrate into the flame region. Using this assumption, they [53]111.2. BACKGROUNDwere also able to address the observed discrepancy between the values of the normalized localand global consumption speeds. Although the studies of [52, 53] addressed the gap between thevalues of the normalized local and global consumption speeds, their calculations were performedbased on presumed penetration of eddies into the flame region. Recently, Mohammadenjad etal. [4, 22] performed PLIF experiments of intensely turbulent premixed flames and showed that,indeed, turbulent eddies can penetrate into the preheat layer. Although penetration of theseeddies into the reaction zone was not experimentally shown in their studies, it was demonstratedthat the swirling strength of the eddies inside the fresh reactants and preheat zones is positivelyrelated to both preheat and reaction zones thicknesses. Mohmamdnejad et al. [4] showed thatthe ratio of the global to local consumption speeds is linearly related to the normalized reactionzone thickness, agreeing with the conclusions of [52, 53].The third remark from the results compiled in [14] is that increasing the turbulence intensityincreases the normalized global consumption speed following a non-linear trend. This is incontrast with the Damko¨hler’s second hypothesis [57] that suggested the above relation shouldbe linear. This is referred to as the bending behavior in the literature.1.2.4 Stratified flames structure and burning rateIn the following section the literature related to the structure and burning rate of turbulentstratified premixed flames is reviewed.Sweeney et al. [61–63] studied both swirling and non-swirling fully-premixed and stratifiedflames. They utilized two concentric annular inner and outer tubes, which could carry mixtureswith varying fuel-air equivalence ratio. The results shown in Sweeney et al. [61] suggest thatchanging the mixture equivalence ratio of the inner and outer tubes from 0.75 to 0.5 and 0.75to 1, respectively, decreases the most probable value of the flame thickness at relatively small121.2. BACKGROUNDdistances downstream of the burner exit plane (10 and 30 mm). At the same heights, furtherstratifying the mixture fed into the inner and outer tubes to 0.375 and 1.125 did not change themost probable value of the flame thickness. At relatively large distances from the burner exitplane (50 and 70 mm), the stratification did not influence the most probable value of the flamethickness. Comparison of the results presented in [61] with those in [62] show that increasingthe swirl number from 0 to 0.79 does not change the most probable value of the flame thickness.Similar results were reported in Bo¨hm et al. [64]. However, compared to [61, 64], results of [65–68] show that stratification increases the hydrodynamic strain on the flames. Results of Robinet al. [68] suggest that such strain can lead to about 10% thinner stratified flames compared totheir tested premixed counterpart.Vena et al. [69] reported that, for globally stoichiometric flames, increasing the fuel-airequivalence ratio gradients resulted in the variation of the incident brush angle of the V-flamebranches. When the flame is slightly stratified, the V-flame branches open up (move away fromthe vertical centerline), and possibly the burning velocity increases. Galizzi et al. [70] reportedthe same behaviour of the flame branches. For large fuel-air equivalence ratio gradients, Vena etal. [69] showed that the V-flame branches come closer to one another making a narrower flame,and possibly the burning velocity decreases. Compared to [69], Anselmo-Filho et al. [71] allowedfor one wing of the V-shaped flame to be exposed to a fuel-air equivalence ratio gradient. Thisparameter changed from 0.54 to 1.16 in their study [71]. They defined a parameter, referred toas the stratification ratio (S), which is the ratio of the relatively richer to the relatively leanertested ϕ. Anselmo-Filho et al. [71] reported that increasing S opens the V-flame towards theinjector exit plane. They suggested that such behavior is due to enhanced burn rate of thestratified mixtures. However, this was not quantified in [71].131.2. BACKGROUNDAlthough the studies of [69, 71] provided insight into the effect of stratification on thepremixed flames, it is unclear how the burning velocity is influenced by such gradient. Bonaldoand Kelman [72] studied how the equivalence ratio gradient influences the burning velocity. Intheir study, the burning velocity is defined as the velocity of the unburnt gas estimated along thedirection normal to the flame front. Their experimental set up carried two separate flows withdifferent fuel-air equivalence ratios through an annular inner tube and an annular outer tube.They [72] varied the mixture equivalence ratio of inner (outer) tube from about 0.63 to 0.78(0.78 to 0.63), stratifying the mixture. Their results [72] suggest that, for all stratified flames,the PDF of the burning velocity is similar to a log-normal distribution skewed towards smallvalues. Bonaldo and Kelman [72] showed that increasing the fuel-air equivalence ratio of theinner and outer tubes from 0.63 and 0.78 to 0.78 and 0.63 increases the most probable value ofthe burning velocity from 1 to 1.5 m/s, with the mean value increasing from about 2.13 to 2.19m/s. Their [72] results suggest that, although the most probable value of the burning velocitycan change by stratifying the mixture, the mean values of this parameter are not sensitive tostratification.Cho and Santavicca [65] studied the effect of varying the fuel-air equivalence ratio of a sparkignited flame kernel. This variation was achieved by keeping the global fuel-air equivalenceratio fixed at 1, but supplying different amounts of fuel at two different locations. The firstand second fuel injection locations were 160 and 10 mm upstream of a dump plane, respectively.Such injection strategy led to the variation of the fuel-air equivalence ratio inside the test section.Specifically, for injection scenarios corresponding to 100/0, 75/25, 50/50, 25/75, 0/100% splitsof the fuel flow-rate between the first and second fuel injection locations, nearly 0, 5, 13, 22and 31% RMS of the fuel-air equivalence ratio fluctuations were reported in [65], respectively.141.2. BACKGROUNDCho and Santavicca [65] obtained the PDF of the fuel-air equivalence ratio, and estimated thelaminar flame speed for the above fuel splits and within the flammability limits of the testedfuel. Their results show that changing the fuel split from 100/0 to 75/25, 50/50, 25/75, and0/100% decreases the laminar flame speed from about 44, 42, 39, 33, and 31 cm/s, respectively.Cho and Santavicca [65] observed that the burning velocity did not feature significant sensitivityto the fuel splits.Zhou et al. [73] used a constant volume combustion chamber to study the effects of stratifica-tion on the flame propagation speed. Their chamber was equipped with two perforated plates,which rotated to mix the air and fuel, increasing the homogeneity of the fuel-air equivalenceratio and decreasing the amount of stratification. Their results showed that decreasing the ro-tation speed of the perforated plates (and as a result, increasing the stratification) increases theflame front length, which corresponds to the amount of the flame front wrinkling. Their re-sults show that increasing the amount of the stratification, first, increases the flame propagationspeed. However, further stratifying the mixture decreases this speed. Zhou et al. [73] argued,initially, as the fuel-air equivalence ratio increases, different locations inside the mixture burn atdifferent velocities. Such spatial variation in the burning velocity induces wrinkling of the flamesurface, which increases the flame speed. However, as suggested by [73], further stratificationof the mixture leads to locations with fuel-air equivalence ratios that do not correspond to theflammability range of the tested fuels. Thus, for large amounts of stratification, the fuel and airmay not burn at the above locations. As a result, the large spatial gradient of the gas velocitymay not exist for highly stratified flames and flame fronts may not be significantly wrinkled.Haworth et al. [74] performed a DNS with detailed combustion chemistry of propane andstudied the heat release rate of both stratified and homogeneous flames. The fuel-air equivalence151.2. BACKGROUNDratio was varied from 0.5 to 2.7 in their study. Their results showed that stratifying the mixturedid not influence the heat release rate (and as a result, the burning velocity) of the perfectlypremixed flames.Pasquier et al. [75] studied the propagation speed of a turbulent stratified flame in a constantvolume chamber. The chamber was filled with a mixture of propane and (with ϕ = 0.6) and air.A jet of propane was injected into the chamber, stratifying the mixture. Their results [75] showthat the fuel-air equivalence ratio varies from 0.6 to 1 and 0.6 to 0.9 along the main jet flowand transverse to this direction, respectively. They performed simultaneous and time-resolvedParticle Image Velocimetry (PIV) and PLIF. Using this, Pasquier et al. [75] conditioned thepropagation speed of their tested flames at several fuel-air equivalence ratios. Their resultsshow that the most probable value of the stratified flame propagation speed of locally leanmixtures is larger than that of the homogeneous flames with the same equivalence ratio. Theyconcluded that some degree of stratification may increase the propagation speed of the propane-air premixed flames. Similar observations are reported for laminar flame simulations by Cruz etal. [76].Mohammadnejad et al. [1] investigated the effect of stratification on a marker of the heatrelease rate for a 60% hydrogen-enriched methane turbulent flames with a global fuel-air equiv-alence ratio of 0.8. They utilized both, a swirling and a non-swirling injector, which operatedat the mean bulk flow velocities of 5 and 25 m/s. For both injectors, the fuel flows throughseveral distributed injection holes, and a mixture of fuel and air exits through four lobes of theinjector. Since the fuel injection holes are relatively small, slight variations of the injection holediameters (as a result of manufacturing) lead to different amounts of fuel to be supplied to eachinjection hole, and as a result; stratification. Mohammadnejad et al. [1] studied the effect of161.3. THESIS OBJECTIVES AND ORGANIZATION OF THE CHAPTERSstratification by calculating the integral of the multiplication of OHPLIF and CH2OPLIF over thedomain of investigation. For a mean bulk flow velocity of 5 m/s, the most probable value of themultiplication integral is about 7% larger for the swirling injector compared to the non-swirlinginjector. For a mean bulk flow velocity of 25 m/s, they reported that the non-swirling injec-tor featured more pronounced stratification than the swirling one. The PDF of the integral ofOHPLIF × CH2OPLIF showed that the most probable value of the non-swirling injector is 23%larger than the swirling injector. In essence, the results presented in the literature suggest thatstratification of homogeneous mixtures may either decrease the flame thickness [68], or it maynot change with the stratification [61, 62, 77]. Despite there exists a discrepancy regarding thedefinition of the burning velocity, past studies suggest that relatively small amount of stratifica-tion may increase the flame strain [65–67], which increases the flame front wrinkling [65, 68, 69]and as a result the flame propagation speed [1, 66, 68, 74–76]. Although such flame strainingmay lead to local extinctions and as a result reduction of the burning velocity, Masri [67] sug-gested that the equivalence ratio gradients may enhance the interaction between the rich andlean regions, which may help the flames to withstand extinctions due to straining.1.3 Thesis objectives and organization of the chaptersFlames related to many engineering applications are influenced by the stratification eitherdue to the design of the fuel and air injectors or due to the mixing with the surrounding gasand/or dilution air streams. The present study follows three objectives. First, this thesis aimsto characterize both the turbulent flow, as well as the mixing fields generated by the injectorused in [1]. This is done for relatively large mean bulk flow velocities (up to 50 m/s comparedto 25 m/s tested in [1]) which are more relevant to engineering applications. Although the171.3. THESIS OBJECTIVES AND ORGANIZATION OF THE CHAPTERScharacterization of the non-reacting flow mixedness is of significant importance, it is not oftenstraightforward to acquire both the mixedness fields for reacting data and the flame-relatedmeasurements. Thus, the second objective of this thesis is to propose a method that is robustand does not rely on simultaneous measurement of the fuel-air equivalence ratio field to studystratified flames characteristics. The third objective of the thesis is to use the above methodand study the flame-related characteristics of premixed and stratified flames.Following this introductory chapter, the experimental methodology for this study is presentedin Chapter 2. This is followed by characterization of the non-reacting flow velocity in Chapter 3and the non-reacting flow mixedness in Chapter 4. These two chapters, together, aim to addressthe first objective of the thesis. The second and third objectives are addressed in Chapter 5.Finally, conclusions of this study and the future work are presented in Chapter 6.18Chapter 2MethodologyThis chapter is composed of three subsections: the burner setup, the diagnostics, and thetested conditions, with details provided in the following.2.1 BurnerThe burner is composed of an air feed section, an expansion section, a settling chamber, anda plenum as shown in Fig. 2.1. The technical drawings of these are provided in Appendix A.The technical drawings of the air feed section, the expansion section, and the settling chamberare similar to those used in [4, 22, 78–81]. The plenum; however, was designed to accommodateindustrial injectors, such as those used by the industrial partner of this project, via an adapterplate. All components of the burner, except the injector, were manufactured in-house.The air feed section, see Fig. 2.1 is composed of four 14 mm diameter air inlets that arepositioned equidistant from one another around the circumference of the air feed section. Thissection carries a fuel line at the center (see the green color tube), which is connected to theinjector. The air feed section is followed by an expansion section, which has an area ratio of4, as well as a settling chamber that is equipped with five mesh screens, which are positionedat a distance of 36 mm from one another. The mesh screens have a wire diameter of 0.5 mmand an opening space size of 0.9 mm similar to [78–80]. Downstream of the settling chamber,192.1. BURNERFig. 2.1. Section view of the utilized burner.a honeycomb (with a cell side length of 5.0 mm and length of 50.8 mm) is positioned for flowconditioning purposes. The settling chamber is followed by a 230.0 mm long plenum, whichholds the injector. The fuel and air flow through four lobes of the injector, which are distributedaround the axis of the burner. The top view of the injector is shown in Fig. 2.2, with thegrey shaded region showing solid material and, white regions presenting the lobes where thefuel-air mixture flows through. The left lobe, L1, and right lobe, L3, centerlines are in theplane of measurements. The terminology L1–L4 is identical to that used in [1]. The geometryof the lobes is such that it induces a swirling motion to the combustible mixture as it entersthe combustion chamber shown by the black arrows in Fig. 2.2. Further details of the injectorcannot be disclosed here due to confidentiality reasons.202.1. BURNERFig. 2.2. Schematic diagram of the injector is reproduced with permission of Springer: Flow,Turbulence and Combustion, Effect of Fuel Stratification on OH and CH2O PLIF Multiplicationof Turbulent Hydrogen-Enriched Flames, Mohammadnejad et al., pp. 263–301, 2021. Thedirection of the salient flow coincides with the y-axis of the coordinate system, also presentedin Fig. 2.1. The green arrows show the directions of fuel injection into the lobes and the blackarrows schematically present the swirling motion of the flow.As discussed in the following, for each test condition, the reacting flow data is collected forboth stratified as well as fully-premixed flames. The stratified premixed flames are generatedusing the fuel and air flow configuration discussed above. For fully-premixed flames, however,the fuel and air streams are fed into a premixing chamber, which is positioned about 2 mupstream of the burner (not shown here). Once the fuel and air are fully mixed, the mixture isfed through the air feed section into the burner. The fuel line shown in Fig. 2.1 is closed for thefully-premixed operation of the burner.212.2. DIAGNOSTICS2.2 DiagnosticsThe hot-wire anemometry (HWA) as well as the Rayleigh scattering technique are utilizedin the present study. The former is used to investigate the characteristics of the non-reactingflow. The latter is used to quantify the mixedness of the non-reacting flow as well as to studythe turbulent flames characteristics. Details related to these diagnostics are discussed in thefollowing.Hot-wire anemometry: The hot-wire anemometry technique is commonly used for charac-terization of the turbulent flows, ranging from flows over cylinders and airfoils [82, 83] to flowsin the wake of fractal turbulence generators [84, 85]. The HWA hardware used in this study isschematically shown in Fig. 2.3 and is composed of (1) a cross-wire probe, (2) the probe support,(3 and 4) two controlled linear translational stages, (5) an sCMOS camera, and (6) a macro lens.The cross-wire probe (model 55P51 by Dantec) is composed of two 5 µm diameter wires, eachof which is 3 mm long. The wires feature resistances of 3.68 and 3.91 Ω. The voltages appliedto the wires are provided by two mini-constant temperature anemometry (mini-CTA) circuits,which are not shown here.Both mini-CTA circuits were set to an overheat ratio of 0.7 for both wires, as recommendedby the producer as well as past studies [86–89]. The probe support is right-angled (model55H26 by Dantec) such that the axis of the probe is positioned parallel with the main flowdirection, see Fig. 2.3. Each motorized translational stage (model MTS50-Z8 from Thorlabs)utilizes a stepper motor with a resolution of 34555 counts per shaft revolution. Each revolutionof the stepper motor shaft leads to 1 mm displacement. As a result, the resolution of thestepper motor displacement is 1 mm/34555 = 29 nm. Each translational stage features a 50 mmrange of operation. Such resolution and range of operation were sufficient for the measurements222.2. DIAGNOSTICSFig. 2.3. The hot-wire anemometry system presents (1) cross-wire and probe, (2) probe holder,(3 and 4) two translational stages (5) camera, and (6) a macro lens. Items (5 and 6) were usedto acquire the position of the cross-wire.presented in this study. A motion control software, referred to as Kinesis (from Thorlabs), wasused to operate the translational stages. The camera is the Andor’s Zyla 5.5 sCMOS from OxforInstruments. The camera sensor is composed of 2560×2160 pixels2. The camera lens has a focallength of f = 105 mm. The combination of the camera and lens presented above allowed forimaging a field of view of 102.4 mm (along the x−axis) × 86.4 mm (along the y−axis). This ledto a pixel resolution of 40 µm.An optical technique was used for proper positioning of the cross-wire for hot-wire anemome-try. First, the probe holder was placed flush-mount with the surface of the burner, and a pictureof the holder was acquired, as shown in Fig. 2.4(a) and the inset presented in Fig. 2.4(b). Usingthis image and the pixel resolution of the imaging system, the vertical location of the exit planeof the burner was obtained. Then, the probe holder was moved along the main flow direction,the probe was mounted on the probe holder, an image was acquired, the angles of the wires withrespect to the burner exit plane were calculated, and the probe holder was adjusted ensuringthe wires generate 45 and 135o angles with the exit plane of the burner. Finally, the distance232.2. DIAGNOSTICSbetween the location of the wires crossing and the burner exit plane was calculated. This dis-tance was set to 3.4 mm, which is shown in Fig. 2.4(d), which is the inset of Fig. 2.4(c). Usingthe translational stages, the probe was then moved to 33.4 mm above the burner exit plane,which corresponds to the lower extent of the collected Rayleigh scattering images.Pixel info: (817, 1252) 392Fig. 2.4. (a) is a picture of the probe touching the burner exit plane. (c) is a picture of the hotwire probe and its holder. (b) and (d) are the insets of (a) and (c), respectively.A calibration procedure was followed to convert the voltage readings of the mini-CTA circuitsto the velocity data [86]. The cross-wire probe and the holder were positioned at the exit ofa free-jet calibrator (model 9054H0101 of Dantec). In the present study, the free-jet velocitywas adjusted using a lever moving from an off position to that corresponding to a maximumflow-rate. A manometer (model HHP8252 from Omega) was used to measure the pressure dropin the calibrator setup. The lever was set to 10 different rotation angles, and for each rotationangle, the pressure drop was recorded and the voltages for both wires were acquired. All voltagedata (for both calibration and flow measurements) was acquired at an acquisition frequencyof 10 kHz. This was the maximum possible acquisition frequency, which was obtained basedon the response time of the mini-CTAs. As discussed later in Section 2.3, a data acquisitionlarger than 77 kHz is required for resolving the Kolmogorov-size fluctuations. Achieving such a242.2. DIAGNOSTICSlarge acquisition frequency for the HWA measurements was not possible, and the 10 kHz set ofthe present study was sufficient for characterizing the non-reacting flow field generated by theutilized injector.The variations of jet centerline velocity versus the mean voltages corresponding to bothwires (referred to as V1 and V2) are presented in Figs. 2.5(a) and (b), respectively, using anopen black circular data symbol. The minimum tested jet centerline velocity is about 5 m/s,and this is recommended by the producer. However, the measurements discussed in the presentstudy include velocity magnitudes ranging from 0 to about 80 m/s. In order to ensure bestdata fitting practices, for each wire, 8 extra data points that allow extrapolating the reading ofthe smallest voltage measured by each wire to V1 = V2 = 0 at zero jet centerline velocity wereadded. These data points are shown by the solid black circular symbol in Fig. 2.5. Following[90], fifth-order polynomials were fit to the data points (solid and open symbols) for each wire,with the corresponding variations for the first and second wires shown by the solid blue andgreen curves in Figs. 2.5(a) and (b), respectively. The values of the polynomial constants wereobtained using MATLAB along with the method of least square fit. These values are providedin Table 2.1.Table 2.1. Calculated polynomial coefficients for curves shown in Fig. 2.5.a1 a2 a3 a4 a5 a60.1925 -4.8359 27.5587 -31.2056 11.1882 -0.3442b1 b2 b3 b4 b5 b60.1889 -4.7413 27.5508 -31.5950 11.5862 -0.4365The flow velocities corresponding to the first (U1) and second (U2) wires frames of referenceare given by:U1 = a1V51 + a2V41 + a3V31 + a4V21 + a5V1 + a6, (2.1a)252.2. DIAGNOSTICS0 0.5 1 1.5 2 2.50204060801001200 0.5 1 1.5 2 2.5020406080100120Fig. 2.5. (a) and (b) are the calibration curves for wire 1 and wire 2, respectively.U2 = b1V52 + b2V42 + b3V32 + b4V22 + b5V2 + b6. (2.1b)Accounting for the directional calibration of the wires, it can be shown [91] thatU ′1 =√22√(1 + k22)U22 − k22U21 , (2.2a)U ′2 =√22√(1 + k21)U21 − k21U22 , (2.2b)where U ′1 and U ′2 are the flow velocities U1 and U2 corrected for the effect of orientation ofthe wires. Such calibration was performed in the present study, and using the imaging system262.2. DIAGNOSTICSintegrated with the cross-wire anemometry, it was confirmed that k1 ≈ k2 ≈ 0 [86]. For k1 =k2 = 0, it can be shown that the flow velocity along the main flow direction as well as normalto the main flow direction (and inside the plane of the wires) are respectively given by:u =12(U ′1 + U′2), (2.3a)v =12(U ′2 − U ′1). (2.3b)In the present study, once the voltages from the mini-CTA circuits were acquired, the coefficientsin Table 2.1 were used to estimate u and v using Eqs. (2.1, 2.3a, and 2.3b). The calibrationexperiments were performed on a daily basis.Rayleigh scattering measurements: The Rayleigh scattering is the elastic scattering of lightfrom molecules, species, particles, etc. that are smaller than the incident laser wavelength[92]. The Rayleigh scattering technique is commonly used in turbulent flames studies, see forexample [37, 93–96], to investigate the structure of fully-premixed flames. In this study, theRayleigh scattering technique is used for both, investigating the stratified and fully-premixedflames structures as well as for quantifying the mixedness of the non-reacting flows. Figure 2.6presents the hardware used for the Rayleigh scattering measurements. In the figure, (1) is anNd:YAG Lab-Series-170 laser from Spectra Physics, which produces a 1064 nm beam. Theoriginal laser beam is converted to 532 nm wavelength and 8 mm in diameter beam with anenergy of about 530 mJ per pulse using a harmonic generator, which is embeded in item (1), seeFig. 2.6. In the figure, (2–4) are sheet forming optics which convert the 532 nm laser beam toa collimated laser sheet. Specifically, items (2), (3), and (4) are a plano-convex cylindrical lenswith a focal length of 1000 mm, a plano-convex cylindrical lens with a focal length of 500 mm,272.2. DIAGNOSTICSand a plano-concave cylindrical lens with a focal length of -100 mm, respectively. Items (5)and (6) are a Macro lens from Sigma, with a focal length of 105 mm and an Andor 5.5 sCMOScamera (which is identical to that used for the hot-wire probe positioning), respectively. Thecamera was controlled using the Micro-Manager software from Andor to set the camera exposuretime to 20 µs. The camera operated under the global shutter mode. The lens aperture size wasfixed at an aperture number of 2.8 to maximize the collected light intensity. Finally, item (7)is a bandpass filter with a center wavelength and Full Width at Half Maximum (FWHM) of532 nm and 20 nm, respectively.Fig. 2.6. The Rayleigh scattering diagnostics hardware. Items (1), (2–4), (5), (6), and (7) arethe laser, the optics, the camera, the lens, and a bandpass filter, respectively.The laser pulse energy is measured using a pyroelectric type detector from Gentec Electro-282.2. DIAGNOSTICSOptics Inc. (model QE25LP-S-MB-QED-INT-D0), after the laser operated for about 30 mins.This energy monitoring equipment is controlled using the Integra software from the same pro-ducer. Figure 2.7 presents the percentile fluctuations of the laser energy (E − E)/E recordedfor a period of 50 s and for the laser operating at 10 Hz. The RMS of (E −E)/E is about 1%,which is deemed small.0 10 20 30 40 50-4-20240 0.5 100.10.20.30.40.50.60.70.80.91Fig. 2.7. The percentile fluctuations of the laser energy over 50 s.The thickness of the laser sheet was estimated by exposing the laser sheet at the loca-tion of measurements to a laser pattern collection sheet, with a representative image shownin Fig. 2.8(a). This image was imported to MATLAB and variation of the number of countsnormal to and along the laser sheet (white line) were obtained and presented in Figs. 2.8(b) and(c), respectively. The FWHM of the variation shown in Fig. 2.8(b) is referred to as the lasersheet thickness and equals 320.8 µm. Similarly, the height of the laser sheet was obtained byestimating the FWHM of the variation shown in Fig. 2.8(c) and equals 42992.0 µm (about 43mm).The Rayleigh scattering signal (IR) at a given pixel is linearly related to the local incidentlaser intensity (Ii), pressure (P ), inverse of temperature (T ), the mixture Rayleigh scattering292.2. DIAGNOSTICS0 8 16 24 32 40 48Height (mm)020040060080010001200Light intensity (counts)0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8Thickness (mm)400600800Light intensity (counts)Fig. 2.8. (a) is an image of a burnt paper for the laser operating at it maximum power after30 mins of operation and at the location of measurements. (b) and (c) are the variations ofthe number of counts for the image in (a) for normal to and along the laser sheet directions,respectively.cross section (σmix), and the efficiency of the collection optics (Copt) [92], which is given byIR = CoptIiPkTσmix, (2.4)where k is the Boltzmann constant. In theory, Copt is not completely independent of the oper-ating conditions. For example, if there exists a temperature gradient, light will follow a curvedpath toward the cold gasses. The refractive index of a cold gas is larger than that of a hotgas due to the density variation. Thus, despite the collection optics may remain unchangedin experiments, Copt could potentially vary. Nonetheless, such variation is usually ignored inRayleigh scattering measurements, and calibration experiments are performed to facilitate mea-surement of temperature by removing Copt from the calculations. In order to do this, reference302.2. DIAGNOSTICSexperiments (performed for non-reacting flow of air) are conducted in addition to the reactingflow experiments. That is, writing and simplifying Eq. (2.4) for both reacting and non-reactingconditions, it can be shown thatTTref=IiIi,refIR,refIRσmixσmix,ref. (2.5)For the experiments performed in this study and as discussed earlier, the laser energy does notchange significantly, see Fig. 2.7, which suggests Ii ≈ Ii,ref . Such observation was also confirmedby spatially integrating the collected laser intensity and assessing its variation during the datacollection period. For single species measurements or for mixtures with known constituentspecies mixture fractions (such as air), σmix,ref is also known. The Rayleigh scattering signal isobtained from [11]:IR = I − IN − ICL − IS, (2.6)where I is the raw signal measured by the camera, IN is the acquired light intensity due toelectric noise, ICL is the collected intensity due to flame chemiluminescence at 532 nm, and ISis the collected light intensity due to background scattering. Ideally, all four parameters on theright-hand-side of Eq. (2.6) should be measured on an instantaneous basis. However, since thisis not feasible in the present study and that the time variations of IN, ICL, and IS are relativelynegligible (compared to I), these intensities are estimated via separate measurements. Time-averaged (for 500 images) 2D variations of I, IN, and ICL are presented in Figs. 2.9(a), (b), and(c), respectively. The results presented in Figs. 2.9(a and b) pertain to a non-reacting flow ofair.The background scattering intensity (IS), with details discussed in [11], is a result of sec-312.2. DIAGNOSTICS605040105165-50 -25 0 25 5060504003605040 110135Pixel info: (X, Y) IntensityPixel ValueFig. 2.9. (a), (b), and (c) are the time-averaged variations of I, IN, and ICL, respectively.ondary scattering (e.g. from the equipment in the lab) collected by the camera. This spatiallyaveraged scattering intensity is relatively small, and is estimated through separate air and he-lium flow experiments. For non-reacting flows of air and helium and for fixed values of theincident laser intensity, Eqs. (2.4) and (2.6) can be used to show thatIR,airIR,He=Iair − IN − ISIHe − IN − IS =σairσHe, (2.7)where σHe is the helium Rayleigh scattering cross section, and σair = 0.21σO2+0.79σN2 , with σO2and σN2 being the oxygen and nitrogen molecules Rayleigh scattering cross sections, respectively.The species Rayleigh scattering cross sections are usually normalized by that of the nitrogenmolecule. For a 532 nm laser excitation, σHe = 0.013σN2 and σO2 = 0.859σN2 [11, 97, 98]. Using322.2. DIAGNOSTICSthe above relations between the helium atom as well as the oxygen and nitrogen molecules,the Rayleigh scattering cross sections along with IR,air and IR,He are measured from separatenon-reacting flow experiments. IS was calculated from Eq. (2.7) to be equal to 17, and does notvary significantly in the domain of investigation.As will be discussed in the results section, estimation of the gas temperature requires a-priori assumptions regarding the variation of combustion species versus temperature. Suchvariations are highly influenced by turbulence, location of the measurements, and the local fuel-air equivalence ratio. Here, instead of temperature, a normalized parameter referred to as T ∗ iscalculated, which is given byT ∗ =Tσmix/σmix,ref= TrefIR,refIR. (2.8)A representative 2D variation of T ∗ is shown in Fig. 2.10(a). As can be seen, T ∗ evaluated inthe products region is contaminated by noise. Figure 2.10(b) presents the T ∗ variation shownin Fig. 2.10(a) after application of a 5×5 median based filter. The size of the filter was obtainedfollowing a trial and error process (to remove noise, while maintaining good spatial resolution)and compares well with that of previous studies, see for example [1, 4].It is important to highlight that IS is necessary to be accounted for in T∗ calculations. Tohighlight this, the T ∗ presented in Fig. 2.10(c) was calculated using IS = 0 (instead of IS = 17 aspresented in Fig. 2.10(b)). As can be seen, mean value of T ∗ is about 1400 K. This is while thenormalized adiabatic flame temperature is T ∗AD ≈ 22270.938/0.9704 = 2304 K, which is significantlydifferent than that of the products region in Fig. 2.10(c) but close to that in Fig. 2.10(b). Thus,the non-zero value of IS needs to be accounted for in the T∗ calculations.332.3. TESTED CONDITIONS6050405001000150020002500500 1000 1500 2000 250060504050010001500200025006050405001000150020002500Pixel info: (X, Y) IntensityFig. 2.10. (a) is a sample of 2D variation of T ∗ and (b) is (a) after median based filtering. (c)is (a) with IS = 0.2.3 Tested conditionsThe tested conditions are discussed for both non-reacting and reacting flows. For the non-reacting flows, the mean bulk flow velocity was changed from 5 to 50 m/s in increments of 5 m/s.For each tested mean bulk flow velocity, the HWA data was collected along the transverse tothe main flow direction from x = −16 mm to x = 16 mm (in increments of 2 mm), wherex = 0 coincides with the injector centerline. For clarity of presentation purposes, the results arepresented only for increments of 4 mm.Methane grade 2 (i.e. methane with 99% chemical purity) was used as the fuel for thetested reacting conditions. The injector utilized in the present study was operated for both342.3. TESTED CONDITIONSfully-premixed and partially premixed conditions, with the corresponding stability maps shownin Figs. 2.11(a) and (b), respectively. The results in Fig. 2.11 are color-coded. That is, cells withgreen and red colors pertain to stable and blow-out conditions. Cells in yellow color correspondto conditions for which the flame was initially stabilized, however, it was extinguished after afew seconds. The results show that, for the conditions that premixed flames may be stabilizedbut extinguished after a few seconds, switching to stratified configuration does not help withthe flame stabilization, except at ϕ = 1. As the results in Fig. 2.11 show, at ϕ = 1, all stratifiedflames are stabilized, however; the premixed flames extinguish after a few seconds at U = 50 m/s.Since both stratified and premixed flames are stabilized for mean bulk flow velocities smallerthan or equal to 45 m/s and at ϕ = 1, the Rayleigh scattering experiments of the reacting flowwere performed only for ϕ = 1.10 20 30 40 5010 20 30 40 500.50.60.70.80.91Pixel info: (4, 1) 0Fig. 2.11. The stability map for (a) premixed and (b) stratified flames. The cells with the greenand red colors pertain to tested conditions that lead to stable flames and blown-out flames,respectively. The cells with yellow color pertain to test conditions for which the flames areinitially stable after ignition, but they blow-out after a few seconds.Table 2.2 presents the tested conditions for which both the Rayleigh scattering and HWAdata were collected. In the table, u′ and v′ are the RMS of the velocity fluctuations measured atx = 0 and y = 33.4 mm. In Table 2.2, lT and ηK are the Taylor and Kolmogorov length scales,respectively, and are given by lT = LuRe− 12T and ηK = LuRe− 34T , with ReT being the turbulent352.3. TESTED CONDITIONSReynolds number. This parameter is given by ReT = u′Lu/ν, where ν is the kinematic viscosityof the reactants estimated at room-temperature (300 K). In the table, Da is the Damko¨hlernumber and is calculated usingDa =(u′SL0)−1(LuδL). (2.9)In estimation of both Da and Ka numbers, the unstretched laminar flame speed (0.37 m/s)and laminar flame thickness (0.17 mm) of stoichiometric methane and air flame were utilized.For comparison purposes, the tested conditions of this study and for fully-premixed flames wereoverlaid on the Borghi–Peters diagram shown in Fig. 2.12. As can be seen, test conditions withU = 5, 10 and 15 m/s, as well as U = 20 − 45 m/s correspond to wrinkled flames, corrugatedflames, and thin reaction zones, respectively.Table 2.2. The reacting flow tested conditions. For all tested conditions, the global fuel-airequivalence ratio is 1. U , SL0, u′, and v′ are in m/s, and Lu, lT, and ηK are in mm. For alltested conditions, SL0 = 0.37 m/s and δL = 0.17 mm.Test Cond. U u′ v′ Lu lT ηK u′/SL0 Lu/δL ReT Da KaU5 5 0.31 0.19 10.8 0.72 0.19 0.8 63.5 225 59.7 0.1U10 10 0.74 0.45 8.6 0.42 0.09 2.0 50.6 425 20.4 0.4U15 15 1.15 0.76 9.5 0.35 0.07 3.1 55.9 739 15.7 0.8U20 20 1.69 1.07 8.5 0.27 0.05 4.6 50.0 976 9.9 1.5U25 25 2.2 1.4 8.7 0.24 0.04 5.9 51.2 1284 7.9 2.1U30 30 2.7 1.8 8.8 0.22 0.03 7.4 51.8 1633 6.5 2.9U35 35 3.4 2.2 9.0 0.20 0.03 9.1 52.9 2041 5.5 3.9U40 40 3.7 2.6 10.0 0.20 0.03 10.0 58.8 2494 5.7 4.2U45 45 4.4 2.9 9.6 0.18 0.02 12.0 56.5 2866 4.7 5.5362.3. TESTED CONDITIONS10-1 100 101 102 10310-1100101102103data1data2data4data3data5data6data7data8data9data10data11data12100 101 102 103Fig. 2.12. The tested experimental conditions overlaid on the Borghi-Peters diagram [3] forfully-premixed flames.37Chapter 3Non-reacting turbulent flowcharacteristicsThe characteristics of the turbulent flow generated by the injector are investigated in thischapter. Of relevance are the mean velocity, RMS velocity fluctuations, as well as the spectralcontent of the velocity data, with details discussed in the following. For comparison purposes,the horizontal extent of the injector is also shown in Fig. 3.1.The mean of the gas velocity along the vertical (u) and horizontal (v) directions were mea-sured for all non-reacting tested conditions, and the results are presented in Figs. 3.1(a) and(b), respectively. The size of the error bars in Figs. 3.1(a) and (b) is the RMS of the velocityfluctuations. The corresponding RMS of the velocity fluctuations normalized by the respectivemean bulk flow velocity are presented in Figs. 3.1(c) and (d). As can be seen, the mean velocityis decelerated near the centerline. This is similar to the results presented in [1]. Also, for alltested conditions, both u′ and v′ feature peaks near 5 ≲ |x| ≲ 10, which is close to the peripheralsurface of the center bluff body. Since the non-reacting flow experiments are performed witha closed fuel line, the large values of u′ and v′ corresponding to 5 ≲ |x| ≲ 10 are not due tothe interaction of fuel and air flows. Such large RMS values are anticipated to be the result ofinteraction of the flow exiting the lobes and the center bluff body wake.380204060-20-100102000.10.20.30.400.10.20.30.4-20 -15 -10 -5 0 5 10 15 20-20 -15 -10 -5 0 5 10 15 20Fig. 3.1. (a) and (b) are the mean of the axial and transverse components of the velocity,respectively. (c) and (d) are the RMS of the axial and transverse components of the velocity,respectively. The square, circular, triangular, and diamond shaped data symbols pertain toU = 5, 20, 35, and 50 m/s, respectively.Fast Fourier Transform analysis was performed to study the spectral content of the non-reacting flow. The collected velocity data was divided into 430 segments of nfft = 211 = 2048data points. Then, the Power Spectrum Density (PSD) was calculated for each segment usingthe 211 frequency bins, and the PSDs were averaged at each frequency bin for best presentationof the results. This was performed for both axial and transverse velocity components, as well asfor all tested mean bulk flow velocities given byEuu =|FFT (u)|2nfft, (3.1)Evv =|FFT (v)|2nfft, (3.2)respectively. Figures 3.2(a) and (b) present the averaged PSDs of the axial (Euu) and transverse(Evv) velocity components measured at x = −8 mm, respectively. This axial location is selected39since it leads to the largest RMS velocity fluctuations, see Fig. 3.1(c and d). The results arepresented for all tested mean bulk flow velocities and are stepped for clarity purposes. As can beseen, a dominant frequency is present (in both Euu and Evv) at about f1 = 90 Hz for the meanbulk flow velocity of 5 m/s. The results in Fig. 3.2(a) and (b) show that there is a −5/3 decay forfrequencies of 520 ≤ f ≤ 1030 Hz and 800 ≤ f ≤ 1020 Hz for a mean bulk flow velocity of 5 m/s,respectively. Further increasing the mean bulk flow velocity to 10 m/s increases the dominantfrequency to about f2 = 190 Hz. At U = 15 m/s, no dominant frequency is detected. However,increasing the mean bulk flow velocity to values larger than 25 m/s leads to the appearanceof nearly periodic velocity fluctuations at f3 = 1790 Hz. As shown in Fig. 3.2, the energy atthis frequency increases with increasing the mean bulk flow velocity from 20 to 50 m/s. Therelatively strong velocity fluctuations at f3 contributes to the large u′ and v′ values reported inFig. 3.1(c) and (d).The velocity fluctuations at f3 = 1790 Hz feature a relatively large PSD amplitude for U =50 m/s. In order to investigate the origin of the detected instability, the PSD calculations wereperformed for the largest tested mean bulk flow velocity at several radial locations. Figures 3.3(a)and (b) present the PSDs of the axial (Euu) and transverse (Evv) velocity components forthe largest tested mean bulk flow velocity at several radial distances away from the injectorcenterline. The results suggest that, for x = 0, the dominant instability is nearly absent, but itis most pronounced near x ≈ ±8 mm. This transverse distance corresponds to the center of theinjector lobes. Since, for the non-reacting flow characterization, all of the air flows through thelobes, and that there is no air being injected through the fuel injection holes, it is speculatedthat the source of the detected instability at f3 = 1790 Hz is hydrodynamic and possibly relatedto the injection lobes.40100 101 102 103 104 105-6-4-20246100 101 102 103 104 105-6-4-20246Fig. 3.2. Effect of the mean bulk flow velocity on the dominant frequencies of the axial andtransverse velocity data collected at x = 8 mm. The vertical axis is a logarithmic (with a baseof 10) scale.Analysis of the results presented in Figs. 3.2 and 3.3 suggests that, for U ≤ 25 m/s, theinstability at f3 = 1790 Hz is absent and is only present at locations displaced from the centerline(x=0) for larger bulk flow velocities. As a result, the integral length scale was estimated only atx = 0 for all tested mean bulk flow velocities. In order to obtain the integral length scales, theauto-correlation of the streamwise (ρu) and transverse (ρv) velocity data were estimated usingρu(∆t) =ΣNi=1u′ [t(i)]u′ [t(i) + i∆t]ΣNi=1u′ [t(i)]u′ [t(i)], (3.3a)ρv(∆t) =ΣNi=1v′ [t(i)] v′ [t(i) + i∆t]ΣNi=1v′ [t(i)] v′ [t(i)], (3.3b)where ∆t is the inverse of the sampling frequency and equates 0.1 ms. The axial (Lu) and lateral(Lv) integral length scales were estimated using the Taylor’s frozen turbulence hypothesis [29],41100 101 102 103 104 105-4-20246810100 101 102 103 104 105-4-20246810Fig. 3.3. The spectral content of the (a) axial and (b) transverse velocity components forU = 50 m/s. The vertical axis is a logarithmic (with a base of 10) scale.which suggests that Lu = Uτu and Lv = Uτv, respectively. τu and τv are the time integral of ρuand ρv from t = 0 to the time that the auto-correlations attain a zero value for the first time.Values of τu and τv as well as Lu and Lv were estimated for all tested mean bulk flow velocities,and the results are presented in Fig. 3.4(a) and (b), respectively. The values of the integrallength scale along the axial direction Lu were listed in Table 2.2 and were used for estimationof the non-dimensional numbers in the table. The integral length scale (Lu) is used for analysisof the burning rate area, which is discussed later in the thesis.420 10 20 30 40 5046810120 10 20 30 40 5000.511.522.5Fig. 3.4. Integral (a) time and (b) length scales versus the tested mean bulk flow velocity. Thecircle and square data points pertain to the axial and transverse components of the velocity,respectively.43Chapter 4Non-reacting flow mixednesscharacteristicsThe Rayleigh scattering technique [92] is used for estimation of the mixedness of the fueland air, which is relevant to the stratified conditions. The results discussed in this chapterpertain to the non-reacting flow. For mixedness calculations, helium is injected through the fuelinjection holes and mixes with the quiescent lab air. The utilized helium is 99.999% chemicallypure, i.e. helium grade 5. Since the experiments are performed for subsonic jets issuing into theatmosphere, the pressure remains at the atmospheric value throughout the field of view of theRayleigh scattering measurements.Helium flows through an aluminum mixing chamber which is in thermal equilibrium withthe lab air and its temperature is 300 K. As a result, the helium temperature equals the roomtemperature. For non-reacting flow conditions and for fuel and air mixture, it is straight forwardto show that the local Rayleigh scattering cross section is the mole fraction-based weightedaverage of the constituent species Rayleigh scattering cross section. This is given byσmix(x, y) = χF(x, y)σF + χO2(x, y)σO2 + χN2(x, y)σN2 , (4.1)where χ is the mole fraction and subscript “F” stands for the fuel. In the present study,44oxygen and nitrogen are not separately provided to the experimental set up, and instead, roomair is provided by a compressor. Assuming that the mole fractions of oxygen and nitrogenare 21% and 79%, respectively, of the air mole fraction (i.e. χO2(x, y) = 0.21χair(x, y) andχN2(x, y) = 0.79χair(x, y)), factoring out σN2 , and considering that χF = 1 − χair, Eq. (4.1)simplifies toσmix(x, y) = σN2{χF(x, y)σFσN2+ [1− χF(x, y)][0.21σO2σN2+ 0.79]}. (4.2)Similar to [1], using the definition of the fuel-air equivalence ratio [99], a correlation betweenthe measured Rayleigh scattering signal for premixed and partially premixed conditions withϕ(x, y) can be theoretically obtained. However, as discussed in Appendix B, the uncertainty inthe Rayleigh scattering measurements negatively influences the ability to estimate the local fuel-air equivalence ratio. For this reason, helium is used in lieu of methane as it features enhancedsensitivity for assessing the quality of mixing, as discussed in the following.Re-writing Eq. (2.4) for the premixed (denoted by subscript P) and stratified (denoted bysubscript S) conditions, and using Eq. (4.2), it can be shown thatIR(x, y)PIR(x, y)S=χF,PσF/σN2 + (1− χF,P)K1χF,SσF/σN2 + (1− χF,S)K1, (4.3)where IR(x, y)P and IR(x, y)S are the measured Rayleigh scattering signals pertaining to thepremixed and stratified conditions, respectively. In Eq. (4.3), χF,P and χF,S are the fuelmole fractions corresponding to the stratified and premixed conditions, respectively, and K1 =0.21σO2/σN2+0.79. Since helium features a relatively small normalized Rayleigh scattering crosssection of 0.013 compared to oxygen of 0.859 (for incident laser light wavelength of 532 nm), thefirst term on the numerator and denominator of Eq. (4.3) can be neglected provided the utilized45“fuel” is helium instead of methane. This suggests that, for helium,IR(x, y)PIR(x, y)S︸ ︷︷ ︸R(x,y)≈ 1− χF,P1− χF,S . (4.4)Variations of the time-averaged IR(x, y)P for helium flow-rates corresponding to methane flow-rates with mean bulk flow velocities of 5, 15, 25, 35, 45, and 50 m/s are presented in Fig. 4.1(a–f),respectively. Similarly, the 2D variations of IR(x, y)S for helium flow-rates set to methane flow-rates of U = 5, 15, 25, 35, 45, and 50 m/s are presented in Fig. 4.2(a–f), respectively. For bothpremixed and stratified conditions, two observations are made. First, IR(x, y)P and IR(x, y)Sare relatively small at the center of the jet and increase by increasing the radial distance fromthe jet centerline. This is due to the helium Rayleigh scattering cross section being significantlysmaller than that of the air. Second, the values of IR(x, y)P and IR(x, y)S become relativelysmall for U = 5 m/s close to the top left corner of the imaging field of view, which is shownby the white dashed boxes in Fig. 4.1(a) and 4.2(a). This means that, at U = 5 m/s, locallylarge values of fuel/air can exist at the top left corner of the imaging field of view. This hasimplications in terms of the generated flame structure for reacting conditions and is discussedlater in Chapter 5.The ratio of IR(x, y)P and IR(x, y)S (that is the LHS of Eq. 4.4) was used for estimationof the mixedness and is referred to as R. A value of R(x, y) < 1 means that, for the strati-fied condition, there exists more fuel compared to the corresponding fully-premixed conditionat (x, y). Similarly, R(x, y) > 1 means that there exists less fuel for the stratified conditioncompared to the perfectly premixed condition at (x, y). R(x, y) estimated for the conditionsshown in Figs. 4.1 and 4.2 are presented in Fig. 4.3. The results in (a–f) pertain to those inFigs. 4.1(a–f) and 4.2(a–f). As can be seen, R(x, y) is nearly unity for the mean bulk flow46605040255075100125150605040-20 0 200-20 0 200-20 0 200L3 L1L1L3L1 L3Fig. 4.1. The time-averaged Rayleigh scattering signals for the premixed condition IR(x, y)P.(a–f) pertain to the helium flow-rates equal to that used for methane flow-rate with mean bulkflow velocities of 5, 15, 25, 35, 45, and 50 m/s, respectively.605040255075100125150605040-20 0 200-20 0 200-20 0 200L3 L1L1L3L1 L3Fig. 4.2. The time-averaged Rayleigh scattering signals for the stratified condition IR(x, y)S.(a–f) pertain to the helium flow-rates equal to that used for methane flow-rate with mean bulkflow velocities of 5, 15, 25, 35, 45, and 50 m/s, respectively.velocity of 5 m/s. However, as the mean bulk flow velocity increases, values of R pertaining toL1 (compared to L3) increase. In order to facilitate comparisons, the integrated values of R for47L1 and L3 were estimated usingRL1 =∫ ymaxymin∫ 0−∆x/2R(x, y)dxdy(∆x/2)∆y, (4.5a)RL3 =∫ ymaxymin∫ ∆x/20 R(x, y)dxdy(∆x/2)∆y, (4.5b)where ymin = 35 mm and ymax = 67 mm are the vertical extents of the integration. In Eqs. (4.5aand 4.5b), ∆x = 40 mm. Changing the horizontal extent of integration changes RL1 and RL3,however, the observed trends remain independent of the horizontal extent of integration.Fig. 4.3. The spatial variation of R, evaluated from the LHS of Eq. (4.4). (a–f) pertain tohelium flow-rates equal to that used for methane flow-rate with mean bulk flow velocities of 5,15, 25, 35, 45, and 50 m/s, respectively.486050406050400.511.5-20 0 200-20 0 200-20 0 200L3 L1L1L3L1 L3Variations of RL1 and RL3 versus the mean bulk flow velocities are presented in Fig. 4.4. Thesize of the error bars in the figure are twice of the standard deviation of R(x, y). It is importantto highlight that the error bars in Fig. 4.4 pertain to the variability in the estimated values of R,rather than uncertainty in the estimation of this parameter. As can be seen in Fig. 4.4, for thecorresponding tested mean bulk flow velocities smaller than 20 m/s, the stratification betweenthe injector is rather small. However, beyond the corresponding mean bulk flow velocity of20 m/s, L1 injects more fuel and the stratification parameter of this lobe is about 14–26% largerthan L3. The above argument suggests that the amount of stratification (or variation in thefuel-air equivalence ratio) is relatively large and non-negligible for U ≥ 20 m/s.0 10 20 30 40 500.811.21.41.61.82Fig. 4.4. Variations of RL1 and RL3 versus the mean bulk flow velocity of the correspondingtested helium flow-rates.49Chapter 5Reacting flow characteristicsIn this chapter, the Rayleigh scattering measurements are used to estimate a parameterthat allows for comparing how fast the tested flames burn for both fully-premixed and stratifiedconditions. The fully-premixed flames are usually visualized using either a marker of the com-bustion species or the flame temperature [14]. Although the present study utilizes the Rayleighscattering measurements, estimation of the gas temperature for reacting conditions is not pos-sible, since this requires instantaneous and spatial information regarding the major combustionspecies variation in the domain of investigation. Traditionally, this is done by assuming a locallylaminar flame structure, relating the normalized Rayleigh scattering cross section to temper-ature using a sixth-order polynomial, and solving the polynomial equation for temperature ateach pixel, see for example [24].The above procedure cannot be used for addressing the objectives of this thesis due to tworeasons. First, the development and application of the relation between the normalized Rayleighscattering cross section and temperature is possible assuming that the fuel-air equivalence ratiois fixed. This assumption is not applicable since the present study is concerned with stratifiedflames, which feature significant deviation compared to the premixed flame counterparts, asdiscussed in Chapter 4. Even for fully-premixed flames, there can exist a significant spatialvariation of the fuel-air equivalence ratio due to the surrounding air entrainment into the re-actants. Second, the assumption of laminar-like structure for turbulent premixed flames is not50reliable at large turbulence intensities. This is extensively discussed in the studies of [4, 22, 81],as well as the review paper by [14]. Thus, instead of temperature, the gas temperature dividedby the normalized mixture Rayleigh scattering cross section was measured and reported, whichis referred to as T ∗ in the present study (see Eq. (2.8)). Characterization of T ∗ is of significantrelevance and importance. First, for the normalized Rayleigh scattering cross section that isclose to unity, T ∗ is nearly the gas temperature. Second, since the information regarding thecombustion species spatial distribution can be available from numerical simulations, T ∗ can beestimated from such simulations and can be reliably compared with the findings of the presentstudy for validation purposes.Figures 5.1(a, c, e, g, and i) present representative 2D variations of T ∗ for fully-premixedflames corresponding to the mean bulk flow velocities of 5, 15, 25, 35, and 45 m/s, respectively.Figures 5.2(a, c, e, g, and i) present representative 2D T ∗ variations of stratified flames, withmean bulk flow velocities of 5, 15, 25, 35, and 45 m/s, respectively. As the mean bulk flowvelocity increases, the results presented in Figs. 5.1(a, c, e, g, and i) and 5.2(a, c, e, g, and i)show that the flames become wrinkled and shredded. For a fully-premixed flame, fixed values oftemperature (and as a result fixed mean progress-variable) have been used in the past to estimatethe preheat and reaction zones thicknesses, see for example [24]. However, since the stratifiedflames experience variation of the fuel-air equivalence ratio in space and time, using fixed valuesof the progress variable for identifying the flame region should not/cannot be implemented here.Instead, an alternative approach, which is developed based on the probability density function(PDF) of the measured T ∗ is proposed and utilized for the entire domain of investigation. Thiswas done by taking the temperature range of 300–2500 K and dividing it into 200 bins for agiven tested condition. The number of the pixels of all frames that correspond to a certain bin51were obtained and divided by the total number of the pixels in all frames to estimate the PDF.605040605040605040605040-20 0 200-20 0 200605040400 1400 2400FullyPremixed(k)(i)(g) (h)(d)(c)(b)(a)(f)(e)L1L3L1 L3,jFig. 5.1. (a, c, e, g, and i) are the reduced temperature fields pertaining to mean bulk flowvelocities of 5, 15, 25, 35, and 45 m/s, respectively. (b, d, f, h, and k) are the binarized flameregions for mean bulk flow velocities of 5, 15, 25, 35, and 45 m/s, respectively. The results arefor fully-premixed flames.52605040605040-20 0 200605040605040605040400 1400 2400-20 0 200PartiallyPremixed(k)(i)(h)(g)(c) (d)(f)(a) (b)(e)L1L3L1 L3Fig. 5.2. (a, c, e, g, and i) are the reduced temperature fields pertaining to mean bulk flowvelocities of 5, 15, 25, 35, and 45 m/s, respectively. (b, d, f, h, and k) are the binarized flameregions for mean bulk flow velocities of 5, 15, 25, 35, and 45 m/s, respectively. The results arefor stratified flames.53Figure 5.3 presents variation of T ∗ PDF for all tested conditions. The results are color-coded based on the tested mean bulk flow velocities. The solid and dashed curves pertain tofully-premixed and stratified conditions, respectively. As can be seen, the PDF of T ∗ for alltested conditions features two peaks at small and large values of this parameter, which pertainto fresh reactants (T ∗R) and fully burnt (T∗B) gases. Also, presented by the dotted-dashed line inthe figure is the normalized adiabatic flame temperature, T ∗AD. Using the Cantera [9] simulationof a fully-premixed and freely propagating stoichiometric methane-air flame, it can be shownthat T ∗AD is 2227/(0.938/0.9704) = 2304 K. The peak corresponding to the fresh gases occursat T ∗R ≈ 344 K. Considering that, in the reactants, σmix ≈ 1.08σN2 and that σref ≈ 0.97σN2 ,the reactants temperature at the location of measurements feature a most probable value of344 × 1.08/0.97 ≈ 380 K. This temperature is larger than the room-air temperature (300 K).The T ∗ measurements are performed at a vertical distance ranging from 35 to 67 mm above theinjector exit plane. This could lead to preheating of the reactants in the domain of investigationand as a result, the 380 − 300 = 80 K difference reported between the reactants temperatureand the lab air temperature.The results presented in Fig. 5.3 show that the peak at larger T ∗ values are related to theburnt gas. The second peak features a relatively broad variation. The reason for this is related tothe nature of the Rayleigh scattering measurements. Specifically, since the Rayleigh scatteringsignal is inversely related to the temperature, small Rayleigh signals correspond to the burntgas. This signal can become comparable to the background noise, which cannot be measured onan instantaneous basis in the present study and can lead to uncertainty in estimation of T ∗ inthe products region. However, such uncertainty can be reduced by increasing the energy of thelaser. Nonetheless, the energy of the laser (530 mJ/pulse) used in this thesis is relatively large54compared to those tested in the literature to the author’s best knowledge.500 1000 1500 2000 250000.050.10.150.20.25Fig. 5.3. The probability density function of the normalized flame temperature. The solid anddashed curves pertain to fully-premixed and stratified conditions, respectively. The results arestepped for clarity. T ∗AD is shown by the dotted-dashed line.Variation of the normalized burnt gas temperature, T ∗B, for all tested conditions are presentedin Fig. 5.4. The size of the error bars in Fig. 5.4 are twice of the standard deviation of T ∗B. Theresults related to premixed and stratified flames are shown by the blue circular and red squaredata symbols, respectively. As can be seen, generally, increasing the mean bulk flow velocityand stratifying the fuel-air mixture decreases the reduced temperature of the burnt gas, exceptfor U ≥ 40 m/s. The reason for this is unknown to the author.555 10 15 20 25 30 35 40 45 50130015001700190021002300Fig. 5.4. Variation of the normalized burnt gas temperature versus the tested mean bulk flowvelocity.The following procedure was used to obtain the instantaneous flame region for all testedconditions. In this thesis, the flame region is defined as where the effects of the reactants andburnt gas are not significant. Specifically, such significance is assessed based on the probabilitydensity function of T ∗. First, T ∗ corresponding to the minimum of the PDF for T ∗R < T∗ < T ∗Bwas obtained. To illustrate this, the PDF of T ∗ for fully-premixed flames at U = 45 m/s is pre-sented in Fig. 5.5. As shown in the figure, the PDF minimizes at T ∗ = 1052 K. This normalizedtemperature is referred to as T ∗M and was then used to estimate the upper bound of the flameregion normalized temperature, which is referred to T ∗2 . At this normalized temperature, thePDF of T ∗ differs by a small value from PDF (T ∗M). This is estimated using a threshold value,th, given byth =PDF (T ∗2 )− PDF (T ∗M)PDF (T ∗B)− PDF (T ∗M). (5.1)56In the present study, th is a small threshold value and was set to 1%. The reason for selectionof this small value is to ensure that the selected upper bound normalized temperature is notinfluenced by the uncertainty of the Rayleigh scattering measurements in the products, see thebell-curve around T ∗B in Fig. 5.5. The lower bound of the flame normalized temperature wasobtained such that the combustion progress variable defined as the flame normalized temperaturevaries by a fixed value of 50% for all tested conditions. That isT ∗1 − T ∗RT ∗B − T ∗R=T ∗2 − T ∗RT ∗B − T ∗R− 12. (5.2)This yieldsT ∗1 = T∗2 −12(T ∗B − T ∗R) . (5.3)The values of T ∗1 and T ∗2 for the condition shown in Fig. 5.5 are 532 K and 1151 K, respectively.The data points with PDFs in between the PDFs of these reduced temperatures highlight theflame region, and are shown by the green color data points in the figure.The variation of T ∗1 and T ∗2 for premixed and stratified flames are presented in Fig. 5.6(a)and (b), respectively. As can been seen, the values of the lower bound normalized temperaturevaries between 372 and 532 K for premixed flames and 487 and 616 K for stratified flames. Theupper bound normalized temperature varies between 1151 and 1265 K for premixed and 1140and 1295 K for stratified flames, respectively. For all tested conditions, the corresponding upperand lower bounds normalized temperatures presented in Fig. 5.6 were used to estimate the flameregion. The flame regions for the representative frames shown in Figs. 5.1 and 5.2(a, c, e, g, andi) are presented in Figs. 5.1 and 5.2(b, d, f, h, and k), respectively.The above procedure allows for obtaining the flame region without a-priori knowledge of thefuel-air equivalence ratio distribution. It is acknowledged that the above results would change57500 1000 1500 2000 250000.0050.010.015Fig. 5.5. The normalized temperatures of the flame region. The PDF pertains to the testedfully-premixed flames with U = 45 m/s.provided th value and the criterion in Eq. (5.3) changed. For comparison purposes, all of theupper and lower bounds of the normalized temperatures were used to estimate the laminarflame thickness, using Cantera [9] simulations of premixed flames with unity fuel-air equivalenceratio. The results show that, for all tested conditions, T ∗1 and T ∗2 are separated by about 0.18to 0.28 mm, which is larger but on the order of the laminar flame thickness of stoichiometricmethane-air premixed flames.In order to estimate the flame burning area (AT), the number of pixels pertaining to T ∗1 <T ∗ < T ∗2 was calculated for all tested conditions. In order to facilitate comparisons and removedependence on the size of the domain of investigation, for each condition, the number of pixelsfor two vertical laminar flames (obtained from the Cantera [9] simulations from a perfectlypremixed and freely propagating stoichiometric methane-air flame) on the left and right sides of584006008001000120010 20 30 40400600800100012001400Fig. 5.6. Variations of T ∗1 and T ∗2 for all tested conditions.the field of view were obtained (AL). Variation of AT/AL versus the mean bulk flow velocity forall tested conditions are presented in Fig. 5.7. The size of the error bars in the figure equal twicethe standard deviation of the normalized burning area. It is acknowledged that the reportedmeasurements of (AT/AL) for L1 and L3 are subject to change for L2 and L4. As highlighted inthe figure, for both fully-premixed and stratified flames, the normalized burning area related tothe mean bulk flow velocities smaller than 25 m/s are relatively larger than those for U ≥ 25 m/s.The reason for the large values of the flame burning area is speculated to be linked to the flamesgenerated by the neighboring (out of plane) lobes. In other words, the flame area corresponding59to U < 25 m/s features contributions from lobes other than L1 and L3. In order to investigatethis, the results related to the non-reacting flow field discussed in Chapter 4 are used.0 10 20 30 40 50051015202530354045Fig. 5.7. Variation of the normalized flame burning area versus the mean bulk flow velocity.The results presented in Fig. 4.1(a) and Fig. 4.2(a) showed that, for U = 5 m/s, the Rayleighscattering intensity at the top left corner (x ≈ −20 mm and y ≈ 60 mm) of the field of viewis relatively small (see the white dashed boxes in the figures). This suggests that a noticeablefuel/air mixture exists in this region. In order to demonstrate this, 3D schematics of the flamestructures corresponding to U = 5 and 45 m/s are employed and presented in Figs. 5.8(a)and (b), respectively. Overlaid on the figure are the speculated trajectories of the injectedfuel/air from the neighboring lobes (L2 and L4). These trajectories are visualized based onthe velocity data presented in [1] assuming an axisymmetric flow. It is speculated, for the testconditions corresponding to U = 5 m/s, the fuel/air injected from L4 is ignited in the domainof investigation (see the pink circular and cross data symbol in Fig. 5.8(a)) leading to formation60of the flame structures shown by the yellow dashed boxes in Figs. 5.1(b) and 5.2(b). In additionto contributions from the flames generated by the neighboring lobes, since the studied flamesare open and the temperature of the burnt gas has to decrease to the room temperature at largehorizontal distances, the reduced temperature attains values corresponding to T ∗1 < T ∗ < T ∗2 ,which pertain to those of a flame. Such structure is highlighted in Fig. 5.8(a) by the blackcurve, and does not pertain to reaction zone/flame region. Compared to the test conditionsrelated to U = 5 m/s, increasing the mean bulk flow velocity pushes the flame generated bythe neighboring lobes (see the red dashed curve and cross data symbol in Fig. 5.8(b)) outsideof the field of view, and the flames are V-shaped. In essence, the above discussions suggestthat, for U < 25 m/s, the relatively large values of AT/AL reported in Fig. 5.7 are influencedby either the flames generated from the neighboring lobes and/or by the intermediate reducedtemperature regions due to mixing.Compared to the flame structure related to U < 25 m/s, those corresponding to U ≥ 25 m/sare not influenced by the above effects and the generated flames only pertain to L1 and L3. Inorder to investigate the effect of turbulence on the flame area ratio, variation of AT/AL versusu′ normalized by SL0 is presented in Fig. 5.9. The overline in SL0 highlights that all testedflames (both premixed and stratified) correspond to globally stoichiometric methane-air flameswith the freely propagating laminar flame speed of 0.37 m/s.To facilitate comparisons, variation of the burning rate estimated from the formulation inMohammadnejad et al. [4] is also presented by two black solid curves in the figure. Two variationsare presented as the normalized integral length scale is not fixed in the present study. Thecurves are estimated based on the minimum and maximum values of the normalized integrallength scales. It is acknowledged that the normalized flame burning area does not equate the61myIAyiguana ygggggggyIggyxzyL3L1L2L4myµyiroupzxL2L4IAyL1L3Fig. 5.8. The 3D schematics of the flame structures for U = 5 and 45 m/s are shown (a) and (b),respectively. Overlaid on the figure are the speculated trajectories of the injected fuel/air fromthe neighboring lobes (L2 and L4) shown by the pink and red circular and cross data symbols,respectively.normalized turbulent flame consumption speed for both premixed and stratified flames. For thepremixed flames, AT/AL does not account for the local variation of the flame stretch and howthis influences the burning rate. For the stratified flames, AT/AL does not account for the localvariation of the fuel-air equivalence ratio and how this parameter changes the flame stretch andas a result the flame burning rate. Nevertheless, the results in Figs. 5.7 and 5.9 suggest thatstratification can slightly increase the normalized burning area. This reconciles the conclusionsreported in [1]. However, compared to the results presented in [1], the present study suggeststhis conclusion can be extended to larger mean bulk flow velocities and turbulence intensities,which are more relevant for industrial applications of the utilized injector.620 5 10 15 20 25510152025Fig. 5.9. Normalized burning area versus the normalized turbulence intensity. The solid linesare the predictions of [4].63Chapter 6Conclusions6.1 Concluding remarksThe non-reacting flow along with the mixing and flame characteristics generated by an in-dustrial injector were investigated experimentally. The mean bulk flow velocity was varied from5 to 50 m/s in increments of 5 m/s for the non-reacting flow experiments. At 50 m/s, the pre-mixed flames cannot be stabilized, however, stratification may facilitate the flame stabilization.For fully-premixed flames, the fuel-air equivalence ratio is set to unity, and the stratified flamesare globally stoichiometric. A burner identical to that in [78] was used, except the nozzle wasreplaced with the injector provided by the industrial partner. The non-reacting flow characteris-tics were studied using cross-wire anemometry. The Rayleigh scattering was used to study boththe mixedness fields as well as the characteristics of the generated flames.Hot-wire anemometry of the non-reacting flow was performed to study mean and RMSvelocity profiles generated by the injector as well as the spectral content of the velocity data.Analysis of the hot-wire anemometry results show that, near the injector centerline, the presenceof a bluff body decelerates the flow and leads to large RMS velocity fluctuations. The powerspectrum density of the velocity data does not suggest existence of a flow instability for U ≤25 m/s. However, for mean bulk flow velocities larger than 25 m/s, the flow features a dominantinstability at 1790 Hz, which is most pronounced near the center of the injection lobes.646.1. CONCLUDING REMARKSA framework was developed and used to study the mixedness of the non-reacting flow gen-erated by the injector. It was shown that, for mean bulk flow velocities smaller than 25 m/s,stratification is not pronounced. However, for mean bulk flow velocities larger than or equalto 25 m/s, the left (right) hand side lobe of the injector generates a rich (lean) mixture. TheLHS lobe injects more fuel and the stratification parameter of this lobe is about 14–26% largerthan the RHS lobe. It was discussed that, while the Rayleigh scattering measurements allow toobtain the mixedness fields, deducing the fuel-air equivalence ratio from these measurements isnot possible.A new parameter, referred to as the reduced temperature, was introduced to establish arobust method for studying the flame structures and how fast both fully-premixed and stratifiedflames burn. The PDF of the normalized temperature showed two peaks for all tested conditions;one at the reactant normalized temperature and the other one at the burnt gas temperature.The results show that, for all tested mean bulk flow velocities (except at U = 40 and 45 m/s),the burnt gas temperature is consistently smaller for the stratified conditions compared to thepremixed counterpart. The reason for this is not known to the author.Using the PDF of the reduced temperature, the flame regions for all tested conditions wereobtained. Using this as well as the results related to the mixedness fields, it was shown that,for mean bulk flow velocities smaller than 25 m/s, the neighboring injection lobes contribute tothe burning area. For mean bulk flow velocities larger than or equal to 25 m/s, the generatedflames only pertain to the investigated lobes; and, the results suggest that stratification slightlyincreases the normalized burning area. This conclusion is in agreement with that reported in[1], but extends it to relatively large and more industrially relevant flow conditions.656.2. FUTURE WORK6.2 Future workThough this thesis aimed to address a gap in the literature related to stratified turbulentflames, future research is required to further support and extend the conclusions and frameworksdeveloped here. In the following, the details of recommended future research are discussed.1. This thesis used an open swirling-type flame in order to generate results comparable tothose of a previous study by Mohammadnejad et al. [1]. It is acknowledged that closedflames are more relevant to industrial applications. Thus, it is recommended that a com-bustion chamber should be integrated with the burner shown in Fig. 2.1, and the resultsshould be compared against those of the present thesis. Such industrially relevant flamescould impact the instability observed and reported in Fig. 3.3.2. Considering that, even perfectly premixed flames used in the literature are exposed tosome degree of mixing with the lab room air, the assumption of fixed fuel-air equivalenceratio is not accurate for premixed flames. The present study proposed a new frameworkfor analysis of either premixed or stratified flames structure. Experiments can be done fora variety of perfectly premixed flames, assessing the validity of the proposed frameworkand investigating if such framework can capture the predicted perfectly premixed flamestructure in the literature.3. Considering that the injector used in the present study is relevant/used for hydrogen-enriched methane-air flames in the industrial partner combustors, future experiments arerequired to extend the findings to such and other cleaner fuels.4. The present thesis is completed for the most industrially relevant type of an injector family.The injector, as shown in [1] features a swirling flow. Although this study extended the666.2. FUTURE WORKfindings reported in [1] to mean bulk flow velocities that are at least twice as large as thosetested in [1], it is unclear how the swirling flow, itself, impacts the reported results. Thisis important since such knowledge can be used for improving the injector design. It isproposed that similar experiments should be carried out for injectors that do not imposethe swirling flow motion.67Bibliography[1] Mohammadnejad, S., Saca, L., Heydarlaki, R., An, Q., Vena, P., Yun, S., Versailles, P.,Bourque, G., and Kheirkhah, S., 2021. “Effect of fuel stratification on OH and CH2O PLIFmultiplication of turbulent hydrogen-enriched flames”. Flow, Turbulence and Combustion,pp. 1–39.[2] Saca, L., Mohammadnejad, S., Versailles, P., Bourque, G., and Kheirkhah, S., 2022. “Pre-heat and reaction zones thicknesses of stratified premixed flames generated by an industrialinjector”. AIAA SciTech Forum, pp. 2057.[3] Peters, N., 1988. “Laminar flamelet concepts in turbulent combustion”. 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Technical drawings of the burnerrodoc#3/8 NPT TYP5.086.205.283.16113°1.120.378.445.289.787.974.543.764x0.130.79O ring groove9.783.768.447.9712 X 0.13 THRUFig.A.2.SolidWorksdrawingoftheexpansionsection.85Appendix A. Technical drawings of the burner8.549.788.008.660.048.6612 x 0.190.508.009.788.4412 x 0.130.508.006.58Fig.A.3.SolidWorksdrawingofthesettlingchamber.86Appendix A. Technical drawings of the burner8.447.978.441.42Fig.A.4.SolidWorksdrawingoftheretainingringsthatholdthemeshscreensinthesettlingchamber.87Appendix A. Technical drawings of the burner12 X 1/4-289.139.786.005.194.484.000.3012 X TBD THRU9.509.000.509.75Fig.A.5.SolidWorksdrawingoftheplenum.88Appendix BThe relation between the fuel-airequivalence ratio and the measuredRayleigh scattering signalUsing the definition of the fuel-air equivalence ratio, ϕ(x, y), it can be shown that [99]:ϕ(x, y) =AF|st χFMWFχairMWair, (B.1)where A/F |st is the air to fuel mass ratio for stoichiometric reaction. Using χair(x, y) = 1 −χF(x, y), Eq. (B.1) simplifies to:χF(x, y) =ϕ(x, y)ϕ(x, y) + AF |st MWFMWair. (B.2)Combining Eqs. (2.4), (4.2), and (B.2), it can be shown that:IR(x, y)CoptIi(x, y)[P/(kT )]σN2=ϕ(x, y)ϕ(x, y) +K2σFσN2+K1(1− ϕ(x, y)ϕ(x, y) +K2), (B.3)where K1 = 0.21σO2/σN2 + 0.79 and K2 = A/F |st(MWF/MWair). K1 varies linearly with theRayleigh scattering cross section of oxygen molecule divided by that for the nitrogen molecule,89Appendix B. The relation between the fuel-air equivalence ratio and the measured Rayleigh scattering signalwhich depends on the wavelength of the incident laser. For the wavelength of the utilized laserin the present study (532 nm), σO2/σN2 = 0.859 [11], and K1 equals 0.97. For a given fuel, K2is fixed. It can be shown that for H2, CO, CH4, and C2H4, K2 equals 2.37, 2.45, 9.48, and 9.48,respectively. Values of σF/σN2 depend on the tested fuel and the laser excitation wavelength.For the wavelength of 532 nm, the values of σF/σN2 were extracted from [11]. For H2, CO, CH4,and C2H4, σF/σN2 equals 0.216, 1.245, 2.134, and 5.803, respectively. Thus, the above argumentcan be used to show that only the fuel-air equivalence ratio is unknown on the right-hand-sideof Eq. (B.3). On the left-hand-side of Eq. (B.3), Copt is unknown as well. In order to removethis unknown, experiments can be conducted for both the stratified (denoted by subscript S),and fully-premixed (denoted by subscript P) non-reacting conditions. Writing Eq. (B.3) forboth stratified and fully-premixed conditions and considering that the fuel-air equivalence ratiois constant and equals unity for fully-premixed condition, it can be shown thatIR(x, y)SCoptIi(x, y)[P/(kT )]σN2=ϕ(x, y)Sϕ(x, y) +K2σFσN2+K1(1− ϕ(x, y)ϕ(x, y) +K2), (B.4a)IR(x, y)PCoptIi(x, y)[P/(kT )]σN2=11 +K2(σFσN2+K1K2). (B.4b)Dividing the LHS and RHS of Eqs. (B.4a) and (B.4b), it is obtained thatϕ(x, y) =K2{K1 − IR(x,y)SIR(x,y)P[11+K2(σFσN2+K1K2)]}IR(x,y)SIR(x,y)P[11+K2(σFσN2+K1K2)]− σFσN2. (B.5)Variations of ϕ(x, y) versus IR(x, y)S/IR(x, y)P were estimated for H2, CO, CH4, and C2H4and the results are presented in Fig. B.1(a). Also, overlaid on the figure is the variation ofIR(x, y)S/IR(x, y)P for helium. Since helium is an inert gas, the air to fuel ratio for a stoichio-90Appendix B. The relation between the fuel-air equivalence ratio and the measured Rayleigh scattering signalmetric condition is not available. Here, it is assumed that A/F |st for hydrogen can be usedto estimate this ratio for helium. As a result, K2 estimated for helium is 4.74. The resultspresented in Fig. B.1(a) suggest similar variations for helium and hydrogen. For clarity pur-poses, an inset of the figure is enlarged and shown in Fig. B.1(b). As can be seen by the graylines, for an arbitrary variation of ϕ(x, y) = 1 ± 0.2, hydrogen features the largest variation ofIR(x, y)S/IR(x, y)P = 1±0.05, closely followed by helium. The estimated sensitivity for methaneis about ±1% (compared to 5% for hydrogen). Such variation/sensitivity is deemed relativelysmall, and as a result, the formulation in Eq. (B.5) cannot be used for estimation of the fuel-airequivalence ratio in the present study [81].0.5 1 1.5051015H2CH4COC2H4He0.8 0.9 1 1.1 1.20.511.52Fig. B.1. Variation of ϕ(x, y) versus IR(x, y)S/IR(x, y)P.91Appendix CUncertainty analysisThis appendix aims to estimate the uncertainty associated with the experimental measure-ments conducted for this investigation. Of primary importance to this thesis are the velocityand the reduced temperature, with relevant uncertainty analysis presented in the following.The uncertainty analysis corresponding to the hot-wire anemometry measurements using across-wire probe was performed following [100]. Moffat [100] stated that the uncertainty (U0.95)associated with an experimentally measured parameter includes the precision error (Se) and thebias error (Bi). U0.95 is given byU0.95 =√Bi2 + (2Se)2, (C.1)The precision error is [100]Se =σN, (C.2)where σ is the standard deviation of the collected data, and N is the number of the data points.A conservative estimation of the precision error was performed by considering the maximumvalue of σ for the velocity data related to the test condition with the largest RMS and is aboutSe = 10−5 m/s, which is deemed insignificant. As a result, U0.95 ≈ Bi. Moffat [100] listed threesources of bias error, which are related to calibration, data acquisition, and data reduction. For92Appendix C. Uncertainty analysishot-wire anemometry, the study of Kawall et al. [101] showed that for a ratio of u′/U ≤ 15%(which is relevant to the present study), the dominant source of error is attributed to calibrationas well as the separation between the wires of the cross-wire probe. While quantifying the formerwas possible in the present study, the latter was not quantified. Jørgensen [86] used a mini-CTA and calibrator identical to that of the present study and concluded that the calibrationuncertainty was ± 1%. Thus, it is concluded that the error for the velocity measurements in thepresent study is U0.95 = 1%.500 1000 1500 2000 250000.020.040.060.080.10.120.140.16500 1000 1500 2000 25002.8%2.7%0.6%6.7%Fig. C.1. The variation of PDF∗ at U = 45 m/s for values of IS = 16, 17 and 18. The results in(a) and (b) are for the fully-premixed and stratified conditions, respectively.It is postulated that the major source of error in the temperature (or T ∗) measurements isassociated with IS. As evident from Eq. (2.4), IR is relatively small in the combustion products,and a small change of this parameter could lead to a significant uncertainty in estimation of T ∗.This uncertainty is present in Fig. 5.3 as the PDF of T ∗ has a broad variation in the products.Following the above discussion, the effect of the variation of IS on the PDF of T∗ wasinvestigated. Figure. C.1(a) and (b) show the PDF∗ for U = 45 m/s of the fully-premixed and93Appendix C. Uncertainty analysisstratified conditions, respectively. Each variation corresponds to a value of IS = 16 (blue), 17(red) and 18 (black). Comparing the values of T ∗B for the fully-premixed condition with IS = 17(used for the calculations of the present study) to values of T ∗B with IS = 16 and 18 suggesteda variation of about 2.7% and 2.8%, respectively. Similarly, the values of T ∗B for the stratifiedcondition with IS = 17 compared to values of T∗B for IS = 16 and 18 suggested a variation of0.6% and 6.74%, respectively.94
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Kheirkhah, Sina
A new framework for analysis of fully-premixed and stratified turbulent flames generated by an industrial injector
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