Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Mollahoseini, Zahra
Master of Applied Science - MASc
University of British Columbia
Characteristics of flame development inside a small-scale power generator model combustor featuring a reverse-flow configuration and the influence of such configuration on these characteristics from early stages of combustion to the steady operation of the combustor are investigated experimentally. Simultaneous and high-speed OH* chemiluminescence and pressure measurements are utilized. Two sets of experiments are performed. In the first set, relatively lean premixed methane/air flames with a fuel-air equivalence ratio of 0.7 have been investigated. For these, four experiments pertaining to air flow rates of 100 and 160 standard liters per minute along with two igniter rod positions are performed. For the second set of experiments, the igniter position was fixed, and two fuel-air equivalence ratios of 0.9 and 1 along with two air flow rates of 120 and 130 standard liters per minute are tested. The results pertaining to the first set of experiments suggest that, prior to the appearance of steady thermoacoustic oscillations, three phases, namely, ignition, stabilization, and transition may exist. During the ignition phase, the normalized flame edge velocity can achieve relatively large maximum values owing to the reverse-flow configuration compared to that for closed chambers. The ignition phase is followed by the stabilization phase during which the flame is formed on the flame-holder. During the transition phase, the flame chemiluminescence features one long-period sinusoidal oscillation. Despite significant influence of the reverse-flow configuration on flame dynamics during the ignition and stabilization phases, the spectral characteristics of pressure and flame chemiluminescence oscillations are similar to those of unconfined flames. The results pertaining to the relatively rich flames suggest, depending on the phase of the flame development, the reverse-flow combustor can serve as either a closed or an open system. It was shown that, during the ignition and stabilization phases, the thermoacoustic fluctuations are dominated by small frequencies associated with the structural and acoustic modes. However, during the steady operation, the intrinsic thermoacoustic modes also become apparent and contribute to the thermoacoustic oscillations. The results of this study have implications for improving the ignition quality and mitigating the thermoacoustic oscillations in reverse-flow combustors used for small-scale power generation purposes.
Flame development characteristicsinside a reverse-flow model combustorfrom early stages of combustion tosteady operationbyZahra MollahoseiniB.Sc., Sharif University of Technology, 2015M.Sc., University of Tehran, 2018A 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)March 2021© Zahra Mollahoseini, 2021The following individuals certify that they have read, and recommend to the College ofGraduate Studies for acceptance, a thesis/dissertation entitled:Flame development characteristics inside a reverse-flow model combustor from early stagesof combustion to steady operationsubmitted by Zahra Mollahoseini in partial fulfillment of the requirements of the degree ofMaster of Applied ScienceDr. Sina Kheirkhah, UBC, School of EngineeringSupervisorDr. Patrick Kirchen, UBC, Mechanical EngineeringCo-supervisorDr. Sunny Li, UBC, School of EngineeringSupervisory Committee MemberDr. Joshua Brinkerhoff, UBC, School of EngineeringSupervisory Committee MemberDr. Morad Abdelaziz, UBC, School of EngineeringUniversity ExamineriiAbstractCharacteristics of flame development inside a small-scale power generator model combustorfeaturing a reverse-flow configuration and the influence of such configuration on these character-istics from early stages of combustion to the steady operation of the combustor are investigatedexperimentally. Simultaneous and high-speed OH∗ chemiluminescence and pressure measure-ments are utilized. Two sets of experiments are performed. In the first set, relatively leanpremixed methane/air flames with a fuel-air equivalence ratio of 0.7 have been investigated. Forthese, four experiments pertaining to air flow rates of 100 and 160 standard liters per minutealong with two igniter rod positions are performed. For the second set of experiments, theigniter position was fixed, and two fuel-air equivalence ratios of 0.9 and 1 along with two airflow rates of 120 and 130 standard liters per minute are tested. The results pertaining to thefirst set of experiments suggest that, prior to the appearance of steady thermoacoustic oscilla-tions, three phases, namely, ignition, stabilization, and transition may exist. During the ignitionphase, the normalized flame edge velocity can achieve relatively large maximum values owingto the reverse-flow configuration compared to that for closed chambers. The ignition phaseis followed by the stabilization phase during which the flame is formed on the flame-holder.During the transition phase, the flame chemiluminescence features one long-period sinusoidaloscillation. Despite significant influence of the reverse-flow configuration on flame dynamicsduring the ignition and stabilization phases, the spectral characteristics of pressure and flameiiiAbstractchemiluminescence oscillations are similar to those of unconfined flames.The results pertaining to the relatively rich flames suggest, depending on the phase of theflame development, the reverse-flow combustor can serve as either a closed or an open system. Itwas shown that, during the ignition and stabilization phases, the thermoacoustic fluctuations aredominated by small frequencies associated with the structural and acoustic modes. However,during the steady operation, the intrinsic thermoacoustic modes also become apparent andcontribute to the thermoacoustic oscillations. The results of this study have implications forimproving the ignition quality and mitigating the thermoacoustic oscillations in reverse-flowcombustors used for small-scale power generation purposes.ivLay SummaryDynamics of ignition and flame propagation inside a power generator model combustor areinvestigated experimentally. The combustor features a stagnation wall that generates a reverse-flow configuration. The results of this study show that such configuration causes non-smoothstart of the combustor which is characterized by high-amplitude and irregular pressure oscilla-tions. For this combustor, it takes about a few seconds to reach the steady-state oscillations.During these few seconds, two distinct phases, namely, the ignition and stabilization have beenidentified. It is demonstrated that, during these phases, the combustor serves as a closed sys-tem. However, after the ignition and stabilization phases, the flame development characteristicsare similar to those of an open system. It is shown that the origins of oscillations are relatedto whether the combustor serves as a closed or open system. This information allows for theimproved design and operation of small-scale power generators.vPrefaceThe research presented in this thesis was conducted by the author under the supervisionof Professor Sina Kheirkhah in the Combustion for Propulsion and Power Laboratory at theUniversity of British Columbia. The experimental apparatus was designed and manufacturedby Etalim Inc. Parts of this thesis were published in the journal of Experimental Fluid andThermal Science [1] and presented in the 73rd annual meeting of the American Physical Society-Division of Fluid Dynamics in November 2020 [2].viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 General overview and problem statement . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Laminar flame speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Early stages of combustion . . . . . . . . . . . . . . . . . . . . . . . . . . 9viiTABLE OF CONTENTS1.2.3 Later stages of combustion . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Chapter 2: Experimental Methodology . . . . . . . . . . . . . . . . . . . . . . . . 202.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3 Tested conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Chapter 3: Flame development at early stages of combustion . . . . . . . . . . 283.1 Pressure and flame chemiluminescence characteristics . . . . . . . . . . . . . . . . 283.2 Flame edge velocity characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3 The relation between pressure, flame chemiluminescence, and flame edge velocity 443.4 The spectral characteristics of pressure, flame chemiluminescence, and flame edgevelocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Chapter 4: Signature of thermoacoustic modes at early stages of combustion 524.1 Temporal variations of pressure, pressure rate, flame chemiluminescence, andflame edge velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 Spectral characteristics of pressure, flame chemiluminescene, and flame edge ve-locity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Chapter 5: Conclusions and future directions . . . . . . . . . . . . . . . . . . . . 635.1 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67viiiTABLE OF CONTENTSAppendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Appendix A: Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Appendix B: Estimation of the heat release rate from the conservation of energy 94ixList of TablesTable 2.1 Experimental parameters for the results discussed in Chapter 3. . . . . . . 25Table 2.2 Experimental parameters for the results discussed in Chapter 4. . . . . . . 25Table 2.3 Tested conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Table 3.1 Parameters pertaining to Flames A–D with the details listed in Table 2.3 30Table 3.2 Parameters utilized in Eqs. (1.1-1.5).  and β are extracted from [29]and [23] for CH4-air and H2-air mixtures, respectively. For all presentedstudies, Pref = 1 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 4.1 The time periods of the ignition (tig.) and stabilization (tst.) phases, per-centile of the excessive OH∗ chemiluminescence (λ), structural (fs), acous-tic (fn), first intrinsic (fI,1), and second intrinsic (fI,2) mode frequenciespertaining to Flames E–H. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Table A.1 Effects of binning window size and median-based filter size on OH∗max. . . 91xList of FiguresFigure 1.1 Diagram schematically presenting propagation of a planar laminar flameinto unburnt and compressed fuel/air mixture. . . . . . . . . . . . . . . . 3Figure 1.2 Schematic of the Darrieus-Landau instability development. The figure isadopted from [30, 32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 1.3 Schematic of the thermal-diffusive instability development. The figure isadopted from [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.4 Schematic of the Rayleigh-Taylor instability development. The figure isadopted from [47]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 1.5 Flame topologies during the premixed flame development inside ducts/tubes. 11Figure 2.1 (a) Technical drawing of the power generator model combustor. (b)Technical drawing of the burner. Please note that in (b), the optically-accessible exhaust tubes are removed for clarity purposes. . . . . . . . . . 21Figure 2.2 Schematic view of the burner shown in Fig. 2.1(a). . . . . . . . . . . . . . 22Figure 2.3 (a) Raw, (b) background subtracted, (c) camera and intensifier sensitivitycorrected, (d) binned, and (e) median-based filtered images. Flow is fromleft to right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26xiLIST OF FIGURESFigure 3.1 (a) and (b) are variations of the normalized pressure (black color) andspatially-averaged flame chemiluminescence (red color) related to the ig-nition and stabilization as well as the transition phases, respectively. Thedashed curve in (b) demonstrates nearly one oscillation of the spatially-averaged flame chemiluminescence during the transition phase. The re-sults pertain to Flame C condition. . . . . . . . . . . . . . . . . . . . . . 29Figure 3.2 (a–h) are the flame chemiluminescence at t = 13.2, 36.6, 91.6, 793.4,884.2, 913.0, 966.0, and 1070.0 ms, respectively. The results pertain toFlame C condition and are related to those shown in Fig. 3.1. Flow isfrom left to right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 3.3 (a) and (b) are variations of the normalized pressure (black color) andspatially-averaged flame chemiluminescence (red color) related to the ig-nition and stabilization phases as well as the steady oscillations, respec-tively. (c) and (d) are the flame chemiluminescence at t = 11.6 and131.6 ms, respectively. The results correspond to Flame D condition. In(c) and (d), flow is from left to right. . . . . . . . . . . . . . . . . . . . . 33Figure 3.4 (a) A representative chemiluminescence image at t = 7.4 ms related toFlame A condition. (b) Edges of the chemiluminescence image detectedby the Sobel algorithm. (c) Flame edge overlaid on the chemiluminescenceimage. The inset of (c) represents the flame edge near y = 0. Flow isfrom left to right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35xiiLIST OF FIGURESFigure 3.5 (a), (b), and (c) are samples of the flame edge position, x(t), during igni-tion, stabilization, and transition phases, respectively. The solid curve isthe flame position after applying the spline smoothing and interpolation.(d), (e), and (f) are the flame edge velocity, V (t), corresponding to theresults presented in (a), (b), and (c), respectively. The results pertain toFlame A condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 3.6 (a) Variation of the normalized flame edge velocity during the ignitionperiod. twall is the time that the flame skirt nearly reaches the combustionchamber side-walls. (b-f) present the flame chemiluminescence during theignition period at t/twall = 0.32, 0.46, 0.57, 0.78, and 1, respectively. Theresults pertain to Flame A condition. In (b–f), flow is from left to right. 38Figure 3.7 Variations of the normalized OH∗ corresponding to (a) Fig. 3.6(e) witht/twall = 0.78 and (b) corresponding to Fig. 3.6(f) with t/twall = 1. . . . . 39Figure 3.8 Variation of the maximum normalized flame edge velocity with the com-bustion chamber aspect ratio. . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.9 Flame chemiluminescence during the stabilization phase. The white solidcurve is the flame edge. The dashed ellipses highlight the flame detach-ment from the flame-holder. The results pertain to the red solid datapoints shown in Fig. 3.5(b) and (d), which are related to Flame A condi-tion. Flow is from left to right. . . . . . . . . . . . . . . . . . . . . . . . . 43xiiiLIST OF FIGURESFigure 3.10 The first and second rows demonstrate variations of the flame edge ve-locity and the derivative of pressure with respect to time versus normal-ized spatially-averaged OH∗ chemiluminescence, respectively. The first,second, and third columns present these variations during ignition, stabi-lization, and transition phases, respectively. . . . . . . . . . . . . . . . . . 45Figure 3.11 (a-d) are spatially-resolved OH∗ chemiluminescence during flame propa-gation inside the exhaust tubes. (e and f) present the OH∗ distributionduring exhaust of the burnt gas from the combustor. Flow is from left toright. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 3.12 Variations of the normalized OH∗ chemiluminescence (red curve) andpressure rate (black curve). . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.13 The normalized power spectrum density of the (a) pressure, (b) spatially-averaged OH∗, (c) pressure rate, and (d) flame edge velocity for the tran-sition phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 3.14 Acoustic response of the experimental setup shown in Fig. 2.1. . . . . . . 49Figure 4.1 (a–d) are the variations of the pressure (black color) and the sliding meansubtracted pressure (gray color) pertaining to Flames E–H, respectively.The insets are related to the ignition and stabilization phases. . . . . . . 53Figure 4.2 (a–d) are the variations of the pressure rate pertaining to Flames E–H,respectively. The insets are related to the ignition and stabilization phases. 54xivLIST OF FIGURESFigure 4.3 (a–d) are the variations of the spatially-averaged flame chemilumines-cence (red color) and the sliding mean subtracted spatially-averaged flamechemiluminescence (orange color) pertaining to Flames E–H, respectively.The insets are related to the ignition and stabilization phases. . . . . . . 55Figure 4.4 (a) and (b) are the variations of the flame edge position and velocity,respectively. (c) and (d) are the spectrogram and power spectrum densityof the flame edge velocity related to the ignition and stabilization phases.(e) and (f) are the spectrogram and power spectrum density of the flameedge velocity related to the steady oscillations. The results pertain toFlame G condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 4.5 The first, second, and third columns are the normalized pressure rate ver-sus normalized spatially-averaged flame chemiluminescence related to theignition phase, stabilization phase, and the steady oscillations, respec-tively. The first, second, third, and fourth rows pertain to Flames E, F,G, and H, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 4.6 The first and second columns are the pressure spectrogram and powerspectrum density related to the ignition and stabilization phases. Thethird and fourth columns are the spectrogram and power spectrum densityof the pressure pertaining to the steady oscillations. The first, second,third, and fourth rows pertain to Flames E, F, G, and H, respectively. . . 59xvLIST OF FIGURESFigure 4.7 The first and second columns are the pressure rate spectrogram and powerspectrum density related to the ignition and stabilization phases. Thethird and fourth columns are the pressure rate spectrogram and powerspectrum density pertaining to the steady oscillations. The first, second,third, and fourth rows pertain to Flames E, F, G, and H, respectively. . 60Figure 4.8 The first and second columns are the spatially-averaged flame chemilumi-nescence spectrogram and power spectrum density related to the ignitionand stabilization phases. The third and fourth columns are the spatially-averaged flame chemiluminescence spectrogram and power spectrum den-sity pertaining to the steady oscillations. The first, second, third, andfourth rows pertain to Flames E, F, G, and H, respectively. . . . . . . . . 61Figure A.1 A sample of the electrical noise as measured by the pressure transducer. . 91Figure A.2 Sensitivity analysis for (a) the effect of the sliding window size (W ) onthe duration of the stabilization phase, and (b) the effect of the steadyoscillations start time on the duration of the estimated transition phase.The results pertain to Flame A condition. . . . . . . . . . . . . . . . . . . 93xviAcknowledgementsI would like to pay my special regards to my supervisor, Professor Sina Kheirkhah, for hisconsistent support and assistance through each stage of the research. He patiently taught mehow to think critically, conduct research efficiently, and communicate research clearly in theacademic world. Undoubtedly, without his insightful comments and guidance, this researchwould have not been possible.I am grateful for financial support from the Natural Sciences Engineering Research Council(NSERC) of Canada and Etalim Inc. during this study. I would like to sincerely acknowledgeMr. Peter Kostka and Mr. William Aitchison in Etalim Inc. for their technical support anddesign/manufacturing of the experimental setup. My sincere thanks to my colleagues in theCombustion for Propulsion and Power Laboratory at the University of British Columbia. Iwould like to express my special thanks to Ramin Heydarlaki for his support in conducting theexperiments and analyses.Last but not least, I would like to express my deepest thanks to my lovely parents whohave suffered the most from the long-distance between us but always have encouraged me tocontinue. I wish to take this opportunity to thank my friends, Kamran Alasvand and SajjadMohammadnejad, who always have been there for me and helped me tackle the challenges.xviiDedicationTo my lovely familyxviiiNomenclatureSymbolsAc Cross-section area of the nozzlec Speed of soundcv Constant volume specific heatD Mass diffusivityD Combustion chamber diameterd Distance between the camera lens and the x− y planed/dt Time derivative(dp/dt)max Maximum pressure rate(dp/dt)s Mean-subtracted pressure rateE Total energyF Camera acquisition frequencyf Frequencyfn Acoustic mode frequencyfI,1 First intrinsic thermoacoustic mode frequencyfI,2 Second intrinsic thermoacoustic mode frequencyfs Structural mode frequencyG Intensifire gainxixNOMENCLATUREh Specific enthalpyhi Inlet specific enthalpyhe Outlet specific enthalpyL Length of the combustion chamberl Length of the wave-guide plus the horizontal distance between the pressuretap and the flame-holderLe Lewis numberL/D Combustion chamber aspect ratio~∇ Gradient vector~∇ρx x-component of the density gradient vector~∇ρy y-component of the density gradient vectorOH∗ Flame chemiluminescence used to study heat release rateOH∗ Spatially-averaged flame chemiluminescenceOH∗max Maximum spatially-averaged flame chemiluminescenceOH∗s Mean-subtracted spatially-averaged flame chemiluminescence〈OH∗〉ig.+st.Time-averaged value of the spatially-averaged flame chemiluminescence dur-ing the ignition and stabilization phases〈OH∗〉s.Time-averaged value of the spatially-averaged flame chemiluminescence dur-ing the steady oscillationsm Mass of the gas inside the control volumem˙i Inlet mass flow ratem˙o Outlet mass flow rateMW Molecular weightxxNOMENCLATUREp Pressurep0 Atmospheric pressurepmax Maximum presssureps Mean-subtracted pressurepref Reference pressurePth Thermal powerQ˙ Time rate of heat transfer across the control volume boundariesQ˙air Air volume flow rateQ˙ch. Heat release rate due to chemical reactionsQ˙fuel Fuel volume flow rateR Gas constant for airRu Universal gas constantS Igniter rod tip positionSL Laminar flame speedSL0 Un-stretched laminar flame speedSL0,ref Reference un-stretched laminar flame speedT TemperatureTref Reference temperaturet Timet0 Initial timeti Start time of the considered time period used for the calculation of the time-averaged value of OH∗tig. Ignition phase durationxxiNOMENCLATUREtst. Stabilization phase durationttr. Transition phase durationtwall Time that the flame skirt reaches the burner side-wallsU Internal energyUch. Chemical internal energyUs Sensible internal energyuDAQ Data acquisition system uncertaintyun Electrical noise uncertaintyup Total pressure measurement uncertaintyut Pressure transducer uncertaintyU Mean bulk flow velocityUb Burnt gas velocityUb,n Normal component of the burnt gas velocityUb,t Tangential component of the burnt gas velocityUu Unburnt gas velocityUu,n Normal component of the unburnt mixture velocityUu,t Tangential component of the unburnt mixture velocityu′ Unburnt mixture RMS velocity fluctuationsV (t) Flame edge velocityV/SL0 Flame edge velocity normalized by the un-stretched laminar flame speedV Control volumex Streamwise directionx(t) Flame edge horizontal positionxxiiNOMENCLATUREy Axis normal to the streamwise directionW Sliding mean window sizeW˙ Time rate of energy transfer due to external work across the boundaries ofthe control volumez Normal to the x− y planeGreek symbolsα Thermal diffusivityβ Exponent presenting the un-stretched laminar flame speed dependence onpressureγ Gas heat capacity ratio∆ The rate of heat transfer across the boundaries of the control volume sub-tracted from the net rate of enthalpy that leaves the control volume∆t Time difference Exponent presenting the un-strenched laminar flame speed dependence ontemperatureη Exponent used for the un-stretched laminar flame speed correctionκ Duration of the time period used for the calculation of the time-averagedvalue of OH∗λ Percentile of the excessive OH∗ chemiluminescenceρb Burnt gas densityρu Unburnt mixture densityσ Expansion ratioτ Time lag used to correct pressure dataxxiiiNOMENCLATUREΦm Mass fluxΦh Heat fluxφ Fuel-air equivalence ratioAbbreviationsDL Darrieus-LandauFFT Fast Fourier transformFOV Field of viewPMT Photomultiplier tubePSD Power spectrum densityPSD∗ Normalized power spectrum densityRes. Imaging resolutionRMS Root mean squareSLPM Standard liters per minutexxivChapter 1Introduction1.1 General overview and problem statementThis thesis is concerned with the operation of an industrial small-scale (1-10 kW) powergenerator combustor. Such generators are composed of two modules, an acoustic generatingmodule and an acoustic energy to electrical energy converting module. The former is the com-bustor which converts the natural gas chemical energy to thermal energy [3]. This process isaccompanied by the generation of pressure oscillations. Such oscillations are converted to elec-trical energy through the latter module using a linear flux switching alternator [4]. However, theamplitude of these oscillations should be controlled at the desired level, since large-amplitudeoscillations can lead to mechanical fatigue of the combustor [5, 6]. Compared to conventionalpower generators, these generators do not require maintenance over the operating life of the gen-erator, due to absence of mechanical friction between the parts [7]. As a result, such generatorsare ideal for remote areas, such as those in Canada [8].The combustors of these power generators usually utilize a stagnation wall that producesa reverse-flow configuration, which facilitates recirculation of exhaust gas. Combustors withreverse-flow configuration have been used in several past investigations, see for example [9–16].The reverse-flow configuration facilitates operation at very lean fuel-air equivalence ratios, whichleads to reduced NOx formation and emission [10–15]. In addition to reduced NOx emission,11.1. General overview and problem statementimprovements related to flame stabilization and ignition delay have also been observed, see forexample [9, 10, 16]. Although these characteristics are of significant importance, our understand-ing related to the effect of reverse-flow configuration on characteristics of flame development atearly stages of combustion (a few seconds after ignition) is limited and requires further inves-tigations. Specifically, at early stages of combustion, the reverse-flow configuration may hindera smooth start of the power generator combustor. Understanding the combustor operation atearly stages of combustion facilitates improved design of such equipment and is of industrialimportance.Characteristics of flame development at early stages of combustion depend substantially onthe end condition of the utilized combustion chamber. These characteristics are primarily studiedfor combustion chambers in the form of a tube/duct with a closed or semi-closed end. However,combustors used for small-scale power generators are not in the form of a tube/duct and feature areverse-flow configuration at the end. Further investigations are required to understand how thereverse-flow configuration (or existence of a stagnation wall) can influence these characteristics.Early stages of combustion are followed by steady-state thermoacoustic oscillations. Theseoscillations arise from the coupling between pressure and heat release oscillations. Depending onthe operation conditions, these oscillations frequencies may lock onto different types of thermoa-coustic modes frequencies. There is a wealth of literature studying steady-state thermoacousticoscillations and their underlying coupling mechanisms. However, the existence of thermoacousticoscillations and their origins at early stages of combustion are not well-understood and requirefurther investigation. This is of importance to develop/utilize efficient methods that can mitigatethe instabilities at both early and later stages of combustion.21.2. Background1.2 BackgroundThe literature related to the laminar flame speed, characteristics of flame development atearly stages of combustion, and thermoacoustic modes are reviewed. In subsection 1.2.1, laminarflame speed, its dependence on parameters such as unburnt mixture pressure and temperature,and the flame front instabilities are discussed. In subsection 1.2.2, literature related to premixedflames dynamics at early stages of combustion is reviewed. The related studies are categorizedinto those investigated premixed flame development in quiescent and flowing mixtures. In sub-section 1.2.3, thermoacoustic instabilities developed at later stages of combustion (during steadyoperation) are discussed.1.2.1 Laminar flame speedThe speed at which an un-stretched flame front propagates relative to unburnt mixture isreferred to as the laminar flame speed [17, 18]. In Fig. 1.1, propagation of a planar and un-stretched laminar flame front into a quiescent unburnt mixture is shown schematically. Theflame front travels at the speed of SL0; and, the burnt gas leaves the flame front at a higherspeed of σSL0, with σ (expansion ratio) being the ratio of the unburnt mixture (ρu) and burntgas (ρb) densities.Fig. 1.1. Diagram schematically presenting propagation of a planar laminar flame into unburntand compressed fuel/air mixture.31.2. BackgroundNumerous studies have been performed to both measure the laminar flame speed and studythe influence of the governing parameters on SL0, see for example [19–30]. Unburnt mixturetemperature (T ) and pressure (p) [19–23, 31, 32], fuel type [24–26, 29, 30, 33], and fuel-airequivalence ratio of the unburnt mixture (φ) [19, 20, 24–28] can influence the laminar flamespeed. An empirical power-law formulation has been developed in the literature to demonstratethe relation between the un-stretched laminar flame speed and the unburnt gas pressure andtemperature [22, 23, 31, 32], which is given bySL0 = SL0,ref(TTref)(ppref)β, (1.1)where the index “ref” highlights the reference condition.  and β are exponents that presentthe dependence of the laminar flame speed on temperature and pressure, respectively. In orderto determine the values of  and β, experimental studies [22, 23] have been performed fordifferent fuel types, and for different ranges of fuel-air equivalence ratios, as well as unburntmixture temperature and pressure. Values of  and β are fuel type dependent. For example, formethane/air mixtures, it is reported in [34] that the values of  and β can be determined by = 1.6 + 0.22(φ− 1), (1.2)β = −0.42− 0.31(φ− 1). (1.3)It can be shown that, for example for stoichiometric methane/air mixtures,  = 1.6 and β =−0.42. However, for stoichiometric hydrogen/air mixtures, values of  and β are 1.4 and 0.19,respectively [28].41.2. BackgroundAssuming that the gas inside the combustion chamber is an ideal gas, and that the unburntgas compression (see Fig. 1.1) is an isentropic process [28, 31, 32], it can be shown that:TTref= (ppref)γ−1γ , (1.4)where γ is the unburnt mixture heat capacity ratio. Combining Eqs. (1.1) and (1.4), it can beshown thatSL0 = SL0,ref(ppref)η, (1.5)where η = β+ (γ−1γ ). Depending on the values of , β, and γ, η may become positive, negative,or zero, which means that the laminar flame speed may increase, decrease, or remain constantduring the flame propagation and pressure change inside a closed/semi-closed environment.Effects of the fuel type and fuel-air equivalence ratio on the laminar flame speed have beeninvestigated in, for example, [19, 20, 24–30, 33]. Studies of [26, 29, 30] show that adding hydro-gen to hydrocarbon fuels increases the laminar flame speed. Investigations of [20, 25–28] suggestthat the laminar flame speed features a parabolic relation with the fuel-air equivalence ratio. Itis shown that the laminar flame speed maximizes for rich mixtures [20, 25–28]. In addition to theabove discussed governing parameters, which are temperature, pressure, fuel type, and fuel-airequivalence ratio, combustion instabilities can also significantly influence the flame propaga-tion speed. These can be grouped into hydrodynamic, thermal-diffusive, and Rayleigh-Taylorinstabilities with details provided in the following.Flame hydrodynamic instabilityPremixed flame propagation is usually accompanied by development and growth of flamefront wrinkling [31, 35–40]. Hydrodynamically unstable flames are those for which the flame51.2. Backgroundfront wrinkling origin is gas expansion. This type of instability is also referred to as Darrieus-Landau (DL) instability in the literature [35–37, 39, 40]. In order to elaborate this instability,a sinusoidally-perturbed flame is schematically shown in Figs. 1.2(a) and (b), see the blue solidcurves. Assuming that the initial flame stretch rate, i.e. the relative rate of change of flamesurface area [38, 41], is negligible, the normal component of the unburnt gas velocity (Uu,n) isnearly constant along the flame front and equals to SL0 [35, 42]. The flame front at the peaksand troughs is normal to the unburnt gas flow, which is similar to the topology shown in Fig. 1.1.At the peaks and troughs, the unburnt mixture reaches the flame front at the speed of Uu = SL0,and the burnt gas leaves the flame at a higher speed of Ub = σSL0. At locations where the flamefront is inclined with respect to the unburnt gas velocity vector, the normal component of theburnt gas velocity (Ub,n) equals σSL0. Neglecting the higher order terms and body forces, for anearly un-stretched flame front, the balance of momentum in the tangential direction leads tothat the tangential components of the unburnt and burnt gas velocities are almost equal, i.e.Ub,t ' Uu,t [35, 39, 42]. The burnt gas velocity vector configuration shown in Fig. 1.2(a) suggeststhe flow streamlines intersect, which is not possible. In reality, the burnt gas vectors deviatefrom the normal axis, leading to deflection of the streamlines [35, 38–40, 42], see the dottedblack curves in Fig. 1.2(b). This induces a relatively larger tangential velocity component onthe burnt gas side, which is nearly equal to that on the reactant side. The large unburntgas velocity component along the flame front causes the unburnt gas streamlines to converge(diverge) when the flame front is concave (convex) with respect to the unburnt mixture, asshown in Fig. 1.2(b). For the two-dimensional and incompressible flow of reactants shown inFig. 1.2(b), the unburnt gas velocity increases (decreases) when the flow streamlines converge(diverge) [35, 38, 40, 42, 43]. This means that the reactant flow is accelerated (decelerated) at61.2. Backgroundregions where the flame front is concave (convex) with respect to the reactants [35, 42, 43]. As aresult, the flame front is recessed (further propagated) into the burnt (unburnt) gas at locationsthat the flame front is concave (convex) towards the reactants. This process increases the initialflame wrinkling [35, 42, 43], as shown by the dashed blue curve in Fig. 1.2(b). This dashed curvepertains to the flame front location at t = t0 + ∆t.Fig. 1.2. Schematic of the Darrieus-Landau instability development. The figure is adopted from[30, 32].Thermal-diffusive instabilityIn addition to the DL instability, the local imbalance between the mass and heat diffu-sions can also develop/mitigate the flame front wrinkling. The Lewis number (Le) is used fordetermining the relation between the mass and heat diffusions [35, 37], which is given byLe =αD , (1.6)where α and D are the thermal and mass diffusivities, respectively.As shown in Figs. 1.3(a) and (b), the heat and mass fluxes (denoted by Φh and Φm, re-spectively) are always in opposite directions for nearly laminar flames [35, 37]. This is because,in nearly laminar flames, the thermal gradient is in the opposite direction of the gradient of71.2. Backgroundthe species concentration [35]. As can be seen in Figs. 1.3(a) and (b), at locations where theflame front is concave towards the unburnt mixture, the heat fluxes are convergent, which canlead to an increase in the local flame temperature [35]. This increases the reaction rate, andas a result, the local laminar flame speed [44]. The opposite holds for the convex part of theflame front [35]. In contrast with the heat fluxes, the mass diffusive fluxes destabilize the flamefront. For the locations where the flame front is convex towards the unburnt mixture, the massdiffusive fluxes locally converge, see Figs. 1.3(a) and (b). Hence, the flux of the species into thereaction zone increases, which can lead to an increase in the local laminar flame speed [35, 37].However, the mass diffusive fluxes diverge at the concave parts moving the reactants away fromthe flame front, which can lead to decrease of the local laminar flame speed [35, 37]. Dependingon the Lewis number, the heat and mass diffusion fluxes may stabilize or destabilize the flamefront [35, 37]. As shown in Fig. 1.3(a), for Le < 1, the mass diffusive fluxes are dominant, andas a result, they destabilize the flame front, see the dashed curve corresponding to t = t0 + ∆t.When Le > 1, see Fig. 1.3(b), the heat diffusive fluxes are dominant, which decreases the flamefront wrinkling and stabilizes the flame front [35, 37].Fig. 1.3. Schematic of the thermal-diffusive instability development. The figure is adopted from[32].Rayleigh-Taylor instability81.2. BackgroundIn addition to the hydrodynamic and thermal-diffusive instabilities, premixed flames mayalso feature another type of instabilities known as the Rayleigh-Taylor instability [45–48]. Thistype of instability occurs due to the baroclinic effect [46–49]. This effect can be elaboratedusing the vorticity transport equation, see [50], suggesting that the misalignment between thepressure and density gradient vectors leads to vorticity generation [49] which wrinkles the flamefront; hence, destabilizing the flame. The baroclinic effect is quantified by the outer product ofdensity and pressure gradient vectors (~∇ρ× ~∇p). As discussed earlier, due to gas expansion, thegas density varies across the flame front [35–37, 39], and the pressure gradient can be inducedby acoustic waves [45, 48, 51, 52] and/or the gravitational acceleration [53, 54]. Figure 1.4shows a perturbed flame front in the presence of the Rayleigh-Taylor instability. The pressureand density gradient vectors are shown by the black and green solid arrows, respectively. Inthis configuration, due to the misalignment between ~∇ρ and ~∇p, vorticity is generated, whichis shown by the red circles in Fig. 1.4. As can be seen, such vortices increase the flame frontwrinkling, destabilizing the flame front [48, 49], see the dotted dashed curve pertaining to theflame front at t = t0 + ∆t. Note that in the schematic shown in Fig. 1.4, if the propagationdirection is changed, the direction of the density gradient changes, the generated vorticity signis switched, and as a result, the flame wrinkling decreases, stabilizing the flame front [46, 49].1.2.2 Early stages of combustionPast studies that investigated flame development at early stages of combustion can be cat-egorized into those for which the reactants are either quiescent [31, 33, 52, 54–77] or flowinginto the combustion chamber [78–81]. In the following, studies related to the former and latterconfigurations are referred to as closed and open system investigations, respectively.Flame development inside closed systems91.2. BackgroundFig. 1.4. Schematic of the Rayleigh-Taylor instability development. The figure is adopted from[47].Studies relevant to closed systems can be categorized into those investigated flame devel-opment inside vessels [20, 75, 76, 82–87] or ducts/tubes [31, 33, 52, 54–74]. Studies relevant tothe closed vessels, e.g. [20, 84], suggest that the characteristics of the flame front structureand velocity can be grouped into those for which the flame propagates into either quiescent orturbulent reactants. For quiescent conditions, two distinct regimes may exist: the stable andunstable regimes [20, 75, 76, 86, 87]. These regimes are categorized based on the value of thespherical flame radius compared to a critical radius. Several factors influence the value of thecritical radius, which are the reactants mixture initial pressure [20, 76, 86] and the Lewis number[75, 76]. Studies of [20, 76, 86] suggest that increasing the initial pressure and decreasing theLewis number decrease the critical radius. For flame radius smaller than the critical radius, theregime is referred to as the stable regime, and the flame features a smooth and spherical front[20, 75, 76, 86, 87]. For the unstable regime, however, the radius of the spherical flame is largerthan the critical radius [20, 75, 76, 86, 87]. This regime is characterized by formation of cellularinstabilities [20, 75, 76, 86, 87]. For the unstable regime, cellular structures increase the flamesurface area, and as a result, the flame propagation speed [20, 75, 76, 86, 87]. For spherical101.2. Backgroundflames propagating into a turbulent environment inside a closed vessel, the flame front structureand velocity are mainly influenced by the turbulent flow characteristics of the reactants, e.g. theturbulence intensity, u′/SL0, where u′ is the reactants RMS velocity fluctuations. In [84, 85],u′/SL0 is controlled by the rotation speed of a fan. In the studies of [84, 85], it is shown thatincreasing the turbulence intensity increases the wrinkling of the flame front and increases theflame surface area.Past studies suggest that, during the premixed flame development inside ducts/tubes, theflame features spherical [31, 33, 52, 54–72, 74], finger-shaped [31, 33, 52, 54–72, 74], planar[31, 33, 52, 54–68, 74], and/or tulip-shaped [31, 33, 52, 54–68, 74] topologies with the corre-sponding schematics shown in Figs.1.5 (a)–(d), respectively. In these studies, high-speed imag-ing [31–33, 55, 57–60, 62, 63, 65, 67, 69–71] and/or numerical [31, 32, 52, 54–59, 61, 63, 64, 66–68, 72, 74] simulations were utilized to investigate the flame topology transition while propagat-ing inside ducts/tubes. The results of [31, 33, 52, 54–72] show that the ignition kernel is originallyFig. 1.5. Flame topologies during the premixed flame development inside ducts/tubes.111.2. Backgroundspherical, which grows into a finger-shaped flame. Such flame is composed of a hemisphericaltip and a cylindrical front, which is referred to as the flame skirt [31, 33, 52, 54–62]. Duringthe transition from a spherical to a finger-shaped flame, both pressure and flame edge velocityincrease exponentially, see for example [31, 52, 55–58]. As the finger-shaped flame grows, thecombustion products volume increases, accelerating the flame edge and increasing the pressure,see for example [31, 52, 55–58]. Once the flame skirt reaches the combustor side-walls, the flamequenches at the walls, decreasing the flame surface area, and as a result, decreasing the growthrate of the pressure [31, 52, 55–58]. As the flame propagates downstream, two recirculationregions are formed near the side-walls, which cause the development of the tulip-shaped flametopology. Compared to the finger-shaped topology, the tulip-shaped topology features a cuspedfront (with a large absolute value of curvature) that is convex towards the burnt gas along thetube axis of symmetry as well as two relatively small curvature fronts that are convex towardsthe fuel and air mixture. The tulip flame topology is believed to be formed due to the DLinstability [63, 64], flame and wall [72, 73], combustion chamber pressure wave and flame front[58], as well as flame-vortex interactions [55, 61, 68, 74]. For hydrogen-air mixtures, after theformation of the tulip flame, secondary cusps (see Fig. 1.5(e)) may also be developed on theflame front [31, 52, 55–57, 88]. This flame topology is referred to as the distorted tulip flameand is shown to be linked to the Rayleigh-Taylor instability [52, 55, 89, 90]. Several investiga-tions show that, for relatively long tubes, a standing pressure wave develops in the tube andcauses pressure fluctuations [31, 52, 55–58, 62]. As the tulip/distorted tulip flame propagatesdownstream, the distance between the flame and the wall at the end of the tube decreases, thetime scale of the wave and the flame interaction decreases, and as a result, the frequency of thepressure oscillations increases [62]. During this period, the flame edge velocity features fluctua-121.2. Backgroundtions similar to the pressure. For tubes that are closed at the end, the flame edge velocity finallydecreases and approaches to zero, as the flame reaches the end-wall [58, 59, 61]. However, fortubes that feature an open end, the flame edge velocity increases as it consumes the reactantsand exits the tube [33, 54, 60].Existence of obstacles inside the ducts/tubes can influence the pressure and flame edgevelocity dynamics. Similar to flame propagation into a duct/tube without an obstacle, theflame kernel is originally spherical and grows into a finger-shaped flame prior to reaching theobstacle. During this period, the pressure and flame tip velocity increase [69, 70]. Once theflame passes the obstacle, a pair of symmetric vortices is formed in the wake of the obstaclewhich is wrapped by the flame front. During this vortex and flame interaction, the flame surfacearea increases [70], which leads to a significant increase in both the pressure and the flame edgevelocity [70]. Johansen and Ciccarelli [70] showed that increasing the blockage ratio, which isthe obstacle height normalized by half of the channel width, increases the flame edge velocity.After the flame passes the obstacle and exits the combustion chamber, suction is created inthe combustion chamber and the pressure decreases [69]. Similar observations are reported forflames passing through several obstacles [71]. For such configurations, after the flame exits thecombustion chamber, unburnt reactants which were trapped in the wake of the obstacles mayburn leading to the increase of the pressure [71].Flame development inside open systemsStudies that investigated flame dynamics in open systems can be categorized into thosethat utilized either single [78, 79, 91] or multi-nozzle injectors [80, 81]. The latter studies pri-marily pertain to non-premixed combustion, which is different from that investigated in thisthesis. Many investigations [92–98] studied turbulent premixed flames in annular multi-nozzle-131.2. Backgroundconfiguration combustors. Although these studies [92–98] provide significant insight into ther-moacoustic oscillations relevant to gas turbine engines, they did not focus on the early stagesof the flame development; and as a result, they are not reviewed here. Renou et al. [79] exper-imentally investigated the flame shape for methane-, propane-, and hydrogen-air flames. Theirresults are similar to those reported for closed systems. Specifically, they [79] show that, fornearly laminar conditions (u′/SL0 ≈ 0), the flames remain spherical. However, for turbulentconditions, hydrogen-air flames (Le < 1) feature cellular structures; whereas, methane- andpropane-air flames (Le & 1) develop wrinkled fronts that are convex towards both burnt andunburnt gases.Cordier et al. [78] utilized a swirl burner and studied the effects of ignition location as wellas the swirl-number [78, 99] on the characteristics of the combustion chamber pressure and heatrelease rate during the early stages of the flame development. For large values of the swirlnumber, the flame kernel moves towards the burner centerline, stabilizes at the burner exit,and then grows downstream consuming the reactants in the combustion chamber. For low swirlnumber flames, the ignition dynamics depends on the ignition location. For ignition inside thecorner recirculation zone, the flame propagation is similar to that for large swirl number flames.However, for ignition inside the inner recirculation zone, the flame grows asymmetrically andaway from the burner centerline, then it propagates towards the end of the combustion chamber.For all tested conditions in Cordier et al. [78], the pressure increases during the flame stabilizationand propagation towards the end of the combustion chamber. The exhaust of the combustionproducts from the chamber generates suction below the atmospheric pressure. After this, thepressure features an oscillatory behaviour, with the corresponding mean plateauing at aboutthe atmospheric pressure [78]. Oscillations during early stages of combustion have also been141.2. Backgroundobserved in the results of Ebi et al. [91] pertaining to the second stage of a sequential combustor.Their results suggest that, at relatively low inlet temperature, the ignition process is dominatedby flame propagation rather than auto-ignition. For this condition, a few milliseconds afterignition, the pressure signal reaches a maximum with a value about ten-folds the RMS of thesteady oscillations. For about 350 ms, the pressure signal features relatively large-amplitudeand low-frequency oscillations. This is followed by the steady oscillations dominated by bothlow- and high frequencies. Similar to the present study, in the studies of Cordier et al. [78] andEbi et al [91], the utilized combustors feature a semi-closed configuration. It is unclear how andif the presence of the relatively large-amplitude and low-frequency oscillations, during the earlystages of combustion, is related to the configuration of the tested combustor.1.2.3 Later stages of combustionFor small-scale power generators, it usually takes about a few seconds for the pressure andheat release rate to reach steady-state oscillations. Later stages of combustion pertain to thetime period during which such oscillations appear. The pressure and heat release rate (ther-moacoustic) oscillations can lead to a wide range of severe effects, including mechanical fatigue,high-amplitude vibrations, inefficient combustion, and noise [5, 6]. Thus, efforts have beenmade to understand the driving mechanisms and/or develop methods to mitigate these oscilla-tions [5, 6, 100–126]. The related studies can be categorized into two groups, those pertaining toself-excited [6, 100–124] and forced oscillations, see for example [5, 126]. For the former group,different mechanisms can lead to coupling between pressure and heat release rate oscillations,which are reviewed in [6, 105, 106]. For the latter, thermoacoustic oscillations are excited byan external actuator, such as a loud-speaker. This thesis is concerned with the first group ofoscillations. In general, three types of modes have been reported for the self-excited thermoa-151.2. Backgroundcoustic oscillations. These are structural [6, 100, 106, 107, 125], acoustic [6, 100, 108–118, 125],and intrinsic [108–110, 119–124] thermoacoustic modes, which are briefly reviewed below.Structural modeFor this mode, the pressure oscillations lead to vibrations of the combustor walls. Thegenerated vibrations perturb the acoustic field by displacing the gas near the walls. This, inturn, causes oscillations in the heat release rate which feeds back to the structural and pressureoscillations [6, 100]. Several numerical [106, 107, 125] and experimental [6, 100, 106, 125] studieshave reported the presence of the structural modes in the past. The frequency of the structuralmode depends on the combustor structure mechanical properties, such as Young’s modulus ofelasticity, wall thickness, and the structure mass [6]. Structural modes can be estimated eitherby utilizing finite element methods [106, 107, 125] or by performing modal experiments [6, 100].For such experiments, the structure is struck by a hammer and an accelerometer records thewall acceleration. Then, the dominant modes observed in the corresponding power spectrumdensity (PSD) are captured.Acoustic modeThere is a wealth of literature reporting the acoustic modes being apparent in thermoacousticoscillations, see e.g. [6, 108–110, 114–118]. Two different types of acoustic modes may exist forconfined combustors. These correspond to standing acoustic [6, 108–110, 114] and Helmholtzmodes [109, 115–118]. The former pertains to the reflection and interference of acoustic waves,and as a result, depends on the acoustic boundary conditions. When gas is trapped inside acavity with a neck, only one mode, i.e. the Helmholtz mode, exists which depends on the volumeof the cavity, its cross-sectional area, length of the neck, and the speed of sound [100]. Suchconfiguration resembles a mass-spring system for which the neck and the gas trapped in the161.2. Backgroundcavity serve as the mass and spring, respectively [100, 116, 117, 127]. For combustion chambersfeaturing a complex geometry, the Helmholtz mode can be estimated using acoustic networksimulations, see for example studies of [108, 109, 128].Intrinsic modeIt is believed that the intrinsic thermoacoustic mode is attributed to a feedback mechanismbetween the upstream velocity, pressure, and heat release rate fluctuations [108–110, 119–124].For this mechanism, the flame causes the acoustic perturbations leading to the upstream velocityfluctuations. The velocity fluctuations, in turn, lead to heat release oscillations, generating afeedback mechanism [108–110, 119–124]. Note that the intrinsic thermoacoustic instability isdifferent from the combustion instabilities discussed earlier in subsection 1.2.1.The intrinsic thermoacoustic modes have been observed in several experimental studies [100,110, 123, 124] with confined configurations. Albayrak et al. [123] observed an inverse relationbetween the intrinsic mode frequency and the flame length. Their results [123] suggest that theintrinsic mode frequency ratio is proportional to the ratio of the corresponding mean bulk flowvelocities raised to the power of 0.8. Study of Heydarlaki [100] suggests that, for a reverse-flowcombustor, all thermoacoustic modes, that are structural, acoustic, and intrinsic modes, can co-exist for premixed flames with φ = 0.9. However, for their [100] relatively leaner tested flameswith φ = 0.7, the intrinsic modes are absent in the power spectrum densities of both the pressureand flame chemiluminescence oscillations. Compared to the acoustic modes, the intrinsic modesare independent of the combustion chamber length. This is investigated by changing the lengthof the experimental apparatus in the studies of [110, 122].171.3. Thesis objectives1.3 Thesis objectivesPast investigations primarily focused on either early stages of flame development or on ther-moacoustic oscillations during the steady-state operation of the tested combustors. The resultsof past studies related to the early stages of combustion pertain to open/closed systems andare not applicable to reverse-flow combustors which feature a stagnation wall. Also, the resultsof a few studies pertaining to semi-closed combustors suggest the presence of relatively large-amplitude and low-frequency pressure oscillations at the early stages of combustion, comparedto those during the steady oscillations. It is of interest to investigate the presence and potentialorigins of such oscillations during the early stages of combustion in our semi-closed and reverse-flow configuration. In addition, the underlying reason for the observed difference between theflame characteristics during the early stages of combustion and those pertaining to the steadyoperation of the combustor is not addressed and requires further investigations. This study aimsto:(i) Identify the phases of flame development prior to steady thermoacoustic oscillations,(ii) Study how the stagnation wall influences the flame edge dynamics and spectral behavioursof flame characteristics at early stages of combustion,(iii) Elaborate the relations between the pressure, flame chemiluminescence, and the flame edgevelocity at early stages of flame development,(iv) Investigate how and if the thermoacoustic oscillations affect the flame dynamics at earlystages of combustion and steady operation of the combustor.In the following, the experimental methodology is elaborated in Chapter 2. The results of thisstudy are presented in Chapters 3 and 4. In Chapter 3, the flame development characteristics181.3. Thesis objectivesat early stages of combustion are discussed. In Chapter 4, it is investigated how the flamedynamics at early stages of combustion and that pertaining to the steady-state operation arerelated. Finally, concluding remarks and future directions are discussed in Chapter 5.19Chapter 2Experimental MethodologyThe utilized experimental setup, diagnostics, and tested conditions are discussed in thischapter.2.1 Experimental setupThe experimental setup technical drawing is shown in Fig. 2.1(a). This is a modified versionof the setup utilized in Heydarlaki et al. [102]. The setup used in [102] did not provide opticalaccessibility, and as a result, information related to the flame chemiluminescence could notbe acquired from the setup elaborated in [102]. In the present investigation, however, thecombustion chamber and the exhaust tubes in [102] were replaced by quartz tubes providingoptical accessibility allowing for flame chemiluminescence measurements. In order to minimizethe effect of reactants preheating and focus on the effect of the stagnation wall on the flamedevelopment characteristics, first, the exhaust gas was removed almost immediately after flowingthrough the optically-accessible exhaust tubes; and, second, the exhaust manifold shown inFig. 2.1(a) was thermally-insulated. Thus, the reactants are not preheated. This was alsoconfirmed by measuring the reactants temperature upstream of the flame-holder. The setuputilized in the present study is similar to that used in [100].Methane grade 2 (i.e. 99% chemical purity) and air are provided through pressurized bottles.202.1. Experimental setup&RPEXVWLRQSURGXFWV 6WDJQDWLRQZDOO7RH[KDXVW0HWKDQHDLUPL[WXUH7RSUHVVXUHWUDQVGXFHU ,JQLWHU 2SWLFDOO\DFFHVVLEOH H[KDXVWWXEHV D Perforated plateMain tubeflow(1.7 mm diameter)Igniter ceramic insulator33mmIgniter tipStagnation platelocation E 2SWLFDOO\DFFHVVLEOH PDLQWXEHNozzle (24 mm diameter)Flame-holderExhaust manifoldMethane/airFig. 2.1. (a) Technical drawing of the power generator model combustor. (b) Technical drawingof the burner. Please note that in (b), the optically-accessible exhaust tubes are removed forclarity purposes.The volume flow rates of methane (Q˙fuel) and air (Q˙air) are measured using SLA5850 andSLA5853 Brooks mass flow controllers, respectively. Methane and air flows are mixed prior toentering a T-shaped joint shown in Fig. 2.1(a). For clarity purposes, details of the burner shownin Fig. 2.1(a) as well as a schematic of its cross-section are presented in Fig. 2.1(b) and Fig. 2.2,respectively. The reactants mixture passes through a perforated plate shown in Fig. 2.1(b) priorto entering the combustion chamber. The perforated plate is composed of 1.7 mm diameterholes that are arranged hexagonally generating a blockage ratio of 70%, see Fig. 2.1(b). Atoroidal flame-holder, with large and small diameters of 24 and 1.5 mm, is utilized to stabilizethe generated flames. A Fenwal igniter is positioned axially along the axis of symmetry of themain tube, see Fig. 2.1(b). The tip of the igniter rod is bent 90o and is positioned at a distanceof S from the flame-holder as shown in Fig. 2.2.After the flame-holder, flow is directed into the main tube and towards the stagnation wall.A TDK-Lambda (model DPP120-24-1) power supply was used to operate the igniter. Since theigniter supplied power can potentially influence the ignition dynamics [129], the supplied powerwas fixed at 120 W for all tested conditions. This corresponds to about 1.5 and 2.5% of the212.2. Diagnosticscombustor thermal power (discussed later) which is relatively small compared to past investiga-tions, see for example [130, 131]. A fixed ignition procedure for all tested conditions is followed.Specifically, control signals are sent to the air flow controller and the igniter simultaneously. Theigniter is programmed to delay the discharge by 15 s. A control signal is then sent to the fuelmass flow controller 3 seconds before the discharge. After ignition, the flames are stabilized onthe flame-holder shown in Figs. 2.1(b) and 2.2. Then, the combustion products are directed intosmall exhaust tubes with inner diameter of 10.6 mm. All exhaust tubes discharge into the sameexhaust manifold which directs the combustion products to a naturally-ventilated exhaust. ACartesian coordinate system is utilized in the present investigation, as shown in Fig. 2.2. Thex−axis of the coordinate system is along the reactants flow direction, the z−axis is along theigniter rod tip direction, and the y−axis is normal to both x and z axes.Fig. 2.2. Schematic view of the burner shown in Fig. 2.1(a).2.2 DiagnosticsTime-resolved pressure and OH∗ flame chemiluminescence data were acquired simultane-ously. The pressure data was collected using a differential pressure transducer (Setra 265). Themeasured pressure data is relative to the laboratory pressure, and the pressure values discussed222.2. Diagnosticsand presented in this manuscript are gauge pressure. The pressure transducer was connectedto a pressure tap located 115.0 mm upstream of the flame-holder using a 642.1 mm-long wave-guide. This arrangement leads to a time-lag, τ , in the pressure data collection. The time-lagrelated to the pressure measurements was estimated using τ = l/c, where l is the length ofthe wave-guide plus the horizontal distance between the pressure tap and the flame-holder(642.1 mm + 115.0 mm = 757.1 mm). c is the speed of sound and is given by c =√γRT ,where γ, R, and T are the air heat capacity ratio, universal gas constant normalized by the airmolecular weight, and the air temperature in the wave-guide, respectively. γ and R are 1.4 and287 J/(kgK), respectively. The temperature near the pressure tap was measured using AD8497K-type thermocouples. T is constant in the wave-guide, equals the room temperature, and is298.2 K. The pressure measurements time-lag is 2.2 ms, and the pressure data was correctedaccounting for this time-lag. Please note that the 115.0 mm length was added to calculate thepressure near the flame-holder, i.e. x = 0. This added length only changes the time-lag byabout 0.3 ms which is close to the imaging resolution and is relatively small. Also, γ could becalculated for the mixture. This was performed and the time-lag did not change significantly.The output of the pressure transducer is in volts (maximum 5 V), and the pressure values werecalibrated using the producer calibration instructions. The resolution of the pressure data is0.8 mV/Pa. The uncertainty of the pressure measurements is ±1.9% of the full-scale pressuretransducer reading, with the corresponding details discussed in Appendix A.The chemiluminescence imaging equipment is composed of a high-speed camera (PhotronFastcam Nova S12), an intensifier (Invisible vision UVi), a UV lens (Nikon, 105 mm, f/4.5), anda band-pass filter (310 nm ± 10 nm). This allows for collecting the OH∗ chemiluminescencenear the wavelength of 306 nm [132]. The camera lens aperture was set to f/4.5 for all tested232.2. Diagnosticsconditions. Following the filter specifications provided by the producer, the peak transmissivityof the band-pass filter is 71.7% at 313 nm. The full width at half maximum of the filtertransmissivity is 9.2 nm. The transmissivity decreases to less than 1% for wavelengths largerthan 318 nm and smaller than 303 nm. The collected chemiluminescence images are usedfor investigating the temporal variation of the normalized spatially-averaged combustion heatrelease rate and the flame edge velocity. Although the collected chemiluminescence signal, inaddition to OH∗, has contribution from a background CO∗2 chemiluminescence [133, 134], thechemiluminescence near 306 nm has been extensively used for studying heat release rate of fullypremixed flames, see for example [135–137]. Since the chemiluminescence imaging is a line-of-sight technique, the turbulent flame structure cannot be studied here. However, the flame edgevelocity can be obtained at locations that the flame propagates into unburnt reactants using thechemiluminescence measurements, see for example the studies of [138–140].The chemiluminescence camera, with a sensor pixel size of 20 µm, is positioned along thez−axis (normal to x − y plane in Fig. 2.2) and the distance between the camera lens and thex− y plane (d) was fixed. For the experiments discussed in Chapters 3 and 4, different settingswere utilized. The values of d, resultant field of view (FOV size), imaging resolution (Res.),camera acquisition frequency (F ), and the intensifier gain (G) pertaining to the results presentedin Chapters 3 and 4 are tabulated in Tables 2.1 and 2.2, respectively. For all experiments, thecamera exposure time and intensifier gate were set to 25 and 20 µs, respectively. A LabJack T7data logger was used to acquire the pressure as well as the camera record signals at a frequency of50 kHz. The camera and the LabJack acquisition signals were used to synchronize the pressuredata and the chemiluminescence images.The OH∗ chemiluminescence images were processed, with the processing steps presented in242.2. DiagnosticsTable 2.1. Experimental parameters for the results discussed in Chapter 3.d (mm) FOV size (mm×mm) Res. (µm/pixel) F (Hz) G (%)730 146.1 × 146.1 143 5000 37Table 2.2. Experimental parameters for the results discussed in Chapter 4.d (mm) FOV size (mm×mm) Res. (µm/pixel) F (Hz) G (%)870 140.1 × 140.1 157 4000 65Fig. 2.3. For presentation purposes, a colormap with colors varying from black to light yellowis used here. A representative raw chemiluminescence image is shown in Fig. 2.3(a). Thecamera sensor background which was collected and averaged for 1000 images was subtractedfrom the raw chemiluminescence images, with the corresponding results shown in Fig. 2.3(b).The sensor background intensity is relatively negligible and the background subtraction does notinfluence the acquired images quality significantly. To obtain the camera and intensifier sensorsensitivity, a FotodioX (C-300RS FlapJack) LED lamp was positioned against the camera lens.The camera and intensifier settings were selected to match those used in the relevant experiments.Then, 1000 images were collected. These images were averaged to obtain the camera andintensifier sensitivity array. The resultant image, after applying the camera sensitivity correction,is presented in Fig. 2.3(c). In order to reduce the post-processing time and increase the signal-to-noise ratio [101, 141, 142], the results in Fig. 2.3(c) were binned. For this purpose, the imageswere divided into 4 × 4 windows; and, the data was averaged inside each window, with thecorresponding results shown in Fig. 2.3(d). After binning, a 4 × 4 median-based algorithm inMATLAB was used to filter the data presented in the figure, with the corresponding resultsshown in Fig. 2.3(e). Specifically, the value of each pixel shown in Fig. 2.3(e) is the medianvalue in a 4× 4 window around the corresponding pixel in Fig. 2.3(d).252.3. Tested conditions1 100 200 300 400 500 600100500Fig. 2.3. (a) Raw, (b) background subtracted, (c) camera and intensifier sensitivity corrected,(d) binned, and (e) median-based filtered images. Flow is from left to right.2.3 Tested conditionsThe tested experimental conditions are tabulated in Table 2.3. To address objectives (i)–(iv)listed in subsection 1.3, in the first set of experiments, characteristics of premixed flames duringearly stages of combustion have been investigated. It is speculated that the inlet flow conditionsand discharging method can influence the flame characteristics at these stages. To furtherinvestigate this speculation, the air flow rate and igniter tip location, which pertain to the inletflow conditions and discharging method, respectively, were varied in the first set of experiments,denoted by Flames A–D. Specifically, two air flow rates of 100 and 160 SLPM along with twoigniter tip positions (see Fig. 2.2) of S = −5 and 1.5 mm were tested. For these experiments,the fuel-air equivalence ratio was kept constant at 0.7. Results of a recent study [100] pertainingto the same experimental setup suggest that, during the steady oscillations, all thermoacousticmodes, that are the structural, acoustic, and intrinsic modes can co-exist for the flames withthe fuel-air equivalence ratio of 0.9. Motivated by this, and to address the last objective of262.3. Tested conditionsthis study, see subsection 1.3, characteristics of relatively rich flames, at different flow rates,during both early and later stages of combustion have been investigated in the second set ofexperiments, i.e. Flames E–H. For this set, relatively rich flames, see Flames E–H in Table 2.3,with two fuel-air equivalence ratios of 0.9 and 1 were examined. For each equivalence ratio, twoair flow rates of 120 and 130 SLPM were tested. For this set of experiments, the igniter positionwas fixed at S = 1.5 mm.In Table 2.3, U is the mean bulk flow velocity and is estimated from U = (Q˙fuel + Q˙air)/Ac,where Ac is the cross-section area of the 24 mm diameter nozzle shown in Fig. 2.1(b). Thecombustor thermal power (Pth) was calculated by multiplying the mass flow rate and lowerheating value of methane. Pth values are tabulated in Table 2.3. Results corresponding toFlames A–D and Flames E–H are discussed in Chapters 3 and 4, respectively.Table 2.3. Tested conditions.φ Q˙air (SLPM) Q˙fuel (SLPM) U (m/s) S (mm) Pth (kW)Chapter3 Flame A 0.7 100 8.0 4 -5.0 4.8Flame B 0.7 160 12.8 6.4 -5.0 7.6Flame C 0.7 100 8.0 4 1.5 4.8Flame D 0.7 160 12.8 6.4 1.5 7.6Chapter4 Flame E 0.9 120 11.7 4.9 1.5 7.0Flame F 0.9 130 12.7 5.3 1.5 7.6Flame G 1 120 13.1 4.9 1.5 7.9Flame H 1 130 14.2 5.3 1.5 8.527Chapter 3Flame development at early stages ofcombustionIn this chapter, dynamics of premixed flames at early stages of combustion is investigated.The results pertain to Flame A–D conditions listed in Table 2.3 and are categorized into foursubsections. First, the characteristics of the pressure and flame chemiluminescence are discussedand the phases of flame development are defined. In the second subsection, the characteristicsof the flame edge velocity are presented. In the third subsection, the dynamics of the flamechemiluminescence and its relation to those of the flame edge velocity and pressure are discussed.In the fourth subsection, the spectral characteristics of the pressure, flame chemiluminescence,and flame edge velocity are presented.3.1 Pressure and flame chemiluminescence characteristicsThe air volume flow rate as well as the igniter rod location can influence the characteristicsof the pressure and flame chemiluminescence. Specifically, Flames A, B, and C feature similarcharacteristics, with representative normalized pressure (p/pmax) presented in Figs. 3.1(a) and(b). The results in the figure pertain to Flame C condition. The maximum values of thepressure for all tested conditions are provided in Table 3.1. Also, overlaid on Figs. 3.1(a)283.1. Pressure and flame chemiluminescence characteristics0 20 40 60 80 100-0.200.20.40.60.81200 400 600 800 1000 1200 1400 160000.20.40.60.8Fig. 3.1. (a) and (b) are variations of the normalized pressure (black color) and spatially-averaged flame chemiluminescence (red color) related to the ignition and stabilization as well asthe transition phases, respectively. The dashed curve in (b) demonstrates nearly one oscillationof the spatially-averaged flame chemiluminescence during the transition phase. The resultspertain to Flame C condition.and (b) is the normalized spatially-averaged chemiluminescence (OH∗/OH∗max) variation. Thespatially-averaged OH∗ is given by the following formulation:OH∗ =∫ ∆y/2−∆y/2∫ ∆x0 OH∗dxdy∆x∆y, (3.1)with ∆x and ∆y being 94.2 and 77.3 mm, respectively. OH∗max is the maximum value of thespatially-averaged OH∗, which is tabulated in Table 3.1. Depending on the sizes of the binningwindow and the median-based filter (discussed in subsection 2.2), the OH∗max values can changeby a maximum of 7% for Flames A–D, as presented in Appendix A. The results in Table 3.1suggest that increasing the mean bulk flow velocity (which is equivalent to increasing the fuel andair volume flow rates) as well as moving the igniter rod upstream increase both the maximumpressure and the maximum spatially-averaged chemiluminescence. The maximum value of thepressure is of significant importance for the mechanical design of the power generator combustor.In Fig. 3.1(a), t = 0 corresponds to the instant at which the flame kernel is first detected in293.1. Pressure and flame chemiluminescence characteristicsTable 3.1. Parameters pertaining to Flames A–D with the details listed in Table 2.3pmax (kPa) OH∗max tig. (ms) tst. (ms) ttr. (ms) λ (%)Flame A 4.2 0.134 13.8 83.2 1178.53 55.8Flame B 4.8 0.183 11.8 102.0 752.7 28.6Flame C 2.9 0.103 13.2 76.4 1256.7 39.2Flame D 4.0 0.154 11.6 120.0 NA -7.6the chemiluminescence images. The accuracy of the time related to the kernel detection equalsthe inverse of the OH∗ chemiluminescence imaging frequency, which is 0.2 ms. The time at whichthe chemiluminescence data equals its global maximum is near t = 13.2 ms, see Fig. 3.1(a), andcorresponds to the instant at which the flame kernel has completely consumed the reactantsinside the main and exhaust tubes, with the spatial variation of the chemiluminescence shownin Fig. 3.2(a). The time period between the initial detection of the flame kernel and completeconsumption of the reactants inside the main and exhaust tubes is referred to as the ignitionphase duration, tig.. This experimental condition was tested two times and a difference of 1 mshas been observed in the corresponding tig. values. For each replication, the uncertainty relatedto estimation of tig. is the inverse of the imaging frequency (0.2 ms). Values of tig. are presentedin Table 3.1 for all tested conditions. As can be seen, tig. varies from about 12 to 14 ms,with Flame D featuring the shortest ignition phase. Please note that, since the igniter rod ispositioned upstream of the flame holder for Flames A and B, the instants related to the initialformation of the flame kernel cannot be recorded for these conditions. The results in the tablesuggest that increasing the mixture volume flow rate (which is equivalent to increasing the meanbulk flow velocity) and the igniter rod position decrease the ignition time. This is expected since,for a fixed fuel-air equivalence ratio, increasing both U and S decrease the required time for theflame to consume the reactants inside the main and exhaust tubes.Following the ignition phase and after about 18 ms, the flame stabilizes on the flame-holder.303.1. Pressure and flame chemiluminescence characteristics-200200 40 8000.010 40 8000.020.040 40 8000.010 40 8000.020.040 40 80-2002000.020.0400.10.20.30.4Fig. 3.2. (a–h) are the flame chemiluminescence at t = 13.2, 36.6, 91.6, 793.4, 884.2, 913.0,966.0, and 1070.0 ms, respectively. The results pertain to Flame C condition and are related tothose shown in Fig. 3.1. Flow is from left to right.Once the flame is stabilized, the flame height increases; and, at t=36.6 ms, the flame tip reachesthe stagnation wall (see Fig. 3.2(b)). After the ignition phase, the flame chemiluminescenceirregularly fluctuates for about 78 ms; and, finally, the flame chemiluminescence decreasessubstantially. During the flame chemiluminescence fluctuations, the flames become partially-detached (as presented later in the manuscript) from the flame-holder. This period is referredto as the stabilization phase. The beginning of this phase is the end of the ignition phase. Inorder to find the end of the stabilization phase, first, a sliding mean with a short duration of10 ms was used to filter the spatially-averaged flame chemiluminescence data. Then, the timeinstants corresponding to the local maxima of the sliding mean of the spatially-averaged flamechemiluminescence were detected using a built-in function (“findpeaks”) in MATLAB. Adjacentpeaks with relative differences smaller than a threshold value of 0.02 in the spatially-averagedflame chemiluminescence peaks were disregarded. Finally, the time instant corresponding to thefirst local minimum after the last local maximum was considered as the end of the stabilization313.1. Pressure and flame chemiluminescence characteristicsphase. This definition is used for identifying the stabilization phase for all tested conditions.A sensitivity analysis was performed to investigate the effect of the sliding mean window sizeon the duration of the stabilization phase, which is discussed in Appendix A. For the resultspresented in Fig. 3.1(a), the sliding mean features a local minimum at t = 91.6 ms, with thecorresponding chemiluminescence image shown in Fig. 3.2(c). The period of 13.2 . t . 91.6 msis referred to as the stabilization phase of Flame C, with the corresponding duration denotedby tst., and the values tabulated in Table 3.1. The uncertainties related to calculation of tst. are11, 7, 13, and 5%, for Flames A, B, C, and D, respectively, as discussed in Appendix A.After the stabilization phase, the flame chemiluminescence features one long-duration (∼1.2s) oscillation, which is followed by the steady flame chemiluminescence oscillations. In orderto demonstrate this one cycle of long-duration flame chemiluminescence oscillation (related tothe transition phase), the mean of the flame chemiluminescence signal inside a relatively largesliding window (200 ms) was calculated, and the results were overlaid on Fig. 3.1(b) by the bluedashed curve. The duration of the long time-period oscillation (shown by the dashed curve) isused to quantify the duration of the transition phase with details discussed in the following.The beginning of the transition phase is the end of the stabilization phase. The end of thetransition phase is identified by finding the instant at which the sliding mean of OH∗, with theduration of 10 ms, equals the time-averaged value of OH∗ corresponding to the steady oscilla-tions. The end of the transition phase depends on the starting time of the steady oscillations.Three different starting times, tstart =1100, 1200, and 1300 ms have been considered for all testedconditions leading to three different time durations for the transient phase. Mean of these pe-riods are considered as the duration of the transition phase, denoted by ttr., with the valuestabulated in Table. 3.1. The uncertainties related to the values of ttr. presented in Table 3.1323.1. Pressure and flame chemiluminescence characteristics200 400 600 800 1000 1200 1400 160000.10.20.30.40.50.60.70.8-200200 20 40 60 80-200200 50 100 150-0.200.20.40.60.81Fig. 3.3. (a) and (b) are variations of the normalized pressure (black color) and spatially-averaged flame chemiluminescence (red color) related to the ignition and stabilization phasesas well as the steady oscillations, respectively. (c) and (d) are the flame chemiluminescence att = 11.6 and 131.6 ms, respectively. The results correspond to Flame D condition. In (c) and(d), flow is from left to right.for all tested conditions are smaller than 7%, as discussed in Appendix A. Note that Flame Ddoes not feature a transition period; hence, ttr. is not provided for this tested condition. Severalchemiluminescence images related to the transition phase are shown in Figs. 3.2(d)-(h). Thenormalized spatially-averaged chemiluminescence signal associated with these instants are high-lighted by the circular data points in Fig. 3.1(b). Comparison of the maximum values of OH∗in Figs. 3.2(d-h) with those in Figs. 3.2(a-c) suggests that, for 790 . t . 1070 ms, the flamechemiluminescence is small, and there exist several instants that the flame is partially-detachedfrom the flame-holder and nearly extinguished. However, as can be seen, the flame does notcompletely detach from the flame-holder, and as a result, the flame blow-out does not happen.For t & tig. + tst. + ttr., the flame is stabilized on the flame-holder, and the burner featuresself-excited thermoacoustic oscillations.Variations of the normalized pressure and spatially-averaged flame chemiluminescence for333.1. Pressure and flame chemiluminescence characteristicsFlame D are presented in Figs. 3.3(a) and (b). Using the above discussed definition, the ignitionphase duration (tig. = 11.6 ms) was estimated for Flame D and tabulated in Table 3.1. Theflame chemiluminescence at t = 11.6 ms is presented in Fig. 3.3(c). Compared to the ignitionand stabilization phases, the transition phase is not present for Flame D condition, and thethermoacoustic oscillations appear after the stabilization phase.The time-averaged OH∗ chemiluminescence signal during the ignition and stabilization phasescompared to that of the steady oscillations can be used to speculate the existence of the tran-sient behaviour. Specifically, for flame conditions with the time-averaged value of OH∗ beingrelatively large (compared to that of the steady oscillations), it is speculated that the transitionphase exists. In order to investigate this speculation, first, the time-averaged values of OH∗ werecalculated using Eq. (3.2), where κ and ti are the duration and start time of the considered timeperiod, respectively.〈OH∗〉 = 1κ∫ ti+κtiOH∗(t)dt. (3.2)Then, the following parameter was calculated using Eq. (3.3).λ =〈OH∗〉ig.+st. − 〈OH∗〉s.〈OH∗〉s., (3.3)where the subscript ig.+st. pertains to the ignition and stabilization phases together, and〈OH∗〉s. is the time-averaged value of the chemiluminescence during steady oscillations. Thevalues of λ are listed in Table 3.1. For conditions with relatively large values of λ (see thoserelated to Flames A–C in Table 2.3), the spatially-averaged flame chemiluminescence is followedby a significant decrease, which is used to characterize the transition period. Compared toFlames A–C, results presented in Table 3.1 show that Flame D features a relatively small value343.2. Flame edge velocity characteristics0 20 40 60 80-200200 20 40 60 80 0 20 40 60 800Fig. 3.4. (a) A representative chemiluminescence image at t = 7.4 ms related to Flame Acondition. (b) Edges of the chemiluminescence image detected by the Sobel algorithm. (c)Flame edge overlaid on the chemiluminescence image. The inset of (c) represents the flame edgenear y = 0. Flow is from left to right.of λ. As a result, the transition phase does not exist for Flame D condition.3.2 Flame edge velocity characteristicsA representative OH∗ chemiluminescence of Flame A at t = 7.4 ms is shown in Fig. 3.4(a).The results pertain to Flame A condition. An edge finding algorithm in MATLAB was usedto detect the flame edge. This algorithm is developed based on the Sobel operator [143], whichdetects the maximum gradient of the OH∗ chemiluminescence and generates a binarized image,see Fig. 3.4(b). In order to obtain the flame edge, for each vertical position, the pixel that isfarthest from the y−axis is selected. The pixels representing the flame edge related to the resultsshown in Fig. 3.4(b) are overlaid on Fig. 3.4(c) and the corresponding inset. The smoothingspline in MATLAB was used to fit a curve to the data points shown in Fig. 3.4(c). This curveis also overlaid on the figure.In order to obtain the flame edge velocity, the horizontal position of the flame edge aty = 0 mm was first selected. Variations of this horizontal position for three time periodsrelated to the ignition, stabilization, and transition phases are shown in Figs. 3.5(a), (b), and353.2. Flame edge velocity characteristics0 2 4 6 8 10 120204060801000 2 4 6 8 10 12-20-100102040 60 80 10040608010040 60 80 100-20-1001020412 414 416 418 420 422708090100412 414 416 418 420 422-20-1001020Fig. 3.5. (a), (b), and (c) are samples of the flame edge position, x(t), during ignition, stabi-lization, and transition phases, respectively. The solid curve is the flame position after applyingthe spline smoothing and interpolation. (d), (e), and (f) are the flame edge velocity, V (t), corre-sponding to the results presented in (a), (b), and (c), respectively. The results pertain to FlameA condition.(c), respectively. The results in the figure pertain to Flame A condition. A smoothing splinealgorithm was used to smooth the position data shown in Fig. 3.5 and to interpolate in betweentwo neighbouring flame position data points. The resultant data is referred to as the flameedge position, denoted by x(t), and shown by the solid curves in Figs. 3.5(a-c). As can be seen,the flame edge position follows the data points in Figs. 3.5(a-c); and as a result, x(t) was usedfor estimation of the flame edge velocity, V (t). This parameter is given by V (t) = dx(t)/dt,and the first order backward finite difference approximation [144] was used to estimate dx/dt.The variation of V (t) pertaining to the results shown in Figs. 3.5(a), (b), and (c) are shownin Figs. 3.5(d), (e), and (f), respectively. During the ignition period, the flame edge velocity ispositive. After the formation of the flame kernel, the flame edge velocity increases from about 4(at t = 0) to 16.5 m/s (at t = 9.4 ms). The flame edge velocity at t = 0 is equal to the mean bulk363.2. Flame edge velocity characteristicsflow velocity inside the nozzle shown in Fig. 2.1(b) for Flame A. For comparison purposes, themean bulk flow velocity inside the 24 mm nozzle is also shown by the dashed-line in Fig. 3.5(d).Similarly, the kernel velocity for Flame B is 6.4 m/s at t = 0, which is equal to the mean bulkflow velocity inside the nozzle shown in Fig. 2.1(b), see Table 2.3. After t = 9.4 ms, the flameedge velocity decreases to zero. This deceleration is due to the presence of the stagnation wall[58, 59, 61].Several studies [31, 33, 52, 54–61, 66, 67, 69, 70, 76, 77, 145] investigated the flame edgevelocity during the ignition period. These investigations mainly utilized either hydrogen- ormethane-air mixtures. The flame edge velocity of the present study was normalized by theun-stretched laminar flame speed (SL0), and the results were presented by the black solid curveshown in Fig. 3.6(a). For clarity, only results related to Flame A are presented. Note that, forthe results presented in the figure, effects of pressure and temperature variations on the value ofthe un-stretched laminar flame speed are considered. The relation presented in Eq. (1.5) alongwith the values of SL0,ref and η = β + (γ−1γ ), pertaining to the present study and past investi-gations [33, 55, 58, 145] were evaluated, presented in Table 3.2, and utilized for normalizing theresults presented in Figs. 3.6(a) and 3.8.Table 3.2. Parameters utilized in Eqs. (1.1-1.5).  and β are extracted from [29] and [23] forCH4-air and H2-air mixtures, respectively. For all presented studies, Pref = 1 atm.Study Mixture φ Tref (K) SL0,ref (m/s) γ  β ηCurrent study CH4/air 0.7 298.2 0.22 1.250 1.54 -0.327 -0.11Yu et al. [33] CH4/air 1 298.2 0.38 1.250 1.6 -0.42 -0.10Chen et al. [58] CH4/air 1 298.2 0.38 1.250 1.6 -0.42 -0.10Zheng et al. [145] CH4/air 1 300.0 0.38 1.250 1.6 -0.42 -0.10Zheng et al. [145] H2/air 1 300.0 2.35 1.245 1.4 0.194 0.47Xiao et al. [55] H2/air 1.28 298.2 2.89 1.249 1.4 0.194 0.47In Table 3.2, SL0,ref and γ are the un-stretched freely propagating laminar flame speed atreference condition and the unburnt mixture heat capacity ratio, respectively, that are estimated373.2. Flame edge velocity characteristics0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80204060801000 20 40 60 80-200200 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80Fig. 3.6. (a) Variation of the normalized flame edge velocity during the ignition period. twall isthe time that the flame skirt nearly reaches the combustion chamber side-walls. (b-f) presentthe flame chemiluminescence during the ignition period at t/twall = 0.32, 0.46, 0.57, 0.78, and1, respectively. The results pertain to Flame A condition. In (b–f), flow is from left to right.using Cantera simulations (with GRI Mech 3.0) [146]. Overlaid on the figure are the results of[33, 55, 58, 145]. The flame edge velocity of these investigations are also normalized by theun-stretched laminar flame speed corrected for the effect of pressure and temperature change inthese studies. Note that Xiao et al. [55], Chen et al. [58], and Zheng et al. [145] performed bothexperimental and numerical simulation studies. Here, their [55, 58, 145] experimental results areextracted and presented. Yu et al. [33] performed their studies for pure and hydrogen-enrichedmethane-air flames for several fuel-air equivalence ratios. Only results related to stoichiometriccondition for pure methane-air mixture are reproduced and presented in Fig. 3.6 for brevity.Similar observations were made for other fuel-air equivalence ratios and hydrogen enrichmentpercentages tested in [33]. Zheng et al. [145] also investigated the flame edge dynamics for bothhydrogen- and methane-air mixtures. The results related to both of these mixtures are overlaidon Fig. 3.6(a).383.2. Flame edge velocity characteristics0 0.1 0.3 0.5 0.7 0.90 0.1 0.3 0.5 0.7 0.9-30-20-100102030Fig. 3.7. Variations of the normalized OH∗ corresponding to (a) Fig. 3.6(e) with t/twall = 0.78and (b) corresponding to Fig. 3.6(f) with t/twall = 1.In Fig. 3.6, t is normalized by the time that the flame skirt reaches the burner side-walls(twall). Several flame chemiluminescence images related to t/twall = 0.32, 0.46, 0.57, 0.78, and 1are shown in Figs. 3.6(b–f), respectively. The flame edges are shown by the white curves in thefigures. The yellow dashed-lines mark the interior of the main tube. The results in Figs. 3.6(band c) show that the ignition kernel is nearly spherical prior to t/twall ≈ 0.5, and it grows insize forming a finger-shaped flame. This is similar to the results of [31, 33, 52, 54–72].Variations of the normalized flame chemiluminescence at x = 10, 20, 30, and 40 mm relatedto the results presented in Figs. 3.6(e) and (f) are presented in Figs. 3.7(a) and (b), respectively.Overlaid on the figures are dashed-lines highlighting the locations of the upper and lower walls.Specifically, the bottom and top wall locations pertain to y = −16.3 ± 1.5 mm and y = 16.3 ±1.5 mm, respectively. The uncertainty associated with the location of the bottom and top wallsis due to a physical clearance for connecting the quartz tubes to the stagnation wall, which was393.2. Flame edge velocity characteristics5 10 15 20 25102030405060708090Fig. 3.8. Variation of the maximum normalized flame edge velocity with the combustion chamberaspect ratio.implemented for mitigating the adverse effect of combustor thermal expansion during long-termoperations. In our analyses, the flame skirt is considered to have touched the side-wall if themeasured chemiluminescence at the wall boundary is larger than or equal to 10% of the totalmaximum chemiluminescence for the corresponding frame, which is OH∗max. This criterion hadto be satisfied for both the bottom and the top walls. As can be seen in Fig. 3.7(b), the resultsrelated to Fig. 3.6(f) and relevant to t/twall = 1, satisfy the above criterion. However, thosepresented in Fig. 3.7(a), related to Fig. 3.6(e) and relevant to t/twall = 0.78, do not satisfy theabove criterion. Thus, the flame skirt in Fig. 3.6(e) has not touched the side-walls, but that inFig. 3.6(f) has touched these.Comparison of the results presented in Fig. 3.6 suggests that V/SL0 maximizes once theflame edge reaches the side-walls, which is in agreement with the results of past investigations[33, 55, 58, 145]. Despite the similarity of the trends presented in Fig. 3.6(a), the maximum403.2. Flame edge velocity characteristicsvalues of V/SL0 are different. In order to investigate the reason for this, the variations ofmaximum V/SL0, denoted by V/SL0|max, versus the combustion chamber aspect ratio (L/D),which is the ratio of the chamber length to diameter, for several past studies and the presentinvestigation are shown in Fig. 3.8. Please note that the values of Vmax pertaining to the presentstudy depend on the smoothing spline fitted to the flame edge position. However, as shown inFig. 3.5(a), the fitted smoothing spline demonstrates an acceptable performance in following theflame edge position data points pertaining to the ignition phase, and as a result, was used tocalculate the flame edge velocity. The results shown in Fig. 3.8 suggest that, for closed tubes, theeffect of the aspect ratio on V/SL0|max depends on the tested fuel type. As can be seen, for themethane-air mixtures, increasing the aspect ratio increases V/SL0|max, while for the hydrogen-air mixtures, the effect of the aspect ratio is relatively small (see the green triangular andred diamond data symbols in Fig. 3.8). As shown in Table 3.2, for the methane-air mixtures,the effect of pressure rise during the flame propagation is not as pronounced as that for thehydrogen-air mixtures. As a result, the un-stretched laminar flame speeds pertaining to studiesof Chen et al. [58] and Zheng et al [145] are almost constant and insensitive to pressure rise, seeTable 3.2. Thus, at t = twall corresponding to V/SL0|max, the observed difference between thevalues of V/SL0|max pertaining to these experiments [58, 145], with the methane-air mixtures,is mainly due to the difference in the maximum value of flame edge velocities. Specifically, for afixed chamber diameter, increasing the length to diameter ratio allows for the flame to accelerateover a longer distance, achieving a relatively large velocity. For the studies of Xiao et al. [55]and Zheng et al. [145] that involved the hydrogen-air mixtures, although the values of SL0 atthe reference condition are nearly close, see Table 3.2, the instantaneous values of SL0 stronglydepend on the corresponding pressure values. As a result, both V and SL0 change during the413.2. Flame edge velocity characteristicsflame propagation, influencing the values of V/SL0|max. Comparison of the results pertainingto the different fuel types tested in Zheng et al. [145] suggests that the values of V/SL0 nearlycollapse. This implies that for identical experimental setups, normalizing the flame edge velocityby the corresponding un-stretched laminar flame speed (corrected for the effect of instantaneouspressure value) allows to eliminate the effect of fuel type on the flame edge velocity.In addition to aspect ratio, existence of a stagnation wall can influence the maximum achievedflame edge velocity. This is specifically relevant to the reverse-flow configuration of the combustorutilized in the present study. This configuration is somewhat similar to that used in the study ofYu et al. [33]. For such configuration, after the flame kernel is formed and accelerated, gas canleave the combustion chamber, generating smaller pressure increase compared to closed tubes.This allows for the flame to accelerate significantly, featuring a large maximum velocity. Ascan be seen in Fig. 3.8, compared to the closed configuration, semi-closed ducts as well as thereverse-flow configuration used in the present study feature larger values of V/SL0|max. Valuesof V/SL0|max obtained from the present study are larger than that related to the study of [33].This is speculated to be linked to the background flow. Flame kernels of the present study aredeveloped inside a tube which features a non-zero mean bulk flow velocity at the ignition time.However, compared to the present study, the mixture used in Yu et al. [33] is initially quiescent.Since the mean bulk flow velocity related to Flames B and D is larger than that of Flames Aand C, V/SL0|max of Flames B and D are larger than those of Flames A and C, as shown inFig. 3.8.Compared to the results presented in Fig. 3.5(d), those in Figs. 3.5(e and f) show that theflame edge velocity fluctuates during both stabilization and transition phases. A sample ofthese fluctuations, demonstrating both positive and negative flame edge velocities, are shown423.2. Flame edge velocity characteristics0 20 40 60 80 100-200200 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100Fig. 3.9. Flame chemiluminescence during the stabilization phase. The white solid curve is theflame edge. The dashed ellipses highlight the flame detachment from the flame-holder. Theresults pertain to the red solid data points shown in Fig. 3.5(b) and (d), which are related toFlame A condition. Flow is from left to right.in Fig. 3.9. The results in Figs. 3.9(a-e) pertain to t = 51.6, 53.0, 56.6, 59.0, and 60.0 ms,respectively. As can be seen, the flame can become nearly detached from the flame-holder duringthe stabilization phase (see the highlighted regions in Figs. 3.9(c-e)). Similar observations weremade for the rest of the tested conditions. Please note that considering the line-of-sight natureof the collected data, regions that feature non-zero values of flame chemiluminescence near theflame-holder (Figs. 3.9(a and b)) may still feature flame detachment. However, this cannot beinvestigated due to the line-of-sight nature of the chemiluminescence measurements.The discussions presented in subsections 3.1 and 3.2 allow for characterizing the flame edgevelocity, pressure, and spatially-averaged flame chemiluminescence separately. Specifically, is-sues such as near flame-out and flame detachment during transition and stabilization phasesare identified. However, the relations between these parameters, and how these relations areinfluenced by the reverse-flow configuration are of importance. Specifically, it is of interest toidentify how the stagnation wall influences the relations between pressure, spatially-averagedflame chemiluminescence, and flame edge velocity, and if the relations can be described bythermodynamics formulations. These are discussed in the following section.433.3. The relation between pressure, flame chemiluminescence, and flame edge velocity3.3 The relation between pressure, flame chemiluminescence,and flame edge velocityVariations of the flame edge velocity versus normalized spatially-averaged chemiluminescence(OH∗/OH∗max) related to the ignition, stabilization, and transition phases are presented inFigs. 3.10(a), (b), and (c), respectively. As can be seen, the results in Fig. 3.10(a) suggestthat the flame edge velocity is positively related to OH∗/OH∗max during 0 . t . 9.4 ms.To investigate this positive relation, a conservation of energy analysis, with the correspondingdetails provided in Appendix B, was performed. The analysis is conducted for a control volumewith projection on x − y plane shown by OH∗ FOV in Fig. 2.2. The results in Appendix Bsuggest that the heat release rate due to chemical reactions, Q˙ch. can be obtained from:Q˙ch. =cvMWRu(dpdtV)+ m˙oho − m˙ihi − Q˙︸ ︷︷ ︸∆, (3.4)where cv, MW , V, Ru, m˙, h, and Q˙ are the specific heat at constant volume, gas molecularweight, the volume of the control volume, the universal gas constant, mass flow rate, the specificenthalpy, and the heat transfer across the boundaries of the control volume, respectively. Theindices “i” and “o” pertain to the inlet and outlet of the control volume. The rate of heattransfer across the boundaries of the control volume subtracted from the net rate of enthalpythat leaves the control volume is ∆.The sequence of chemiluminescence images presented in Figs. 3.6(b–f) as well as the resultspresented in Fig. 3.10(a) suggest that, during the ignition phase and prior to t = 9.4 ms, the flamechemiluminescene increases. This generates an increasing volume of hot combustion productswhich pushes the finger-shaped flame and increases the flame edge velocity; hence, the positive443.3. The relation between pressure, flame chemiluminescence, and flame edge velocity0 0.2 0.4 0.6 0.8 100.5100.510.2 0.4 0.6 0.8 1-20-10010200.2 0.4 0.6 0.8 1-1-0.500.510.1 0.2 0.3 0.4-200200.1 0.2 0.3 0.4-0.0500.050 0.2 0.4 0.6 0.8 105101520Fig. 3.10. The first and second rows demonstrate variations of the flame edge velocity and thederivative of pressure with respect to time versus normalized spatially-averaged OH∗ chemilu-minescence, respectively. The first, second, and third columns present these variations duringignition, stabilization, and transition phases, respectively.relation presented in Fig. 3.10(a). Variations of dp/dt versus OH∗/OH∗max, during the ignition,stabilization, and transition phases, are presented in Figs. 3.10(d–f), respectively. A slidingmean with the duration of 2 ms was used to filter the pressure rate data and the filtered resultsare shown in Figs. 3.10(d–f). Prior to reaching the stagnation wall (t = 11.4 ms), the flame edgedecelerates and the pressure rate increases rapidly, see Fig. 3.10(d). During 11.4 . t . 13.8 ms,the flame propagates into the exhaust tubes. The spatial distribution of OH∗ at t = 11.4, 12.2,13.0, and 13.8 are presented in Figs. 3.11(a–d), respectively. During the above period, both flamechemiluminescence and pressure rate increase. The flame speed, with the definition discussedearlier, is zero since the flame edge has reached to the stagnation wall. Thus, V ≈ 0 aftert = 11.4 ms in Fig. 3.11(a). During 0 . t . 9.4 ms as well as 11.4 . t . 13.8, ∆ in Eq. (3.4)is nearly negligible, and as a result, the pressure rate and the normalized spatially-averagedchemiluminescence are linearly correlated.453.3. The relation between pressure, flame chemiluminescence, and flame edge velocity0 20 40 60 800 20 40 60 800 20 40 60 80-20020-20020Fig. 3.11. (a-d) are spatially-resolved OH∗ chemiluminescence during flame propagation insidethe exhaust tubes. (e and f) present the OH∗ distribution during exhaust of the burnt gas fromthe combustor. Flow is from left to right.During 13.8 . t . 15.4 ms, the hot combustion products leave the exhaust tubes, with tworepresentative OH∗ chemiluminescence images shown in Figs. 3.11(e and f). This period pertainsto the beginning of the stabilization phase, with the corresponding flame edge velocity, pressurerate, and spatially-averaged flame chemiluminescence relations presented in Figs. 3.10(b and e).During the above time period, the main tube is filled with combustion products, and for thisreason, V is set to zero as can be seen in Fig. 3.10(b). Discharge of the combustion productsfrom the exhaust tubes generates suction inside the main tube, which decreases the pressure rateto negative values as shown in Fig. 3.10(e). Similar conclusions can be made from the pressurevariations presented in the studies of [69, 71, 78].For t & 15.4 ms, the results shown in Fig. 3.10(b) do not suggest a relation between the flameedge velocity and the normalized OH∗ chemiluminescence. However, the results presented in463.4. The spectral characteristics of pressure, flame chemiluminescence, and flame edge velocity13.8 31 75 100-1-0.500.510 0.5 1 1.5 200.20.40.60.811.21.41.61.82Fig. 3.12. Variations of the normalized OH∗ chemiluminescence (red curve) and pressure rate(black curve).Fig. 3.10(e) show that the pressure rate and the normalized chemiluminescence are nearly related.In order to further demonstrate this, the normalized (by maximum) of both OH∗ and dp/dt timehistories related to the stabilization phase are shown in Fig. 3.12. As can be seen, these twoparameters nearly follow during 31 ms . t . 75 ms. The results in Figs. 3.10(e) suggest that thevalues of dp/dt are smaller than those predicted by the first-law of thermodynamics for ∆ = 0.The flame edge velocity, pressure rate, and OH∗ feature a cyclical behaviour superimposedby noise during the transition period as shown in Figs. 3.10(c and f). Spectral analysis wasperformed to investigate this behaviour, which is discussed in the next subsection.3.4 The spectral characteristics of pressure, flamechemiluminescence, and flame edge velocitySpectral analysis was performed to study the characteristics of pressure, pressure rate,spatially-averaged flame chemiluminescence, and flame edge velocity during the transition pe-riod. The normalized power spectrum density (PSD∗) of the pressure, pressure rate, spatially-473.4. The spectral characteristics of pressure, flame chemiluminescence, and flame edge velocity101 102 10310-810-610-410-2100101 102 103101 102 10310-610-410-2100100 101 102 103Fig. 3.13. The normalized power spectrum density of the (a) pressure, (b) spatially-averagedOH∗, (c) pressure rate, and (d) flame edge velocity for the transition phase.averaged OH∗, and flame edge velocity for Flames A–C pertaining to the transition period wereobtained and presented in Figs. 3.13(a)–(d), respectively. Please note that for Flames A–C, asliding mean was subtracted from the spatially-averaged OH∗ signal prior to the spectral analy-sis. Also, as shown in Fig. 3.3(b), Flame D does not feature a transition period, and as a result,this condition is not considered for the spectral analysis.In order to investigate the dominant acoustic mode of the setup, the plenum was struck witha hammer, and the pressure data was collected. For this experiment, the apparatus containsquiescent air. The PSD of the pressure data normalized by the corresponding maximum value(PSD∗) is presented in Fig. 3.14. As can be seen, PSD∗ features a dominant frequency atabout 61 Hz (fn). The harmonics of this frequency (2fn, 3fn, etc.) are also apparent, which arehighlighted in the figure.483.4. The spectral characteristics of pressure, flame chemiluminescence, and flame edge velocity101 102 10310-410-310-210-11000 1 2012Fig. 3.14. Acoustic response of the experimental setup shown in Fig. 2.1.Results presented in Fig. 3.13(a) show that the PSD∗ of the pressure data features a dom-inant peak at the burner acoustic frequency. As can be seen, for f . fn, the values of PSD∗depend on the corresponding tested condition. However, for f & fn, the PSD∗ values of thepressure data nearly collapse for Flames A–C. A least-square technique was used to fit lines tothe results presented in Fig. 3.13(a) for f & fn. The slopes of the lines vary from -2.7 to -2.9depending on the tested condition, with the mean value being -2.8. A dotted dashed-line is usedto present the decay with the slope of -2.8 in Fig. 3.13(a). Also overlaid on Fig. 3.13(a) are theresults of Clavin and Siggia [147]. They [147] performed a theoretical investigation, and theirresults suggest that, for the inertial range of turbulence where the fluid velocity PSD features a-5/3 power-law, the PSD of pressure oscillations should follow a -2.5 power-law relation. Thisrelation is shown by the blue dashed line in Fig. 3.13(a). The validity of the theory discussed inClavin and Siggia [147] is limited to burners with diameters larger than 30 cm [148]. This maybe the reason for the small difference between the values of the slopes related to the presentstudy and that of [148]. In fact, Lieuwen et al. [149, 150] investigated the PSD of the pressureoscillations for relatively small-diameter burners (1–3 cm) similar to that of the present study.For comparison purposes, the results of [149, 150] were reproduced and overlaid on Fig. 3.13(a).493.4. The spectral characteristics of pressure, flame chemiluminescence, and flame edge velocityThe PSDs presented in [149] and [150] are normalized by their corresponding maximum values.Rajaram and Lieuwen [149] results show that the slope of PSD∗ can vary from -2.1 to -3.2depending on the tested condition, which is similar to the slopes obtained in the present study.The PSD∗ values of the spatially-averaged OH∗ chemiluminescence signals are calculatedfor Flames A–C and presented in Fig. 3.13(b). As can be seen, the OH∗ chemiluminescencesignals feature a broader spectrum around the acoustic dominant frequency (about 61 Hz).For the tested conditions of the present study, the PSD∗ values of the spatially-averaged OH∗chemiluminescence nearly collapse. As the results in Fig. 3.13(b) show, the slopes of the powerspectrum density are -2.4 and -5.8 for fn . f . 1400 Hz and f & 1400 Hz, respectively. Theresults of [149, 151] are reproduced and presented in Fig. 3.13(b) for comparison purposes as well.Hirsch et al. [151] developed a theoretical model for the PSD of the flame chemiluminescence andvalidated their model against their experimental results (which are not shown in Fig. 3.13(b) forclarity purposes). The variation of PSD∗ versus frequency related to the present study agreeswith those of Rajaram and Lieuwen [149] as well as Hirsch et al. [151].The PSD∗ values of the pressure rate (dp/dt) are presented in Fig. 3.13(c). Similar to thepressure power spectrum density, pressure rate PSD also features a dominant frequency at fnfor Flames A–C. However, the power-law relations presented for the pressure data and the OH∗chemiluminescence shown in Figs. 3.13(a) and (b) are not observed for the pressure rate.The PSD∗ values of the flame edge velocity for Flames A–C are presented in Fig. 3.13(d). Forf . 500 Hz, the PSD∗ values depend on the tested mean bulk flow velocity. For f & 500 Hz, thepower spectrum density of the flame edge velocity collapses for all tested conditions featuring thetransition phase. For this range, the PSD∗ values follow a -5.2 power-law relation. The powerspectrum density of gas velocity for spherically-expanding flames is extracted from Bradley et503.4. The spectral characteristics of pressure, flame chemiluminescence, and flame edge velocityal. [83] and is presented in Fig. 3.13(d). As can be seen, the gas velocity PSD follows the -5/3power-law relation related to the inertial range. The difference between the power-law relationof the flame edge velocity (−5.2) and gas velocity (−5/3) is expected as they correspond to twodifferent physical parameters. However, the results in Fig. 3.13(d) show that the PSD of theflame edge velocity decays faster compared to that of the gas velocity for f & 500 Hz.In essence, the results discussed in subsections 3.1–3.4 suggest that the presence of thestagnation wall (and as a result, the reverse-flow configuration) allows for the flames to attainrelatively large velocities compared to closed configurations. After the flame reaches the stag-nation wall, and the flow turns into the exhaust tubes, the pressure rate increases significantly.Once the flame stabilizes on the flame-holder and after the transition phase, the pressure andflame chemiluminescene feature cyclic behaviour superimposed with random fluctuations. Forthese fluctuations, the power spectral densities of the pressure, flame chemiluminescene, andflame edge velocity feature power-law relations with different decay rates. However, the decayrates of PSDs reported for pressure and flame chemiluminescene fluctuations are similar to thosereported in the literature for unconfined flames. This suggests, despite the significant influenceof the reverse-flow configuration during the ignition and stabilization phases, this configurationdoes not influence the pressure and flame chemiluminescence spectra during the transition phaseand results similar to unconfined flames are obtained.51Chapter 4Signature of thermoacoustic modesat early stages of combustionCharacteristics of flame development at early stages of combustion were investigated inChapter 3 for relatively lean flames (φ = 0.7). However, our understanding related to thesecharacteristics pertaining to relatively rich conditions is limited. In a recent study related tothe same setup, Heydarlaki [100] showed that the pressure and flame chemiluminescence featuredominant frequencies associated with the structural, acoustic, and intrinsic modes during steady-state oscillations. It is of interest to investigate whether these modes can be detected at theearly stages of flame development inside our reverse-flow combustor. This is of importance forproviding guidelines that can be used to mitigate and control the thermoacoustic instabilities.The results presented in this chapter pertain to Flames E–H conditions with details tabulatedin Table 2.3. In the following, first, the temporal variations of thermoacoustic parameters arepresented for relatively rich flames. Then, the signature of thermoacoustics at both early andlater stages of combustion is sought.524.1. Temporal variations of pressure, pressure rate, flame chemiluminescence, and flame edge velocity4.1 Temporal variations of pressure, pressure rate, flamechemiluminescence, and flame edge velocityPressure variations (see black curves) pertaining to Flames E–H conditions are shown inFigs. 4.1(a–d), respectively. The first and second rows pertain to φ = 0.9 and 1; and, the firstand second columns correspond to air flow rates of 120 and 130 SLPM, respectively.0 200 400 600 800 1000 1200 1400 1600 1800-4-202460 50 100 150 20002460 200 400 600 800 1000 1200 1400 1600-4-2024680 50 100 150 200-2024680 500 1000 1500 2000-4-202460 50 100 150-202460 500 1000 1500-4-2024680 50 100 150 200 250-202468800 850 900 950 1000 1050-0.200.20.40024800 850 900 950 1000 1050-0.200.20.40024800 850 900 950 1000 1050-0.200.20.4800 850 900 950 1000 1050-0.200.20.40-202468Fig. 4.1. (a–d) are the variations of the pressure (black color) and the sliding mean subtractedpressure (gray color) pertaining to Flames E–H, respectively. The insets are related to theignition and stabilization phases.Variations of the pressure rate and spatially-averaged flame chemiluminescence are presentedin Figs. 4.2 and 4.3, respectively. In both figures, the first and second rows highlight results forφ = 0.9 and 1; and, the first and second columns are for air flow rates of 120 and 130 SLPM.For clarity purposes, two insets relating to the early stages of combustion, with the duration534.1. Temporal variations of pressure, pressure rate, flame chemiluminescence, and flame edge velocitycorresponding to the ignition and stabilization phases, and a 250 ms window of the steadythermoacoustic oscillations are enlarged and shown in Figs. 4.1–4.3. The time periods of theignition (tig.) and stabilization (tst.) phases for Flames E–H are provided in Table. 4.1.0 200 400 600 800 1000 1200 1400 1600 1800-1-0.500.511.520 200 400 600 800 1000 1200 1400 1600-1.5-1-0.500.511.520 50 100 150 200-1010 500 1000 1500-1.5-1-0.500.511.520 50 100 150 200 250-1010 50 100 150 200-1-0.500 50 100 150-202460 500 1000 1500 2000-1.5-1-0.500.511.520 50 100 150-101800 850 900 950 1000 1050-1-0.500 200-1-0.50800 850 900 950 1000 1050-0.100.1800 850 900 950 1000 1050-0.100.10 200-101800 850 900 950 1000 1050-0.100.1Fig. 4.2. (a–d) are the variations of the pressure rate pertaining to Flames E–H, respectively.The insets are related to the ignition and stabilization phases.Table 4.1. The time periods of the ignition (tig.) and stabilization (tst.) phases, percentile ofthe excessive OH∗ chemiluminescence (λ), structural (fs), acoustic (fn), first intrinsic (fI,1), andsecond intrinsic (fI,2) mode frequencies pertaining to Flames E–H.tig. (ms) tst. (ms) λ (%) fs (Hz) fn (Hz) fI,1 (Hz) fI,2 (Hz)Flame E 10 221.3 -31.5 21.0 61.0 238.0 293.0Flame F 9.75 147 -31.93 21.0 61.0 244.1 293.0Flame G 10.5 191.5 -86.11 21.0 61.0 244.1 299.1Flame H 10 274.3 -45.96 21.0 61.0 256.3 299.1The flame edge position and velocity were estimated, and the results are shown in Figs. 4.4(a)and (b), respectively. From all tested conditions, Flame G pertains to the most rich and smallest544.1. Temporal variations of pressure, pressure rate, flame chemiluminescence, and flame edge velocity0 200 400 600 800 1000 1200 1400 1600 1800-0.2-0.100.10.20.30 50 100 150 200-0.0500.050.10.150 200 400 600 800 1000 1200 1400 1600-0.2-0.100.10.20.30 500 1000 1500 2000-0.2-0.100.10.20.30 500 1000 1500-0.100.10.20.30 50 100 150 200 250-0.100.10.20 50 100 150-0.0500.050.10.150 50 100 150 200-0.0500.050.10.15800 850 900 950 1000 105000.050.10-0.0500.050.10.15800 850 900 950 1000 105000.050.10 200-0.0500.050.10.15800 850 900 950 1000 105000.050.1800 850 900 950 1000 105000.050.10-0.100.10.2Fig. 4.3. (a–d) are the variations of the spatially-averaged flame chemiluminescence (red color)and the sliding mean subtracted spatially-averaged flame chemiluminescence (orange color) per-taining to Flames E–H, respectively. The insets are related to the ignition and stabilizationphases.tested flow rates. As a result, this flame hits the stagnation wall the least frequently comparedto the rest of the test conditions. Thus, the flame edge velocity was estimated only for Flame G.The flame edge position and velocity were estimated using the procedures discussed in Chapter3.The results shown in Fig. 4.3 suggest that neither of Flames E–H features the transitionphase, and the stabilization phase is immediately followed by the steady thermoacoustic oscil-lations. This can be linked to the negative values of parameter λ, calculated using Eq. (3.3)and tabulated in Table 4.1. As can be seen, the values of λ are negative. This is similar toλ reported for Flame D condition. Similar to Flames E–H, Flame D also did not feature the554.1. Temporal variations of pressure, pressure rate, flame chemiluminescence, and flame edge velocity0 200 400 600 800 1000 1200 1400 16000501000 200 400 600 800 1000 1200 1400 1600-40-200200 200 400 60000.511.52 1080 200 400 60002468 1070 100 200 0 100100200300400500600400 600 800 1000 1200100200300400500600Fig. 4.4. (a) and (b) are the variations of the flame edge position and velocity, respectively.(c) and (d) are the spectrogram and power spectrum density of the flame edge velocity relatedto the ignition and stabilization phases. (e) and (f) are the spectrogram and power spectrumdensity of the flame edge velocity related to the steady oscillations. The results pertain to FlameG condition.transient condition. This observation further confirms that negative values of λ are associatedwith absence of the transition phase.As can be seen in Figs. 4.1–4.4, during the ignition and stabilization phases, the pressure,pressure rate, spatially-averaged OH∗, and flame edge velocity feature an oscillatory behaviourwith a relatively large-amplitude and small frequency. However, once the steady thermoacousticoscillations are established, these parameters feature both low- and high-frequency oscillations.Similar observations were reported in the studies of [78, 91].In Chapter 3, it was shown that, for lean methane/air flames with φ = 0.7, the flame de-velopment characteristics during the ignition and stabilization phases (∼100 ms) follow thoseof a closed system. However, such a conclusion could not be drawn for the transition phase.Analyses similar to those performed in Chapter 3 are performed in this chapter to assess the564.1. Temporal variations of pressure, pressure rate, flame chemiluminescence, and flame edge velocity0 0.2 0.4 0.6 0.8 100.510 0.2 0.4 0.6 0.8 1-1010 0.2 0.4 0.6 0.8 100.510 0.2 0.4 0.6 0.8 1-1010.4 0.5 0.6-0.100.10.4 0.5 0.6-0.100.10 0.2 0.4 0.6 0.8 100.510 0.2 0.4 0.6 0.8 1-1010.2 0.3 0.4 0.5 0.6-0.100.10 0.2 0.4 0.6 0.8 100.510 0.2 0.4 0.6 0.8 1-1010.3 0.35 0.4 0.45 0.5 0.55-0.0500.05Fig. 4.5. The first, second, and third columns are the normalized pressure rate versus normalizedspatially-averaged flame chemiluminescence related to the ignition phase, stabilization phase,and the steady oscillations, respectively. The first, second, third, and fourth rows pertain toFlames E, F, G, and H, respectively.system behaviour during the ignition and stabilization phases as well as the steady thermoa-coustic oscillations for relatively rich flames, that are Flames E–H. Results presented in Fig. 4.5show the variations of the normalized pressure rate, (dp/dt)/(dp/dt)max, versus the normal-ized spatially-averaged flame chemiluminescence (OH∗/OH∗max). The first, second, third, andfourth rows of Fig. 4.5 pertain to Flames E, F, G, and H, respectively. The results related tothe ignition phase, stabilization phase, and steady oscillations are presented in the first, second,and third columns of Fig. 4.5, respectively. Also, overlaid on the figures shown in the first and574.2. Spectral characteristics of pressure, flame chemiluminescene, and flame edge velocitysecond columns is a blue dashed line ((dp/dt)/(dp/dt)max = OH∗/OH∗max), which pertains tothe linear relation between the pressure rate and heat release rate predicted by the first law ofthermodynamics simplified for a closed system, see Eq.(3.4) for ∆ = 0.The results presented in Fig. 4.5 suggest that, during the ignition and stabilization phases,the normalized pressure rate and spatially-averaged flame chemiluminescence are related, andthe values of the normalized pressure rate during these phases are relatively close to those onthe blue dashed line. However, for the steady thermoacoustic oscillations, see the last columnin Fig. 4.5, no linear relation between the pressure rate and flame chemiluminescence can beobserved. Assuming negligible heat transfer across the control volume boundaries, ∆ is negligiblein closed systems and the relation between pressure and heat release rate is linear. Thus, theresults shown in Fig. 4.5 confirm that, during the ignition and stabilization phases, the systemserves as a closed system for relatively rich flames similar to lean flames. The relations betweenpressure rate and flame chemiluminescence presented in Figs. 4.5 and 3.10 suggest that theutilized combustor features characteristics of closed and open systems at early and later stagesof combustion, respectively. This behaviour may have implications in terms of the modes of thethermoacoustic oscillations. In order to further investigate this, spectral analysis was performed,and the results are discussed in the next subsection.4.2 Spectral characteristics of pressure, flamechemiluminescene, and flame edge velocitySpectral analysis was performed for the pressure, pressure rate, and the spatially-averagedflame chemiluminescence pertaining to Flames E–H, with the corresponding results presentedin Figs. 4.6, 4.7, and 4.8, respectively. In these figures, the first, second, third, and fourth584.2. Spectral characteristics of pressure, flame chemiluminescene, and flame edge velocityrows pertain to Flames E, F, G, and H, respectively. The first and second columns are thespectrograms and power spectrum densities related to the ignition and stabilization phases. Thethird and fourth columns present the spectrograms and power spectrum densities pertaining tothe steady thermoacoustic oscillations. For Flame G, spectral analysis was also performed tostudy the characteristics of the flame edge velocity, with the corresponding results shown inFig. 4.4. The spectral analysis of the flame edge velocity related to Flame G for the ignition andstabilization phases as well as the steady thermoacoustic oscillations are shown in Figs. 4.4(cand d) and (e and f), respectively.0 100 200 300 400 500 6000121060 50 100 150 200200400600500 1000 15002004006000 100 200 300 400 500 6000121040 100 200 300 400 500 60001231060 50 100 1502004006000 100 200 300 400 500 600012104500 1000 1500 20002004006000 100 200 300 400 500 60002461060 50 100 150 200200400600500 1000 15002004006000 100 200 300 400 500 6000121040 100 200 300 400 500 6000510 1060 50 100 150 200 2502004006000 100 200 300 400 500 600012 104400 600 800 1000 1200200400600Fig. 4.6. The first and second columns are the pressure spectrogram and power spectrumdensity related to the ignition and stabilization phases. The third and fourth columns are thespectrogram and power spectrum density of the pressure pertaining to the steady oscillations.The first, second, third, and fourth rows pertain to Flames E, F, G, and H, respectively.To generate the spectrograms and power spectrum densities in Fig. 4.4 and Figs. 4.6–4.8, first,a sliding mean with a window size of 100 ms was constructed and the mean was subtracted fromthe original signal. The mean-subtracted signals pertaining to the pressure and the spatially-averaged flame chemiluminescence were shown by the gray and orange colors in Figs. 4.1 and 4.3,594.2. Spectral characteristics of pressure, flame chemiluminescene, and flame edge velocityrespectively. Note that for the pressure rate data and flame edge velocity, the mean value issmall and about zero. Thus, for clarity purposes, only the original signals are shown in Figs. 4.2and 4.4(b). After this, the sliding fast Fourier transform (FFT) of the mean-subtracted signalwas calculated for time windows with 50% overlap. For the steady thermoacoustic oscillations,200 ms windows with 8192 FFT points were used providing a resolution of 6.1 Hz. However, inthe spectral analyses pertaining to the ignition and stabilization phases, due to the relativelyshort duration, the window size and number of FFT points were set to 100 ms and 4096 FFTpoints leading to a resolution of 12.2 Hz.0 100 200 300 400 500 600051010100 50 100 150 200200400600500 1000 15002004006000 100 200 300 400 500 6000246 1090 100 200 300 400 500 6000510 10100 50 100 1502004006000 100 200 300 400 500 60002461090 100 200 300 400 500 600024 10110 50 100 150 200200400600500 1000 15002004006000 100 200 300 400 500 6000510151090 100 200 300 400 500 60001210110 50 100 150 200 2502004006000 100 200 300 400 500 6000123 109400 600 800 1000 1200200400600500 1000 1500 2000200400600Fig. 4.7. The first and second columns are the pressure rate spectrogram and power spectrumdensity related to the ignition and stabilization phases. The third and fourth columns are thepressure rate spectrogram and power spectrum density pertaining to the steady oscillations.The first, second, third, and fourth rows pertain to Flames E, F, G, and H, respectively.As can be seen in the results presented in Fig. 4.4 and Figs. 4.6–4.8, all thermoacoustic modes,which are the structural (fs), acoustic (fn), and intrinsic modes (fI,1 and fI,2) with the valuestabulated in Table 4.1, are captured for the steady state. The results pertaining to the ignitionand stabilization phases suggest that, during these phases, the flame dynamics is dominated604.2. Spectral characteristics of pressure, flame chemiluminescene, and flame edge velocityFig. 4.8. The first and second columns are the spatially-averaged flame chemiluminescencespectrogram and power spectrum density related to the ignition and stabilization phases. Thethird and fourth columns are the spatially-averaged flame chemiluminescence spectrogram andpower spectrum density pertaining to the steady oscillations. The first, second, third, and fourthrows pertain to Flames E, F, G, and H, respectively.by the low-frequency fluctuations with the peaks near the structural and acoustic modes, seeFigs. 4.4 (c and d) and the first two columns of Figs. 4.6–4.8. However, as shown in Figs. 4.4(eand f) and the last two columns of Figs. 4.6–4.8, during the steady-state operation, in addition tothe structural and acoustic modes, the intrinsic modes (with frequencies of fI,1 and fI,2) becomepronounced. These results are similar to those presented in the studies of [78, 91]. This impliesthat for a semi-closed configuration, such as a reverse-flow configuration, the instabilities duringthe early stages of flame development, that are the ignition and stabilization phases, feature thestructural and/or acoustic modes. However, as the flame development transitions from ignitionand stabilization phases to steady-state oscillations, the intrinsic thermoacoustic modes appear.In essence, it was shown that, during the ignition and stabilization phases, the flame devel-opment characteristics follow those of a closed system. Thus, during these phases, the intrinsic614.2. Spectral characteristics of pressure, flame chemiluminescene, and flame edge velocitymodes which are related to the upstream velocity oscillations [100, 120] are less pronounced.However, during the steady oscillations, the system behaviour is similar to that of an open sys-tem, and as a result, the intrinsic modes co-exist with the structural and acoustic modes. Thisinformation has implications for mitigation and control of the instabilities during both the earlystages of flame development and the steady operation of the combustor. Specifically, our resultsshow, when the instabilities at early stages of flame development in a reverse-flow combustorare of concern, it is important to utilize methods that allow for mitigating structural and/oracoustic modes. Modifying the combustor rigidity could allow to change the structural mode [6].Also, past investigations suggest both passive [153–156] and active [157–159] control methodscould significantly mitigate thermoacoustic oscillations associated with acoustic modes. For thesteady-state operation of the reverse-flow combustor, however, in addition to the structural andacoustic modes, thermoacoustic oscillations associated with the intrinsic modes are pronounced.Hydrogen enrichment is recently suggested as a promising method to mitigate intrinsic thermoa-coustic instabilities [160]. Specifically, the results of Ghani et al. [160] show that the addition ofhydrogen to the methane/air mixtures decreases the flame length, changing the intrinsic modefrequency to large values. Their [160] results suggest increasing the hydrogen mass fraction sig-nificantly decreases the maximum pressure fluctuation from about 175 Pa for pure methane/airmixtures to about 25 Pa for 40% hydrogen-enriched methane/air flames.62Chapter 5Conclusions and future directionsThe concluding remarks and future directions are discussed below.5.1 Concluding remarksCharacteristics of premixed flame development and propagation inside a reverse-flow combus-tor of a small-scale power generator were investigated experimentally. Two sets of experimentswere performed. For all experiments, high-speed OH∗ chemiluminescence and pressure werecollected simultaneously, and methane was used as the fuel. In the first set of experiments, twomean bulk flow velocities of 4.0 and 6.4 m/s, two igniter rod positions of -5 and 1.5 mm, anda fuel-air equivalence ratio of 0.7 were tested. In the second set of experiments, relatively richflames (φ = 0.9 and 1) with two mean bulk flow velocities of 4.9 and 5.3 m/s for igniter rodposition of 1.5 mm were examined.The results pertaining to the first set of experiments suggest three phases, namely, the ig-nition, stabilization, and transition may exist at the early stages of flame development. Theignition phase (with a duration of ∼10 ms) is characterized by a significant increase in the pres-sure and flame chemiluminescence. This is followed by high-amplitude oscillations during thestabilization phase (∼100 ms). During the transition phase, the spatially-averaged OH∗ chemi-luminescence data features a relatively long-duration (∼1 s) and high-amplitude oscillations.635.1. Concluding remarksDuring this phase, the flame is nearly extinguished, but the flame-out does not take place. Allthree phases were present for the tested conditions, except that one flame condition did notfeature the transition phase. This was linked to the relatively small value of the time-averagedflame chemiluminescene during the ignition and stabilization phases relative to that of the steadyoscillations.During the ignition phase and prior to the flame reaching the stagnation wall, the flame kernelgrows into a finger-shaped flame, and the flame edge velocity maximizes once the flame skirtreaches the combustor side-walls, agreeing with the results of past investigations [33, 55, 58, 145].It is shown that the reverse-flow configuration of the present study allows for the flames toachieve relatively large normalized edge velocities. During the ignition phase, the time rate ofthe pressure change is proportional to the spatially-averaged flame chemiluminescene. Afterthis, the flame reaches the stagnation wall; and, over a 2 ms period, the flame decelerates, andthe time rate of pressure change increases significantly. Then, for a duration of about 5 ms,the flame propagation direction is reversed and the flame enters the exhaust tubes. During thisperiod, the time rate of pressure change is nearly proportional to the spatially-averaged flamechemiluminescene. After the combustion products leave the combustor, the time rate of pressurechange decreases and becomes negative.During the stabilization phase, the flame edge velocity fluctuates significantly, leading tosubstantial variation in the flame height. Although the time rate of pressure change nearlyfollows the spatially-averaged flame chemiluminescene, the flame edge velocity does not followthis parameter and features a cyclical behaviour superimposed with random fluctuations. Theresults pertaining to the transition phase suggest that there does not exist a correlation betweenthe spatially-averaged flame chemiluminescene, the time rate of pressure change, and the flame645.1. Concluding remarksedge velocity.Despite the lack of relation between the spatially-averaged flame chemiluminescene, pressurerate, and flame edge velocity during the transition phase, these parameters feature similar spec-tral behaviour. Pressure, pressure rate, and spatially-averaged flame chemiluminescene feature apeak at about 61 Hz during the transition phase. This peak is less pronounced for the spatially-averaged flame chemiluminescene and corresponds to the acoustic mode of the combustor. Thenormalized power spectrum densities of the pressure and spatially-averaged flame chemilumi-nescene collapse and follow power-law relations which agree with the results reported in theliterature for unconfined flames. This suggests, although the presence of the stagnation wallsignificantly influences the relations between the pressure and flame chemiluminescene duringthe ignition phase as well as the maximum attained flame edge velocity, the spectral behavioursof pressure and flame chemiluminescence are not influenced by the presence of the stagnationwall and are similar to those of the unconfined flames.The results pertaining to relatively rich flames, similar to those of lean flames show thatthe flame development features the ignition and stabilization phases. However, the transitionphase is absent, and the stabilization phase is followed by steady thermoacoustic oscillations forthe relatively rich flames. This was linked to the values of the time-averaged flame chemilumi-nescene during the ignition and stabilization phases relative to those of the steady oscillations.The results suggest the flame development during the early stages of combustion, that are theignition and stabilization phases, follows that of a closed system. However, during the steady-state operation, the flame dynamics is similar to that of an open system. Specifically, duringthe ignition and stabilization phases, the fluctuations are dominated by the small frequenciesassociated with the structural and acoustic modes. However, in addition to the structural and655.2. Future directionsacoustic oscillations, high-frequency oscillations associated with the intrinsic modes appear forthe steady-state thermoacoustic oscillations.5.2 Future directionsFive future research directions are recommended here. First, all flames studied in this the-sis are stabilized on a toroidal flame-holder. Flame-holder geometry can affect both early andlater stages of the flame development. Future experiments should be conducted for differentflame-holder geometries. Second, the combustor tested in this study features a reverse-flowconfiguration due to the presence of a stagnation wall, which was at room temperature for alltested conditions studied here. Effects of wall temperature and heat flux on flame develop-ment characteristics at early stages of combustion are of interest and should be investigated.Third, methane was used as the fuel in this study. However, several investigations have sug-gested that substituting pure methane with hydrogen-enriched methane can alleviate issuessuch as emissions and intrinsic thermoacoustic oscillations [160–164]. Future investigations canbe performed for hydrogen-enriched methane/air mixtures with different hydrogen enrichmentpercentages. Fourth, in this study, the fuel was introduced three seconds before the igniterdischarge. 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B., 1988. “Fundamentals of internal combustion engines”. Tata McGrawHills, New York.88Appendix89Appendix AUncertainty analysisUncertainties related to the values of pressure (p), maximum spatially-averaged OH∗ (OH∗max),time periods of the ignition (tig.), stabilization (tst.), and transition (ttr.) phases are discussedin the following.The total pressure measurement uncertainty (up) includes contributions from the data ac-quisition system (uDAQ), pressure transducer (uT), and electrical noise (uN). up is given by[165–167]:up =√u2DAQ + u2T + u2N. (A.1)The data acquisition system uncertainty is due to resolution (±300 µv, equivalent to ±0.1 Pa)and accuracy (±2 mv, equivalent to ±2.5 Pa) based on the specifications provided by the pro-ducer. Thus, uDAQ =√0.12 + 2.52 ≈ 2.5 Pa. The pressure transducer uncertainty is due toaccuracy (±50 mv, equivalent to ±62.3 Pa), non-linearity (±49 mv, equivalent to ±61.0 Pa),hysteresis (±5 mv, equivalent to ±6.2 Pa), non-repeatability (±2.5 mv, equivalent to ±3.1 Pa),and long-term (estimated for one year) stability (±25 mv, equivalent to ±31.1 Pa), based on theinformation provided by the producer. The contribution of pressure transducer to uncertaintyof pressure measurements is uT =√62.32 + 612 + 6.22 + 3.12 + 31.1 ≈ 92.8 Pa. The electri-cal noise is primarily due to electrical wiring. A sample of the noise is presented in Fig. A.1.uN was estimated by finding the root-mean-square of the signal presented in Fig. A.1 and is90Appendix A. Uncertainty analysis0 2 4 6 8 10 12-20-1001020Fig. A.1. A sample of the electrical noise as measured by the pressure transducer.approximately 2.7 mv (equivalent to 3.4 Pa). Please note that the spikes near ±20 mv areless frequent and the majority of the noise is near 0 mv; hence, the relatively small reportedroot-mean-square. Following Eq. (A.1), the total uncertainty of the pressure measurements isup =√2.52 + 92.82 + 3.42 = 92.9 Pa. This is about ±1.9% of the pressure transducer full-scalereading.The values of OH∗max are influenced by the size of the utilized median-based filter as wellas the size of the binning window. A sensitivity analysis was performed to study the influencesof these parameters on the reported values of OH∗max. The reported values are highlighted bythe green cells in Table A.1. The last row presents percentile of maximum deviation from theresults reported in the row highlighted by the green color. As can be seen, the reported valuesof OH∗max for Flames A–H can change between 5 to 8%.Table A.1. Effects of binning window size and median-based filter size on OH∗max.Bin size Filter size Flame A Flame B Flame C Flame D Flame E Flame F Flame G Flame H2×2 2×2 0.137 0.186 0.105 0.156 0.147 0.147 0.166 0.1962×2 4×4 0.134 0.183 0.103 0.154 0.147 0.147 0.166 0.1962×2 8×8 0.132 0.181 0.101 0.152 0.146 0.146 0.165 0.1954×4 2×2 0.135 0.185 0.105 0.156 0.144 0.143 0.161 0.1914×4 4×4 0.134 0.183 0.103 0.154 0.142 0.142 0.160 0.1884×4 8×8 0.130 0.179 0.100 0.150 0.140 0.139 0.158 0.1868×8 2×2 0.137 0.186 0.106 0.157 0.142 0.143 0.161 0.1918×8 4×4 0.133 0.182 0.102 0.153 0.139 0.140 0.158 0.1878×8 8×8 0.125 0.173 0.096 0.146 0.131 0.131 0.145 0.177Maximum deviation (%) 6.7 5.5 6.8 5.0 7.9 7.7 7.3 6.091Appendix A. Uncertainty analysisThe uncertainty related to the ignition time period (tig.) is the inverse of the imaging fre-quency (0.2 ms). The stabilization (tst.) and transition (ttr.) time periods can slightly changedepending on the relevant utilized window sizes in the analyses. tst. is the time between theinstant that the spatially-averaged flame chemiluminescence features a global maximum andthe time that the sliding mean of OH∗ features a local minimum after the last local maximum.A sensitivity analysis was performed for estimation of tst.. Specifically, three different windowsizes of 10, 20 and 30 ms were utilized for the sliding mean calculations. As can be seen inFig. A.2(a), the window size of 10 ms follows the fluctuations of the spatially-averaged OH∗.Thus, this window size is selected for the reported data in Tables 3.1 and 4.1. Depending on theselected window size, the values of tst. can vary from 83.2 to 90.4 ms for Flame A condition. Theblue square, orange circle, and green triangular data points highlight the instants correspondingto the end of the stabilization period. The sensitivity analysis was also performed for FlamesB–H. The maximum deviations from the reported values are about 9, 8, 10, 6, 3, 4, 40, and11 ms for Flames A–H, respectively.The transition phase duration is defined as the instant that the sliding mean of OH∗ intersectswith the time-averaged value of the spatially-averaged OH∗ corresponding to the steady oscil-lations. The duration of the considered steady oscillations for estimation of the time-averagedOH∗ was changed, and the sensitivity of the transition time period to this was investigated. Byselecting the start time of the considered steady oscillations as tstart =1100, 1200, and 1300 ms,three different transition phase periods of 1130.2, 1142.2, and 1263.2 ms are estimated for FlameA. The transition period end instants related to these are highlighted by the blue square, orangecircle, and green triangle data points in Fig. A.2(b). The averaged value of the above periodsis reported in Table 3.1. The maximum deviations from the values of ttr. presented in Table 3.192Appendix A. Uncertainty analysis90 100 110 120 130 140 1500.150.20.250.30.350.4600 800 1000 1200 1400 160000.050.10.150.20.250.30.35Fig. A.2. Sensitivity analysis for (a) the effect of the sliding window size (W ) on the durationof the stabilization phase, and (b) the effect of the steady oscillations start time on the durationof the estimated transition phase. The results pertain to Flame A condition.are about 7% for Flames A and C, and 0.02% for Flame B. Please note that Flame D–H do notfeature the transition phase.93Appendix BEstimation of the heat release ratefrom the conservation of energyA control volume with the projection on the x − y plane being the field of view shown inFig. 2.2 was used for the analysis. Assuming negligible kinetic and potential energies, the tempo-ral change of the total energy (dE/dt) can be estimated by that of the internal energy (dU/dt).The temporal change of the control volume internal energy is due to change in temperature forfixed gas composition (dUs/dt), and due to change in the gas composition because of chemicalreactions (dUch./dt). That is dU/dt = dUs/dt+dUch./dt. As a result, dE/dt=dUs/dt+dUch./dt.Assuming that cv is constant and spatially-invariant with the value equal to that pertaining tothe reactant mixture at T = 298.2 K, implementing the chain rule for dUs/dt leads to [168]dEdt=dmdtcvT +mcvdTdt− Q˙ch., (B.1)where Q˙ch. is the time rate of heat release due to chemical reactions. Please note that dUch./dt =−Q˙ch.. Considering the ideal gas equation of state, i.e., (p+ p0)V = mRuT/MW , and assumingthat the molecular weight of the gas is constant, it can be shown thatcvMWRu[d(p+ p0)dtV + (p+ p0)dVdt]=dmdtcvT +mcvdTdt. (B.2)94Appendix B. Estimation of the heat release rate from the conservation of energyIn Eq. (B.2), Ru and p0 are the universal gas constant and the atmospheric pressure, respectively.The conservation of energy for the above discussed control volume suggests thatdEdt= Q˙− W˙ + m˙ihi − m˙oho, (B.3)where Q˙, W˙ , m˙, and h are the time rate of heat transfer across the control volume boundaries,the time rate of energy transfer due to external work across the boundaries of the control volume,the total fuel and air mass flow rate, and the specific enthalpy, respectively. The indices “i” and“o” pertain to the inlet and outlet of the control volume. Combining Eqs. (B.1), (B.2), and (B.3)leads tocvMWRu[d(p+ p0)dtV + (p+ p0)dVdt]− Q˙ch. = Q˙− W˙ + m˙ihi − m˙oho. (B.4)Considering V and p0 are constant values and the time rate of external work done on the controlvolume is zero, Eq. (B.4) simplifies toQ˙ch. =cvMWRu(dpdtV)+ m˙oho − m˙ihi − Q˙. (B.5)95
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Flame development characteristics inside a reverse-flow model combustor from early stages of combustion to steady operation
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