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Flame characteristics in quasi-2D channels: stability, rates and scaling
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Flame characteristics in quasi-2D channels: stability, rates and scaling
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Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA Presented in Partial Fulfillment of the Requirements of the Degree Doctor of Philosophy (Mechanical Engineering) December 2019 Si Shen Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 1 Table of Contents List of Figures ......................................................................................................................... 4 Nomenclature ....................................................................................................................... 14 Abstract ................................................................................................................................ 17 Chapter 1: Introduction ......................................................................................................... 19 1.1 Combustion in the modern world ............................................................................................. 19 1.2 Combustion in Narrow Channels .............................................................................................. 22 1.3 Literature Review ..................................................................................................................... 24 1.3.1 Darrieus-Landau Instability ...................................................................................................................... 24 1.3.2 Rayleigh-Taylor Instability ........................................................................................................................ 26 1.3.3 Saffman-Taylor Instability ........................................................................................................................ 27 1.3.4 Diffusive-thermal Instability ..................................................................................................................... 28 1.3.5 Flames in Narrow Channels and Hele-Shaw cells ..................................................................................... 29 1.4 Proposal ................................................................................................................................... 33 Chapter 2: Background ......................................................................................................... 35 2.1 Hele-Shaw Flow ....................................................................................................................... 35 2.2 Laminar Premixed Flame .......................................................................................................... 36 2.3 Darrieus-Landau Instability ...................................................................................................... 37 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 2 2.4 Rayleigh-Taylor Instability ........................................................................................................ 40 2.5 Saffman-Taylor Instability ........................................................................................................ 42 2.6 Joulin-Sivashinsky Parameter ................................................................................................... 44 2.7 Diffusive-thermal Instability ..................................................................................................... 47 Chapter 3: Methods .............................................................................................................. 53 3.1 Experimental Setup .................................................................................................................. 53 3.2 Video Processing Method ......................................................................................................... 55 3.3 Scaling Parameters ................................................................................................................... 58 3.3.1 Computational Local Characteristic Flame Speed (Ucomp) ..................................................................... 59 3.3.2 Experiment Based Local Characteristic Flame Speed (Uexp) ................................................................... 61 Chapter 4: Results and Discussion ......................................................................................... 62 4.1 Flame Shape Variations ............................................................................................................ 62 4.2 Flame Propagation Speed (S T) .................................................................................................. 71 4.3 Scaling Parameters ................................................................................................................... 78 4.3.1 Joulin-Sivashinsky Parameter ................................................................................................................... 78 4.3.2 Computational local characteristic Flame Speed (Ucomp) ...................................................................... 81 4.3.2 Experiment Based Laminar Flame Speed (Uexp) ..................................................................................... 85 4.3.3 Ucomp vs.Uexp ....................................................................................................................................... 90 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 3 Chapter 5: Conclusion ........................................................................................................... 92 Chapter 6: Future Work ........................................................................................................ 93 6.1 Continue Investigation into Scaling Parameters ................................................................. 93 6.2 Interactions between Darrieus-Landau Instability and Diffusive-thermal Instability ........... 93 6.4 New Experiment Apparatus and other Aspects of Flame in Narrow Channels ........................... 94 Appendix .............................................................................................................................. 97 Appendix I – Video Processing Program Output Example ............................................................... 97 Appendix II – Supplement Plots of Individual Fuel-inert gas mixtures ............................................. 98 Reference ........................................................................................................................... 104 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 4 List of Figures Figure 1 History of world total primary energy supply (TPES) in Mtoe (Million Tons of Oil Equivalent) by fuel from 1971 to 2016.[2] ................................................................................... 20 Figure 2 2015 World energy consumption history and projections by energy source from 1990 to 2040 in unit of quadrillion Btu.[3] ............................................................................................ 21 Figure 3 World CO 2 emission history and projection by energy source from 1990 to 2040 in unit of billion metric tons.[3] ............................................................................................................... 22 Figure 4 diagram showing combustion chamber and crevice volume in a typical internal combustion engine. ...................................................................................................................... 23 Figure 5 diagram of a curved flame front in a Hele-Shaw cell. ..................................................... 33 Figure 6 detailed premixed flame structure diagram. .................................................................. 37 Figure 7 diagram of flow and a curved flame front interaction[79]. ............................................ 38 Figure 8 Darrieus-Landau instability growth rate vs. wavelength for an example of U = 28 cm/s, e = 0.2 and l cell = 40 cm. ................................................................................................................ 39 Figure 9 Diagram of upward (left) and downward (right) propagating flame and buoyancy effects [80]. .................................................................................................................................. 40 Figure 10 Combined Darrieus-Landau instability and Rayleigh-Taylor instability growth rate vs. wavelength for an example of U = 28 cm/s, e = 0.2 and l cell= 40 cm. ........................................... 41 Figure 11 Oil-water interface experiment demonstrates Saffman-Taylor Instability by Tabeling et al. (1987) [48] ........................................................................................................................... 42 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 5 Figure 12 diagram of Saffman-Taylor instability mechanism. ...................................................... 43 Figure 13 Effects of ST and RT instabilities on DL instability’s dimensionless growth rate (𝛺) for a range of example hydrocarbon-air flames with U=20cm and d=1.27cm. .................................... 46 Figure 14 diagram of thermal and molecular mass diffusions of a curved flame front [79]. ....... 48 Figure 15 Joulin and Mitani estimated reduced Lewis number (same as Le eff in this study) in hydrogen-oxygen flames as a function of hydrogen-oxygen ratio. [81] ....................................... 50 Figure 16 Images of laser-induced fluorescence of OH for 1.89%H 2–10.06%O 2–88.05N 2 flame Le eff »0.3 at 1 atm.[58] ................................................................................................................. 50 Figure 17 cellular structure in hydrocarbon-O 2-N 2 flames at atmosphere pressure in Markstein (1951). [82] ................................................................................................................................... 51 Figure 18 typical growth rate of a cellular flame with Le eff < Le c as a function of k [79]. ............. 52 Figure 19 Experimental apparatus, A: partial pressure mixing system, B: mixing chamber, C: fuel-oxidizer-inert gas supplies, D: ignition system, E: exhaust ball valve, F: vacuum pump, G: high-speed camera. ...................................................................................................................... 54 Figure 20 example of a frame of a video recorded then imported into the Matlab program, flame is propagating toward right, red line represent location of recognized flame position. Left: flame in gas mixture with Le eff > 1; Right: flame in gas mixture with Le eff < 1. ............................. 55 Figure 21 example of experimentally measured flame position (blue) and corresponding pressure in the combustion chamber (orange). ........................................................................... 57 Figure 22 Exemplary plot of wrinkled flame length ratio lflame /lcell vs. time generated from Matlab program. .......................................................................................................................... 58 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 6 Figure 23 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.2s in steady state region) in 8.17%CH 4-17.28%O 2-74.55%N 2 mixture, horizontal propagation, d=1.27cm, Le eff ≈1. .............................................................................. 63 Figure 24 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.2s in steady state region) in (a) 8.17%CH 4-17.28%O 2-74.55%N 2 mixture, upward propagation, d=1.27cm, Le eff ≈1, (b) 8.17%CH 4-17.28%O 2-74. 55%N 2 mixture, downward propagation, d=1.27cm Le eff ≈1. .............................................................................. 63 Figure 25 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.2s in steady state region) in 12.16%CH 4-21.62%O 2-66.22%N 2 mixture, horizontal propagation, d=0.3175cm, Le eff ≈1. ............................................................ 64 Figure 26 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.4s in steady state region) in 4.70%C 3H 8-28.95%O 2-66.35%N 2 mixture, horizontal propagation, d=1.27cm, Le eff ≈1.7. ............................................................. 64 Figure 27 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~0.25s in steady state region) in (a) 4.70%C 3H 8-28.95%O 2-66.35%N 2 mixture, upward propagation, d=1.27cm, Le eff ≈1.7, (b) 4.70%C 3H 8-28.95%O 2-66.35%N 2 mixture, downward propagation, d=1.27cm Le eff ≈1.7. ............................................................. 65 Figure 28 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.4s in steady state region) in 1.99%H 2-9.95%O 2-88.06%N 2 mixture, horizontal propagation, d=1.27cm Le eff » 0.4 ...................................................................................................................................... 66 Figure 29 Dendrite growing into a supercooled melt of pure succinonitrile.[89] ........................ 67 Figure 30 (a) Illustration of a horizontal steady flame in gas mixture of Le eff = 1.5 front represented by the reaction rate iso-contour and the flow field by the streamline pattern calculated. (b) picture of a quasi-steady flame shape, 2.46%C 3H 8-24.63%O 2-72.91%N 2, Le eff » Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 7 1.6. (c) Illustration of a horizontal steady flame in gas mixture of Le eff = 0.3 front represented by the reaction rate iso-contour and the flow field by the streamline pattern. (d) picture of a quasi- steady flame shape, 12.59%H 2-7.87%O 2-79.54%N 2, Le eff » 0.4. ................................................... 67 Figure 31 Normalized temperature (Θ ) for the large-scale DNS (Lx = 800 l F , or d T) at a simulation time t = 200 τ F (τ F = l F/S L) after initialization [88]. ....................................................... 68 Figure 32 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.3s in steady state region) in 1.11%H 2-9.88%O 2-89.01%N 2 mixture, horizontal propagation, d=1.27cm, Le eff » 0.3. ..................................................................................................................................... 69 Figure 33 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~0.4s in steady state region) in (a) 0.80%H 2-15.96%O 2-83.24%N 2 mixture, upward propagation, d=1.27cm, Le eff ≈0.4, (b) 0.80%H 2-15.96%O 2-83.24%N 2 mixture, downward propagation, d=1.27cm, Le eff ≈0.4. .......................................................................... 69 Figure 34 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.15s in steady state region) in 2.52%H 2-12.61%O 2-84.87 %N 2, horizontal propagation, d=0.1375cm Le eff » 0.4. ..................................................................................................................................... 70 Figure 35 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.3s in steady state region) in 0.36%H 2-57.14%O 2-42.5 %N 2, horizontal propagation, d=0.1375cm Le eff » 0.3. ................................................................................................................................................ 70 Figure 36 exemplary flame fronts of CH 4-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 =0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. .................. 73 Figure 37 S T’ vs. Pe for CH 4-O 2-N 2 gas mixtures with Le eff » 1 for various chamber thickness and propagation directions. ................................................................................................................ 73 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 8 Figure 38 exemplary flame fronts of for rich H 2-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 =0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. .................. 74 Figure 39 S T ’ vs. Pe for H 2-O 2-N 2 gas mixtures with equivalent ratio of 2.0 (Le eff » 1.4) and for C 3H 8-O 2-N 2 gas mixtures with equivalent ratio of 0.5 (Le eff ≈1.7) for various chamber thickness and propagation directions. ......................................................................................................... 74 Figure 40 exemplary flame fronts of for lean H 2-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 =0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. .................. 75 Figure 41 S T ’ vs. Pe for H 2-O 2-N 2 gas mixtures with equivalent ration of 0.8 (Le eff » 0.4) for various chamber thickness and propagation directions. .............................................................. 75 Figure 42 Fernandez-Galisteo et al. simulating results of S T’ º S T/S L vs time for 𝐿𝑒 =1,𝛽 = 10,𝜀 =0.2 and µ u/µ b = 0.7. G is their own gravity factor (𝐺 ≡ −𝑎2𝒈𝛿𝑇/(12𝑃𝑟𝑆𝐿2)). ........ 76 Figure 43 Fernandez-Galisteo et al. simulating results of S T’ º S T/S L vs time for various Le,𝛽 = 10,𝜀 =0.33 and µ u/µ b = 0.7. G is their own gravity factor (𝐺 ≡ −𝑎2𝒈𝛿𝑇/(12𝑃𝑟𝑆𝐿2)=0). ...................................................................................................................................................... 76 Figure 44 exemplary flame fronts of for ultra-lean H 2-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 =0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. ..... 78 Figure 45 Effect of adiabatic flame temperature, chamber thickness and propagation direction on flame propagation speeds (S T) for ultra-lean H 2-O 2-N 2 and H 2-O 2-CO 2, 𝐿𝑒𝑒𝑓𝑓 » 0.3. ............. 78 Figure 46 S T’ vs. JS Parameter for CH 4-O 2-N 2 gas mixtures with equivalent ratios of 1.0 (Le eff » 1), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1) and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm. ....................................................... 80 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 9 Figure 47 S T’ vs. JS Parameter for C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 1.7), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 2.0 (Le eff » 1.3), and H 2-O 2-N 2 gas mixtures with equivalent ratios of 2.0 (Le eff » 1.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm. ................................... 80 Figure 48 S T’ vs. JS Parameter for CH 4-O 2-CO 2 gas mixtures with equivalent ratio of 0.5 (Le eff » 0.7), H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.8 (Le eff » 0.4) and 0.4 (Le eff » 0.3), and H 2-O 2-CO 2 gas mixtures with equivalent ratios of 0.8 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm. ...... 81 Figure 49 S T/U comp vs. JS Parameter for experimental data: lean CH 4-O 2-N 2 gas mixtures (Le eff » 1); CH 4-O 2-CO 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 0.8); H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.3), 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4), 1.25 (Le eff » 1.3) and 2 (Le eff » 1.4); H 2-O 2-CO 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.2), 0.2 (Le eff » 0.2), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.3), 1.25 (Le eff » 1.1) and 2 (Le eff » 1.3); and C 3H 8-O 2- N 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 1.7) and 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .......................................................................................................................................... 82 Figure 50 S T/U COMP vs. JS Parameter for experimental data: rich CH 4-O 2-N 2 gas mixtures (Le eff » 1) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .................................................................................................... 83 Figure 51 Calculated K ext vs.1/T ad for C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 and 2 and CH 4-O 2-N 2 gas mixtures with equivalent ratios of 0.6, 1 and 1.6. ......................................... 84 Figure 52 S L vs.1/T ad for C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 and 2 and CH 4-O 2- N 2 gas mixtures with equivalent ratios of 0.6, 1 and 1.6. ............................................................. 84 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 10 Figure 53 Law (2010) calculated extinction strain rates for (a) top: lean methane-air flames; bottom: lean propane-air flames in a counterflow, with heat loss [78]; (b) Evans et al. (1988) simulation data of extinction limit comparison with the Law, et al. data and the Stahl, et al. computation. [90] ......................................................................................................................... 85 Figure 54 S T/U exp vs. JS Parameter for near unity Leeff experimental data: CH 4-O 2-N 2 gas mixtures with equivalent ratios of 1.0 (Le eff » 1), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1) and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .................................................................................................... 86 Figure 55 S T/ U exp vs. JS Parameter for high Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 2 (Le eff » 1.4), H 2-O 2-CO 2 with equivalent ratios of 2 (Le eff » 1.3), and C 3H 8-O 2-N 2 mixtures with equivalent ratios of 0.5 (Le eff » 1.7) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ....................... 87 Figure 56 S T/ U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.1 (Le eff » 0.3), 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4), and H 2-O 2-CO 2 with equivalent ratios of (Le eff » 0.3), 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .......................................................................................................................... 87 Figure 57 U exp /S L vs. Péclet number for near unity Le eff experimental data: CH 4-O 2-N 2 gas mixtures with equivalent ratios of 1.0 (Le eff » 1), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1) and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .................................................................................................... 88 Figure 58 U exp /S L vs. Péclet number for high Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 2 (Le eff » 1.4), H 2-O 2-CO 2 with equivalent ratios of 2 (Le eff » 1.3), and C 3H 8-O 2-N 2 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 11 mixtures with equivalent ratios of 0.5 (Le eff » 1.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ....................... 88 Figure 59 U exp /S L vs. Péclet number for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4), and H 2-O 2-CO 2 with equivalent ratios of 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ....................... 89 Figure 60 U comp and U exp vs. S L for H 2-O 2-N 2 flames with equivalent ratios of 0.8 and 2.0 propagating through a Hele-Shaw cell of (a) h = 1.27cm and (b) h = 0.635cm. ........................... 90 Figure 61 U comp and U exp vs. S L for C 3H 8-O 2-N 2 flames with equivalent ratios of 0.5 and 2.0 propagating through a Hele-Shaw cell of h = 1.27cm. ................................................................. 91 Figure 62 CAD demonstration of the new Hele-Shaw cell ............................................................ 95 Figure 63 Stage demonstrations and explanations of new support structure and rotation mechanism. .................................................................................................................................. 96 Figure 64 example of the output from the video processing program. ....................................... 97 Figure 65 S T/U comp vs. JS Parameter for experimental data: CH 4-O 2-CO 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 0.8); H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele- Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .................................................................. 98 Figure 66 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-CO 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.2), 0.2 (Le eff » 0.2), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .......................................................................................................................... 98 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 12 Figure 67 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.3), 0.2 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ....................... 99 Figure 68 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-CO 2 gas mixtures with equivalent ratios of 2 (Le eff » 1.3); and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ...................................................................................... 99 Figure 69 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-N 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.3) and 2 (Le eff » 1.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .............. 100 Figure 70 S T/U comp vs. JS Parameter for experimental data: lean CH 4-O 2-N 2 gas mixtures (Le eff » 1); H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1); and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ..................... 100 Figure 71 S T/U exp vs. JS Parameter for high Le eff experimental data: H 2-O 2-CO 2 with equivalent ratios of 2 (Le eff » 1.3) and C 3H 8-O 2-N 2 mixtures with equivalent ratios of 0.5 (Le eff » 1.7) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. .................................................................................................. 101 Figure 72 S T/ U exp vs. JS Parameter for high Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 1.25 (Le eff » 1.3) and 2 (Le eff » 1.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ..................... 101 Figure 73 S T/ U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-CO 2 with equivalent ratios of 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ..................... 102 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 13 Figure 74 S T/U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ..................... 102 Figure 75 S T/U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele- Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ................................................................ 103 Figure 76 S T/U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-CO 2 with equivalent ratios of 0.1(Le eff » 0.3) and 0.2 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. ..................... 103 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 14 Nomenclature α Thermal diffusivity of unburned gas mixtures β Zel’dovich number c Specific heat capacity C N Constant pressure specific heat d Hele-Shaw cell thickness D Coefficient of mass diffusivity δ Q Flame thickness E S Overall activation energy ε Expansion coefficient f Exchange coefficient of momentum f V Exchange coefficient of momentum of unburned gas mixture f W Exchange coefficient of momentum of product gas mixture f SX Average exchange coefficient of momentum F Dimensionless friction factor Fr Froude number 𝐠 Gravity field parallel to the plate G Dimensionless gravity factor h Exchange coefficient of heat loss k Wavenumber =2π/λ Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 15 k RT Rayleigh-Taylor instability’s critical wavenumber =2π/l ^_`` k ST Saffman-Taylor instability’s critical wavenumber =2π/l ^_`` L Hele-Shaw cell length l ^_`` Hele-Shaw cell width l a`Sb_ Two-dimensional wrinkled flame length Le _aa Effective Lewis number Le ^ Critical Lewis number characterizes occurring of cellular flame by DT insta- bility λ Flame wavelength λ ^ Critical wavelength characterizes occurring of cellular flame by DT insta- bility λ dQ Saffman-Taylor instability wavelength Λ Dimensionless wavelength µ Dynamic viscosity of gas mixture µ V Dynamic viscosity of fresh unburned gas mixture µ W Dynamic viscosity of burned gas mixture µ SX Average dynamic viscosity of both fresh unburned gas mixture and burned gas mixture n Reaction order ω Growth rate of flame wrinkle base on Joulin and Sivashinsky analysis ω̇ Overall reaction rate Ω Dimensionless growth rate Pe Péclet number Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 16 P Pressure ℜ Universal gas constant ρ Gas mixture density ρ V Unburned gas mixture density ρ W Products mixture density S T Flame propagation speed S L Laminar flame speed S valley Local flame speed at a valley of a curved flame front S peak Local flame speed at a peak of a curved flame front t time T Sm Adiabatic flame temperature T Temperature T V Temperature of unburned gas mixture u Two-dimensional velocity field =(u, v) u and v Velocity components U Local characteristic flame speed U ^nbN Local characteristic flame speed estimated base on 1-D extinction strain rate simulations U _oN Local characteristic flame speed extrapolated from experimental data Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 17 Abstract Understanding propagation and behaviors of premixed flames in narrow channels, tubes, gaps or slots is important and relevant to several areas of combustion research and applications. For instance, in internal combustion engines (ICEs), combustion chambers at the time of combustion (when the piston is at top dead center position, TDC) are in narrow channel like shapes with high aspect ratios. Flames in such environment exhibit different behaviors and instabilities comparing to ones in mostly commonly used open configurations with little flame-wall interactions, includ- ing opposing jets and fan-stir reactors. This study focuses on the behaviors and propagation rates of flames in a confined environment, such as a narrow channel. A Hele-Shaw cell with varying gap thicknesses (h) is used as the combustion chamber for its high aspect ratio and simple geometry. The flame shapes and propagation rates (S T) of quasi-2D pre- mixed-gas flames in fuel-O 2-inert mixtures having a range Lewis numbers (Le eff), adiabatic tem- peratures (T ad) and orientation (upward (g=1), horizontal (g=0) and downward (g=-1) propagation) are studied. Instabilities due to thermal expansion of the burned gas (Darrieus-Landau, DL), Lewis number (diffusive-thermal, DT), buoyancy (Rayleigh-Taylor, RT) and viscosity contrast across the flame (Saffman-Taylor, ST) were found to have substantial effects on these shapes and rates. Classic cusp shapes of DL instability are observed in flames with Le eff ³ 1, while flames with Le eff < 1 present dendritic flame fronts under the combined effect of DL and DT instabilities. Further- more, due to DT instability, S T of flames with Le eff < 1 is much faster than its of flames with Le eff ³ 1. RT instability destabilizes upward propagating flames and stabilizes downward propagating flames. Upward propagating flames also exhibit higher S T than downward propagating flames because of RT instability. ST instability is most prominent in fast propagating flames propagating through the Hele-Shaw cell with the smallest h. JS parameter (s) is developed base on derivations of Joulin and Sivashinsky (1994) as a scaling parameter of the “driving force” for flame wrinkling. Although, the original derivations are limited Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 18 in describing DT instability, s estimated using Le eff scaled local characteristic flame speed (U º pαK _or , K ext = extinction strain rate) is found to be effective characterizing flames under various conditions. It is can be seen as an analog to 𝑢’/S L in premixed turbulent flame studies (𝑢’ = tur- bulence intensity, S L = laminar flame speed). However, rich methane flames are the exceptions. Overall, it is asserted that these flame-generated instabilities in the absence of forced turbulence have a significant influence on S T in practical combustion devices such premixed-charge internal combustion engines and lean-burn stationary gas turbines. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 19 Chapter 1: Introduction 1.1 Combustion in the modern world Combustion has been the corner stone of modern society. In late 18 th century. In Britain, by using fire, people had transformed their society from an agrarian and handcraft centered economy into an industrial and machine manufacturing dominated system. [1] Such revolution, then, propa- gated throughout the world. This was the beginning of the industrial revolution. It is the single most important human development in past several centuries. The industrial revolution has shaped nearly every aspects of modern society, such as the transportation system, the clothing and accessory manufacturing, the information system, etc. At its core, such momentous devel- opment in human history was powered predominantly by combustion. Since then, the world’s total primary energy supply (TPES), which measures the world total en- ergy consumption based on raw energy supplies without human intervention, has Increased ex- ponentially. International Energy Agency (IEA) published world’s TPES data has more than dou- bled for the past several decades, as shown in Figure 1.[2] Although, there has been significant developments in technologies, the market domination of natural gas, oil and coal has little changes for the entire time. Moreover, this trend is also unlikely to change anytime soon in the future according to the pro- jections from the US Energy Information Administration (EIA). They predict another 28% increase in world energy consumption by 2040.[3] While renewable energy’s share has increased steadily, liquid fuel, natural gas and coal, which mostly utilize combustion, remain the largest energy pro- duction sources. Together, they will account for 77% of total energy consumption in 2040 as shown in Figure 2. Coal has shown little change in market share, but liquid fuels and natural gas are forecasted to have continuous growth in coming decades. This insurances combustion as the dominant energy production method for a long time into the future. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 20 Figure 1 History of world total primary energy supply (TPES) in Mtoe (Million Tons of Oil Equivalent) by fuel from 1971 to 2016.[2] Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 21 Figure 2 2015 World energy consumption history and projections by energy source from 1990 to 2040 in unit of quadrillion Btu.[3] On the other hand, current combustion energy production methods present major environmen- tal issues. One of the most discussed is emissions of CO 2, a major greenhouse gas (GHG) that is identified to have major contribution to climate change in recent decades. Growing fossil fuel centric energy production means rapid increase in CO 2 emissions as shown in Figure 3.[3] Similar to projections of energy consumption, while CO 2 emissions from use of coal stays relatively con- stant, CO 2 emissions from liquid fuels and natural gas will grow with their increasing usage. More- over, other emissions, including NO x, also pose serious environmental issues and health risks.[4] Reducing CO 2 and other pollution emissions from combustion applications has become essential for sustainability of the future. Therefore, this trend of growing energy demand, combustion dominating production methods, increasing concern over emissions and environment highlight the growing importance of better combustion efficiencies and emissions through research and innovations. Currently, some of widely used combustion applications for energy production including gas tur- bine, jet engines and Internal combustion engines (ICEs). All of these are brilliant inventions but have room for improvement. For example, in ICEs, the typical efficiency currently is around 25% to 30% for some high-volume production vehicles. However, if hydrogen is used as fuel, lean hydrogen-air mixtures with lower flame temperatures and higher gas specific heat ratios (g = 1.4 compared to g = 1.1 for typical gasoline), the efficiency of ICEs engine can theoretically reach 33.1% 27.5% 22.4% 12.5% 4.5% 30.7% 25.0% 21.8% 17.4% 5.1% History Projection Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 22 about 41% [5]. It is also a green energy source as its combustion product including only water and zero CO 2. Moreover, the wide range of hydrogen flammability means it can burn at a much lower temperature than conventional gasoline. This is essential for reducing NOx production as its emissions are proportional to flame temperature. However, the technology still needs much development and optimization. There are also many other researchers and inventors looking into innovations that improve or replace existing applications for better efficiency and emissions us- ing variety of fuels. The insight into the chemical kinetics, transport, thermodynamics and heat transfer can certainly help to achieve such a goal and push the limits of combustion applications, which is so important to supply energy to the world for decades to come. Figure 3 World CO 2 emission history and projection by energy source from 1990 to 2040 in unit of billion metric tons.[3] 1.2 Combustion in Narrow Channels Several of most commonly used combustion research experiment apparatus, including opposing jets, Bunsen flames and fan-stir reactors, create a flame burning either in an open area or away from chamber walls to avoid flame-wall interactions. Although, such experiments provide im- portant information on chemical kinetics, flame instabilities, etc., considering the majority of combustion applications for energy production, such as furnaces, internal combustion engines (ICEs), and jet engines, almost of them utilize flames housing in small combustion chambers. Those flames are highly subjective to the effects of boundary conditions. As expected, flames can 43.8% 36.1% 20.1% 38.4% 36.8% 24.8% History Projection Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 23 behave rather different propagating in an open area away from walls rather than being enclosed in a tight space. One aspect of such influence is the distortion of the flow field in such confine- ments. For instance, due to the high temperature of burned gas behind a flame, the viscosity of the gas increases, thus creating a sizable difference in fluid viscosity across the flame. This differ- ence has little effect on free propagating flames in an open environment, but can severely wrinkle the interface between the two sections of fluid, due to imposing friction on the flow by the walls, in this case, the flame front, as results in a narrow chamber.[6] Consequently, it is important to study combustion and flame behaviors in confinement. Narrow channels, tubes, gaps or slots are some of the simplest configurations to study. Under- standing propagation and behaviors of premixed flames in such an apparatus is particularly im- portant and relevant to several areas of combustion research and applications. First of all, there is an increasing interest in micro-combustion related portable power generation applications with high aspect ratios to compete with batteries. [7]–[11] One major benefit of these devices as power generators is that they take advantage of the high energy density of fossil fuels, compared with batteries on the market. Figure 4 diagram showing combustion chamber and crevice volume in a typical internal combustion engine. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 24 Moreover, in a typical internal combustion engines (ICEs), as shown in Figure 4, the combustion chamber at the time of combustion (when the piston is at top dead center position, TDC) is in narrow channel like shapes with high aspect ratios, typically 1cm in height and 10cm in diameter. Likewise, to understand the combustion in crevice volume in ICEs, the narrow gap between the piston and the cylinder wall, is essential for studying engine hydrocarbon emissions related to partial burning and flame quenching. [12], [13] Therefore, this study attempts to gain more fun- damental understanding of flame behaviors in confinement resemble similar conditions. 1.3 Literature Review It is anticipated that several instabilities would manifest themselves in narrow channels and wrin- kle flame fronts even in laminar flows. Such instabilities include, • Thermal expansion (Darrieus-Landau (DL) instability) • Buoyancy driven instability (Rayleigh-Taylor (RT) instability) • Viscosity fingering (Saffman-Taylor (ST) instability) • diffusive-thermal (DT) instability Although there is a substantial literature that looks at each individual instability, investigations, especially experimental works, involving multiple or all of the aforesaid instabilities and their ef- fect on flame behaviors and propagation velocity are limited. 1.3.1 Darrieus-Landau Instability Darrieus-Landau instability is a hydrodynamic instability that has been studied for years. It origi- nates from gas expansion of the hot products; thus, it is inherent to all highly exothermal com- bustion processes. This is also the reason that later studies of other instability often include DL instability. It is difficult to isolate other instability from DL instability both theoretically and ex- perimentally. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 25 Darrieus, (1938), and Landau (1988) first well defined the instability phenomena, hence others named it Darrieus-Landau instability. [14][15] It is found that DL instability can significantly am- plify the flame velocities and create curved flame fronts. Such curvature can interact with local flow field and distort streamlines across the flame, thus, destabilize the flame. [16] DL instability has no characteristic length scale in one dimensional analysis and positive growth for all wave perturbation wavelength with zero flame thickness assumption. In two dimensional and three dimensional structures, a typical length scale is in the order of the flame thickness base on Darrius-Landau solutions, but experimental observations reveled at least two orders of mag- nitude larger. [17]–[20] It is believed that the commonly used zero flame thickness assumption in early theoretical analysis is to be blamed. In general, most believe that a finite flame thickness and transport processes need to be considered for such decency. [21] Pelce and Calvin (1982) presents one of the early rigorous analytical studies reflecting the effects of flame thickness and diffusion process on DL instability in an Arrhenius reaction. [22] In addition, the second-order theories have also been developed for DL instability. For instance, Sivashinsky and Clavin (1986) finds the difference between the first-order and the second-order effects can be represented by lonely changing the coefficients in growth rate equations. [23] Experimentally, Clanet and Searby (1998) directly measures the growth rate of DL instability. [24] They use acoustic re-stabilization to create a laminar planar flame and forced acoustic signal to impose standing waves on flame. The measured growth rates agreed well with pervious theoretical studies. Due to the wide influence of DL instability on flames in all type of flow fields, there are numerous studies investigates such effects in different flame regimes. For instance, Calvin (1985) shows an overall review of DL instability’s fundamental theoretical developments in premixed laminar and turbulent flame regimes. [25] It discusses the effects of weak flame front wrinkling on heat and active species distributions and streamlines of the flow. Matalon and Creta (2012) has pushed the analysis further into wrinkled-to-corrugated framelet regime. [26] Th study extends the as- ymptotic perturbative approach developed by Calvin and Williams (1979) and Calvin and Williams Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 26 (1982). [27], [28] It shows the classic cups shapes of DL instability and the significant influence of it on streamlines at the flame fronts. Matalon et al. (2013) focuses on weak turbulent flows. [29] In this study, a weak homogenous turbulence is used instead of more commonly used quiescent weak wrinkles as the inflow field to study DL instability. It finds substantial increase of flame surface areas and flame propagation speeds due to DL instability. There is also a most effective perturbed turbulent length scale as a direct consequence of DL instability. Furthermore, Matalon et al. (2015) presents an experi- mental study of DL instability with higher turbulent intensity. [30] The study defines a subcritical and supercritical regimes base on present or absent of DL instability’s classic cups shaped corru- gation. With high enough of turbulent intensity, the flame becomes a single turbulence-driven propagation mode instead of dual modes with both turbulence and instability effects. Although, DL instability would destabilize flames in nearly all regimes, it is found that the effect of stretch can counter the growth of the instability. [31] Moreover, other instabilities can also stabilize DL instability driven flames, such as Rayleigh-Taylor instability. 1.3.2 Rayleigh-Taylor Instability Rayleigh-Taylor instability is generated from a well-known buoyancy effect first discovered in liq- uid. [19][32][33] Kull (1991) offerings a well summarized review on fundamental theories of RT instability in non-reactive fluid. [34] In combustion, the question raised when fast flame propa- gation speeds observed in multiple studies that can’t be explained by DL instability. [35][36] Then, scholars started to draw similarity between non-reactive interface between two fluids of differ- ent viscosity to flame sheet. It is found that experimental measurements of slow propagation fuel-lean methane flame velocity subject to buoyancy effects in a glass tube is comparable to theoretical calculation of a rising hot air bubble. [37][38] It can be characterized by the gravitational field parallel to flame propagation directions. In up- ward propagating flames, RT instability destabilizes the flame front. Liberman et al. (1993) and Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 27 Bychkov et al. (2007) show analytical derivation of the instability’s growth rate and good com- parison with numerical simulations. [38][39] However, RT instability can also stabilize the flame front in downward propagating flames, which also provides counter effects to DL instability at large hydrodynamic wavelengths.[41][42] While most research of RT instability were done on a flame propagating in vertical tubes, a horizontal tube of large diameter also can facilitate such effects. Rakib and Sivashinsky (1988) shows an analytical derivation of RT instability growth rate and strong influence of it on flame behaviors in a wide horizontal channel. [43] RT instability also has huge impact on flammability limit. Azarbarzin et al. (1982) demonstrated the different mech- anism of extinction for upward and downward propagating tube flames under the influence of RT instability. [44] The upward propagating flame is extinguished by stretch, while the downward propagating flame extinguishes due to heat loss to the wall. Moreover, in flame ball studies, at first, flame ball was considered not to be able to stabilize experimentally. Then, it was found that a stable flame ball can be obtained under microgravity condition, free of RT instability. [45] On the other hand, the two dimensional simulation study by de Goey et al. (2014) shows the transition from a curved flame front to a ball-like shape with or without gravity under very specific conditions. [46] 1.3.3 Saffman-Taylor Instability Another instability that was also first discussed in liquid between water and oil is ST instability. [6] [46] [47] The instability is largely studied and modeled in Hele-Shaw cell, which has a frame sandwiched between two clear plates to form a narrow channel, due to its requirements on con- finement. [48][49] Hele-Shaw cell is also utilized in this study. It has one of most simple geometry, and flow behavior has been studied extensively in Homsy (1987) [51]. Although, ST instability is well studied in non-reactive fluid, developed theories that can be used on a flame is limit. The is due to the fundamental differences between a self-propagating flame and a passive non-reactive interface. For example, the importance of surface tension in ST instability has been proven in studies of non-reactive interfaces.[50], [52], [53] There is no surface tension in combustion. In Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 28 some ways that curvature effects on flame sheet would have similar influence on flames as sur- face tension has on liquid interfaces. However, such effect can be more effectively studied with diffusive-thermal instability. Therefore, combustion focused study on ST instability is necessary in understand the full picture of flame behaviors in confinements. In combustion, ST instability usually is studied as additional to DL, RT and other instabilities in tube flame. Although, ST instability is not the center of Denet (1992), it discusses the mathematic representation of ST instability on curved flames. [42] Aldredge (2004) put more efforts in under- standing the impact of ST instability, in particular with acoustically excited flow. [54] ST instability is also found numerically to be expected at small Péclet numbers (Pe) in a channel flame, it can impose significant impacts on flame shape and propagation speed.[55] However, ST instability centered combustion research is very limited. It is clear that ST instability is not as well studied as DL and RT inabilities in combustion. This may be caused by the requirement of confinement for such instability restricting numerical and experimental studies. 1.3.4 Diffusive-thermal Instability The fourth instability is studied in this research is diffusive-thermal instability. Transport pro- cesses of mass and heat are closely associated with instabilities of premixed planar flames. Dif- fusive-thermal instability is the result of the competition between mass and heat diffusion of flames. [19][56] It is characterized by the ratio of thermal diffusivity and molecular mass diffusiv- ity of reactants that is consumed completely in the flame, or an effective Lewis number (Le eff). DT instability’s growth rate is associated with diffusive length scale, which is much smaller than the other hydrodynamic instabilities discussed. [57] The characteristic wavelength (λ ^ ) happens at critical Le eff, usually slightly less than 1. At small wavelength compare to λ ^ , flames favor cur- vatures and create broken cellular flames. At large wavelength, DT instability can stabilize the flame front,[58] thus, provide stability oppose to DL instability at small wavelength compare to DL effective wavelength range, which is overall much larger. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 29 Kadowaki et al. (2005) performed a numerical simulation study on 2D flame solving adiabatic compressible Navier–Stokes equation including a one-step irreversible chemical reaction. It ob- tains critical length scales for a range of Lewis numbers (Le), as well as displays cellular and cusp flame front corresponding to flame with low and unity Le. 1.3.5 Flames in Narrow Channels and Hele-Shaw cells Combustion in narrow channels is a well-studied topic. Daou and Matalon (2002) presents an extensive analytical study of heat loss in a narrow channel. [59] It discovers the two extinction modes: total extinction and partial extinction mode due to heat loss under certain conditions. However, the study does not discuss any possible effects of heat loss on instabilities. Narrow channels pose questions about effects on a length scale comparable to flame thickness (d-scale). It is found heat loss through walls poses significant influence on flammability and prop- agation velocity of planar flames with unity Le eff. In channels with width comparable to flame length (d~15δ Q ), the flames can experience partial extinction due to excessive heat loss.[60] For flames with Le eff < 1 experiencing high heat loss through walls, broken cellular structure with dead space both at the center and near the wall can be observed.[61] In another numerical simulation study that laminar flames with Le eff > 1 exhibit lower flame velocity in a narrow channel with isothermal cold walls than with adiabatic walls. However, laminar flames with Le eff < 1 have un- expected higher flame velocity in the channel with isothermal cold walls than with adiabatic walls. This is due to the effect of increased flame curvature near the isothermal cold walls creates pock- ets of higher temperature product gas behind the flame.[62] Moreover, Kadowaki (2015) investigated the heat loss effects on DL and DT instability in a time dependent two-dimensional unbounded simulation.[63] It shows that while DL instability is sup- pressed by heat loss, DT instability can promote unstable behaviors in flames with lower than unity Le eff as heat loss increases. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 30 Kurdyumov and Jiménez (2013) focuses on heat loss effects on flame symmetry. [64] It studies a stable state two-dimensional flame subject to a Poiseuille flow in a narrow channel with a single Lewis number (Le). It finds that for Le equal to or larger than 1, there is always a symmetric solu- tion. Moreover, When Le is larger than 1, high heat loss can generate oscillations of the flame front. On the other hand, for L f smaller than 1 with high heat loss, certain flow rates give no steady state solution, and sufficiently high flow rates can result in a non-symmetric steady state solution. Furthermore, increasing heat loss can delay the transition from a symmetric flame front to a non-symmetric one, when Le is smaller than 1. However, realistically, such non-symmetric flame would be hard to produce in three dimensions, especially in high aspect ratio combustion chamber like the one used in the study. This study is followed by another study of the same group to extend the analysis in a two reac- tants, and investigates the effects of equivalent ratios. [65] It confirms that for sufficient lean or rich mixtures, flames behave similar to flames of a single Le (Le of the deficient reactant). When near stoichiometry, flames acts like ones of a single Le that is weighted between the two reac- tants base on the equivalent ratio. In additional to heat loss, a narrow channel’s width can also restrain flame propagation. When the channel width is comparable to flame thickness, meaning either channel is extremely narrow, or flame thickness is large, the flame can be flattened out. Under such condition, Dold et al. (2004) has found that burning rate would be no longer heavily influenced by Le _aa .[66] Although, it is useful to understand flame behaviors in a narrow channel, it is not the focus of this study. This study is aimed to investigate flame instabilities in a combustion chamber of high as- pect ratios. Therefore, the point of interest is the flame behaviors in the two large dimensions of the chamber. However, instability studies in such conditions are limited comparing to research on narrow channel combustions. One of profound theoretical and numerical studies regarding several of discussed flame instabil- ities in the two large length scale dimensions of narrow channels (size of the domain much larger Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 31 than the flame thickness (δ Q )) is Joulin and Sivashinsky.[67] It derives a dispersion relation ex- pressing a combined instability growth rate of a qusi-2D flame in a Hele-Shaw cell utilizing a linear stability analysis. It incorporates DL, RT and ST instabilities, but with an assumption of unity Le eff, it omitted DT effects. The model treats the flame front as an infinitely thin discontinuity (zero flame thickness assumption) with specified local normal propagation speeds. The study showed that due to persistent density increases and viscosity decreases across flame fronts (modified by heat losses though chamber walls), DL and ST instabilities are unconditionally destabilizing, while RT effects can be destabilizing or stabilizing for upward or downward propagation directions re- spectfully. Kang et al.[68] extended Joulin and Sivashinsky’s analysis by preforming numerical simulations utilize a 2D compressible reactive Navier-Stokes model within the Poiseuille flow as- sumption to compute linear growth rates of DL, ST and RT instabilities. Their results show agree- ments with previous theoretical and numerical studies [68], [69] regarding DL instability with variances concerning ST instabilities. In additional, Fernandez-Galisteo et al. [70] performed an extensive analysis of quasi-isobaric, quasi-2D flames in Hele-Shaw cell using average flow properties across the channel gap, similar to the experimental setup of this research. The simulations incorporate all aforesaid instabilities (DL, RT, ST and DL). Although the study uses only one-step chemistry, constant heat capacity and variable transport coefficients, it shows very good qualitative and, in some case, quantitative agreement with the experiments in this study which will be discussed in chapter 4. Moreover, for a 2D planar lean hydrogen flame in a sufficiently large domain free of confinement effects, the flame velocity is found to be independent of the domain size. [71] This numerical simulation also shows extremely similar flame shapes influenced by instabilities as in Fernandez- Galisteo et al. [70] despite the simulated flame is only 2D (no third-dimension viscosity effect) utilizing multi-step chemistry and large-scale Direct Numerical Simulations (DNS). Fernández-Galisteo and Kurdyumov (2018) performed an analytical study on flames propagating in a Hele-Shaw cell. [72] The study looks into DL instability, DT instability and effect of gravity (RT Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 32 instability). It finds that gravity does not only stabilizing/destabilizing DL instability on the large scale, it can also affect small scale wrinkling and oscillations generated by DT instability. In term of experimental studies, although there are some investigations of flames propagating through a narrow channel,[73]–[76] nearly all of them analyze flame extinction and propagation velocities in d-scales (10-30δ Q ), and few explanation in the contribution of multiple instabilities. Compare to amount of research done in narrow channels, there are only few experiments uti- lizing a high aspect ratio combustion chamber, like a Hele-Shaw cell. Villermaux et al. (2015) displays a beautiful image of propane-air flame obtained through experiments in a Hele-Shaw cell from, but it offers little explanations on any associating instabilities. [77] Yakush et al. (2018) preformed an experimental study on propane-air flame of equivalent ratios ranging from 1 to 1.25. The combustion chamber has a single center ignition point (can be changed to two at different locations) with open edge. Flames would propagate outwards cre- ates circular shapes with wrinkles and cells caused by instabilities. The study looks at flame ve- locities, cell sizes and Long-exposure flame patterns in relation with propagating time, chamber thickness, heat loss and equivalent ratio. The study also talks about interaction between two immerging flames from separate ignition positions. The concluding mainly confirmed existing theories. Although, the experiments were well done, the paper provide little development on scaling parameters or growth rate analysis. The several theoretical and numerical studies have provided some understanding of the multiple in- stabilities combined effects in the large 2D dimensions of a narrow channel. There is an absent of experiments to verify those investigations and to look at an overall effect from all four aforementioned instabilities on flame behaviors and propagation velocity. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 33 1.4 Proposal Figure 5 diagram of a curved flame front in a Hele-Shaw cell. Based on the aforementioned considerations and issues discussed, especially the lack of experi- mental data in the field, the main goal of this study is to assess of the combined effects of the aforesaid instabilities, DL, RT, ST and DT. In particular, their influence on flame shapes and flame propagation speed (S T) in a closed configuration, a narrow channel in this case as shown in Figure 5. To gain a full picture of effects from all instabilities, experiments will be performed for a wide range of following parameters: • Mixture strength (% of inert gas, affects adiabatic flame temperature (T ad)) • Effective Lewis numbers (Le eff) • Equivalence ratio (𝜙) • Fuel and inert gas types • Propagation directions • Combustion channel thickness (d) A sufficiently long narrow channel of open ignition end, one can hypothesize to observe a quasi- steady region of S T. If so, the second objective of this investigation aims to develop scaling pa- rameters for combined instability effects on S T. JS parameter (σ) is developed base on a linear derivation of Joulin and Sivashinsky [67], that included major instabilities present in a narrow Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 34 channel flame propagation (DL, RT and ST instabilities). Its shortcoming is the lack of representa- tion of DT instability. Therefore, this study would expand on JS parameter to include influence of DT instability through modifications of the local characteristic flame speed (U) used in Joulin and Sivashinsky analysis [67]. This study uses an estimated local characteristic flame speed (U ^nbN ) based on extinction strain rate (K _or ) for its dependence on flame curvature and Le _aa similar to DT instability, and its relatively simple 1-D calculation process. Then, the validity of U ^nbN is eval- uated by comparing to the local characteristic flame speed inferred from experiments (U _oN ). To obtain U _oN , one proposes to deconstruct S T into two factors: 1. The wrinkled flame length in the 2D plane (S Q /U _oN ), which can be measured for the quasi-steady region. It is hypotheses to be influence by large scale hydrodynamic and body force instabilities such as DL, RT and ST instabilities. 2. An effective laminar burning velocity (U _oN ) representing the curvature effects and heat loss in d-scale. Therefore, d z d { =| d z } ~ } ~ d { 1 U _oN can be inferred from the measurable quantities of S T, S L and S Q /U _oN as it will be explained later. The organization of this document is as follows: Chapter 2 provides background information on the four instabilities studied in this research (DL, RT, ST and DT). Chapter 3 will discuss experi- mental setup, data processing methods and scaling parameters used. Chapter 4 presents the re- sults of the experiments and the performance of the scaling parameters. Then, Chapter 5 gives a conclusion of the entire study. Chapter 6 is dedicated to future plans to complete this proposed study. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 35 Chapter 2: Background 2.1 Hele-Shaw Flow DL, RT and DT instabilities have been studied in various combustion experiments, such as Bunsen flame burners, expanding spherical flame chambers and glass tubes. However, majority of exper- imental studies about ST instability uses Hele-Shaw cells. This is due to the specific requirements needed to observe the instability, which is described in section 2.5 Saffman-Taylor Instability. There are few studies utilize porous materials, but those materials are mostly opaque, thus the experiments often have limited optical access. A Hele-Shaw cell provide an easy optical oppor- tunity. The flow field of a Hele-Shaw model is also relatively easy to describe. Figure 5 in last chapter has shown a demonstration of propagating flame in a Hele-Shaw cell. It seeks to portray a two-dimensional flow with depth-average over the thin channel, or a quasi-2D flow. For such flow fields, a set of two-dimensional single-phase conservation equations satisfying the limit of low-Reynold’s number and d/l ^_`` ≪1 can be used, ∇∙𝐮=𝟎 2 ∇p =− 𝐮 m +ρ𝐠 3 Therefore, this flow satisfies Darcy’s law. Although, the basic governing equation of Hele-Shaw model is the same for the liquid often used in non-reactive experiments and the gas used in com- bustion experiments, it is actually simpler to use Hele-Shaw model in combustion. For example, in liquid non-reactive experiments, one issue is that the residue liquid film left on the wall after displacement. It was shown in Saffman and Taylor (1958) that this film has a constant thickness, which complicates the boundary conditions and question the depth-average method. [6] In gas, such issue is minimized. However, combustion research in a Hele-Shaw cell faces other issues, such as heat loss, which directly affects important properties like density and viscosity ratios across flames. Furthermore, unlike non-reactive fluid, a self-sustaining flame would generate its Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 36 own driving force. Consequently, the analysis of flame propagations in a Hele-Shaw cell will also have to include energy equations and understanding of combustion theories. 2.2 Laminar Premixed Flame Laminar premixed flame is a combustion wave that combines thermodynamics, chemical kinetics, fluid mechanics and transport phenomena. It propagates in a gas or a mixture of gas with laminar flow characteristics. [78] Figure 6 shows an example of flame structure for a one-dimensional, adiabatic, steady laminar premixed flame propagating in a channel. The flame zone is mainly sep- arated into upstream transport region or preheat zone and high heat release region or reaction zone. The upstream unburned gas is heated through conduction and radiation, while combustion reactants and chemically active species diffuse downstream by molecular transport in the pre- heat region. When the unburned gas temperature reaches a sufficient high level to sustain chem- ical reactions at a high rate in the reaction zone, the flame becomes self-propagating, as the fast- chemical reactions release large amount of heat increasing upstream unburned gas temperature, which continuously sustaining the high chemical reaction rate. Eventually, after combustion pro- cess, hot reaction products would reach equilibrium at downstream.[45] However, when the thickness of this flame, including preheating zone and reaction zone, is extremely small compare to the length of the channel, the flame can be seen as a sheet or a discontinuity of fluid properties in the flow. This assumption allows the flow to be separated by the flame into two regions, un- burned region and burned region. Each region can be evaluated independently, with the assump- tion that chemistry is frozen between the two end boundaries of the channel and the flame sheet. Moreover, this study mainly considers flame propagations under a constant pressure (atmos- phere pressure). The analysis is within the framework of isobaric approximation (low Mach num- ber). This means that fluid and thermal properties, such as density (ρ), viscosity (µ), thermal dif- fusivity (α) and gas composition, are constant in each unburned and burned regions. One of the fundamental properties of a laminar premixed flame is the laminar flame speed (S L). It is measured with respect to the velocity of the unburned fresh gas mixture. The laminar flame Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 37 speed is defined as the speed of an ideal planar propagating laminar flame front, meaning a 2-D, adiabatic, planar, laminar premixed flame. This also means the laminar flame speed is normal to the local flame front. It is given that: S ∝√αω̇ 4 As shown in the above equation, S L is related to the overall reaction rate of the gas mixture, ω̇ ∝ e ℜz , which is heavily dependent on flame temperature. S L also is related to the diffusivity of the gas mixtures. With its sensitivity to molecular transport and flame chemical kinetics, it is com- monly used as a measurement for the transport properties and reactivity of flames. S L is consid- ered a flame property. It is not influenced by flow properties or heat loss, etc. Therefore, it is one of the widely used baseline normalizing parameter for flame propagation speeds, thus along with the absent of turbulence in unburned gas mixture of this study, it is used as one of the normaliz- ing parameters in studying instabilities influenced S T in this investigation. Figure 6 detailed premixed flame structure diagram. 2.3 Darrieus-Landau Instability Combustion is a strong exothermal chemical reaction process. Large heat release from the flames results in high temperature of product gas. This creates a sharp rise of temperature between T ad 𝜌 𝜇 Products T atm 𝜌 𝜇 𝛼 Reactants Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 38 fresh unburned reactant gas and burned product gas crossed the flame. With ideal gas assump- tion, P=ρℜT, under a constant pressure, the density of a gas mixture is inverse proportional to the temperature of the mixture. Therefore, the difference in temperature of unburned gas mix- ture and burned gas mixture creates large density ratio at the flame front. Figure 7 shows a dia- gram of the flow and flame interactions affected by this hydrodynamic instability. The arrows crossing the flame front are streamlines. They indicate flow cross section area variations due to curved flame front. Here, the hydrodynamic length scale associated with DL instability is much larger than flame thickness, so that the flame is approximated to have zero thickness. Therefore, based on simple Bernoulli’s equation (conservation of momentum crossed the flame), P+ ρ𝐮 =constant 5 Figure 7 diagram of flow and a curved flame front interaction[79]. Local velocity increases at valleys of the flame front and decreases at peaks as shown in Figure 7, and favors curvature and destabilized the curved flame front even more. This generates multidi- mensional flame and flow interactions (DL instability).[14][15] This is true for all flames under any conditions. Therefore, a planar flame as described earlier is unconditionally unstable. DL in- stability’s growth rate does not depend on internal flame structures due to the assumption of zero flame thickness. It also does not have any characteristic wavelength, as such curvature effect Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 39 is independent from the wavelength (λ≡2π/k) of flame wrinkles. k are the transversally har- monic wrinkles of wavenumber. DL instability’s growth rate depends only on the ratio between the density of unburned gas, ρ V , and burned gas, ρ W . It can be characterized by the thermal expansion coefficient, ε=ρ W /ρ V . It has a growth rate of [79], ω = ¡¢ £ ¤( ¥ ¦ )§¨ ¤ ¥ ¦ 6 Or as described by Joulin and Sivashinsky [67] in their linear analysis of a qusi-2D flame, including only DL instability, the dimensionless growth rate (σ≡ω /kU) is, (1+ε)σ +2σ− § § =0 7 Because ε<1 for all combustion processes, σ is always positive for all wavelength. It confirms that DL instability would always destabilizing a flame front. Figure 8 Darrieus-Landau instability growth rate vs. wavelength for an example of U = 28 cm/s, e = 0.2 and l cell = 40 cm. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 40 2.4 Rayleigh-Taylor Instability The density variance across flame is also subject to the influence of buoyancy when flame prop- agates vertically upward or downward. This buoyant convection creates RT instability.[19] In flames propagating upward, a less-dense fluid, high temperature products gas mixture, is be- neath a more-dense fluid, low temperature reactants gas mixture. This arrangement is buoyantly unstable. Therefore, an upward propagating flame is expected to experience instability due to buoyant convection. This effect also results in flame stretch at the top of the flame front in tube flames as shown in Figure 9. The situation is reversed in a flame propagating downward. Now, the less-dense fluid is above the more-dense fluid, thus produce a stable balance at the interface, and stabilize the flame. However, in a tube flame, due to heat loss at tube walls, product gas near the wall can becomes cold faster than gas in away from the wall. This cooling effect can create sinking boundary layers as shown in Figure 9. Figure 9 Diagram of upward (left) and downward (right) propagating flame and buoyancy effects [80]. RT insatiability, as a body force instability, presents most impacts on larger hydrodynamic scales than smaller diffusive scales, which makes it also independent from flame structures. The char- acteristic parameters of RT instability are the density ratio and the gravitational field parallel to flame propagation directions. Theoretically, the largest wavelength of RT insatiability is the one Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 41 that would fit into the experimental combustion chamber, thus, the width of the chamber (l ^_`` ). Therefore, the critical wavenumber of RT instability is, k ªQ = 2π l ^_`` It overlaps with effective wavelength of DL instability. Hence, RT instability would interact with DL instability and affects the overall dimensionless growth rate (σ≡ω &ªQ /kU) of flame insta- bility. Joulin and Sivashinsky [67] derived this combination growth rate as, (1+ε)σ +2σ− § § −¬ (§)𝐠` ~®® } ¯ ¡` ~®® =0 8 σ increases for upward propagating flames and decreases for downward propagating flames as shown in Figure 10. Moreover, under certain conditions, σ can be imaginary. It represents the oscillatory behaviors of flames propagating downward, which this study observed as shown in section 4.1 Flame Shape Variations Figure 10 Combined Darrieus-Landau instability and Rayleigh-Taylor instability growth rate vs. wavelength for an example of U = 28 cm/s, e = 0.2 and l cell= 40 cm. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 42 2.5 Saffman-Taylor Instability Saffman-Taylor instability (ST instability), or viscous fingering was first discovered in studies of non-reactive interface between fluids of different viscosities.[6] Tabeling conducted a detailed experimental study showing the effect of ST instability on oil-water interface. Figure 11 from the study showed the clear characteristic finger shape growth pattern. Such instability is only ob- served in narrow channels when the more-viscous fluid is displaced by the less-viscous fluid. Figure 11 Oil-water interface experiment demonstrates Saffman-Taylor Instability by Tabeling et al. (1987) [48] Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 43 Similar behavior would happen on any interface between fluids of different viscosity, including on flame sheet between burned and unburned gas. The rapid increase of gas temperature across flame changes the viscosity of gas mixtures (µ W /µ V ∝(T ^n`m /T ±nr ) ².³ ). The hot products gas mix- ture would have a higher viscosity than the cold reactants gas mixture, thus creates imbalanced friction force across the flame. This results in small variation of pressure at the flame front. Kan, Im & Baek (2003) [55] demonstrates a simulation study of the instability. It shows significant velocity increase in the burned gas right behind the flame front. Then, the net effect of increase velocity and the friction force of more viscous fluid excides the resistance of incoming fluid (un- burned gas). The incoming flow would be deflected the less viscous fluid (unburned gas) as shown in Figure 12. Figure 12 diagram of Saffman-Taylor instability mechanism. Similar to DL and RT instabilities, ST instability is a hydrodynamic instability. Its influential wave- length is much larger than flame thickness. Therefore, it doesn’t depend on flame structure, and has most effects on larger hydrodynamic scales. However, due to its friction driven nature, ST instability is only observed in confined environment (e.g., in a Hele-Shaw cell) with dependence on its geometry (d). Consequently, the instability can be characterized by the dynamic viscosity Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 44 ratio between products gas mixtures and reactants gas mixture (µ W /µ V ), and the thickness (d) of the narrow channel. Kan, Im & Baek (2003) [55] also finds that ST instability is most prominent at long wavelengths. This means that high viscosity contrast (fast flames) propagating thin channel (small d) would present the largest effects of ST instability. Detailed analysis is discussed in the following section (2.7 Joulin-Sivashinsky Parameter). Furthermore, different from the interface between oil and water, a flame front is exotherm self- propagating interface. Variation of density is unavoidable, while viscosity changes across the flame front. Therefore, ST instability is always coupled with DL instability in experimental studies. A linear analysis on all three hydrodynamic instabilities is presented by Joulin and Sivashinsky [67] in 1994. This analysis is used as baseline characterizing parameter in this study. 2.6 Joulin-Sivashinsky Parameter This investigation focuses on flame in flow without any forced turbulence. Therefore, the combi- nation growth rate of all instabilities exhibited by flame can be seen as the driving force for the flame propagation. In order to get an estimate on such combined growth rate, Joulin and Si- vashinsky [67] presents a linear stability analysis of the three hydrodynamic instabilities men- tioned earlier in background chapter: DL instability, RT instability and ST instability. In the deriva- tion, flame is assumed to be a quasi-2D laminar thin flame propagating in the direction of S T as noted through a Hele-Shaw cell as shown in Figure 5. The authors used non-adiabatic Euler-Darcy equations, ´µ ´r =∇∙(ρ𝐮) =0 9 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 45 ρ ´𝐮 ´r +𝐮∙∇𝐮=−∇p−f𝐮+𝐠ρ 10 ρc ´Q ´r +𝐮∙∇T=−h(T−T V ) 11 𝐮 is the 2-D velocity field in a flame propagating against unburned gas mixtures with stationary Hele-Shaw cell walls. The density (ρ) and temperature (T) are averaged over the thickness of the cell (d). g is gravity field taken aligned with x-axis (g<0 for downward propagation, g=0 for hori- zontal propagation and g>0 for upward propagation). As explained in earlier sections, the flame is modelled as a reactive discontinuity in the flow. f and h are momentum and energy exchange coefficients base on plate temperature, which is different in front (unburned area) and behind (burned area) the flame. Therefore, the derivation uses different f and h for each region. This analysis allows separate representations of thermal and transport properties for unburned gas mixture and burned product gas mixture. Typically, one has exchange coefficient of momentum, f~µ/d . Then, for flow in a Hele-Shaw cell f V =12µ V /d , f W =12µ W /d and f SX ≡(f W +f V )/2. The final growth rate (ω) of transversally harmonic wrinkles of wavenumber (k) is represented as: ω (ρ V +ρ W )+ω(2|k|ρ V U+f W +f V )= k ρ V U(U W −U)+|k|(f W U W −f V U+(ρ V −ρ W )g) 12 With expansion coefficient (ε), above equation can be written as, 13 Defining dimensionless growth rate, dimensionless wavelength, dimensionless friction factor and dimensionless gravity factor, ω 2 1+ε ( ) 2 2 2 k 2 U 2 + ω 1+ε ( ) 2kU 1+ f av ρ u Uk ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ − 1−ε 2 4ε ⎛ ⎝ ⎜ ⎞ ⎠ ⎟− f b −εf u ( ) 4ε f av 1+ε ( ) f av ρ u Uk − 1+ε ( ) 1−ε ( ) ρ u g 4f av U f av ρ u Uk =0 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 46 Ω≡ ω(1+ε) 2kU ;Λ≡ f SX ρ V kU ;F≡ f W −f V ε εf SX ;G≡ (1−ε)ρ V 𝐠 f SX U The final simplified equation becomes, Ω 𝟐 +(1+Λ)Ω− § ¼§ ¬1+ § § (F+G)Λ¯ =0 14 G represent RT instability. F symbolizes ST instability and has wavelength measured as λ dQ ≡ ½ ¾ µ ¿ }m À ∝(Pe)(d), where Pe≡Ud/α is Péclet number. DL instability doesn’t have any char- acteristic wavenumber. However, RT instability and ST instability have preferred wavelength. In this study’s experimental set-up, such wavelength would be the largest that can be fitted within the width of the cell (l ^_`` ). Therefore, a characteristic wavenumber, k=2π/l ^_`` , is used for this study. The analytical growth rates are shown in Figure 13 Effects of ST and RT instabilities on DL instability’s dimensionless growth rate (𝛺) for a range of example hydrocarbon-air flames with U=20cm and d=1.27cm. In order to observe ST instability in a Hele-Shaw cell, one must have λ dQ <l ^_`` . Therefore, for a fixed lcell, Pe or d has to be small. Although to have a small Pe requires low flame speed, to avoid quenching, fast flame with high flame temperature is needed. Moreover, decreasing d means Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 47 increasing effects of heat loss. This can suppress density and viscosity variation across the flame, which would also suppress DL, RT and ST instabilities. Therefore, in the experiments, ST instabil- ity is mostly observed in fast flames propagating through a cell with the smallest d. JS parameter (σ), a linear growth rate, is defined to be a dimensionless parameter of the growth rate (σ≡ω/kU). It measures the growth rate of flame wrinkling from DL, RT and ST in- stability as shown in Figure 13. The hypothesis is that such linear growth rate can be character- ize the driven force of instability wrinkled flames and is used to scale the flame propagation speed measured (S T) normalized by a linear flame speed, such as S L, similar to how turbulent intensity (u′) is used to describe turbulent flame propagation speed. However, due to the assumption of unity Le eff, Diffusive-thermal instability (DT instability), a small length scale effect, is not considered. Moreover, experimental wise, a prefect 2-D flame is impos- sible to produce. The inevitable third dimensional curvature effects, also another small length scale effect in d-scale, of flame propagating through a narrow gap also contribute into the uncer- tainty and limitation of the utilizing JS parameter. 2.7 Diffusive-thermal Instability Unlike the other three instabilities which consider the flame as a discontinuity of fluid properties, thus, ignore flame internal structure, DT instability depends on the thermal and molecular diffu- sion processes within the flame. The unequal values of thermal and molecular diffusion coeffi- cients generate DT instability.[19][56] For a curved or stretch flame front, heat diffuses from the flame front into unburned gas, while radicals molecules diffuse from unburned gas toward flame’s reaction zone to sustain the flame, as shown in Figure 14, where the arrows indicate the directions of the heat and species net fluxes, and S valley and S peak are local flame speed at the valleys and peaks of the flame front respectively. The bulge of the flame acts like a local source for heat and a sink for reactants radicals. The local flame speeds are affected by the two diffusion processes. The net fluxes of each diffusion processes are characterized by coefficient of thermal diffusivity, α, and coefficient of mas diffusivity, D, of the reactant gas mixture respectively. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 48 The ratio between those two coefficients is Lewis number, Le≡α/D. However, for a two reac- tants system with Le 1 ¹ Le 2, the estimation of Le for the gas mixture becomes more complicated. Therefore, effective Lewis number (Le eff) is used. A traditional approach is to estimate it base on deficient reactant, the reactant that has less mass in the gas mixture than what is needed to consume all mass of other reactants, thus, it depends on equivalent ratio (ϕ). ϕ=1 means all fuel and oxidizer in the gas mixture are consumed (stoichiometric). ϕ= S^rVS` aV_` rn noÄmÄÅ_Æ bSÇÇ ÆSrÄn ÇrnÄ^±Änb_rÆÄ^ aV_` rn noÄmÄÅ_Æ bSÇÇ ÆSrÄn 15 Figure 14 diagram of thermal and molecular mass diffusions of a curved flame front [79]. For a two reactants reaction, Le eff is closer to Le of the fuel in a lean combustion (fuel is the defi- cient reactant, ϕ<1) and is assumed to be similar to Le of the oxidizer in a rich combustion (oxidizer is the deficient reactant, ϕ>1). Therefore, for examples, a lean H 2-O 2-N 2 flame will has a Le eff smaller than 1, while a rich H 2-O 2-N 2 flame will has a Le eff larger than 1. There are several methods used to quantified Le eff in multi-gas mixtures. One of which is base a linear stability analysis by Joulin and Mitani. [81] The analysis considers reaction rates and weights by the abundant reactant. The results vary based on the reaction order of the global Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 49 reaction. For example, the study plots the estimated reduced Lewis number, L c, (same as Le eff in this study) against mole ratio between hydrogen and oxygen (n É /n Ê ), for various reaction or- ders as shown in Figure 15. However, in this study, the exact value of Le eff is not considered im- portant. Therefore, as simplification, all overall reaction order is assumed to be 1. The simplified result has for rich gas mixture with fuel being the abundant reactant, Le _aa = _ Ë¿~® ¤Ì ÍÎÏ _ ÐÎÎÑ~Í ¤Ì ÍÎÏ 16 A ÆÄ^± =1+β(ϕ−1) 17 Where β is Zel’dovich number based on global activation energy (Ea), β= Ó ªQ Q Q ¿ Q 18 For lean gas mixtures with oxidizer being the abundant reactant, Le _aa = _ ÐÎÎÑ~Í ¤Ì ®~Ù _ Ë¿~® ¤Ì ®~Ù 19 A `_SÛ =1+β Ü −1 20 A unity Le eff implies a balance between thermal and mass diffusion of the flame. The local flame temperature would be unaffected. Flames in gas mixtures of methane-air would mostly exhibit a unity Le eff. When Le eff > 1, thermal diffusion is more promenade than mass diffusion. Therefore, the faster thermal diffusion means the flame losses more heat than gaining reactant radicals for chemical reactions. The local flame temperature will decrease as result; thus, the local flame speed will drop as well. It is easy to see from the geometry showed in the diagram (Figure 14) S peak is more vulnerable to such effect. As S peak decreases, the flame will tend to flatten. Most hydrocarbon-air gas mixtures and rich hydrogen-air gas mixtures would have Le eff >1. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 50 Figure 15 Joulin and Mitani estimated reduced Lewis number (same as Le eff in this study) in hydrogen-oxygen flames as a func- tion of hydrogen-oxygen ratio. [81] Figure 16 Images of laser-induced fluorescence of OH for 1.89%H 2–10.06%O 2–88.05N 2 flame Le eff »0.3 at 1 atm.[58] Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 51 Figure 17 cellular structure in hydrocarbon-O 2-N 2 flames at atmosphere pressure in Markstein (1951). [82] Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 52 One the other hand, the opposite is true for Le eff <1. Now, mass diffusion is much greater than thermal diffusion. More reactant radical molecule influx for the flame means higher reactivity and higher local flame temperature. S peak will increase as a result. This effect favors flame curva- tures and in gas mixtures with sufficient low Le eff, it can break the flame into small cellular struc- tures as example shown in Figure 16. Markstein (1951) also performed a famous experiment to demonstration such cellular structure, as show in Figure 17.[82] This type of flame is mostly ob- served in lean H 2-O 2-iner and rich hydrocarbon-O 2-N 2 gas mixtures, which have Le eff < 1 due to the high mass diffusivity of hydrogen and the low mass diffusivity of hydrocarbon correspond- ingly. DT instability uniquely depends on the flame structure and exhibit a maximum growth rate at wavelengths comparable to thermal thicknesses of flames (δ Q ≡α/S ). As explained earlier, it is characterized by Le eff of the reactants gas mixtures, which is defined by the stoichiometrically deficient reactant. DT is destabilizing for flames in gas mixture with Le eff smaller than a critical value, Le ^ , and can be stabilizing of flames in gas mixture with Le eff larger than Le ^ . Le ^ is in gen- eral slightly less than 1 and characterizes when the broken cellular flame structures appear. The typical growth rate is demonstrated in Figure 18. Figure 18 typical growth rate of a cellular flame with Le eff < Le c as a function of k [79]. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 53 Chapter 3: Methods 3.1 Experimental Setup This investigation requires enclosed combustion chamber with optical access. Therefore, Hele- Shaw cell is used due to its simple geometry and large optical window. It is made of two acrylic plates separated by a hollow aluminum frame to create a combustion chamber that is 59.5 cm long (L), 39.5 cm wide (lcell). With different acrylic inserts, the chamber thickness (d) varies be- tween 1.27cm, 0.635cm and 0.3175cm. In order to create a flame that can be analyzed as a quasi- 2D flame, it is important that d is large enough to allow flame propagation (d>10α/S and is also small enough to prevent instability driven flame wrinkling perpendicular to the plates (d< O(10 Þ α/S )). In addition, the Hele-Shaw cell is installed on a metal stand with rotating ability. Therefore, the chamber can be set up in different positions to force the flame to propagate in upward, horizontal or downward. The chamber also has three spark electrodes installed at one end so that after ignition, three circular flames quickly merge into a single flame. The power to the sparks is pro- vided by a custom-built spark generator (D). At the ignition end of the cell, an exhaust manifold is connected to the atmosphere through a ball valve (E). The experimental system also includes a separate mixing chamber (B), a custom-built partial pressure mixing system (A), a Vision Re- search Miro eX2 high speed camera (later upgraded to a Phantom v711) (G), a vacuum pump (F), and a computer controlling the system through LabVIEW programs. The overall diagram of this experimental setup is illustrated below in Figure 19 . Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 54 Figure 19 Experimental apparatus, A: partial pressure mixing system, B: mixing chamber, C: fuel-oxidizer-inert gas supplies, D: ignition system, E: exhaust ball valve, F: vacuum pump, G: high-speed camera. At the beginning of each experiment, the Hele-Shaw cell and the mixing chamber are first evac- uated to eliminate the interference of residual gas from previous experiments. Then the mixing chamber is filled with a desired gas mixture using the partial pressure method. Dalton’s Law states that the total pressure of a gas mixture is equal to partial pressure of each individual gas, which is assumed to be an ideal gas. Multiple gas mixtures are used to study the effects of Le eff. Fuel, oxidizer and inert gas are all filled from separate gas tank to achieve desired gas mixtures. Hydrocarbon (e.g., CH 4, C 3H 8)-O 2-inert gas (e.g. N 2, CO 2) mixtures are used to study flame behav- iors in gas with high and near unity Le eff, and H 2-O 2-inert gas (e.g. N 2, CO 2) mixtures are used for their ability to achieve low Le eff. Next, the Hele-Shaw cell is filled with the mixed gas to a pressure slightly above 1atm to prevent back flow of air when the ball valve opens. Just before ignition, the ball valve opens so that com- bustion takes place at a nearly constant pressure (as confirmed by time-resolved chamber pres- sure measurements). The whole set-up is placed in an enclosure to block environment light in- terference. This is especially important for hydrogen experiments. Depending on the inert gas, hydrogen flames has little or no color due to lack of excited CH* in the reaction zone. The camera using the Vision Research Phantom Camera Control software records the flame propagation by filming the chemical illumination from hydrocarbon flames and the near inferred light emission from the hot product gas, mainly water vapor, from the hydrogen flames. The conditions of each Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 55 experiment, including date, mixture types, target and actual filled mixture mole fractions and target T ad, is documented in its video’s file name. Then, recorded actual filled mixture fractions are used to calculate S L in Chemkin Pro with USC Mech II chemical kinetic model, and K ext is esti- mated using a twin flames opposing jet model,“jet1”, with USC Mech II chemical kinetic model. [83] More details about K ext is discussed in section 3.3.1 Computational Local Characteristic Flame Speed (U ^nbN ). 3.2 Video Processing Method Figure 20 example of a frame of a video recorded then imported into the Matlab program, flame is propagating to- ward right, red line represent location of recognized flame position. Left: flame in gas mixture with Le eff > 1; Right: flame in gas mixture with Le eff < 1. Each experiment’s video is processed through a custom built Matlab program. It first extrapolates information about the experiment from video’s file name. Then, the program imports the video and transforms each frame into a 2-D matrix of light intensity as show in Figure 20 (left). Each frame is traded as an independent image. The goal is to obtain the estimated position of the flame in each frame, which is assumed to have the highest gradient of illumination contrast. In hydrocarbon flames, such light is from excited CH* particles. In hydrogen flames (mostly H 2-O 2- N 2 flames), such light is mostly from near inferred light emitted by hot water vapor in products gas. First, the background noise is determined using first and last frame of the video (the frame right before the ignition, and the frame right after flame extinguish at the end wall) and subtracted Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 56 from each frame. A median filter is used to remove background salt and paper noise. Then, each frame is put through a Gaussian filter. It has a cut-off length scale of the chamber thickness (d) and gamma of 0.7. This is an attempt to separate Diffusive-Thermal generated small wavelength wrinkling from hydrodynamic instability dominated large wavelength wrinkling on 2-D flame length measurement. In a depth averaged 2-D flame image, any wavelength smaller than the cell thickness can be seen as small-scale wrinkles. Next, changes in contrast can be found by calculating the 2-D gradient of each frame. The MATLAB program uses function “edge” with Canny method.[84] It is one of the most commonly used edge detection method. Canny method looks for local maxima of image gradient that is calculated using the derivative of a Gaussian filter. It can detect both strong and weak edge by using two thresholds instead of one in other method, such as Sobel and Prewitt.[85] Weak edges are only included if it is connected to a strong edge. This method is proven to show less noise. However, result gradient mask tend to show many broken lines because high degree of noise near flame fronts. In order to find a smooth outline, detected edges need to be dilated using linear structuring elements. The dilation has a size of the chamber thickness (d), so that it will not eliminate any wrinkles or gaps of larger wavelength. This also connects each cell that is less than the chamber thickness apart in a broken flame typically observed in gas mixtures with Le _aa less than one, as shown in Figure 20 (right). Then, the dilated gradient mask is put through “imfill” and “bwareaopen” functions to fill in small open holds within the mask and noise that wasn’t eliminated. The result binary image will give a smooth representation of the flame fronts. The program recognizes the front edge of the illuminated area in the direction of propagation as the flame position, shown as red trace in Figure 20. By summing all pixels behind this flame edge and normalizing it with the width and length of the cell, the program will generate an average flame position and combustion chamber pressure vs. time plot as shown in Figure 21. This time plot reveals that after the initial thermal expansion dominated transient period, a quasi-steady state period with nearly constant slope (thus steady propagation speed) is observed until the Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 57 flame approaches the opposite end of the Hele-Shaw cell. During the quasi-steady state period, the pressure in combustion chamber is relatively constant. This ensured that the unburned gas is not compressed, and the flame is free of pressure effects. The flame propagation speed, S T, is assumed to be the average slope of the flame position plot in the quasi-steady state region. Such method ensured that filter size used in the Gaussian filter will not affect estimate of flame prop- agation speeds. The root-mean-square error (RMSE) is calculated for each S T base on equation 21, where S Tn is the slope of each frame, and N is the number of frame within the quasi-steady state region. RMSE= £ ád z Ù d z â ã 21 Figure 21 example of experimentally measured flame position (blue) and corresponding pressure in the combustion chamber (orange). Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 58 Figure 22 Exemplary plot of wrinkled flame length ratio l flame /l cell vs. time generated from Matlab program. One more measurement that the video can provide us is the length of the 2-D flame wrinkled by instabilities (lflame). This quantity is extrapolated simply by measuring the length of the flame edge that already identified while measureing S T. The estimation uses Vossepoel and Smeulder’s althgorisum on priemeter length calculations with 8-connectivity [86]. Then, the results are nor- malized using the width of the cell (lcell). As shown in Figure 22 Wrinkled flame length ratio (lflame /lcell) vs. time plot has the same regions of developments as the exemplary plot of flame position vs. time, including thermal expansion dominated region, quasi-steady state region and end-wall region. The value of wrinkled flame length ratio for each experiment is estimated as the average value in the quasi-steady state region. Its RMSE is also calculated using the same method as for S T. Some exemplary outputs from this process can be find in Appendix. 3.3 Scaling Parameters As explained in section 2.6 Joulin-Sivashinsky Parameter, JS parameter (σ) is limited by its deri- vation and can’t reflect DT instability of flames studied in this research. Therefore, to minimize impacts of the issue, instead of the commonly used laminar flame speed S L, a computational local characteristic flame speed (U comp) is calculated. Although, a 2-D simulation of curved flame prop- 0 0.5 1 1.5 2 2.5 3 0 20 40 60 80 100 Wrinkled Flame Length Ratio (lflem/lcell) Time [ms] Quasi Steady State Region End-wall Region Thermal Expansion Dominated Average = Wrinkle Flame Length Ratio (lflame/lcell) Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 59 agating through narrow channels under each experimental condition should return the most ac- curate estimation of U comp, it is too costly and cumbersome. Therefore, this study attempts to use U comp based on extinction strain rate (K ext), a property that can be calculated through much simpler 1-D simulations. Then, in order to access the validity of U comp, U exp is extrapolated from experimental data as a comparison to U comp. 3.3.1 Computational Local Characteristic Flame Speed (U ^nbN ) Wrinkled flames, such as the ones studied in this research, is highly suggestable to effects of flame stretch. When flames propagate toward close end of a channel, like in the Hele-Shaw cell used in this study, under constant pressure, it is reasonable to assume unburned gas in front of the flame is at rest, as explained earlier. A wrinkled flame surface propagating toward resting gas, flame stretch can be manifested through curvature effect. At the valleys of the flame sheet, the unburned gas is heated diffusively. Then, it may be possible to achieve higher temperature than the unburned gas near the peaks. On the other hand, the concentration of reactants can be de- focused due to this curvature, which can also change flame speeds. It is found to be especially important in gas mixtures with unbalanced thermal and mass diffusion rates, which is closely accessioned with one of the instability studied, diffusive-thermal instability, as explain in section 2.7 Diffusive-thermal Instability. Therefore, this study attempts to use stretched flame theories to incorporate effects of Le eff in the scaling parameter. The key parameter of flame stretching is the stretch rate, [78] κ= Ì mÌ mr 22 Where A is the flame sheet surface area. One dimensionless property often used in describing stretch is Karlovitz number (Ka). It is defined as the ratio between chemical time scale for un- stretched flame (δ Q /S ) and Karlovitz time scale, which measures the physical flow time scale of a stretched flame (κ ). It is found that flame spontaneous extinction happens when those two Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 60 scales are comparable. In strong stretch, the time of flow can be too short for sufficient chemical reaction to complete, thus extinguishes the flame. In strong stretch, the stretch rate is proportional to laminar flame speed and thermal diffusivity, κ~S /α. At its limit, it can extinguish the flame. It may have, S ∝ √ακ 23 As shown in section 2.2 Laminar Premixed Flame, S ∝√αω̇ . Therefore, it can be said the stretch rate κ would scale with the overall reaction rate ω̇ (κ~ω̇ ). Then, the extinction stain rate (K _or ) would be associated with the highest reaction rate. Then, this study hypothesis a “computational local characteristic flame speed” (U ^nbN ) defined as, U ^nbN ≡ pαK _or This U ^nbN should be a function of Le _aa of the gas mixture. Therefore, by scaling S Q with U ^nbN , the goal is to describe Le _aa effects and DT instability to make up the shortcoming of JS parameter (σ). To estimate the premixed extinction stain rate (K _or ), a counter flow model is commonly used. This study chose to use a twin flames counter flow model. This is because for single flame coun- ter flow model, there is no clear justification for a specific temperature for the non-reactive side. The high level of heat loss of a cold flow can make it impossible to sustain a low tempera- ture flame at any strain rate. With flames of low adiabatic flame temperature being the focus of this study, this is not ideal choice. Using an adiabatic boundary condition is also not possible, because there would simply not be a spontaneous extinction. Therefore, the extinction stain Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 61 rate (K _or ) is estimating in a twin flame model, because it exists for the full range of experi- ment’s gas mixtures and is relatively easy to calculate (opposing jet simulations with 1atm, 289K inlet temperature and 1.4cm gap distance). 3.3.2 Experiment Based Local Characteristic Flame Speed (U _oN ) In order to extrapolate an experimental base local characteristic flame speed, S T is decomposed base on the length scale of influential factors. On the large length scale, the flame is subjected to hydrodynamic effects, mainly DL, RT and ST instabilities. In other words, S T/U _oN is assumed to depend on ε, 𝐠, µ V /µ W and d. Wrinkled flame length ratio (lflame /lcell) measured from experi- mental videos is expected to catch such large length scale characteristics. Therefore, it has, d z } ~ ≡ ` Ë®å~ ` ~®® 24 For small length scale, it brings the introduction of modified laminar flame speed (U _oN ). It is assumed to represent a hypothetical flame speed that is subjective to all small length scaled ef- fects, including DT instability, d-scale curvature and heat loss. Naturally, this factor is proposed to scale with Le eff which is a characteristic measure for DT instability, and Péclet number (Pe≡ S d/α), which describes the d-scale curvature and heat loss effects. Then, the decomposition model of S T is shown as, d z d { =| d z } ~ } ~ d { 25 Where S T and S T/U _oN are measured quantities, and S L is calculated using Chemkin Pro and USC Mech II. Therefore, U _oN /S L can be inferred base on above equation. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 62 Chapter 4: Results and Discussion 4.1 Flame Shape Variations To categorized flame in a narrow channel, it was hypothesized since steady, spherical flame balls can exist in large chambers [56], a 2D analog (flame circles) could be possible in the quasi-cylin- drical geometry in a Hele- Shaw cell. As in the case of flame balls, such structures would not be possible under the influence of buoyancy. However, unlike flame balls, for which buoyancy must be eliminated using microgravity experiments, in the case of flame circles, it may be possible to observe them in a horizontally oriented Hele-Shaw cell. While flame circles cannot be perfectly steady because Laplace's equation does not have a steady solution in cylindrical, unconfined ge- ometry due to the boundary condition, which cannot be satisfied as r→∞, unlike the spherical case. The singularity as r→∞ is very weak (logarithmic), and thus one might expect such struc- tures to persist on long time scales [87]. In fact, no such behavior was observed in this study. It can be stated that, in current experimental setup, flames in a Hele-Shaw cell behave more like propagating flames influenced by instabilities rather than flame circles with weak effects of prop- agation. Combined effects of DL, RT, ST and DT instabilities can originate differences on propagating flame shapes. Selective sequential, superimposed images of CH 4-O 2-N 2 flames are shown in Figure 23, Figure 24 and Figure 25. As the mass diffusivities of CH 4 and O 2 in N 2 are very similar. A horizontal propagating flame of a gas mixture with near unity Le eff is displayed in Figure 23. Effected by DL instability, the flame front has a smooth and cusp shape. Figure 24a shows a similar flame but propagates upward. RT instability destabilizes the flame generating a large curved front. As ex- pected, shown in Figure 24b, the downward propagating flame front is flattened by RT instability Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 63 as the less dense burned product gas resides on the top of denser unburned gas. Figure 25 dis- plays a tulip shaped methane flame, because of viscous fingering that is characteristic of thin plate spacing (d=0.3175cm) when ST instabilities are prominent. Figure 23 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.2s in steady state region) in 8.17%CH 4-17.28%O 2-74.55%N 2 mixture, horizontal propagation, d=1.27cm, Le eff ≈1. Figure 24 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.2s in steady state region) in (a) 8.17%CH 4-17.28%O 2-74.55%N 2 mixture, upward propagation, d=1.27cm, Le eff ≈1, (b) 8.17%CH 4- 17.28%O 2-74. 55%N 2 mixture, downward propagation, d=1.27cm Le eff ≈1. (a) (b) Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 64 Figure 25 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.2s in steady state region) in 12.16%CH 4-21.62%O 2-66.22%N 2 mixture, horizontal propagation, d=0.3175cm, Le eff ≈1. Flames in gas mixture with higher than unity Le eff exhibit similar behaviors. Flame fronts present smooth cusp shapes, as shown in Figure 26. Figure 27 shows that upward propagating flames exhibit large stretch due to RT instability, while downward propagating flames are flattened. However, due to gas mixtures’ higher Le eff, DT instability will stabilize flame fronts. Faster thermal diffusion of the gas mixture compare to its mass diffusion works against flame curvature effects. As explained in background chapter, the speeds of flame fronts’ valleys would increase. Flame fronts exhibit less wrinkling in general comparing to CH 4-O 2-N 2 flames. Figure 26 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~ 0.4s in steady state region) in 4.70%C 3H 8-28.95%O 2-66.35%N 2 mixture, horizontal propagation, d=1.27cm, Le eff ≈1.7. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 65 Figure 27 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~0.25s in steady state region) in (a) 4.70%C 3H 8-28.95%O 2-66.35%N 2 mixture, upward propagation, d=1.27cm, Le eff ≈1.7, (b) 4.70%C 3H 8- 28.95%O 2-66.35%N 2 mixture, downward propagation, d=1.27cm Le eff ≈1.7. One the other hand, flames in gas mixtures with lower than unity Le eff present dramatically dif- ferent shapes. Instead of smooth flame fronts, the flame Figure 28. is cellular and angular due to both small-scale DT instabilities and larger-scale hydrodynamic DL instabilities. The cellular struc- ture is a classic characteristic of DT instabilities. In the background chapter, it explains that faster mass diffusion of the gas mixture increases the speeds of flame’s peaks, thus favors flame curva- ture effects. Flames in gas mixtures with Le eff lower than a critical value would have broken flame fronts as shown in Figure 28. (a) (b) Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 66 Figure 28 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.4s in steady state region) in 1.99%H 2-9.95%O 2-88.06%N 2 mixture, horizontal propagation, d=1.27cm Le eff » 0.4 However, flame fronts showed also exhibit a large-scale angular shape. Such pattern presents striking similarity with dendrite solidification process as shown in Figure 29. Similar observations are also displayed in simulation works of flames with similar conditions. Fernandez-Galisteo et al. [70] presents a single step chemistry numerical study of a quisi-2D flame propagating through a Hele-Shaw cell utilized a set of similar conditions as in this experimental study. It shows flames with different Le eff shapes like it have been seen in this study. For instance, Figure 30 shows much similarities in a comparison of example flames in gas mixtures with high (>1) and low (<1) Le eff between simulations and our experiments. High Le eff gas mixtures create cusped shape flames, while flames become cellular and angular in low Le eff gas mixtures. Similar behaviors have also shown in Altantzis et al. [69] with a single step chemistry in a channel and Bergera et al. [88] (Figure 31) with detailed chemistry with neither confinement effects nor wall friction. Although, unfortunately, neither work offers a good, complete explanation on the theory behind such be- haviors, they together show such effects of DT instability on hydrodynamic structure of flame fronts can exist with only DT and DL instabilities presents. There is no need for viscosity effects from the channel wall, detail chemistry or even confinement. The reason on the formation of such flame shapes exists in interactions between those two instabilities. Although, such behav- iors deserve a well-rounded and detailed investigation, it is beyond the current scope for this experimental study. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 67 Figure 29 Dendrite growing into a supercooled melt of pure succinonitrile.[89] Figure 30 (a) Illustration of a horizontal steady flame in gas mixture of Le eff = 1.5 front represented by the reaction rate iso-contour and the flow field by the streamline pattern calculated. (b) picture of a quasi-steady flame shape, 2.46%C 3H 8-24.63%O 2-72.91%N 2, Le eff » 1.6. (c) Illustration of a horizontal steady flame in gas mixture of Le eff = 0.3 front represented by the reaction rate iso-contour and the flow field by the streamline pattern. (d) picture of a quasi- steady flame shape, 12.59%H 2-7.87%O 2-79.54%N 2, Le eff » 0.4. (b) (a) (c) (d) Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 68 Figure 31 Normalized temperature (Θ ) for the large-scale DNS (Lx = 800 l F , or d T) at a simulation time t = 200 τ F (τ F = l F/S L) after initialization [88]. Figure 32 shows the effects of heat lost on flame shapes. It is a horizontal propagating, close to extinction flame. Due to substantial heat loss in the burned gas, large-scale hydrodynamic wrin- kling caused by DL and ST effects are suppressed, but the small-scale DT cells are retained. There- fore, it shows only the cellular structures with a smooth large-scale curve front instead an angular one in previous figures. Figure 33 shows upward and downward propagating flames in gas mixtures with lower than unity Le eff, where the RT effect is destabilizing and stabilizing the flames accordingly as the same as in CH 4-O 2-N 2 flames. In upward propagating flames, Figure 33a, the large-scaled angular shapes are enhances, yet, Figure 33b shows that the suppression of the large-scale structures in downward propagating flames. Such flame has a saw tooth shape that is nearly flat on a large scale but still presents a cellular and angular front. Similarly, as in CH 4-O 2-N 2 flames, Figure 34 displays a tulip shaped flame. It is affected by ST in- stability. However, due to its small Le eff the flame is affected by DT instability, and the flame front shape is changed into angular peaks just like other flames with Le eff much smaller than 1. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 69 Figure 32 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.3s in steady state region) in 1.11%H 2-9.88%O 2-89.01%N 2 mixture, horizontal propagation, d=1.27cm, Le eff » 0.3. Figure 33 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell with constant time interval (~0.4s in steady state region) in (a) 0.80%H 2-15.96%O 2-83.24%N 2 mixture, upward propagation, d=1.27cm, Le eff ≈ 0.4, (b) 0.80%H 2-15.96%O 2-83.24%N 2 mixture, downward propagation, d=1.27cm, Le eff ≈0.4. (a) (b) Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 70 Figure 34 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.15s in steady state region) in 2.52%H 2-12.61%O 2-84.87 %N 2, horizontal propagation, d=0.1375cm Le eff » 0.4. Figure 35 Sequential, superimposed images of a flame propagating in a Hele-Shaw cell (~0.3s in steady state region) in 0.36%H 2- 57.14%O 2-42.5 %N 2, horizontal propagation, d=0.1375cm Le eff » 0.3. One additional interesting observation is in upward propagating ultra-lean H 2-O 2-N 2 flames. Such flames have extremely low Le _aa (~0.3). Theoretically, the flame front is expected to be very cellular. It is the case in downward and horizontal propagating flames. However, the flame front is changed when it propagates upward. As shown in Figure 35, the flame front appears to be smooth. It forms a propagating pattern similar to a lava lamp. One possible research is that Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 71 the flame is under extreme stretch while under the influence of RT instability. However, the evi- dence supports are not sufficient. Further investigation would be necessary to determine the driving force of such flame behavior. However, it is beyond the scope of this study. 4.2 Flame Propagation Speed (S T ) Flame propagation speeds are directly associated with the surface area of a flame, which is pro- portional to the amount of wrinkling the flame front exhibit. Therefore, similar to how flame shapes are influenced by aforementioned instabilities, the experimentally measured flame prop- agation speeds (S T) is also affected by DL, RT, ST and DT instabilities. In order to gain a better understanding of such effects, S T is nondimensionalized with calculated laminar burning speed (S L) of the mixture to create scaled flame propagation speed (S Q æ ≡S Q /S ). Figure 37 shows S T’ data plotting against another nondimensional quantity, Péclet number (Pe≡ S d/α), for CH 4-O 2-N 2 flames propagating through the Hele-Shaw cell of different thickness and in directions. Due to near unity Le eff, CH 4-O 2-N 2 flames are free from effects of DT instability. The flames propagating in the horizontal direction also are not influenced by RT instability. More- over, in the Hele-Shaw cell of 1.27cm thickness, ST instability is not prominent. Therefore, DL instability is the driving force for such flames. Although there isn’t any forced turbulence in the experiments, as shown in Figure 37, S T’ of horizontally propagating flames through 1.27cm thick Hele-Shaw cell averages around 3. It shows the significant effects of DL instabilities on laminar flames propagating speeds. Furthermore, in Figure 37, slow propagating flames (low Pe) display profound effects from RT instabilities as there is much variance between S T’ of similar S L, but of different propagation di- rections. The destabilizing nature of RT instability in upward propagating flames amplified larger scale wrinkling of flame fronts, thus increasing overall flame surface area and S T, while in down- ward propagating flames, RT instability stabilizes and decreases flame surface areas, thus slowing Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 72 down flames. However, such effects are observed less in fast propagating flames, where DL in- stability dominate and both S T and S L are relatively large compare to buoyance convection. as shown in Figure 36, the effect of ST instability is apparent, forming tulip shaped flame front in the thing chamber. This reflect on flame propagation speeds (S Q ) as shown in Figure 37. At similar Pe, S Q æ is relative the same for flames propagating upward through all three different cell thick- ness. This is due to the possible increase of flame surface is limited by cell length (60cm). In up- ward propagating flames, the flame front has reached a situation level of large scale wrinkling due to RT and ST instabilities, thus, the propagation speeds vary few between flames in the thick cell and the thin one. However, the horizontal and downward propagating rates increases signif- icantly for flames in thin cell due to ST instability promoting large scale wrinkling. shows experi- mental data of H2-O2-N2 flames with equivalence ratio of 2 (Le eff > 1). Higher Le eff means that DT instability is working against flame’s curvature, thus, stabilizing flames and de-creasing ST. There- fore, in Figure 39, although due to DL instability, average S T’ of horizontally propagating flames in 1.27cm cell is still higher than 1 (S T = S L), it is much lower than its of CH 4-O 2-N 2 flames. Unlike CH 4-O 2-N 2 flames, DT instability also make high Le eff flames much more sensitive to cham- ber thickness. Flames’ curvature in the small, third dimension is weakened, which slows down flames as d decreases. RT instability is also affected. It has a stronger present and make bigger variances between flames of different propagation directions in the thicker than in the thinner chamber for slow flames. Moreover, as shown in Figure 38, ST instability appears to wrinkly the flame front in the thin cell. However, S Q æ is still lower than flames propagating in thicker cells due to the strong DT instability effect. In Figure 41, it shows experimental data of H 2-O 2-N 2 flames with equivalence ratio of 0.8. Due to low Le eff of the gas mixtures, DT instabilities present in all the cases. The dominated effect of DT instabilities results in not only little variances between experiments in chamber of different thicknesses. This results in little effects of ST instability on S T’. Moreover, it shows much higher overall average S T’ compare to experiments of flames in gas mixtures with higher Le eff as shown Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 73 in Figure 37 and Figure 39. One the other hand, similarly to other two cases, RT instabilities shows a strong effect on slow propagating flames causing S T’ of different propagation directions to deviate from each other. Then, as the Pe, or flame propagation speed, increase, S T’ of differ- ent propagation directions merge due to overall fast flame propagation speeds. Figure 36 exemplary flame fronts of CH 4-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 =0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. Figure 37 S T’ vs. Pe for CH 4-O 2-N 2 gas mixtures with Le eff » 1 for various chamber thickness and propagation directions. Upward Horizontal Downward 0.31cm 1.27cm Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 74 Figure 38 exemplary flame fronts of for rich H 2-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 = 0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. Figure 39 S T ’ vs. Pe for H 2-O 2-N 2 gas mixtures with equivalent ratio of 2.0 (Le eff » 1.4) and for C 3H 8-O 2-N 2 gas mixtures with equiv- alent ratio of 0.5 (Le eff ≈1.7) for various chamber thickness and propagation directions. Upward Horizontal Downward 0.31cm 1.27cm Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 75 Figure 40 exemplary flame fronts of for lean H 2-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 = 0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. Figure 41 S T ’ vs. Pe for H 2-O 2-N 2 gas mixtures with equivalent ration of 0.8 (Le eff » 0.4) for various chamber thickness and propagation directions. Upward Horizontal Downward 0.31cm 1.27cm Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 76 Figure 42 Fernandez-Galisteo et al. simulating results of S T’ º S T/S L vs time for 𝐿𝑒 =1,𝛽 =10,𝜀 =0.2 and µ u/µ b = 0.7. G is their own gravity factor (𝐺 ≡−𝑎 𝒈𝛿 ç /(12𝑃𝑟𝑆 è )). Figure 43 Fernandez-Galisteo et al. simulating results of S T’ º S T/S L vs time for various Le,𝛽 =10,𝜀 =0.33 and µ u/µ b = 0.7. G is their own gravity factor (𝐺 ≡−𝑎 𝒈𝛿 ç /(12𝑃𝑟𝑆 è )=0). Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 77 Fernandez-Galisteo et al. [70] simulates 2-D flames in similar conditions as this study. Their re- sults are also comparable with the experimental measurements. They have shown purely insta- bilities driven flames with high S Q æ in good agreements with our experiments for some cases. For example, S T’ in near or above unity Le eff gas mixtures from simulations are similar to those meas- ured from experiments as show in Figure 42. However, S T’ in low Le eff gas mixtures from simula- tions are about half of those measured from experiments, as shown in Figure 43. This may be contributed by one-step chemistry and constant heat capacity assumption used in the simula- tions. Another possible explanation is their way of processing heat loss through the wall. There is no active calculation of heat loss, instead in Figure 43, the expansion ratio (ε) is lowered. This may also result in variations between their simulations and the experiment in this study. Going lower with Le _aa , ultra-lean H 2-O 2-N 2 and H 2-O 2-CO 2 flames have displayed a very interest- ing case. As shown in Figure 44. The flame shapes with different propagation orientations in the chamber with various thickness are largely diverse from one and another, which is consistent with flame behaviors with other equivalence ratios. Experimental data of those flames are showed in Figure 45. For those gas mixtures, it either is impossible to form a self-sustaining adi- abatic unstarched planar flame or may forms an extremely weak one. This means there is no associated S L or S L is way too small, which can’t be used as an adequate characteristic scale for S T. Therefore, the figure plots S T vs. T ad instead. However, despite similar flame shape as shown in Figure 44, Figure 45 does not show any dependence of S T on propagation orientations and chamber thicknesses. This is different from results of other hydrocarbon and hydrogen flames that discussed earlier. The propagation speeds appear to depend only on T ad of the flame. One likely explanation is the domination and saturation of DT instabilities considering the extreme low Le eff of those gas mixtures (Le eff » 0.3). This also suggests that combined effects of different instabilities result in similar overall driven force of the flames under the tested conditions. More- over, possible effects from different curvatures in the third dimension that is not observed in this experiment set up may also be a potential factor. Further investigations of those behaviors are planned. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 78 Figure 44 exemplary flame fronts of for ultra-lean H 2-O 2-N 2 with the same mixture ratio, but various chamber thickness (𝑑 = 0.31𝑐𝑚 or 1.27𝑐𝑚) and propagation directions as noted. Figure 45 Effect of adiabatic flame temperature, chamber thickness and propagation direction on flame propagation speeds (S T) for ultra-lean H 2-O 2-N 2 and H 2-O 2-CO 2, 𝐿𝑒 éêê » 0.3. 4.3 Scaling Parameters 4.3.1 Joulin-Sivashinsky Parameter First, in this section, JS parameter is scaled with S L, (σ≡ω/kS ). Base on the derivation of JS parameter explain in Chapter 2: Background, horizontal propagating flames would have σ≈1; Upward Horizontal Downward 0.31cm 1.27cm Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 79 upward propagating flame would have σ>1; and downward propagating flame would have σ< 1. In addition, the closer the value of σ to 1, the higher the corresponding Pe would be (higher S L). Figure 46 displayed a linear relationship between S T ’ and corresponding JS parameter, which make JS parameter a good linear measurement for S T ’ for gas mixtures with Le eff » 1. The mixtures include CH 4-O 2-N 2 with equivalent ratio around 1, C 3H 8-O 2-N 2 with equivalent ratio around 2, and H 2-O 2-CO 2 with equivalent ratio around 1.25. It can be augured that JS parameter is a good po- tential characteristic scale for instabilities driven, near unity Le eff flames of numerous fuel types propagating through narrow channels of different thickness in various directions. However, experimental data of flames in gas mixtures with Le eff deviated far from unity exhibits different correlations with JS parameters, as shown in Figure 47 and Figure 48. In Figure 47, H 2- O 2-N 2 and H 2-O 2-CO 2 gas mixtures have equivalent ratio of 2, and C 3H 8-O 2-N 2 gas mixtures have equivalent ratio of 0.5. Both mixtures groups exhibit Le eff much larger than unity. For data of σ< 1 (downward propagating), there is little changes, while S T’ scatters when σ>1 (upward prop- agating). In Figure 48, it displays data of H 2-O 2-N 2 gas mixtures having equivalent ratio of 0.8 and 0.4, and H 2-O 2-CO 2 gas mixtures having equivalent ratio of 0.8, and CH 4-O 2-CO 2 gas mixtures having equiv- alent ratio of 0.5. Giving their Le eff much smaller than unity. S T’ increases as σ decreases, when σ<1 (downward propagating). If σ>1 (upward propagating), S T’ would increase as σ increases. Horizontally propagating flames of this set of experiments have σ close to 1. Large variation of S T’ creates a radial pattern in Figure 48. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 80 Figure 46 S T’ vs. JS Parameter for CH 4-O 2-N 2 gas mixtures with equivalent ratios of 1.0 (Le eff » 1), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1) and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm. Figure 47 S T’ vs. JS Parameter for C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 1.7), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 2.0 (Le eff » 1.3), and H 2-O 2-N 2 gas mixtures with equivalent ratios of 2.0 (Le eff » 1.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 81 Figure 48 S T’ vs. JS Parameter for CH 4-O 2-CO 2 gas mixtures with equivalent ratio of 0.5 (Le eff » 0.7), H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.8 (Le eff » 0.4) and 0.4 (Le eff » 0.3), and H 2-O 2-CO 2 gas mixtures with equivalent ratios of 0.8 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm. Those behavioral differences of flames with different Le eff are to be expected as Joulin and Si- vashinsky’s analysis assumes unity Le eff, thus, eliminates effects of DT instability in its derived growth rate (ω) and JS parameter (σ). Therefore, it is important to incorporate DT instability in the scaling analysis, in order to create a more complete picture of flame behaviors of different gas mixtures under various conditions propagating narrow channels. As mentioned in Method chapter, this study attempts two different methods: (1) extinction strain rate based estimated laminar flame speed U ^nbN ) and (2) modified 2-D laminar flame speed (S L * ). 4.3.2 Computational local characteristic Flame Speed (U ^nbN ) Figure 49 shows experimentally measured flame propagation speeds (S T) scaled with computa- tional local characteristic flame speed (U ^nbN ) plotted against JS parameter (σ) calculated base on U ^nbN . Although, σ is no longer associated with regular laminar flame speed (S L), its behavior and representation are the same as explained in pervious section. Here, as shown in Figure 49, the overall trend of S T/U ^nbN is much improved compare to S T/S L in previous section for various Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 82 gas mixtures, cell thickness and propagation directions. Although, it is not perfectly clean, there is a linear growth of S T/U ^nbN proportional to σ. U ^nbN shows protentional in its ability to cap- ture Le _aa effects. Figure 49 S T/U comp vs. JS Parameter for experimental data: lean CH 4-O 2-N 2 gas mixtures (Le eff » 1); CH 4-O 2-CO 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 0.8); H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.3), 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4), 1.25 (Le eff » 1.3) and 2 (Le eff » 1.4); H 2-O 2-CO 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.2), 0.2 (Le eff » 0.2), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.3), 1.25 (Le eff » 1.1) and 2 (Le eff » 1.3); and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 1.7) and 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. However, one set of data is not displaced in Figure 49: rich CH 4-O 2-N 2 flames. As shown in Figure 50, rich CH 4-O 2-N 2 flames exhibit much higher S T/U comp compare to all other gas mixtures tested in this study. This is due to their low value of estimated extinction strain rates (K _or ) as shown in Figure 51 compare to propane flames and lean methane flames. Majority of scholar works meas- uring or calculating K _or uses fuel-air mixtures. Therefore, the estimation of this study can only be spot checked. K _or of lean methane-air mixtures and lean propane-air mixtures are compara- ble with Law (2010) [78], and Evans et al. (1988) as shown in Figure 53 [90] . This proves certain level of confident in the method used to estimate of K _or in this study. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 83 However, as shown in Figure 52, the regular laminar flame speeds (S ) for methane flames do not deviate much from propane flames for similar equivalent ratios and adiabatic flame temper- atures. This raises a question of the reason for such different in K _or . One possibility is that due to the influence of Le _aa on lean propane flames. The high Le _aa works against flame stretch, thus, lowers its K _or . In addition, with rich propane having lower Le _aa , which favors flame stretch, K _or would increase. As a result, K _or of both rich and lean propane flames collapse. CH 2-O 2-N 2 flames are free from Le _aa effects, thus, their K _or spreads apart for different equivalent ratios. This produces low U COMP, thus, high S T/U COMP for rich CH 2-O 2-N 2 flames. Figure 50 S T/U COMP vs. JS Parameter for experimental data: rich CH 4-O 2-N 2 gas mixtures (Le eff » 1) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 84 Figure 51 Calculated K ext vs.1/T ad for C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 and 2 and CH 4-O 2-N 2 gas mixtures with equivalent ratios of 0.6, 1 and 1.6. Figure 52 S L vs.1/T ad for C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 0.5 and 2 and CH 4-O 2-N 2 gas mixtures with equivalent ratios of 0.6, 1 and 1.6. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 85 Figure 53 Law (2010) calculated extinction strain rates for (a) top: lean methane-air flames; bottom: lean propane-air flames in a counterflow, with heat loss [78]; (b) Evans et al. (1988) simulation data of extinction limit comparison with the Law, et al. data and the Stahl, et al. computation. [90] 4.3.2 Experiment Based Laminar Flame Speed (U _oN ) U _oN is considered to represent small scale wrinkling base on experimental measurements. As explained in previous chapters, S T/U _oN is assumed to be represented by measured lflame /lcell. JS parameter is also modified to be calculated based on U _oN rather than S L (σ≡ω/kU _oN ). The behavior of σ stays the same. The trends of S T/U _oN are much more uniformed than when plot- ting S T ’ . Figure 54 shows the experimental results for gas mixtures with near unity Le eff. For σ> 1, S T/U _oN increasing steadily with a slope about 0.75, while for σ<1, S T/U _oN levels out near 1. (a) (b) Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 86 The results are showed in Figure 55 for gas mixture with relatively high Le eff. The average value and increasing slop of S T/U _oN is comparable the values in Figure 54. However, Figure 56 for gas mixtures with relatively low Le _aa . Again, residual Le _aa effects persist. Not only the overall aver- age of S T/U _oN is higher than it in gas mixtures with near unity Le _aa , S T/U _oN also increases faster, when σ>1. There are several possible reasons for such difference base on Le eff. Flames with sufficiently small Le eff display as broken flames with cellular structures. The method of measuring lflame /lcell uses peak to peak estimation to connect the broken flames. This may result in inaccuracy in measured S T/U _oN . Moreover, this method by diffuses curved cellular structures into U _oN , it thickens the flame brush and increased corresponding σ. Therefore, the “true” σ would be smaller than ones displayed in Figure 56. The combined effect is difficult to quantify. Figure 54 S T/U exp vs. JS Parameter for near unity Leeff experimental data: CH 4-O 2-N 2 gas mixtures with equivalent ratios of 1.0 (Le eff » 1), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1) and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 87 Figure 55 S T/ U exp vs. JS Parameter for high Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 2 (Le eff » 1.4), H 2-O 2-CO 2 with equivalent ratios of 2 (Le eff » 1.3), and C 3H 8-O 2-N 2 mixtures with equivalent ratios of 0.5 (Le eff » 1.7) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 56 S T/ U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.1 (Le eff » 0.3), 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4), and H 2-O 2-CO 2 with equivalent ratios of (Le eff » 0.3), 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 88 Figure 57 U exp /S L vs. Péclet number for near unity Le eff experimental data: CH 4-O 2-N 2 gas mixtures with equivalent ratios of 1.0 (Le eff » 1), H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1) and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 58 U exp /S L vs. Péclet number for high Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 2 (Le eff » 1.4), H 2-O 2-CO 2 with equivalent ratios of 2 (Le eff » 1.3), and C 3H 8-O 2-N 2 mixtures with equivalent ratios of 0.5 (Le eff » 1.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 89 Figure 59 U exp /S L vs. Péclet number for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4), and H 2-O 2-CO 2 with equivalent ratios of 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adia- batic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Another possibility is due to flame front being broken by DT instability for flame with sufficiently small Le eff, not all fuel-oxidizer gas is consumed. Therefore, ε is overestimated, as well as the growth rate of hydrodynamic instabilities, σ. However, this would end in similar situation as per- vious possibility. The “true” σ is smaller than current calculation, and scaling parameter perfor- mance is worsened. Another possibility is that although DT instability exhibit a maximum growth rate at wavelengths comparable to thermal thicknesses of flames, its present also affect large scale flame wrinkling. The curvature of each cell in the cellular structure may disturbed local streamlines and intensifies local flame propagation speed, similar as DL instability. This explains flames of Le eff <1 having higher S T/U _oN than flame of Le eff >1. On the other hand, the small length scale effects measured using U _oN /S L shows good trends (Figure 57, Figure 58 and Figure 59) as a function of Pe and Le eff. U _oN /S L of gas mixtures with Le eff smaller than unity (H 2-O 2-N 2 with equivalent ratio of 0.8) declines as Pe increases, while U _oN /S L of gas mixtures with Le eff larger than unity (H 2-O 2-N 2 with equivalent ratios of 2.0, and C 3H 8-O 2N 2 Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 90 mixtures with equivalent ratios of 0.5 and 2.0) are relative constant through the range of Pe measured. Furthermore, in general has a higher average value that U _oN /S L of gas mixtures with Le eff smaller than unity. This is due to the fact that U _oN is dominated by cellular structures from DT instability and favors more curvature in gas mixture of smaller than 1 Le eff than ones of larger than 1 Le eff. 4.3.3 U ^nbN vs.U _oN As shown in previous two sections, U ^nbN and U _oN give slightly different resulted JS parame- ters. It also can be seen in comparison between the two local characteristic flame speeds. As shown in Figure 60 and Figure 61, it shows comparison between U _oN and scaled U ^nbN for H 2- O 2-N 2 flames and C 3H 8-O 2-N 2 flames. In Figure 60, 𝑈 ìíîï /𝑈 éðï ≈1/6, and in Figure 61, 𝑈 ìíîï /𝑈 éðï ≈1/3. The reason for this mixture dependence for the ratios between U ^nbN and U _oN is unclear. The further investigation is necessary, but beyond the scope of this study. (a) (b) Figure 60 U comp and U exp vs. S L for H 2-O 2-N 2 flames with equivalent ratios of 0.8 and 2.0 propagating through a Hele-Shaw cell of (a) h = 1.27cm and (b) h = 0.635cm. Moreover, as shown in Figure 60, U _oN exhibits a propagation direction dependence for slow propagating flames (small S L) in the thick cell (h=1.27cm). This is the evidence of RT instability Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 91 effect in the x-z plane. However, U ^nbN is independent of such effects. This is another limitation of U ^nbN as a local characteristic flame speed. Figure 61 U comp and U exp vs. S L for C 3H 8-O 2-N 2 flames with equivalent ratios of 0.5 and 2.0 propagating through a Hele-Shaw cell of h = 1.27cm. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 92 Chapter 5: Conclusion Flames propagating in narrow channels exhibit a wide range of behaviors in terms of flame shapes and propagation speeds due to combined effects of Darrieus-Landau (DL), Rayleigh-Taylor (RT), Saffman-Taylor (ST) and diffusive-thermal (DT) effects. Thermal expansion (DL) effects are present in all flames, except when suppressed by excessive heat loss in very slow flame. Buoyancy (RT) effects are destabilizing/stabilizing at long wavelengths for upward/downward propagation and presenting stronger influence in thicker chambers than in thinner chambers. For fast flames in thinner chamber, strong ST instability is observed. Moreover, some new phenomena have been observed, e.g. stable saw-tooth patterns for downward propagation (Figure 33b), cusped for Le eff>1 (Figure 23) vs. angular large-scale structures for Le eff<1 (Figure 28) which is also wit- nessed in numerical simulation studies, and ultra-lean hydrogen lava lamp shaped flame (Figure 35). Moreover, this study has shown that even without forced turbulence at all, flame propagation speeds can be significantly larger than laminar flame speeds due to instabilities along. Usually, the instability driven flames propagate two to three times of laminar flame speeds. In some cases, such as upward propagating flames with low Le _aa , can have a propagation speeds that is more than 10 times of the corresponding laminar flame speeds. Proposed scaling parameters, JS parameter bases on laminar flame speed S L shows very limited validity range (Le eff » 1). JS parameter bases on computational local characteristic flame speed U ^nbN shows partially promising results. Flame propagation speeds with various Le _aa presents improved trends associating with JS parameter. However, rich CH 4-O 2-N 2 flames appear to be problematic. Moreover, compare to JS parameter base on experimental extrapolated local char- acteristic flame speed U _oN , U ^nbN showed dependence on gas mixtures and lack of representa- tion of propagation direction effects. Though, more works and analysis are preferable in several areas as will be discussed in the following chapter, the current study have shown a good and valuable results. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 93 Chapter 6: Future Work 6.1 Continue Investigation into Scaling Parameters As shown in Chapter 4: Results and Discussion, the results of scaling parameters investigated show promising outcomes. More experimental data is needed establishing a more complete globe trend. The study will extend analysis onto more diverse equivalent ratios, adiabatic flame temperatures and fuel gas mixtures, which will allow further examination into one of the most important aspect, the effect of DT instability. This study is aiming in producing comprehensive sets of data in 4 groups of Le eff , including high Le eff , such as H 2-O 2-N 2 gas mixtures with ϕ=2, Le _aa ≈1.4; Le _aa ≈1, such as CH 4-O 2-N 2 gas mixtures; low Le eff , such as H 2-O 2-N 2 gas mixtures with ϕ=0.8, Le _aa ≈0.4; and very low Le eff, such as H 2-O 2-N 2 gas mixtures with ϕ=0.2, Le _aa ≈0.3. One hope that a set of comprehensive experimental data and analysis will give a solid foundation in promoting future model development. In experiments of flames with cellular structures, only partial fuel-oxidizer gas is consumed is very possible as discussed previously. To verify such possibility, gas analysis of a gas sample extracted from the cell right after the flame past is needed. Therefore, the experiment apparatus needs to be modified to extract such gas sample. 6.2 Interactions between Darrieus-Landau Instability and Diffusive-thermal Instability In section 4.1 Flame Shape Variations, the angular flame front is discussed. The phenomenon is also observed in simulation works. However, the fundamental theory of such behavior is unclear. There has not been any scholar work preform any type of in-depth investigation of the issue. This study, along with comparison to simulation works mentioned, has confirmed the driving force of the angular flame front is the result of interaction between DL and DT instabilities. The origin is not rooted RT, ST instabilities or chemical kinetics. Further research is necessary to understand this flame behavior and its grow rate. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 94 6.4 New Experiment Apparatus and other Aspects of Flame in Narrow Channels A new Hele-Shaw cell is built to overcome several restrictions of the current experiment appa- ratus. Experiments of fast flame are proven to be difficult in current Hele-Shaw cell. First, it is important that the flame is propagating under constant pressure, thus, unburned gas is not pushed by increased pressure from expansion of less dense burned products behind the flame. It is to ensure that the measured flame speeds are the flame speeds with respect to relative stationary unburned fresh gas. Such pressure of variation is constrained by out volume flow of excessive pressure of the products, which depends on the size of exhaust pipe cross area. There- fore, the new set-up with much wider exhaust pipes will allow experiments with much faster flame. Moreover, the range of quasi-steady state region decreases as the flame speed increases. A longer quasi-steady state region can help improve measurement accuracy. One way to extend the range is simply to have a longer cell. Furthermore, ST instability has a dependence on k, which varies base on the width of the Hele-Shaw cell. A larger cell width will also allow studies of ST instability of flames with a different k. As shown in Figure 62, the new Hele-Shaw cell will be 106cm long and 46cm wide, with four ignition sparks instead of three. Thus, the original ignition system will not be able to support the new needed power. A one is designed using four separate spark ignitors. There is also a new bypass gas line at ignition positions, so that if needed, additional fuel or oxidizer can be inserted to assist ignition in near limit gas mixtures. In addition, the original box that enclosed the entire Hele-Shaw cell to ensure total darkness in order to eliminate environmental light noise has been extended to accommodate the new cell. Moreover, due to the new size and weight of the Hele-Shaw cell, there is an update for supporting structure and rotating mechanism, as shown in Figure 63. An electric hoist is installed to lift the cell into different positions. There is also an upgrade for the camera. The new camera, Phantom v771, has much higher res- olution with 7,530 pixels and light sensitivity with ISO at 6,400. This will allow an improved video Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 95 quality and visual possibility of low temperature, dim flames. With those hardware upgrades, one hope to acquire experimental data of much wider range than current set-up allows in order to present a much more comprehensive picture of the behaviors flame and effects of instabilities. Figure 62 CAD demonstration of the new Hele-Shaw cell Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 96 Figure 63 Stage demonstrations and explanations of new support structure and rotation mechanism. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 97 Appendix Appendix I – Video Processing Program Output Example Examples from the video processing program, Figure 64 example of the output from the video processing program. In Figure 64, the original light intensity frame is displayed at the top right corner. The top center image shows the filtered light intensity frame using the Gaussian filter described earlier. Then, using the edge finding method discussed, the top right corner image shows the outline of the hot products region. The bottom left image shows the result after filling everything behind the flame front. This is the final binary image used to estimate flame propagation speed. At last, to minimize measurement error for flame length and possible reflection of light from the alumi- num frame of the Hele-Shaw cell, near wall regions of the bottom left image is cut off. The re- sult is the last image, which is used for flame length estimation. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 98 Appendix II – Supplement Plots of Individual Fuel-inert gas mixtures Figure 65 S T/U comp vs. JS Parameter for experimental data: CH 4-O 2-CO 2 gas mixtures with equivalent ratios of 0.5 (Le eff » 0.8); H 2- O 2-N 2 gas mixtures with equivalent ratios of 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propa- gating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 66 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-CO 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.2), 0.2 (Le eff » 0.2), 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 99 Figure 67 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-N 2 gas mixtures with equivalent ratios of 0.1 (Le eff » 0.3), 0.2 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 68 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-CO 2 gas mixtures with equivalent ratios of 2 (Le eff » 1.3); and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 100 Figure 69 S T/U comp vs. JS Parameter for experimental data: H 2-O 2-N 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.3) and 2 (Le eff » 1.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 70 S T/U comp vs. JS Parameter for experimental data: lean CH 4-O 2-N 2 gas mixtures (Le eff » 1); H 2-O 2-CO 2 gas mixtures with equivalent ratios of 1.25 (Le eff » 1.1); and C 3H 8-O 2-N 2 gas mixtures with equivalent ratios of 2 (Le eff » 0.8) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 101 Figure 71 S T/U exp vs. JS Parameter for high Le eff experimental data: H 2-O 2-CO 2 with equivalent ratios of 2 (Le eff » 1.3) and C 3H 8- O 2-N 2 mixtures with equivalent ratios of 0.5 (Le eff » 1.7) of various adiabatic flame temperature and propagating through Hele- Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 72 S T/ U exp vs. JS Parameter for high Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 1.25 (Le eff » 1.3) and 2 (Le eff » 1.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 102 Figure 73 S T/ U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-CO 2 with equivalent ratios of 0.4 (Le eff » 0.3), 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Figure 74 S T/U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.2 (Le eff » 0.3), 0.4 (Le eff » 0.3) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. Flame Characteristics in Quasi-2D Channels: Stability, Rates and Scaling 103 Figure 75 S T/U exp vs. JS Parameter for low Le eff experimental data: H 2-O 2-N 2 with equivalent ratios of 0.8 (Le eff » 0.4) of various adiabatic flame temperature and propagating through Hele-Shaw cell of 1.27cm, 0.635cm and 0.3175cm height. 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Abstract (if available)
Abstract
Understanding propagation and behaviors of premixed flames in narrow channels, tubes, gaps or slots is important and relevant to several areas of combustion research and applications. For instance, in internal combustion engines (ICEs), combustion chambers at the time of combustion (when the piston is at top dead center position, TDC) are in narrow channel like shapes with high aspect ratios. Flames in such environment exhibit different behaviors and instabilities comparing to ones in mostly commonly used open configurations with little flame-wall interactions, including opposing jets and fan-stir reactors. This study focuses on the behaviors and propagation rates of flames in a confined environment, such as a narrow channel. ❧ A Hele-Shaw cell with varying gap thicknesses is used as the combustion chamber for its high aspect ratio and simple geometry. The flame shapes and propagation rates of quasi-2D premixed-gas flames in fuel-O₂-inert mixtures having a range effective Lewis numbers, adiabatic temperatures and orientation (upward (g=1), horizontal (g=0) and downward (g=−1) propagation) are studied. Instabilities due to thermal expansion of the burned gas (Darrieus-Landau, DL), Lewis number (diffusive-thermal, DT), buoyancy (Rayleigh-Taylor, RT) and viscosity contrast across the flame (Saffman-Taylor, ST) were found to have substantial effects on these shapes and rates. ❧ Classic cusp shapes of DL instability are observed in flames with effective Lewis numbers ≥ 1, while flames with effective Lewis numbers < 1 present dendritic flame fronts under the combined effect of DL and DT instabilities. Furthermore, due to DT instability, ST of flames with effective Lewis numbers < 1 is much faster than its of flames with effective Lewis numbers ≥1. RT instability destabilizes upward propagating flames and stabilizes downward propagating flames. Upward propagating flames also exhibit higher ST than downward propagating flames because of RT instability. ST instability is most prominent in fast propagating flames propagating through the Hele-Shaw cell with the smallest h. ❧ JS parameter (σ) is developed base on derivations of Joulin and Sivashinsky (1994) as a scaling parameter of the “driving force” for flame wrinkling. Although, the original derivations are limited in describing DT instability, σestimated using effective Lewis number scaled local characteristic flame speed ⎷(αΚₑₓₜ), Κₑₓₜ = extinction strain rate) is found to be effective characterizing flames under various conditions. It can be seen as an analog to turbulence intensity in premixed turbulent flame studies. However, rich methane flames are the exceptions. ❧ Overall, it is asserted that these flame-generated instabilities in the absence of forced turbulence have a significant influence on ST in practical combustion devices such premixed-charge internal combustion engines and lean-burn stationary gas turbines.
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Shen, Si
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Core Title
Flame characteristics in quasi-2D channels: stability, rates and scaling
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Viterbi School of Engineering
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Doctor of Philosophy
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Mechanical Engineering
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10/23/2019
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08/05/2019
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combustion,Darrieus-Landau instability,diffusive-thermal instability,flame instability,flame propagation,Hele-Shaw cell,JS parameter,laminar flame,narrow channel,OAI-PMH Harvest,Rayleigh–Taylor instability,Saffman-Taylor instability
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English
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Ronney, Paul D. (
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sishen@usc.edu,sishen0525@gmail.com
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Tags
combustion
Darrieus-Landau instability
diffusive-thermal instability
flame instability
flame propagation
Hele-Shaw cell
JS parameter
laminar flame
narrow channel
Rayleigh–Taylor instability
Saffman-Taylor instability