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AME 514 Applications of Combustion Lecture 9: Nonpremixed flames, edge flames
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2 AME 514 - Spring 2015 - Lecture 9 Turbulent combustion (Lecture 3) Motivation (Lecture 1) Basics of turbulence (Lecture 1) Premixed-gas flames Turbulent burning velocity (Lecture 1) Regimes of turbulent combustion (Lecture 1) Flamelet models (Lecture 1) Non-flamelet models (Lecture 1) Flame quenching via turbulence (Lecture 1) Case study I: “Liquid flames” (Lecture 2) (turbulence without thermal expansion) Case study II: Flames in Hele-Shaw cells (Lecture 2) (thermal expansion without turbulence) Nonpremixed gas flames (Lecture 3) Edge flames (Lecture 3)
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3 AME 514 - Spring 2015 - Lecture 9 Non-premixed flames Nonpremixed: no inherent propagation rate (unlike premixed flames where propagation rate = S L ) No inherent thickness (unlike premixed flames where thickness ~ /S L ) - in nonpremixed flames, determined by equating convection time = /U = -1 to diffusion time 2 / ~ ( / ) 1/2 Have to mix first then burn Burning occurs near stoichiometric contour where reactant fluxes in stoichiometric proportions (otherwise surplus of one reactant) Burning must occur near highest T since ~ exp(-E/RT) is very sensitive to temperature (like premixed flames) Simplest approach: “mixed is burned” - chemical reaction rates faster than mixing rates Recall stoichiometric mixture fraction Z st = mass fraction of fuel stream in a stoichiometric mixture of fuel and oxidant streams = stoichiometric coefficient, M = molecular weight, Y = mass fraction
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4 AME 514 - Spring 2015 - Lecture 9
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5 Nonpremixed turbulent jet flames Laminar: L f ~ U o d o 2 /D Turbulent (Hottel and Hawthorne, 1949) D ~ u'L I ; u' ~ U o ; L I ~ d o L f ~ d o (independent of Re) High U o high u' Da small – flame “lifts off” near base (why base first?) Still higher U o - more of flame lifted When lift-off height = flame height, flame "blows off" (completely extinguished)
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6 AME 514 - Spring 2015 - Lecture 9 Scaling of turbulent jets Hinze (1975) Determine scaling of mean velocity ( ), jet width (r jet ) and mass flux through jet ( ) with distance from jet exit (x) Assume u'(x) ~, L I (x) ~ r jet (x) Note that mass flux is not constant due to entrainment! Conservation of momentum flux (Q): Kinetic energy flux (K) (not conserved - dissipated!) KE dissipation
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7 AME 514 - Spring 2015 - Lecture 9 Scaling of turbulent jets dodododo UoUoUoUo r jet (x) x u(x)_entrainment m(x).≈12˚
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8 AME 514 - Spring 2015 - Lecture 9 Scaling of turbulent jets Combine
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9 AME 514 - Spring 2015 - Lecture 9 Liftoff of turbulent jets Scaling suggests mean strain ~ Re do 3/2 /x 2 For fixed fuel & ambient atmosphere (e.g. air), strain rate at flamelet extinction ( ext ) ≈ constant Liftoff height (x LO ) ~ ( / ext ) 1/2 Re do 3/4 ~ u o 3/4 d o 3/4 Experiments - closer to x LO ~ u o 1 d o 0 - but how to make dimensionless? Need time scale, i.e. x LO ~ u o 1 d o / , where S L 2 / S L 2 /, leading to x LO S L / ~ u o /S L G. Mungal (Stanford) Cha and Chung, 1996
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10 AME 514 - Spring 2015 - Lecture 9 Liftoff of turbulent jets Similar trend (x LO ~ u o 1 d o / ) seen in other fuels, scaled by highest S L of fuel/air mixture and fuel density ratio function g X LO S L / X LO S L / gU O /S L Kalghatgi (1984)
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11 AME 514 - Spring 2015 - Lecture 9 Liftoff of turbulent jets Summary of theories / experiments in Lyons (2007) Premixed flame theory: S L ≈ at x = x LO Critical scalar dissipation (Peters & Williams, 1983): ≈ mean turbulent strain at x = x LO Turbulent intensity theory S T ≈ at x = x LO (Kalghatgi, 1984) - but which S T ? Flamelet or distributed? Which model? Need to have stoichiometric (or close) mixture for maximum S T - 2 conditions need to be satisfied - stabilization point may not be at jet centerline Large eddy concept (Pitts, 1988) – flame is somehow attached to large eddies Lifted flame stabilized as ensemble of edge flames (next) What are predictions? Homework problem!
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12 AME 514 - Spring 2015 - Lecture 9 EDGE FLAMES - motivation Reference: Buckmaster, J., “Edge flames,” Prog. Energy Combust. Sci. 28, 435-475 (2002) Laminar flamelet model used to describe local interaction of premixed & nonpremixed flames with turbulent flow Various regions of turbulent flow will be above/below critical extinction strain ( ext ) Issues Can flame “holes” or “edges” persist? Will extinguishment in high- region spread to other regions? Will burning region re-ignite extinguished region? Will at edge locate ( edge ) be at higher or lower strain than extinction strain for uniform flame ( ext )? How is edge propagation rate affected by ? Lewis number effects?
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13 AME 514 - Spring 2015 - Lecture 9 Edge flames Flame propagates from a burning region to a non-burning region, or retreats into the burning region Could be premixed or non-premixed Kim et al., 2006 FLOW Non-premixed edge-flame in a counterflow
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14 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - theory Daou and Linan, 1998 Configuration as in previous slide No thermal expansion Non-dimensional stretch rate = ( /S L 2 ) 1/2 or Damköhler number ~ S L 2 / ~ -2 S L = steady unstretched S L of stoichiometric mixture of fuel & air streams Effects of stretch Low : flame advances, "triple flame" structure - lean premixed, rich premixed & trailing non-premixed flame branches Intermediate : flame advances, but premixed branches weaker High : flame retreats, only nonpremixed branch survives Note that stretch rate corresponding to zero edge speed is always less than the extinction stretch rate for the uniform (edgeless, infinite) flame sheet - edge flames always weaker than uniform flames - retreat in the presence of less strain than required to extinguish uniform flame Le effects: as expected - lower Le yields higher edge speeds, broader extinction limits
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15 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - theory Daou et al., 2002
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16 AME 514 - Spring 2015 - Lecture 9 Daou and Linan, 1998 (l F = (Le Fuel - 1)) Edge flames - nonpremixed - theory
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17 AME 514 - Spring 2015 - Lecture 9 Thermal expansion effect (Ruetsch et al., 1995): U/S L ~ ( ∞ / f ) 1/2 with proportionality constant shown Edge flames - nonpremixed - theory ( ∞ / f ) 1/2
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18 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - with heat loss Daou et al., 2002 = dimensionless heat loss ≈ 7.5 /Pe 2 ; Pe S L d/ (see Cha & Ronney, 2006) With heat loss: trailing non-premixed branch disappears at low - nonpremixed flame extinguishes because mixing layer thickness ~ ( / ) 1/2 (thus volume, thus heat loss) increases while burning rate decreases
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19 AME 514 - Spring 2015 - Lecture 9 Daou and Linan, 1999 - similar response of U edge to stretch as nonpremixed flames - also note "spots" Edge flames - premixed - theory
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20 AME 514 - Spring 2015 - Lecture 9 Experiments - nonpremixed edge-flames Cha & Ronney (2006) Use parallel slots, not misaligned slots Use jet of N 2 to "erase" flame, then remove jet to watch advancing edge, or establish flame, then zap with N 2 jet to obtain retreating flame
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21 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment Retreating "Tailless" Propagating
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22 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment Behavior very similar to model predictions with heat loss - negative at low or high , positive at intermediate with U edge /S L ≈ 0.7( ∞ / f ) 1/2 (prediction: ≈ 1.8) Propagation rates ≈ same for different gaps when scaled by strain rate except at low (thus low V jet ) where smaller gap more heat loss (higher )
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23 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment Dimensional U edge vs. stretch ( ) can be mapped into scaled U edge vs. scaled stretch rate ( ) for varying mixtures Little effect of mixture strength when results scaled by , except at low , where weaker mixture lower S L higher DimensionalDimensionless Numbers refer to molar N 2 dilution when fuel and oxidant streams are mixed in stoichiometric proportions (CH 4 :O 2 :N 2 = 1:2:N)
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24 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment High stretch ( ) or heat loss ( ) causes extinction - experiments surprising consistent with experiments, even quantitatively Very difficult to see "tailless" flames in experiments Model assumes volumetric heat loss (e.g. radiation) - mixing layer thickness can increase indefinitely, get weak non-premixed branch that can extinguish when premixed branches do not Experiment - heat loss mainly due to conduction to jet exits, mixing layer thickness limited by jet spacing Experiment (Cha & Ronney, 2006) Prediction (Daou et al., 2002)
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25 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment Lewis number effects VERY pronounced - at low Le, MUCH higher U edge than mixture with same S L (thus ) with Le ≈ 1 Opposite trend for Le > 1 Low Le (CH 4 -O 2 -CO 2 ) High Le (C 3 H 8 -O 2 -N 2 ) (Le fuel = 0.74; Le O2 = 0.86) (Le fuel = 1.86; Le O2 = 1.05)
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26 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment Z st = "stoichiometric mixture fraction" = fraction of fuel + inert in a stoichiometric mixture of (fuel+inert) & (O 2 +inert) (1 > Z st > 0) High Z st : flame sits near fuel side; low Z st : flame sits near O 2 side …but results not at all symmetric with respect to Z st = 0.5! Due to shift in O 2 concentration profile as Z st increases to coincide more closely with location of peak T, increases radical production (Chen & Axelbaum, 2005) (not symmetrical because most radicals on fuel side, not O 2 side)
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27 AME 514 - Spring 2015 - Lecture 9 Edge flames - nonpremixed - experiment Heat loss limit (low , thus low strain) - relationship between and independent of mixture strength, gap, Le, Z st, etc. Recall high (high strain) limit depends strongly on Le but almost independent of (page 24) Suggests relatively simple picture of non-premixed edge flames
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28 AME 514 - Spring 2015 - Lecture 9 Edge flames - premixed - theory Again larger U edge for low Le Again 2 nd extinction limit at low strain rates Daou & Linan, CNF 1999; Daou et al., CTM 2003
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29 AME 514 - Spring 2015 - Lecture 9 Edge flames – twin premixed - images Clayton, Cha, Ronney (2015?) Lewis number effects very evident – curvature effects on leading edge
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30 AME 514 - Spring 2015 - Lecture 9 Edge flames – twin premixed - U edge Propagation rates scale with ( u / b ) 1 not ( u / b ) 1/2 Again 2 extinction limits, high & low strain rates Clayton, Cha, Ronney (2015?) Raw data Scaled data
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31 AME 514 - Spring 2015 - Lecture 9 Edge flames – twin premixed - U edge Lewis number effects similar to nonpremixed edge flames Clayton, Cha, Ronney (2015?) Low fuel LeHigh fuel Le
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32 AME 514 - Spring 2015 - Lecture 9 Edge flames – twin premixed - regimes Regimes of behavior similar to nonpremixed edge flames Experiments Model predictions Clayton, Cha & Ronney, 2015? Daou et al., CTM 2003
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33 AME 514 - Spring 2015 - Lecture 9 Edge flames – single premixed - images Clayton, Cha, Ronney (2015?)
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34 AME 514 - Spring 2015 - Lecture 9 Edge flames – single premixed - U edge Propagation rates scale with ( u / b ) 1/2 Structure similar to nonpremixed flame – large temperature gradients on both sides of reaction zone, unlike twin premixed flame Less Lewis number effect than nonpremixed or twin premixed, especially for Le > 1
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35 AME 514 - Spring 2015 - Lecture 9 References Buckmaster, J. D., Combust. Sci. Tech. 115, 41 (1996). Buckmaster, J., "Edge flames," Prog. Energy Combust. Sci. 28, 435-475 (2002). Buckmaster, J. D. and Short, M. (1999). Cellular instabilities, sub-limit structures and edge-flames in premixed counterflows. Combust. Theory Modelling 3, 199-214. M. S. Cha and S. H. Chung (1996). Characteristics of lifted flames in nonpremixed turbulent confined jets. Proc. Combust. Inst. 26, 121–128 M. S. Cha and P. D. Ronney, "Propagation rates of non-premixed edge-flames, Combustion and Flame, Vol. 146, pp. 312 - 328 (2006). R. Chen, R. L. Axelbaum, Combust. Flame 142 (2005) 62–71. R. Daou, J. Daou, J. Dold (2002). "Effect of volumetric heat-loss on triple flame propagation" Proc. Combust. Inst., Vol. 29, pp. 1559 - 1564. R. Daou, J. Daou, J. Dold (2003). "Effect of heat-loss on flame edges in a premixed counterflow,” Combust. Theory Modelling, Vol. 7, pp. 221–242 J. Daou, A Liñán (1998). "The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers," Combust. Theory Modelling 2, 449–477 J. Daou and A. Liñán (1999). "Ignition and extinction fronts in counterflowing premixed reactive gases," Combust. Flame. 118, 479-488. Hinze, J. O. (1975) "Turbulence," McGraw-Hill. Hottel, H. C., Hawthorne, W. R., Third Symposium (International) on Combustion, Combustion Institute, Pittsburgh, Williams and Wilkins, Baltimore, 1949, pp. 254-266. Joulin, G. and Clavin, P. (1979). Linear stability analysis of nonadiabatic flames: diffusional- thermal model. Combust. Flame 35, 139. Kalghatgi, G. T. (1984). Lift-Off Heights and Visible Lengths of Vertical Turbulent Jet Diffusion Flames in Still Air. Combust. Sci. Tech. 41, 17-29.
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36 AME 514 - Spring 2015 - Lecture 9 References Kaiser, C., Liu, J.-B. and Ronney, P. D., "Diffusive-thermal Instability of Counterflow Flames at Low Lewis Number," Paper No. 2000-0576, 38 th AIAA Aerospace Sciences Meeting, Reno, NV, January 11-14, 2000. N. I. Kim, J. I. Seo, Y. T. Guahk and H. D. Shin (2006). " The propagation of tribrachial flames in a confined channel, " Combustion and Flame, Vol. 146, pp. 168 - 179. Liu, J.-B. and Ronney, P. D., "Premixed Edge-Flames in Spatially Varying Straining Flows," Combustion Science and Technology, Vol. 144, pp. 21-46 (1999). Lyons, K. M. (2007). “Toward an understanding of the stabilization mechanisms of lifted turbulent jet flames: Experiments,” Progress in Energy and Combustion Science, Vol 33, pp. 211–231 Pitts, W. M. (1988). “Assessment of theories for the behavior and blowout of lifted turbulent jet diffusion flames,” 22 nd Symposium (International) on Combustion, pp. 809–16. Ruetsch, G. R., Vervisch, L. and Linan, A. (1995). Effects of heat release on triple flames. Physics of Fluids 7, 1447. Shay, M. L. and Ronney, P. D., "Nonpremixed Flames in Spatially-Varying Straining Flows," Combustion and Flame, Vol. 112, pp. 171-180 (1998). Sivashinsky, G. I., Law, C. K. and Joulin, G. (1982). On stability of premixed flames in stagnation- point flow. Combustion Science and Technology 28, 155-159. R. W. Thatcher and J. W. Dold (2000). " Edges of flames that do not exist: flame-edge dynamics in a non-premixed counterflow. " Combust. Theory Modelling 4, 435-457. Vedarajan, T. G., Buckmaster, J. D. and Ronney, P. D., " Two-dimensional Failure Waves and Ignition Fronts in Premixed Combustion, " Twenty-Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 537-544.
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