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AME 513 Principles of Combustion Lecture 9 Premixed flames II: Extinction, stability, ignition

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2 AME Fall Lecture 9 - Premixed flames II Outline Flammability limits Chemical considerations Aerodynamics (i.e. stretch effects) Lewis number Heat losses to walls Buoyancy Radiative heat losses Flame instabilities Flame ignition Simple estimate Effects of Lewis number Effects of ignition source

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3 AME Fall Lecture 9 - Premixed flames II Flammability / extinction limits Too lean or too rich mixtures won’t burn - flammability limits Even if mixture is flammable, still won’t burn in certain environments Small diameter tubes Strong hydrodynamic strain or turbulence High or low gravity High or low pressure Understanding needed for combustion engines & industrial combustion processes (leaner mixtures lower T ad lower NO x ); fire & explosion hazard management, fire suppression,...

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4 AME Fall Lecture 9 - Premixed flames II Flammability limits - basic observations Limits occur for mixtures that are thermodynamically flammable - theoretical adiabatic flame temperature (T ad ) far above ambient temperature (T ∞ ) Limits usually characterized by finite (not zero) burning velocity at limit Models of limits due to losses - most important prediction: burning velocity at the limit (S L,lim ) - better test of limit predictions than composition at limit

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5 AME Fall Lecture 9 - Premixed flames II 2 limit mechansims, (1) & (2), yield similar fuel % and T ad at limit but very different S L,lim Premixed-gas flames – flammability limits

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6 AME Fall Lecture 9 - Premixed flames II Flammability limits in vertical tubes Upward propagation Downward propagation Most common apparatus - vertical tube (typ. 5 cm in diameter) Ignite mixture at one end of tube, if it propagates to other end, it’s “flammable” Limit composition depends on orientation - buoyancy effects

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7 AME Fall Lecture 9 - Premixed flames II Chemical kinetics of limits Recall crossover of H + O 2 OH + O vs. H + O 2 + M HO 2 + M at low T – but this just means that at low T ad, flame will propagate very slowly due to absence of this branching route Computations show no limits without losses – no purely chemical criterion (Lakshmisha et al., 1990; Giovangigli & Smooke, 1992) - for steady planar adiabatic flames, S L decreases smoothly towards zero as fuel concentration decreases (domain sizes up to 10 m, S L down to 0.02 cm/s) …but as S L decreases, d increases - need larger computational domain or experimental apparatus Also more buoyancy & heat loss effects as S L decreases …. Giovangigli & Smooke, 1992 Left: H 2 -air Right: CH 4 -air

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8 AME Fall Lecture 9 - Premixed flames II Chemical kinetics of limits Ju, Masuya, Ronney (1998) Ju et al., 1998

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9 AME Fall Lecture 9 - Premixed flames II Aerodynamic effects on premixed flames Aerodynamic effects occur on a large scale compared to the transport or reaction zones but affect S L and even existence of the flame Why only at large scale? Re on flame scale ≈ S L / ( = kinematic viscosity) Re = (S L / )( ) = (1)(1/Pr) ≈ 1 since Pr ≈ 1 for gases Re flame ≈ 1 viscosity suppresses flow disturbances Key parameter: stretch rate ( ) Generally ~ U/d U = characteristic flow velocity d = characteristic flow length scale

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10 AME Fall Lecture 9 - Premixed flames II Aerodynamic effects on premixed flames Strong stretch ( ≥ ~ S L 2 / or Karlovitz number Ka /S L 2 ≥ 1) extinguishes flames Moderate stretch strengthens flames for Le < 1 S L /S L(unstrained, adiabatic flame) Buckmaster & Mikolaitis, 1982a ln(Ka)

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11 AME Fall Lecture 9 - Premixed flames II Lewis number tutorial Le affects flame temperature in curved (shown below) or stretched flames When Le < 1, additional thermal enthalpy loss in curved/stretched region is less than additional chemical enthalpy gain, thus local flame temperature in curved region is higher, thus reaction rate increases drastically, local burning velocity increases Opposite behavior for oppositely curved flames

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12 AME Fall Lecture 9 - Premixed flames II TIME SCALES - premixed-gas flames Chemical time scale t chem ≈ /S L ≈ ( /S L )/S L ≈ /S L 2 = thermal diffusivity [typ. 0.2 cm 2 /s], S L = laminar flame speed [typ. 40 cm/s] Conduction time scale t cond ≈ T ad /(dT/dt) ≈ d 2 /16 t cond ≈ T ad /(dT/dt) ≈ d 2 /16 d = tube or burner diameter Radiation loss time scale t rad ≈ T ad /(dT/dt) ≈ T ad /( / C p ) ( = radiative loss per unit volume) Optically thin radiation: = 4 a p (T ad 4 – T ∞ 4 ) a p = Planck mean absorption coefficient [typ. 2 m -1 at 1 atm] Planck mean absorption coefficient Planck mean absorption coefficient ≈ 10 6 W/m 3 for HC-air combustion products t rad ~ P/ a p (T ad 4 – T ∞ 4 ) ~ P 0, P = pressure Buoyant transport time scale t ~ d/V; V ≈ (gd( / )) 1/2 ≈ (gd) 1/2 (g = gravity, d = characteristic dimension) Inviscid: t inv ≈ d/(gd) 1/2 ≈ (d/g) 1/2 (1/t inv ≈ inv ) Inviscid: t inv ≈ d/(gd) 1/2 ≈ (d/g) 1/2 (1/t inv ≈ inv ) Viscous: d ≈ /V t vis ≈ ( /g 2 ) 1/3 ( = viscosity [typ cm 2 /s]) Viscous: d ≈ /V t vis ≈ ( /g 2 ) 1/3 ( = viscosity [typ cm 2 /s])

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13 AME Fall Lecture 9 - Premixed flames II Time scales (hydrocarbon-air, 1 atm) Conclusions Buoyancy unimportant for near-stoichiometric flames (t inv & t vis >> t chem ) Buoyancy strongly influences near-limit flames at 1g (t inv & t vis < t chem ) Radiation effects unimportant at 1g (t vis << t rad ; t inv << t rad ) Radiation effects dominate flames with low S L (t rad ≈ t chem ), but only observable at µg Small t rad (a few seconds) - drop towers useful Radiation > conduction only for d > 3 cm Re ~ Vd/ ~ (gd 3 / 2 ) 1/2 turbulent flow at 1g for d > 10 cm

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14 AME Fall Lecture 9 - Premixed flames II Flammability limits due to losses Golden rule: at limit Why 1/ not 1? T can only drop by O(1/ before extinction - O(1) drop in T means exponentially large drop in , thus exponentially small S L. Could also say heat generation occurs only in / region whereas loss occurs over region

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15 AME Fall Lecture 9 - Premixed flames II Flammability limits due to losses Heat loss to walls t chem ~ t cond S L,lim ≈ (8 1/2 /d at limit or Pe lim S L,lim d/ ≈ (8 1/2 ≈ 9 Actually Pe lim ≈ 40 due to temperature averaging - consistent with experiments (Jarosinsky, 1983) Upward propagation in tube Rise speed at limit ≈ 0.3(gd) 1/2 due to buoyancy alone (same as air bubble rising in water-filled tube (Levy, 1965)) Pe lim ≈ 0.3 Gr d 1/2 ; Gr d = Grashof number gd 3 / 2 Causes stretch extinction (Buckmaster & Mikolaitis, 1982b): t chem ≈ t inv or 1/t chem ≈ inv Note f(Le) 1 for Le > 1 - flame can survive at lower S L (weaker mixtures) when Le 1 for Le > 1 - flame can survive at lower S L (weaker mixtures) when Le < 1

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16 AME Fall Lecture 9 - Premixed flames II long flame skirt at high Gr or with small f (low Lewis number, Le) (but note S L not really constant over flame surface!) Difference between S and S L

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17 AME Fall Lecture 9 - Premixed flames II Flammability limits due to losses Downward propagation – sinking layer of cooling gases near wall outruns & “suffocates” flame (Jarosinsky et al., 1982) t chem ≈ t vis S L,lim ≈ 1.3(g ) 1/3 Pe lim ≈ 1.65 Gr d 1/3 Can also obtain this result by equating S L to sink rate of thermal boundary layer = 0.8(gx) 1/2 for x = Consistent with experiments varying d and (by varying diluent gas and pressure) (Wang & Ronney, 1993) and g (using centrifuge) (Krivulin et al., 1981)

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18 AME Fall Lecture 9 - Premixed flames II Flammability limits in vertical tubes Upward propagation Downward propagation

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19 AME Fall Lecture 9 - Premixed flames II Flammability limits in tubes Upward propagation - Wang & Ronney, 1993

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20 AME Fall Lecture 9 - Premixed flames II Flammability limits in tubes Downward propagation - Wang & Ronney, 1993

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21 AME Fall Lecture 9 - Premixed flames II Big tube, no gravity – what causes limits? Radiation heat loss (t rad ≈ t chem ) (Joulin & Clavin, 1976; Buckmaster, 1976) What if not at limit? Heat loss still decreases S L, actually 2 possible speeds for any value of heat loss, but lower one generally unstable Flammability limits – losses - continued…

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22 AME Fall Lecture 9 - Premixed flames II Doesn’t radiative loss decrease for weaker mixtures, since temperature is lower? NO! Predicted S L,lim (typically 2 cm/s) consistent with µg experiments (Ronney, 1988; Abbud-Madrid & Ronney, 1990) Flammability limits – losses - continued…

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23 AME Fall Lecture 9 - Premixed flames II Reabsorption effects Is radiation always a loss mechanism? Reabsorption may be important when a P -1 < d Small concentration of blackbody particles - decreases S L (more radiative loss) More particles - reabsorption extend limits, increases S L Abbud-Madrid & Ronney (1993)

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24 AME Fall Lecture 9 - Premixed flames II Reabsorption effects on premixed flames Gases – much more complicated because absorption coefficient depends strongly on wavelength and temperature & some radiation always escapes (Ju, Masuya, Ronney 1998) Absorption spectra of products different from reactants Spectra broader at high T than low T Dramatic difference in S L & limits compared to optically thin

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25 AME Fall Lecture 9 - Premixed flames II Spherical expanding flames, Le < 1: stretch allows flames to exist in mixtures below radiative limit until flame radius r f is too large & curvature benefit too weak (Ronney & Sivashinsky, 1989) Adds stretch term (2S/R) (R = scaled flame radius; R > 0 for Le 1) and unsteady term (dS/dR) to planar steady equation Dual limit: radiation at large r f, curvature-induced stretch at small r f (ignition limit) Stretched flames - spherical

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26 AME Fall Lecture 9 - Premixed flames II Theory (Ronney & Sivashinsky, 1989) Experiment (Ronney, 1985) (Ronney, 1985) Stretched flames - spherical

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27 Mass + momentum conservation, 2D, const. density ( ) ( u, v = velocity components in x, y directions) ( u, v = velocity components in x, y directions) admit an exact, steady (∂/∂t = 0) solution which is the same with or without viscosity (!!!): = rate of strain (units s -1 ) = rate of strain (units s -1 ) Similar result in 2D axisymmetric (r, z) geometry: Very simple flow characterized by a single parameter , easily implemented experimentally using counter-flowing round jets… AME Fall Lecture 9 - Premixed flames II Stretched counterflow or stagnation flames

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28 = du z /dz – flame located where u z = S L Increased stretch pushes flame closer to stagnation plane - decreased volume of radiant products Similar Le effects as curved flames AME Fall Lecture 9 - Premixed flames II Stretched counterflow or stagnation flames z

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29 AME Fall Lecture 9 - Premixed flames II Premixed-gas flames - stretched flames Stretched flames with radiation (Ju et al., 1999): dual limits, flammability extension even for Le >1, multiple solutions (which ones are stable?)

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30 Dual limits & Le effects seen in µg experiments, but evidence for multivalued behavior inconclusive Guo et al. (1997) AME Fall Lecture 9 - Premixed flames II Premixed-gas flames - stretched flames

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31 Stability of premixed flames Many types, e.g. Thermal expansion (Darrieus-Landau, DL) – always occurs due to lower density of products than reactants Rayleigh-Taylor (buoyancy-driven, RT) – upward propagating flames unstable (more dense reactants on top of products), downward propagating stable Diffusive-thermal (DT) (Lewis number, already discussed) Viscous fingering (Saffman-Taylor, ST) in confined geometries when viscous fluid (e.g. oil) displaced by less viscous fluid (e.g. water) – occurs in flames because products are more viscous than reactants AME Fall Lecture 9 - Premixed flames II

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32 Effects of thermal expansion Darrieus-Landau instability - causes infinitesimal wrinkle in flame to grow due simply to density difference across front Williams, 1985 A flame , u , P A flame , u , P A flame , u , P Bernoulli: P+1/2 u 2 = const FLOW

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33 Apparatus for studying flame instabilities Aluminum frame sandwiched between Lexan windows 40 cm x 60 cm x 1.27 or or 0.32 cm test section CH 4 & C 3 H 8 fuel, N 2 & CO 2 diluent - affects Le, Peclet # Upward, horizontal, downward orientation Spark ignition (3 locations, ≈ plane initiation) Exhaust open to ambient pressure at ignition end - flame propagates towards closed end of cell AME Fall Lecture 9 - Premixed flames II

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34 Results - video - “baseline” case, DL-dominated 6.8% CH 4 -air, horizontal, 12.7 mm cell AME Fall Lecture 9 - Premixed flames II

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35 Upward propagation – RT enhanced 6.8% CH 4 -air, upward, 12.7 mm cell AME Fall Lecture 9 - Premixed flames II

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36 Downward propagation – RT suppressed 6.8% CH 4 -air, downward, 12.7 mm cell AME Fall Lecture 9 - Premixed flames II

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37 3.0% C 3 H 8 -air, horizontal, 12.7 mm cell (Le ≈ 1.7) High Lewis number AME Fall Lecture 9 - Premixed flames II

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38 Low Lewis number 8.6% CH % O % CO 2, horizontal, 12.7 mm cell (Le ≈ 0.7) AME Fall Lecture 9 - Premixed flames II

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39 9.5% CH % air, horizontal, 3.1 mm cell Horizontal, but ST not DL dominated AME Fall Lecture 9 - Premixed flames II

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40 Minimum ignition energy (mJ) Ignition - basic concepts Experiments (Lewis & von Elbe, 1987) show that a minimum energy (E min ) (not just minimum T or volume) required to ignite a flame E min lowest near stoichiometric (typ. 0.2 mJ) but minimum shifts to richer mixtures for higher HCs (why? Stay tuned…) Prediction of E min relevant to energy conversion and fire safety applications

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41 AME Fall Lecture 9 - Premixed flames II Basic concepts E min related to need to create flame kernel with dimension ( ) large enough that chemical reaction ( ) can exceed conductive loss rate ( / 2 ), thus > ( / ) 1/2 ~ /( ) 1/2 ~ /S L ~ E min ~ energy contained in volume of gas with T ≈ T ad and radius ≈ ≈ 4 /S L

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42 AME Fall Lecture 9 - Premixed flames II Predictions of simple E min formula Since ~ P -1, E min ~ P -2 if S L is independent of P E min ≈ 100,000 times larger in a He-diluted than SF 6 - diluted mixture with same S L, same P (due to and differences) Stoichiometric CH 4 1 atm: predicted E min ≈ mJ ≈ 30x times lower than experiment (due to chemical kinetics, heat losses, shock losses …) … but need something more (Lewis number effects): 10% H 2 -air (S L ≈ 10 cm/sec): predicted E min ≈ 0.3 mJ = 2.5 times higher than experiments Lean CH 4 -air (S L ≈ 5 cm/sec): E min ≈ 5 mJ compared to ≈ 5000mJ for lean C 3 H 8 -air with same S L - but prediction is same for both

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43 AME Fall Lecture 9 - Premixed flames II Lewis number effects Ok, so why does min. MIE shift to richer mixtures for higher HCs? Le effective = effective /D effective D eff = D of stoichiometrically limiting reactant, thus for lean mixtures D eff = D fuel ; rich mixtures D eff = D O2 Lean mixtures - Le effective = Le fuel Mostly air, so eff ≈ air ; also D eff = D fuel CH 4 : D CH4 > air since M CH4 air since M CH4 < M N2&O2 thus Le CH4 < 1, thus Le eff < 1 Higher HCs: D fuel 1 - much higher MIE Rich mixtures - Le effective = Le O2 CH 4 : CH4 > air since M CH4 air since M CH4 < M N2&O2, so adding excess CH 4 INCREASES Le eff Higher HCs: fuel M N2&O2, so adding excess fuel DECREASES Le eff Actually adding excess fuel decreases both and D, but decreases more

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44 AME Fall Lecture 9 - Premixed flames II Effect of spark gap & duration Expect “optimal” ignition duration ~ ignition kernel time scale ~ R Z 2 / Duration too long - energy wasted after kernel has formed and propagated away - E min ~ t 1 Duration too short - larger shock losses, larger heat losses to electrodes due to high T kernel Expect “optimal” ignition kernel size ~ kernel length scale ~ R Z Size too large - energy wasted in too large volume - E min ~ R 3 Size too small - larger heat losses to electrodes Detailed chemical model 1-step chemical model Sloane & Ronney, 1990 Kono et al., 1976

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45 AME Fall Lecture 9 - Premixed flames II Effect of flow environment Mean flow or random flow (i.e. turbulence) (e.g. inside IC engine or gas turbine) increases stretch, thus E min Kono et al., 1984 DeSoete, 1984

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46 AME Fall Lecture 9 - Premixed flames II Effect of ignition source Laser ignition sources higher than sparks despite lower heat losses, less asymmetrical flame kernel - maybe due to higher shock losses with shorter duration laser source? Lim et al., 1996

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