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

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

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,...

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

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

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

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

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

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

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)

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

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])

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

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

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

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

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)

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

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

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

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…

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…

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)

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

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

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

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

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

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?)

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

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

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 

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

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

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

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

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

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

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

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

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

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

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

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

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

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