1 / 46

AME 513 Principles of Combustion

AME 513 Principles of Combustion. Lecture 9 Premixed flames II: Extinction, stability, ignition. Outline. Flammability limits Chemical considerations Aerodynamics (i.e. stretch effects) Lewis number Heat losses to walls Buoyancy Radiative heat losses Flame instabilities

mira
Download Presentation

AME 513 Principles of Combustion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 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 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  3. 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 Tadlower NOx); fire & explosion hazard management, fire suppression, ... AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  4. Flammability limits - basic observations • Limits occur for mixtures that are thermodynamically flammable - theoretical adiabatic flame temperature (Tad) 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 (SL,lim) - better test of limit predictions than composition at limit AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  5. Premixed-gas flames – flammability limits 2 limit mechansims, (1) & (2), yield similar fuel % and Tad at limit but very different SL,lim AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  6. 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 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  7. Chemical kinetics of limits • Recall crossover of H + O2 OH + O vs. H + O2 + M  HO2 + M at low T – but this just means that at low Tad, flame will propagate very slowly due to absence of this branching route • Computations show no limits without losses – no purely chemical criterion (Lakshmishaet al., 1990; Giovangigli & Smooke, 1992) - for steady planar adiabatic flames, SL decreases smoothly towards zero as fuel concentration decreases (domain sizes up to 10 m, SL down to 0.02 cm/s) • …but as SL decreases, d increases - need larger computational domain or experimental apparatus • Also more buoyancy & heat loss effects as SL decreases …. Giovangigli & Smooke, 1992 Left: H2-air Right: CH4-air AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  8. Chemical kinetics of limits Ju, Masuya, Ronney (1998) Ju et al., 1998 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  9. Aerodynamic effects on premixed flames • Aerodynamic effects occur on a large scale compared to the transport or reaction zones but affect SL and even existence of the flame • Why only at large scale? • Re on flame scale ≈ SL/ ( = kinematic viscosity) • Re = (SL/)() = (1)(1/Pr) ≈ 1 since Pr ≈ 1 for gases • Reflame ≈ 1  viscosity suppresses flow disturbances • Key parameter: stretch rate () • Generally  ~ U/d U = characteristic flow velocity d = characteristic flow length scale AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  10. Aerodynamic effects on premixed flames • Strong stretch ( ≥  ~ SL2/ or Karlovitz number Ka /SL2 ≥ 1) extinguishes flames • Moderate stretch strengthens flames for Le < 1 Buckmaster & Mikolaitis, 1982a SL/SL(unstrained, adiabatic flame) ln(Ka) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  11. 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 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  12. TIME SCALES - premixed-gas flames • Chemical time scale tchem ≈ /SL≈ (a/SL)/SL≈ a/SL2 a = thermal diffusivity [typ. 0.2 cm2/s], SL = laminar flame speed [typ. 40 cm/s] • Conduction time scale tcond ≈Tad/(dT/dt) ≈ d2/16a d = tube or burner diameter • Radiation losstime scale trad ≈Tad/(dT/dt) ≈ Tad/(L/rCp) (L = radiative loss per unit volume) Optically thin radiation: L = 4sap(Tad4 – T∞4) ap = Planck mean absorption coefficient [typ. 2 m-1 at 1 atm] • L ≈ 106 W/m3 for HC-air combustion products • trad ~ P/sap(Tad4 – T∞4) ~ P0, P = pressure • Buoyant transport time scale t ~ d/V; V ≈ (gd(Dr/r))1/2 ≈ (gd)1/2 (g = gravity, d = characteristic dimension) Inviscid: tinv ≈ d/(gd)1/2 ≈ (d/g)1/2 (1/tinv ≈ Sinv) Viscous: d ≈ n/V Þtvis ≈ (n/g2)1/3 (n = viscosity [typ. 0.15 cm2/s]) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  13. Time scales (hydrocarbon-air, 1 atm) • Conclusions • Buoyancy unimportant for near-stoichiometric flames (tinv & tvis >> tchem) • Buoyancy strongly influences near-limit flames at 1g (tinv & tvis < tchem) • Radiation effects unimportant at 1g (tvis << trad; tinv << trad) • Radiation effects dominate flames with low SL (trad ≈ tchem), but only observable at µg • Small trad (a few seconds) - drop towers useful • Radiation > conduction only for d > 3 cm • Re ~ Vd/n ~ (gd3/n2)1/2Þ turbulent flow at 1g for d > 10 cm AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  14. Flammability limits due to losses • Golden rule: at limit • Why 1/b not 1? T can only drop by O(1/b) before extinction - O(1) drop in T means exponentially large drop in , thus exponentially small SL. Could also say heat generation occurs only in /bregion whereas loss occurs over region AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  15. Flammability limits due to losses • Heat loss to walls • tchem ~ tcond SL,lim ≈ (8)1/2a/d at limit or Pelim SL,limd/a ≈ (8)1/2 ≈ 9 • Actually Pelim ≈ 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)) Pelim ≈ 0.3 Grd1/2; Grd = Grashof number gd3/n2 • Causes stretch extinction (Buckmaster & Mikolaitis, 1982b): tchem ≈ tinv or 1/tchem ≈ Sinv Note f(Le) < 1 for Le < 1, f(Le) > 1 for Le > 1 - flame can survive at lower SL (weaker mixtures) when Le < 1 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  16. Difference between S and SL • long flame skirt at high Gr or with small f (low Lewis number, Le) (but note SL not really constant over flame surface!) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  17. Flammability limits due to losses • Downward propagation – sinking layer of cooling gases near wall outruns & “suffocates” flame (Jarosinskyet al., 1982) • tchem ≈ tvisÞSL,lim ≈ 1.3(ga)1/3 • Pelim ≈ 1.65 Grd1/3 • Can also obtain this result by equating SL to sink rate of thermal boundary layer = 0.8(gx)1/2 for x =  • Consistent with experiments varying d and a (by varying diluent gas and pressure) (Wang & Ronney, 1993) and g (using centrifuge) (Krivulin et al., 1981) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  18. Flammability limits in vertical tubes Upward propagation Downward propagation AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  19. Flammability limits in tubes Upward propagation - Wang & Ronney, 1993 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  20. Flammability limits in tubes Downward propagation - Wang & Ronney, 1993 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  21. Flammability limits – losses - continued… • Big tube, no gravity – what causes limits? • Radiation heat loss (trad ≈ tchem) (Joulin & Clavin, 1976; Buckmaster, 1976) • What if not at limit? Heat loss still decreases SL, actually 2 possible speeds for any value of heat loss, but lower one generally unstable AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  22. Flammability limits – losses - continued… • Doesn’t radiative loss decrease for weaker mixtures, since temperature is lower? NO! • Predicted SL,lim (typically 2 cm/s) consistent with µg experiments (Ronney, 1988; Abbud-Madrid & Ronney, 1990) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  23. Reabsorption effects • Is radiation always a loss mechanism? • Reabsorption may be important when aP-1 < d • Small concentration of blackbody particles - decreases SL (more radiative loss) • More particles - reabsorption extend limits, increases SL Abbud-Madrid & Ronney (1993) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  24. 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 SL & limits compared to optically thin AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  25. Stretched flames - spherical • Spherical expanding flames, Le < 1: stretch allows flames to exist in mixtures below radiative limit until flame radius rf is too large & curvature benefit too weak (Ronney & Sivashinsky, 1989) • Adds stretch term (2S/R) (R = scaled flame radius; R > 0 for Le < 1; R < 0 for Le > 1) and unsteady term (dS/dR) to planar steady equation • Dual limit: radiation at large rf, curvature-induced stretch at small rf (ignition limit) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  26. Stretched flames - spherical Theory (Ronney & Sivashinsky, 1989) Experiment (Ronney, 1985) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  27. Stretched counterflow or stagnation flames • Mass + momentum conservation, 2D, const. density () (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) • 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 513 - Fall 2012 - Lecture 9 - Premixed flames II

  28. z Stretched counterflow or stagnation flames • S = duz/dz – flame located where uz = SL • Increased stretch pushes flame closer to stagnation plane - decreased volume of radiant products • Similar Le effects as curved flames AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  29. 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?) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  30. Premixed-gas flames - stretched flames • Dual limits & Le effects seen in µg experiments, but evidence for multivalued behavior inconclusive Guo et al. (1997) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  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 513 - Fall 2012 - 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 Bernoulli: P+1/2u2 = const Aflame , u , P  Aflame, u, P FLOW  Aflame , u , P  Aflame, u, P AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  33. Apparatus for studying flame instabilities • Aluminum frame sandwiched between Lexan windows • 40 cm x 60 cm x 1.27 or 0.635 or 0.32 cm test section • CH4 & C3H8 fuel, N2 & CO2 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 513 - Fall 2012 - Lecture 9 - Premixed flames II

  34. Results - video - “baseline”case, DL-dominated 6.8% CH4-air, horizontal, 12.7 mm cell AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  35. Upward propagation – RT enhanced 6.8% CH4-air, upward, 12.7 mm cell AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  36. Downward propagation – RT suppressed 6.8% CH4-air, downward, 12.7 mm cell AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  37. High Lewis number 3.0% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  38. Low Lewis number 8.6% CH4 - 32.0% O2 - 60.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  39. Horizontal, but ST not DL dominated 9.5% CH4 - 90.5% air, horizontal, 3.1 mm cell AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  40. Ignition - basic concepts • Experiments (Lewis & von Elbe, 1987) show that a minimum energy (Emin) (not just minimum T or volume) required to ignite a flame • Emin lowest near stoichiometric (typ. 0.2 mJ) but minimum shifts to richer mixtures for higher HCs (why? Stay tuned…) • Prediction of Emin relevant to energy conversion and fire safety applications Minimum ignition energy (mJ) AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  41. Basic concepts • Emin related to need to create flame kernel with dimension () large enough that chemical reaction () can exceed conductive loss rate (/2), thus  > (/w)1/2 ~ /(w)1/2 ~ /SL ~  • Emin ~ energy contained in volume of gas with T ≈ Tad and radius ≈ ≈ 4/SL AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  42. Predictions of simple Emin formula • Since  ~ P-1, Emin ~ P-2 if SL is independent of P • Emin ≈ 100,000 times larger in a He-diluted than SF6-diluted mixture with same SL, same P (due to  and differences) • Stoichiometric CH4-air @ 1 atm: predicted Emin ≈ 0.010 mJ ≈ 30x times lower than experiment (due to chemical kinetics, heat losses, shock losses …) • … but need something more (Lewis number effects): • 10% H2-air (SL ≈ 10 cm/sec): predicted Emin ≈ 0.3 mJ = 2.5 times higher than experiments • Lean CH4-air (SL ≈ 5 cm/sec): Emin ≈ 5 mJ compared to ≈ 5000mJ for lean C3H8-air with same SL - but prediction is same for both AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  43. Lewis number effects • Ok, so why does min. MIE shift to richer mixtures for higher HCs? • Leeffective = effective/Deffective • Deff = D of stoichiometrically limiting reactant, thus for lean mixtures Deff = Dfuel; rich mixtures Deff = DO2 • Lean mixtures - Leeffective = Lefuel • Mostly air, so eff ≈ air; also Deff = Dfuel • CH4: DCH4 > air since MCH4 < MN2&O2 thus LeCH4 < 1, thus Leeff < 1 • Higher HCs: Dfuel < air, thus Leeff > 1 - much higher MIE • Rich mixtures - Leeffective = LeO2 • CH4: CH4 > air since MCH4 < MN2&O2, so adding excess CH4 INCREASES Leeff • Higher HCs: fuel < air since Mfuel > MN2&O2, so adding excess fuel DECREASES Leeff • Actually adding excess fuel decreases both  and D, but decreases  more AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  44. Effect of spark gap & duration • Expect “optimal” ignition duration ~ ignition kernel time scale ~ RZ2/ • Duration too long - energy wasted after kernel has formed and propagated away - Emin ~ t1 • Duration too short - larger shock losses, larger heat losses to electrodes due to high T kernel • Expect “optimal” ignition kernel size ~ kernel length scale ~ RZ • Size too large - energy wasted in too large volume - Emin ~ R3 • Size too small - larger heat losses to electrodes Sloane & Ronney, 1990 Kono et al., 1976 Detailed chemical model 1-step chemical model AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  45. Effect of flow environment • Mean flow or random flow (i.e. turbulence) (e.g. inside IC engine or gas turbine) increases stretch, thus Emin Kono et al., 1984 DeSoete, 1984 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

  46. 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 AME 513 - Fall 2012 - Lecture 9 - Premixed flames II

More Related