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Turbulent combustion (Lecture 3)

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)

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Turbulent combustion (Lecture 3)

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  1. 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) AME 514 - Spring 2013 - Lecture 9

  2. Non-premixed flames • Nonpremixed: no inherent propagation rate (unlike premixed flames where propagation rate = SL) • No inherent thickness  (unlike premixed flames where thickness ~ /SL) - 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 w~ 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 Zst= mass fraction of fuel stream in a stoichiometric mixture of fuel and oxidant streams n = stoichiometric coefficient, M = molecular weight, Y = mass fraction AME 514 - Spring 2013 - Lecture 9

  3. AME 514 - Spring 2013 - Lecture 9

  4. Nonpremixed turbulent jet flames • Laminar: Lf ~ Uodo2/D • Turbulent (Hottel and Hawthorne, 1949) • D ~ u'LI; u'~ Uo; LI ~ doLf ~ do (independent of Re) • High Uo highu' Da small – flame “lifts off”near base (why base first?) • Still higher Uo - more of flame lifted • When lift-off height = flame height, flame "blows off"(completely extinguished) AME 514 - Spring 2013 - Lecture 9

  5. Scaling of turbulent jets • Hinze (1975) • Determine scaling of mean velocity ( ), jet width (rjet) and mass flux through jet ( ) with distance from jet exit (x) • Assume u'(x) ~ , LI(x) ~ rjet(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 AME 514 - Spring 2013 - Lecture 9

  6. . m(x) _ u(x) Scaling of turbulent jets Uo ≈12˚ x rjet(x) do entrainment AME 514 - Spring 2013 - Lecture 9

  7. Scaling of turbulent jets • Combine AME 514 - Spring 2013 - Lecture 9

  8. Liftoff of turbulent jets • Scaling suggests mean strain ~ Redo3/2/x2 • For fixed fuel & ambient atmosphere (e.g. air), strain rate at flamelet extinction (ext) ≈ constant • Liftoff height (xLO) ~ (/ext)1/2 Redo3/4 ~ uo3/4do3/4 • Experiments - closer to xLO ~ uo1do0 - but how to make dimensionless? Need time scale, i.e. xLO ~ uo1do/w, where w ≈ SL2/≈ SL2/, leading to xLOSL/ ~ uo/SL G. Mungal (Stanford) Cha and Chung, 1996 AME 514 - Spring 2013 - Lecture 9

  9. Liftoff of turbulent jets • Similar trend (xLO ~ uo1do/w) seen in other fuels, scaled by highest SL of fuel/air mixture and fuel density ratio function g Kalghatgi (1984) XLOSL/ gUO/SL AME 514 - Spring 2013 - Lecture 9

  10. Liftoff of turbulent jets • Summary of recent theories / experimentsin Lyons (2007) • Premixed flame theory: SL ≈ at x = xLO • Critical scalar dissipation (Peters & Williams, 1983): w≈ mean turbulent strain at x = xLO • Turbulent intensity theory ST≈ at x = xLO (Kalghatgi, 1984) But which ST? Flamelet or distributed? Which model? Need to have stoichiometric (or close) mixture for maximum ST - 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! AME 514 - Spring 2013 - Lecture 9

  11. 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? AME 514 - Spring 2013 - Lecture 9

  12. 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  FLOW  Non-premixed edge-flame in a counterflow Kim et al., 2006 AME 514 - Spring 2013 - Lecture 9

  13. Edge flames - nonpremixed - theory • Daou and Linan, 1998 • Configuration as in previous slide • No thermal expansion • Non-dimensional stretch rate  = (/SL2)1/2 or Damköhlernumber ~ SL2/ ~ -2 SL = steady unstretched SL 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 AME 514 - Spring 2013 - Lecture 9

  14. Edge flames - nonpremixed - theory • Daou et al., 2002 AME 514 - Spring 2013 - Lecture 9

  15. Edge flames - nonpremixed - theory • Daou and Linan, 1998 (lF = (LeFuel - 1)) AME 514 - Spring 2013 - Lecture 9

  16. Edge flames - nonpremixed - theory • Thermal expansion effect (Ruetsch et al., 1995): U/SL ~ (∞/f)1/2 with proportionality constant shown (∞/f)1/2 AME 514 - Spring 2013 - Lecture 9

  17. Edge flames - nonpremixed - with heat loss • Daou et al., 2002 •  = dimensionless heat loss ≈ 7.5/Pe2; Pe  SLd/ (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 AME 514 - Spring 2013 - Lecture 9

  18. Edge flames - premixed - theory • Daou and Linan, 1999 - similar response of Uedge to stretch as nonpremixed flames - also note "spots" AME 514 - Spring 2013 - Lecture 9

  19. Experiments - nonpremixed edge-flames • Cha & Ronney (2006) • Use parallel slots, not misaligned slots • Use jet of N2to "erase"flame, then remove jet to watch advancing edge, or establish flame, then zap with N2 jet to obtain retreating flame AME 514 - Spring 2013 - Lecture 9

  20. Edge flames - nonpremixed - experiment Propagating Retreating "Tailless" AME 514 - Spring 2013 - Lecture 9

  21. Edge flames - nonpremixed - experiment • Behavior very similar to model predictions with heat loss - negative at low or high , positive at intermediate  with Uedge/SL ≈ 0.7(∞/f)1/2 (prediction: ≈ 1.8) • Propagation rates ≈ same for different gaps when scaled by strain rate  except at low  (thus low Vjet) where smaller gap  more heat loss (higher ) AME 514 - Spring 2013 - Lecture 9

  22. Edge flames - nonpremixed - experiment • Dimensional Uedge vs. stretch () can be mapped into scaled Uedge vs. scaled stretch rate () for varying mixtures • Little effect of mixture strength when results scaled by , except at low , where weaker mixture  lower SL  higher  Dimensional Dimensionless Numbers refer to molar N2 dilution when fuel and oxidant streams are mixed in stoichiometric proportions (CH4:O2:N2 = 1:2:N) AME 514 - Spring 2013 - Lecture 9

  23. 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) AME 514 - Spring 2013 - Lecture 9

  24. Edge flames - nonpremixed - experiment • Lewis number effects VERY pronounced - at low Le, MUCH higher Uedge than mixture with same SL (thus ) with Le ≈ 1 • Opposite trend for Le > 1 Low Le (CH4-O2-CO2) High Le (C3H8-O2-N2) (Lefuel = 0.74; LeO2 = 0.86) (Lefuel = 1.86; LeO2 = 1.05) AME 514 - Spring 2013 - Lecture 9

  25. Edge flames - nonpremixed - experiment • Zst= "stoichiometric mixture fraction"= fraction of fuel + inert in a stoichiometric mixture of (fuel+inert) & (O2+inert) (1 > Zst > 0) • High Zst: flame sits near fuel side; low Zst: flame sits near O2 side • …but results not at all symmetric with respect to Zst = 0.5! • Due to shift in O2 concentration profile as Zst 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 O2 side) AME 514 - Spring 2013 - Lecture 9

  26. Edge flames - nonpremixed - experiment • Heat loss limit (low , thus low strain) - relationship between  and  independent of mixture strength, gap, Le, Zst, etc. • Recall high  (high strain) limit depends strongly on Le but almost independent of  (page 21) • Suggests relatively simple picture of non-premixed edge flames AME 514 - Spring 2013 - Lecture 9

  27. Edge flames in low Le mixtures • Diffusive-thermal instability for Lewis number <> 1 • High Le - imaginary growth rates - pulsating, travelling waves • Low Le - real growth rates with maximum value at finite wave number - cellular flames • Low-Le instability well known for premixed flames • Encouraged by heat losses (Joulin & Clavin, 1979), but near extinction conditions (high  or low Da) not required • Discouraged by stretch (Sivashinskyet al., 1981) • Computations (Buckmaster & Short 1999; Daou & Liñán 1999) (premixed) • Le << 1: Instabilities not suppressed (or reappear) at high  • Sequence of behavior as  increased: wrinkled continuous flames, travelling "flame tubes,"isolated tubes • Analogous to "flame balls"- curvature/stretch induced enhancement of flame temperature at low Le • Similar for nonpremixed flames (Thatcher & Dold, 2000) AME 514 - Spring 2013 - Lecture 9

  28. Edge flames in low Lewis number mixtures Moving train of tubes • Computations by Buckmaster & Short (1999) Stationary single tube AME 514 - Spring 2013 - Lecture 9

  29. Edge flames with low Lewis number • Kaiser et al., 2000 • Twin premixed, single premixed, nonpremixed • H2-N2 vs. O2-N2 AME 514 - Spring 2013 - Lecture 9

  30. Edge flames with low Lewis number AME 514 - Spring 2013 - Lecture 9

  31. Results - twin premixed - high Da • Nearly flat (low ) or moderately wrinkled (higher ) flames Moderately wrinkled flame 8.10%H2,  = 120 s-1 (high Da, high ) Nearly flat flame 8.77%H2  = 45 s-1 (high Da, low ) AME 514 - Spring 2013 - Lecture 9

  32. Results - twin premixed - lower Da • Moving tubes emanating from center • Still lower Da - stationary multiple tubes Moving tubes Stationary multiple tubes 6.96%H2,  = 60 s-1 AME 514 - Spring 2013 - Lecture 9

  33. Schematic of tube formation AME 514 - Spring 2013 - Lecture 9

  34. Results - twin premixed - very near limit • Very low Da - stationary single or twin tubes • High s - near wall - lower  - slightly farther from limit • Low s - near center - higher  - slightly farther from limit Stationary twin tube near center (low ) (6.68%H2,  = 60 s-1) Stationary single tube near center (low ) (6.64%H2,  = 60 s-1) Stationary single tube near wall (high ) (6.11%H2,  = 100 s-1) AME 514 - Spring 2013 - Lecture 9

  35. Results - twin premixed - orthogonal view • Verifies tube-like character of flames • Upward curvature due to buoyancy much weaker than flame tube curvature Single tube standard view (6.64%H2,  = 60 s-1) Single tube orthogonal view (6.50%H2,  = 100 s-1) AME 514 - Spring 2013 - Lecture 9

  36. Results - twin premixed - turbulence • High s - sudden transition to "turbulent"flow • Occurs for all flame structures • Rejet = Vw/n ≈ 600 (w = jet width),  ≈ 140 s-1 • Re at transition ≈ independent of gap (d) • Similar results found for inert counterflowing jets • Slightly lower Re for single premixed & nonpremixed (≈ 500) • Prevents examination of lower Da via higher  6.9%H2,  = 158 s-1 AME 514 - Spring 2013 - Lecture 9

  37. Results - non-premixed AME 514 - Spring 2013 - Lecture 9

  38. Results - non-premixed • Flat flames at high Da - Burke-Schumann (infinite-rate chemistry, mixing limited) solution unconditionally stable Fuel/N2 side Fuel/N2 side Air side Air side Normal view Orthogonal view AME 514 - Spring 2013 - Lecture 9

  39. Results - non-premixed • Moving tubes at lower Da - similar to premixed flames • How can non-premixed flames exhibit premixed flame instabilities? Near extinction, fuel or O2"leaks"through flame front, causing partial premixing of fuel and O2, creating quasi-premixed-flame behavior Fuel/N2 side Fuel/N2 side Air side Air side Normal view Orthogonal view AME 514 - Spring 2013 - Lecture 9

  40. Results - non-premixed • Stationary multiple or single tubes at still lower Da Fuel/N2 side Fuel/N2 side Air side Air side 3 tubes 1 tube AME 514 - Spring 2013 - Lecture 9

  41. 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 Modelling3, 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. • 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. AME 514 - Spring 2013 - Lecture 9

  42. References • Kaiser, C., Liu, J.-B. and Ronney, P. D., "Diffusive-thermal Instability of Counterflow Flames at Low Lewis Number,"Paper No. 2000-0576, 38th 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,” 22nd 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., "NonpremixedFlames 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. AME 514 - Spring 2013 - Lecture 9

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