AME 514 Applications of Combustion Lecture 9: Nonpremixed flames, edge flames

2 AME Spring 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)

3 AME Spring 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

4 AME Spring Lecture 9

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)

6 AME Spring 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

7 AME Spring Lecture 9 Scaling of turbulent jets dodododo UoUoUoUo r jet (x) x u(x)_entrainment m(x).≈12˚

8 AME Spring Lecture 9 Scaling of turbulent jets  Combine

9 AME Spring 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

10 AME Spring 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)

11 AME Spring 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!

12 AME Spring Lecture 9 EDGE FLAMES - motivation  Reference: Buckmaster, J., “Edge flames,” Prog. Energy Combust. Sci. 28, (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?

13 AME Spring 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

14 AME Spring 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

15 AME Spring Lecture 9 Edge flames - nonpremixed - theory  Daou et al., 2002

16 AME Spring Lecture 9  Daou and Linan, 1998 (l F =  (Le Fuel - 1)) Edge flames - nonpremixed - theory

17 AME Spring 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

18 AME Spring 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

19 AME Spring Lecture 9  Daou and Linan, similar response of U edge to stretch as nonpremixed flames - also note "spots" Edge flames - premixed - theory

20 AME Spring 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

21 AME Spring Lecture 9 Edge flames - nonpremixed - experiment Retreating "Tailless" Propagating

22 AME Spring 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  )

23 AME Spring 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)

24 AME Spring 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)

25 AME Spring 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)

26 AME Spring 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)

27 AME Spring 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

28 AME Spring 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

29 AME Spring Lecture 9 Edge flames – twin premixed - images Clayton, Cha, Ronney (2015?)   Lewis number effects very evident – curvature effects on leading edge

30 AME Spring 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

31 AME Spring 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

32 AME Spring 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

33 AME Spring Lecture 9 Edge flames – single premixed - images Clayton, Cha, Ronney (2015?)

34 AME Spring 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

35 AME Spring Lecture 9 References  Buckmaster, J. D., Combust. Sci. Tech. 115, 41 (1996).  Buckmaster, J., "Edge flames," Prog. Energy Combust. Sci. 28, (2002).  Buckmaster, J. D. and Short, M. (1999). Cellular instabilities, sub-limit structures and edge-flames in premixed counterflows. Combust. Theory Modelling 3,  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 (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  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,  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  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,

36 AME Spring Lecture 9 References  Kaiser, C., Liu, J.-B. and Ronney, P. D., "Diffusive-thermal Instability of Counterflow Flames at Low Lewis Number," Paper No , 38 th AIAA Aerospace Sciences Meeting, Reno, NV, January 11-14,  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  Liu, J.-B. and Ronney, P. D., "Premixed Edge-Flames in Spatially Varying Straining Flows," Combustion Science and Technology, Vol. 144, pp (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,  Shay, M. L. and Ronney, P. D., "Nonpremixed Flames in Spatially-Varying Straining Flows," Combustion and Flame, Vol. 112, pp (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,  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,  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