1. Advanced fundamental topics
Flammability & extinction limits
Description of flammability limits
Chemical kinetics of limits
Mechanisms of limits
Buoyancy effects - upward & downward
Conduction heat loss to tube walls
Radiation heat loss
Aerodynamic stretch
Chemical fire suppressants
Ignition limits
Basic mechanisms
Theory
Lewis number effects
Influence of geometry, flow, ignition source
AME Spring Lecture 2

2. Flammability and extinction limits
Reference: Ju, Y., Maruta, K., Niioka, T., "Combustion Limits," Applied Mechanics Reviews, Vol. 53, pp (2001)
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 Spring Lecture 2

3. 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 Spring Lecture 2

4. Premixed-gas flames – flammability limits
2 limit mechanisms, (1) & (2), yield similar fuel % and Tad at limit but very different SL,lim
AME Spring Lecture 2

5. Flammability limits in vertical tubes
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
Upward propagation Downward propagation
AME Spring Lecture 2

6. Chemical kinetics of limits
Lean hydrocarbon-air flames: main branching reaction (promotes combustion) is
H + O2  OH + O; d[O2]/dt = [H][O2]T-0.8e-16500/RT
[ ]: mole/cm3; T: K; R: cal/mole-K; t: sec
Depends on P2 since [ ] ~ P, strongly dependent on T
Why important? Only energetically viable way to break O=O bond (120 kcal/mole), even though [H] is small
Main H consumption reaction
H + O2 + M  HO2 + M; {M = any molecule}
d[O2]/dt = [H][O2][M]T0e+1000/RT for M = N2
(higher rate for CO2 and especially H2O)
Depends on P3, nearly independent of T
Why important? Inhibits combustion by replacing H with much less active HO2
Branching or inhibition may be faster depending on T and P
AME Spring Lecture 2

7. Chemical kinetics of limits
Rates equal ("crossover") when
[M] = 101.5T-0.8e-17500/RT
Ideal gas law: P = [M]RT thus
P = 103.4T0.2e-17500/RT (P in atm)
 crossover at 950K for 1 atm, higher T for higher P
…but this only indicates that chemical mechanism may change and perhaps overall W drop rapidly below some T
Computations show no limits without losses – no purely chemical criterion (Lakshmisha et al., 1990; Giovangigli & Smooke, 1992) - for steady planar adiabatic flames, burning velocity 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 ….
AME Spring Lecture 2

8. Chemical kinetics of limits
Ju, Masuya, Ronney (1998)
Ju et al., 1998
AME Spring Lecture 2

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 Spring Lecture 2

10. Aerodynamic effects on premixed flames
Strong stretch ( ≥ w ~ SL2/ or Karlovitz number Ka  /SL2 ≥ 1) extinguishes flames
Moderate stretch strengthens flames for Le < 1
Buckmaster &
Mikolaitis, 1982a (Ze = b in my notation), cold reactants against adiabatic products
SL/SL(unstrained, adiabatic flame)
ln(Ka)
AME Spring Lecture 2

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 Spring Lecture 2

12. TIME SCALES - premixed-gas flames
See Ronney (1998)
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 time scale
trad ≈ Tad/(dT/dt) ≈ Tad/(L/rCp) (L = radiative heat 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 Þ tvis ≈ (n/g2)1/3 (n = viscosity [typ cm2/s])
AME Spring Lecture 2

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)1/2 Þ turbulent flow at 1g for d > 10 cm
AME Spring Lecture 2

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 reaction rate w, thus exponentially small SL (could also say heat generation occurs only in /b region whereas loss occurs over  region)
AME Spring Lecture 2

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 (USE Pelim ≈ 40 NOT 9) 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 Spring Lecture 2

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 Spring Lecture 2

17. Flammability limits due to losses
Downward propagation – sinking layer of cooling gases near wall outruns & "suffocates" flame (Jarosinsky et al., 1982)
tchem ≈ tvis Þ SL,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 Spring Lecture 2

18. Flammability limits in vertical tubes
Upward propagation Downward propagation
AME Spring Lecture 2

19. Flammability limits in tubes
Upward propagation - Wang & Ronney, 1993
AME Spring Lecture 2

20. Flammability limits in tubes
Downward propagation - Wang & Ronney, 1993
AME Spring Lecture 2

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 Spring Lecture 2

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 Spring Lecture 2

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 Spring Lecture 2

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 Spring Lecture 2

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 Spring Lecture 2

26. Stretched flames - spherical
Theory (Ronney & Sivashinsky, 1989)
Experiment
(Ronney, 1985)
AME Spring Lecture 2

27. Stretched counterflow or stagnation flames
Mass + momentum conservation, 2D, const. density ()
(ux, uy = 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 geometry:
Very simple flow characterized by a single parameter , easily implemented experimentally using counter-flowing round jets…
AME Spring Lecture 2

28. Stretched counterflow or stagnation flames
S = dux/dx – flame located where ux = SL
Increased stretch pushes flame closer to stagnation plane - decreased volume of radiant products
Similar Le effects as curved flames
Homework problem – determine effect of stretch rate S on SL, and extinction limit in terms of Damköhler number Z/S
AME Spring Lecture 2

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 Spring Lecture 2

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 Spring Lecture 2

31. Chemical fire suppressants
Key to suppression is removal of H atoms
H + HBr  H2 + Br
H + Br2  HBr + Br
Br + Br + M  Br2 + M
H + H  H2
Why Br and not Cl or F? HCl and HF too stable, 1st reaction too slow
HBr is a corrosive liquid, not convenient - use CF3Br (Halon 1301) - Br easily removed, remaining CF3 very stable, high CP to soak up heat
Problem - CF3Br very powerful ozone depleter - banned!
Alternatives not very good; best ozone-friendly chemical alternative is probably CF3CH2CF3 or CF3H
Other alternatives (e.g. water mist) also being considered
AME Spring Lecture 2

32. Chemical fire suppressants
AME Spring Lecture 2

33. Flame ignition - basic concepts
Experiments (Lewis & von Elbe, 1987) show that a minimum energy (Emin) (not just minimum T or volume) required for ignition
Emin lowest near stoichiometric (typically 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
Lewis & von Elbe, 1987
Minimum ignition energy (mJ)
AME Spring Lecture 2

34. Flame ignition - basic concepts
Emin related to need to create flame kernel with dimension () large enough that chemical reaction (w) 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 Spring Lecture 2

35. 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 k [thermal conductivity] differences)
Stoichiometric 1 atm: predicted Emin ≈ 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 Spring Lecture 2

36. Predictions of simple Emin formula
 hard to measure, but quenching distance (q) (min. tube diameter through which flame can propagate) should be ~  since Pelim = SL,lim q/ ~ q/ ≈ 40 ≈ constant, thus should have Emin ~  q3P
Correlation so-so
AME Spring Lecture 2

37. More rigorous approach
Assumptions: 1D spherical; ideal gases; adiabatic (except for ignition source Q(r,t)); 1 limiting reactant (e.g. very lean or rich); 1-step overall reaction; D, k, CP, etc. constant; low Mach #; no body forces
Governing equations for mass, energy & species conservations (y = limiting reactant mass fraction; QR = its heating value)
AME Spring Lecture 2

38. More rigorous approach
Non-dimensionalize (note Tad = T∞ + Y∞QR/CP)
leads to, for mass, energy and species conservation
with boundary conditions
(Initial condition: T = T∞, y = y∞,
U = 0 everywhere)
(At infinite radius, T = T∞, y = y∞,
U = 0 for all times)
(Symmetry condition at r = 0 for all times)
AME Spring Lecture 2

39. Steady (?!?) solutions
If reaction is confined to a thin zone near r = RZ (large )
This is a flame ball solution - note for Le < > 1, T* > < Tad; for Le = 1, T* = Tad and RZ = 
Generally unstable
R < RZ: shrinks and extinguishes
R > RZ: expands and develops into steady flame
RZ related to requirement for initiation of steady flame - expect Emin ~ Rz3
… but stable for a few carefully (or accidentally) chosen mixtures
AME Spring Lecture 2

40. Steady (?!?) solutions AME 514 - Spring 2017 - Lecture 2
How can a spherical flame not propagate???
Space experiments show ~ 1 cm
diameter flame balls possible
Movie: 500 sec elapsed time
AME Spring Lecture 2

41. Computations by Tromans and Furzeland, 1986
Lewis number effects
Energy requirement very strongly dependent on Lewis number!
10% increase in Le: 2.5x increase in Emin (PDR); 2.2x (Tromans & Furzeland)
Computations by Tromans and Furzeland, 1986
AME Spring Lecture 2

42. Lewis number effects
Why does minimum 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 Spring Lecture 2

43. Dynamic analysis
RZ is related (but not equal) to an ignition requirement
Joulin (1985) analyzed unsteady equations for Le < 1
(,  and q are the dimensionless radius, time and heat input)
and found at the optimal ignition duration
which has the expected form
Emin ~ {energy per unit volume} x {volume of minimal flame kernel} ~ {adCp(Tad - T∞)} x {Rz3}
AME Spring Lecture 2

44. Dynamic analysis Joulin (1985) Radius vs. time Minimum ignition energy
vs. ignition duration
AME Spring Lecture 2

45. 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 Spring Lecture 2

46. Effect of flow environment
Mean flow or random flow (i.e. turbulence) (e.g. inside IC engine or gas turbine) increases stretch, thus Emin
Ballal and Lefebrve, 1975
AME Spring Lecture 2

47. 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 Spring Lecture 2

48. References
Abbud-Madrid, A., Ronney, P. D., "Effects of Radiative and Diffusive Transport Processes on Premixed Flames Near Flammability Limits," Twenty Third Symposium (International) on Combustion, Combustion Institute, 1990, pp
Abbud-Madrid, A., Ronney, P. D., "Premixed Flame Propagation in an Optically-Thick Gas," AIAA Journal, Vol. 31, pp (1993).
Ballal, D. R., Lefebvre, A. H., “The influence of flow parameters on minimum ignition energy and quenching distance,” 15th Symposium (International) on Combustion, Combustion Institute, 1975, pp
Buckmaster, J. D. (1976). The quenching of deflagration waves, Combust. Flame 26,
Buckmaster, J. D., Mikolaitis, D. (1982a). The premixed flame in a counterflow, Combust. Flame 47,
Buckmaster, J. D., Mikolaitis, D. (1982b). A flammability-limit model upward propagation through lean methan-air mixtures in a standard flammability tube. Combust. Flame 45, pp
De Soete, G. G., 20th Symposium (International) on Combustion, Combustion Institute, 1984, p. 161.
Dixon-Lewis, G., Shepard, I. G., 15th Symposium (International) on Combustion, Combustion Institute, 1974, p
Frendi, A., Sibulkin, M., "Dependence of Minimum Ignition Energy on Ignition Parameters," Combust. Sci. Tech. 73, , 1990.
Joulin, G., Combust. Sci. Tech. 43, 99 (1985).
AME Spring Lecture 2

49. References
Giovangigli, V. and Smooke, M. (1992). Application of Continuation Methods to Plane Premixed Laminar Flames, Combust. Sci. Tech. 87,
Guo, H., Ju, Y., Maruta, K., Niioka, T., Liu, F., Combust. Flame 109: (1997).
Jarosinsky, J. (1983). Flame quenching by a cold wall, Combust. Flame 50, 167.
Jarosinsky, J., Strehlow, R. A., Azarbarzin, A. (1982). The mechanisms of lean limit extinguishment of an upward and downward propagating flame in a standard flammability tube, Proc. Combust. Inst. 19,
Joulin, G., Clavin, P. (1976). Analyse asymptotique des conditions d'extinction des flammes laminaries, Acta Astronautica 3, 223.
Ju, Y., Masuya, G. and Ronney, P. D., "Effects of Radiative Emission and Absorption on the Propagation and Extinction of Premixed Gas Flames" Twenty-Seventh International Symposium on Combustion, Combustion Institute, 1998, pp
Ju, Y., Guo, H., Liu, F., Maruta, K. (1999). Effects of the Lewis number and radiative heat loss on the bifurcation of extinction of CH4-O2-N2-He flames, J. Fluid Mech. 379,
Krivulin, V. N., Kudryavtsev, E. A., Baratov, A. N., Badalyan, A. M., Babkin, V. S. (1981). Effect of acceleration on the limits of propagation of homogeneous gas mixtures, Combust. Expl. Shock Waves (Engl. Transl.) 17,
Lakshmisha, K. N., Paul, P. J., Mukunda, H. S. (1990). On the flammability limit and heat loss in flames with detailed chemistry, Proc. Combust. Inst. 23,
Levy, A. (1965). An optical study of flammability limits, Proc. Roy. Soc. (London) A283, 134.
AME Spring Lecture 2

50. References
Kingdon, R. G., Weinberg, F. J., 16th Symposium (International) on Combustion, Combustion Institute, 1976, p
Kono, M., Kumagai, S., Sakai, T., 16th Symposium (International) on Combustion, Combustion Institute, 1976, p. 757.
Kono, M., Hatori, K., Iinuma, K., 20th Symposium (International) on Combustion, Combustion Institute, 1984, p. 133.
Lewis, B., von Elbe, G., Combustion, Flames, and Explosions of Gases, 3rd ed., Academic Press, 1987.
Lim, E. H., McIlroy, A., Ronney, P. D., Syage, J. A., in: Transport Phenomena in Combustion (S. H. Chan, Ed.), Taylor and Francis, 1996, pp
Ronney, P.D., "Effect of Gravity on Laminar Premixed Gas Combustion II: Ignition and Extinction Phenomena," Combustion and Flame, Vol. 62, pp (1985).
Ronney, P.D., "On the Mechanisms of Flame Propagation Limits and Extinction Processes at Microgravity," Twenty Second Symposium (International) on Combustion, Combustion Institute, 1988, pp
Ronney, P. D., "Understanding Combustion Processes Through Microgravity Research," Twenty-Seventh International Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp
Ronney, P.D., Sivashinsky, G.I., "A Theoretical Study of Propagation and Extinction of Nonsteady Spherical Flame Fronts," SIAM Journal on Applied Mathematics, Vol. 49, pp (1989).
Sloane, T. M., Ronney, P. D., "A Comparison of Ignition Phenomena Modeled with Detailed and Simplified Kinetics," Combustion Science and Technology, Vol. 88, pp (1993).
AME Spring Lecture 2

51. References
Tromans, P. S., Furzeland, R. M., 21st Symposium (International) on Combustion, Combustion Institute, 1986, p
Wang, Q., Ronney, P. D. (1993). Mechanisms of flame propagation limits in vertical tubes, Paper no. 45, Spring Technical Meeting, Combustion Institute, Eastern/Central States Section, March 15-17, 1993, New Orleans, LA.
AME Spring Lecture 2