Advanced fundamental topics (3 lectures)

Why study combustion? (0.1 lectures) Quick review of AME 513 concepts

(0.2 lectures) Flammability & extinction limits (1.2 lectures) Ignition (0.5 lectures) Emissions formation & remediation (1 lecture)

2AME 514 - Spring 2015 - Lecture 2

Min

imum

igni

tion

ener

gy (

mJ)

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 applications

3AME 514 - Spring 2015 - Lecture 2

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

4AME 514 - Spring 2015 - Lecture 2

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 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

5AME 514 - Spring 2015 - Lecture 2

Predictions of simple Emin formula Emin ~  3∞

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

6AME 514 - Spring 2015 - Lecture 2

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)

7AME 514 - Spring 2015 - Lecture 2

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)

8AME 514 - Spring 2015 - Lecture 2

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 ~ Rz

3

… but stable for a few carefully (or accidentally) chosen mixtures

9AME 514 - Spring 2015 - Lecture 2

Steady (?!?) solutions How can a spherical flame not propagate???

Space experiments show ~ 1 cmdiameter flame balls possibleMovie: 500 sec elapsed time

10AME 514 - Spring 2015 - Lecture 2

Energy requirement very strongly dependent on Lewis number! 10% increase in Le: 2.5x increase in Emin (PDR); 2.2x (Tromans &

Furzeland)

Lewis number effects

From computations by Tromans and Furzeland, 1986

11AME 514 - Spring 2015 - Lecture 2

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

12AME 514 - Spring 2015 - Lecture 2

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 {Rz

3}

13AME 514 - Spring 2015 - Lecture 2

Dynamic analysis

Joulin (1985)

Radius vs. time Minimum ignition energy vs. ignition duration

14AME 514 - Spring 2015 - Lecture 2

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

Detailed chemical model

1-step chemical model

Sloane & Ronney, 1990 Kono et al., 1976

15AME 514 - Spring 2015 - Lecture 2

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

16AME 514 - Spring 2015 - Lecture 2

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

17AME 514 - Spring 2015 - Lecture 2

References

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. 1483.Frendi, A., Sibulkin, M., "Dependence of Minimum Ignition Energy on Ignition Parameters," Combust.

Sci. Tech. 73, 395-413, 1990.Joulin, G., Combust. Sci. Tech. 43, 99 (1985).Kingdon, R. G., Weinberg, F. J., 16th Symposium (International) on Combustion, Combustion Institute,

1976, p. 747-756. 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. 176-184.Ronney, P. D., Combust. Flame 62, 120 (1985).Sloane, T. M., Ronney, P. D., "A Comparison of Ignition Phenomena Modeled with Detailed and

Simplified Kinetics," Combustion Science and Technology, Vol. 88, pp. 1-13 (1993).Tromans, P. S., Furzeland, R. M., 21st Symposium (International) on Combustion, Combustion Institute,

1986, p. 1891.