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)

2 AME Spring Lecture 2 Minimum ignition energy (mJ) Basic concepts  Experiments (Lewis & von Elbe, 1987) show that a minimum energy (E min ) (not just minimum T or volume) required for ignition  E min lowest near stoichiometric (typically 0.2 mJ) but minimum shifts to richer mixtures for higher HCs (why? Stay tuned…)  Prediction of E min relevant to energy conversion and fire safety applications

3 AME Spring Lecture 2 Basic concepts  E min related to need to create flame kernel with dimension (  ) large enough that chemical reaction (  ) can exceed conductive loss rate (  /  2 ), thus  > (  /  ) 1/2 ~  /(  ) 1/2 ~  /S L ~   E min ~ energy contained in volume of gas with T ≈ T ad and radius ≈  ≈ 4  /S L

4 AME Spring Lecture 2 Predictions of simple E min formula  Since  ~ P -1, E min ~ P -2 if S L is independent of P  E min ≈ 100,000 times larger in a He-diluted than SF 6 -diluted mixture with same S L, same P (due to  and k [thermal conductivity] differences)  Stoichiometric CH 4 1 atm: predicted E min ≈ mJ ≈ 30x times lower than experiment (due to chemical kinetics, heat losses, shock losses …)  … but need something more (Lewis number effects):  10% H 2 -air (S L ≈ 10 cm/sec): predicted E min ≈ 0.3 mJ = 2.5 times higher than experiments  Lean CH 4 -air (S L ≈ 5 cm/sec): E min ≈ 5 mJ compared to ≈ 5000mJ for lean C 3 H 8 -air with same S L - but prediction is same for both

5 AME Spring Lecture 2 Predictions of simple E min formula  E min ~  3  ∞   hard to measure, but quenching distance (  q ) (min. tube diameter through which flame can propagate) should be ~  since Pe lim = S L,lim  q /  ~  q /  ≈ 40 ≈ constant, thus should have E min ~  q 3 P  Correlation so-so

6 AME Spring 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, C P, etc. constant; low Mach #; no body forces  Governing equations for mass, energy & species conservations (y = limiting reactant mass fraction; Q R = its heating value)

7 AME Spring Lecture 2 More rigorous approach  Non-dimensionalize (note T ad = T ∞ + Y ∞ Q R /C P ) 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)

8 AME Spring Lecture 2 Steady (?!?) solutions  If reaction is confined to a thin zone near r = R Z (large  )  This is a flame ball solution - note for Le 1, T * > < T ad ; for Le = 1, T * = T ad and R Z =   Generally unstable  R < R Z : shrinks and extinguishes  R > R Z : expands and develops into steady flame  R Z related to requirement for initiation of steady flame - expect E min ~ R z 3  … but stable for a few carefully (or accidentally) chosen mixtures

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

10 AME Spring Lecture 2  Energy requirement very strongly dependent on Lewis number!  10% increase in Le: 2.5x increase in E min (PDR); 2.2x (Tromans & Furzeland) Lewis number effects From computations by Tromans and Furzeland, 1986

11 AME Spring Lecture 2 Lewis number effects  Ok, so why does min. MIE shift to richer mixtures for higher HCs?  Le effective =  effective /D effective  D eff = D of stoichiometrically limiting reactant, thus for lean mixtures D eff = D fuel ; rich mixtures D eff = D O2  Lean mixtures - Le effective = Le fuel  Mostly air, so  eff ≈  air ; also D eff = D fuel  CH 4 : D CH4 >  air since M CH4 < M N2&O2 thus Le CH4 < 1, thus Le eff < 1  Higher HCs: D fuel 1 - much higher MIE  Rich mixtures - Le effective = Le O2  CH 4 :  CH4 >  air since M CH4 < M N2&O2, so adding excess CH 4 INCREASES Le eff  Higher HCs:  fuel M N2&O2, so adding excess fuel DECREASES Le eff  Actually adding excess fuel decreases both  and D, but decreases  more

12 AME Spring Lecture 2 Dynamic analysis  R Z 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 E min ~ {energy per unit volume} x {volume of minimal flame kernel} ~ {  ad C p (T ad - T ∞ )} x {R z 3 }

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

14 AME Spring Lecture 2 Effect of spark gap & duration  Expect “optimal” ignition duration ~ ignition kernel time scale ~ R Z 2 /   Duration too long - energy wasted after kernel has formed and propagated away - E min ~ t 1  Duration too short - larger shock losses, larger heat losses to electrodes due to high T kernel  Expect “optimal” ignition kernel size ~ kernel length scale ~ R Z  Size too large - energy wasted in too large volume - E min ~ R 3  Size too small - larger heat losses to electrodes Detailed chemical model 1-step chemical model Sloane & Ronney, 1990 Kono et al., 1976

15 AME Spring 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 E min Kono et al., 1984 DeSoete, 1984

16 AME Spring 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

17 AME Spring Lecture 2 References De Soete, G. G., 20th Symposium (International) on Combustion, Combustion Institute, 1984, p 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, , Joulin, G., Combust. Sci. Tech. 43, 99 (1985). 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 Kono, M., Hatori, K., Iinuma, K., 20th Symposium (International) on Combustion, Combustion Institute, 1984, p Lewis, B., von Elbe, G., Combustion, Flames, and Explosions of Gases, 3rd ed., Academic Press, 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., 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 (1993). Tromans, P. S., Furzeland, R. M., 21st Symposium (International) on Combustion, Combustion Institute, 1986, p