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)
Basic concepts
Minimum ignition energy (mJ)
 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
AME 514 - Spring 2015 - Lecture 2
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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
k T -T¥ )
4p 3
4p 3
2 ¥ ( ad
Þ Emin »
d rC p (Tad -T¥ ) » 0.3 d r¥C p (Tad -T¥ ) » 34a¥
3
3
S L3
AME 514 - Spring 2015 - Lecture 2
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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
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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
AME 514 - Spring 2015 - Lecture 2
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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)
¶r 1 ¶ 2
rT = r¥T¥ = constant
+ 2 ( r rv ) = 0
¶t r ¶r
¶T
1 ¶ 2
k ¶ æ 2 ¶T ö
rC p + rC p 2 ( r vT ) = 2 ç r
÷ + rQR yZ exp
¶t
r ¶r
r ¶r è ¶r ø
¶y
1 ¶ 2
rD ¶ æ 2 ¶y ö
-E
r + rv 2 ( r y ) = 2 ç r
÷ - ryZ exp ÂT
¶t
r ¶r
r ¶r è ¶r ø
( ) + Q(r,t)
-E
ÂT
( )
AME 514 - Spring 2015 - Lecture 2
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More rigorous approach
 Non-dimensionalize (note Tad = T∞ + Y∞QR/CP)
T
e-b Z
v
E
-b
qº
;t º te Z;R º r
;U º
;b º
-b
Tad
a¥
ÂTad
Za ¥e
leads to, for mass, energy and species conservation
¶(1/q ) 1 ¶ æ 2 1 ö
+ 2 ç R U÷ = 0
¶t
R ¶R è q ø
¶Y
1 ¶ 2
1 q 1 ¶ æ 2 ¶Y ö
+U 2
R
Y
=
çR
÷ -Yexp - b (q1 -1)
(
)
2
¶t
R ¶R
Le e R ¶R è ¶R ø
(
with boundary conditions
q(R,0) = e;Y(R,0) =1;U(R,0) = 0 for all R
(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 514 - Spring 2015 - Lecture 2
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)
Steady (?!?) solutions
 If reaction is confined to a thin zone near r = RZ (large )
1- e Rz
R
R > Rz : q =
+ e; Y = 1- z R
T*
1- e
T -T
*
q º
=e+
or T * = T¥ + ad ¥
Le R
Tad
Le
Le
R < Rz : q = q * = constant; Y = 0
æ b æ 1 öö
æ -b ö
2eLea¥ Z
d
a
Rz = expç ç * -1÷÷;d = ;SL =
expç ÷
øø
è 2ø
Le è 2 è q
SL
b
 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 514 - Spring 2015 - Lecture 2
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Steady (?!?) solutions
 How can a spherical flame not propagate???
Space experiments show ~ 1 cm
diameter flame balls possible
Movie: 500 sec elapsed time
AME 514 - Spring 2015 - Lecture 2
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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)
From the relation Rz =
æ b æ 1 öö
expç ç * -1÷÷
øø
Le è 2 è q
d
From computations by Tromans
and Furzeland, 1986
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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
a eff = a mix
Const1
Const 2 Const 3
~
;DO2 ~
+
M mix
M mix
MO2
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Dynamic analysis
 RZ is related (but not equal) to an ignition requirement
 Joulin (1985) analyzed unsteady equations for Le < 1
s
q(s )
dc (s) ds
c (s ) ln( c (s )) +
= c (s ) ò
2
ds s - s
0
æ * 2
ö2
q )
(
R(s )
Le ÷ at
Q
ç
cº
;s º 4 p
2 ;q º
* 2
ç 1 - e 1 - Le ÷ Rz
Rz
4 plRzTad (q )
è
ø
(,  and q are the dimensionless radius, time and heat input)
and found at the optimal ignition duration
E min
2
æ
ö
æ1- e ö 1- Le
3
» 14 bç
֍ *
÷ rad C p (Tad - T¥ ) Rz
è e øè q Le ø
which has the expected form
Emin ~ {energy per unit volume} x {volume of minimal flame kernel} ~
{adCp(Tad - T∞)} x {Rz3}
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Dynamic analysis
 Joulin (1985)
Radius vs. time
Minimum ignition energy
vs. ignition duration
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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
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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
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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
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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.
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