Ignition

Advanced fundamental topics  Ignition      

Basic concepts Mathematical theory Dynamics of ignition Effects of the state of the combustible mixture Effects of the characteristics of the ignition source Effects of the flow environment

 More detailed information: http://ronney.usc.edu/Lecture2/AME514F06/AME514.ignition.review.pdf

AME 514 - Fall 2006 - Lecture 2

1

Basic concepts

Minimum ignition energy (mJ)

 Experiments (Lewis & von Elbe, 1961) show that a minimum energy (Emin) (not just minimum T or volume) required to ignite a flame  Emin lowest near stoichiometric (typ. 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 - Fall 2006 - Lecture 2

2

Basic concepts

Unsuccessful ignition

Successful ignition Initial profile

Later Still later

TEMPERATURE

TEMPERATURE

 Emin related to need to create flame kernel with dimension (δ ) large enough that chemical reaction (Ω ) can exceed conductive loss rate (α /δ 2), thus δ > (α /Ω )1/2 ~ α /(α Ω )1/2 ~ α /SL ~ δ  Emin ~ energy contained in volume of gas with T ≈ Tad and radius ≈ δ ≈ 4α /SL T 4 π3 4 π3 (T ) 2k ∞ a d− ∞ ⇒ E ≈ δ ρ C T − T ≈ 0 . 3 δ ρ C T − T ≈ 3 4 α ) ) m in p(a d ∞ ∞ p(a d ∞ ∞ 3 3 3 S L

Initial profile Later

δ

DISTANCE

AME 514 - Fall 2006 - Lecture 2

Still later

SL

DISTANCE

3

Predictions of simple Emin formula  Since α ~ P-1, Emin ~ P-2 if SL is independent of P  Emin ≈ 100,000 times larger in a He-diluted than SF6diluted mixture with same SL, same P (due to α and λ 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

AME 514 - Fall 2006 - Lecture 2

4

Predictions of simple Emin formula

Minimum ignition energy (mJ)

 Emin ~ δ 3ρ ∞  δ hard to measure, but quenching distance (δ q) (min. tube diameter through which flame can propagate) should be ~ δ since Pelim = SL,lim δ q/α ~ δ q/δ ≈ 40 ≈ constant, thus should have 2 Emin ~ δ q3P 10 Hydrogen (lean) Slope = 0.739  Correlation so-so Hydrogen (rich) 10

1

10

0

10

-1

10

-2

10

-3

Methane (lean) Methane (rich) Ethane (lean) Ethane (rich) Propane (lean) Propane (rich) Best fit to all data

Slope = 1

10

-6

10

-5

10

-4

10

-3

10

-2

Pressure * (quenching distance)

AME 514 - Fall 2006 - Lecture 2

10 3

-1

10 3

(atm cm )

5

0

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; ρ D, λ , CP, etc. constant; low Mach #; no body forces  Governing equations for mass, energy & species conservations (y = limiting reactant mass fraction; QR = its heating value)

∂ρ 1 ∂ 2 T = ρ T = c o n s t a n t +2 ( r ρv)=0 ρ ∞ ∞ ∂t r ∂r  ∂ T 1∂ 2 k ∂ 2∂ T − E ρ C + ρ C r v T = r + ρ Q y Z e x p +Q (r,t)   ( ) () p p 2 R 2 ℜ T ∂ t r∂ r r∂ r ∂ r ∂y 1∂ 2 ρ D∂ 2∂ y − E ρ +ρ v2 ( ry) = 2 r −ρ y Ze x p() ℜ T ∂t r∂ r r ∂ r ∂ r

AME 514 - Fall 2006 - Lecture 2

6

More rigorous approach  Non-dimensionalize (note Tad = T∞ + Y∞QR/CP)

T Z e−β v E −β θ≡ ;τ≡tA e ;R≡r ;U≡ ; β ≡ T α∞ ℜ T α∞Z e−β a d a d T

y

k

Q (r,t)

ε≡ ∞;Y≡ ;L e≡ ;Ω ≡ T y∞ ρC ρ∞C Z e−β a d pD pT ∞ leads to, for mass, energy and species conservation

∂Y 1 ∂ 2 1θ1 ∂ 2∂ Y ∂(1/θ) 1 ∂  21  + U R Y = R Y e x p  − + 2 R U ( ) =0 2 2  ∂  ∂τ R∂R L e εR∂ R R ∂τ R ∂R θ  ∂ θ 1 ∂ 2 θ1 ∂ 2∂ θ 1 +U 2 ( Rθ = 2 R +( 1 − ε) Y e x p −β( − 1 + Ω (R ,τ)θ ) θ )  ∂  ∂ τ R∂ R εR∂ R R

(( ))

( )

with boundary conditions

θ ( R , 0 ) = ε ; Y ( R , 0 ) = 1 ; U ( R , 0 ) = 0 f o r a l R

(Initial condition: T = T∞, y = y∞, U = 0 everywhere)

θ ( R , τ ) = ε ; Y ( R , τ ) = 1 ; U ( R , τ ) = 0 a s R → ∞ (At infinite radius, T = T , y = y , ∞

∂θ ∂Y ∂U = = =0a tR =0 a n d a s R ∂R ∂R ∂R

∞

U = 0 for all times)

→ ∞

(Symmetry condition at r = 0 for all times)

AME 514 - Fall 2006 - Lecture 2

7

1 − β − 1

θ

Steady (?!?) solutions  If reaction is confined to a thin zone near r = RZ (large β ) 1−ε Rz R R >Rz : θ= +ε; Y=1− z R T* 1−ε * * L e R R < Rz : θ=θ* =constant ; Y=0

θ≡

T a d

=ε+

T T a d− ∞ o r T =T + ∞ L e L e

2 εL eα Z − δ β1  α β ∞ R = e x p − 1 ; δ = ; S = e x p      z L  2 L e 2θ*  SL β

 This is a flame ball solution - note for Le < > 1, T* > < Tad; for Le = 1, T* = Tad and RZ = δ  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 - Fall 2006 - Lecture 2

8

Steady (?!?) solutions  How can a spherical flame not propagate??? 1.2 Temperature

T*

Fuel concentration T ~ 1/r

T Interior filled with combustion products

Reaction zone

Normalized temperature (T - T ) / (T - T ) f  

C ~ 1-1/r

1 0.8 0.6

Propagating flame (δ/r = 1/10) f

0.4 0.2 0 0.1

Fuel & oxygen diffuse inward

Flame ball

1 10 Radius / Radius of flame

100

Heat & products diffuse outward

Space experiments show ~ 1 cm diameter flame balls possible Movie: 500 sec elapsed time

AME 514 - Fall 2006 - Lecture 2

QuickTime™ and a Video decompressor are needed to see this picture.

9

Lewis number effects  Energy requirement very strongly dependent on Lewis number!

1000 ε = 1/7 β = 10

R 3 / R 3(Le = 1) z z

100 10 1 0.1 0.01 0.001 0

0.5

1

1.5

2

Lewis number

F ro m th e re la tio n

β1  R e x p  −1  z= L e 2θ* 

δ

From computations by Tromans and Furzeland, 1986

AME 514 - Fall 2006 - Lecture 2

10

Lewis number effects   

Ok, so why does min. MIE shift to richer mixtures for higher HCs? Leeffective = α 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 α eff ≈ α air ; also Deff = Dfuel  CH4: DCH4 > α air since MCH4 < MN2&O2 thus LeCH4 < 1, thus Leeff < 1  Higher HCs: Dfuel < α air , thus Leeff > 1 - much higher MIE  Rich mixtures - Leeffective = LeO2  CH4: α CH4 > α air since MCH4 < MN2&O2 , so adding excess CH4 INCREASES Leeff  Higher HCs: α fuel < α air since Mfuel > MN2&O2 , so adding excess fuel DECREASES Leeff  Actually adding excess fuel decreases both α and D, but decreases α more

C o n s t 1 C o n s t 2 C o n s t 3 αeff =αm ;D ~ + ix ~ O 2 M M M m ix m ix O 2 AME 514 - Fall 2006 - Lecture 2

11

Dynamic analysis  RZ is related (but not equal) to an ignition requirement  Joulin (1985) analyzed unsteady equations for Le < 1

σ q( σ) dχ(s) d s χσ ( )ln(χσ ( ))+ =χσ ( )∫ 2 σ σ−s 0 d  θ* 2 2 ( ) Θ R(σ) L e  αt  q≡ ;χ≡ ;σ≡4π 2 * 2   R 1 − ε R 1 − L e 4πλRzTad ( θ) z   z

(χ , σ and q are the dimensionless radius, time and heat input) and found at the optimal ignition duration 2

1−ε1− L e 3 Em ≈ 1 4 β ρ C T − T R     ( ) in a d p a d ∞ z  ε  θ*L e 

which has the expected form Emin ~ {energy per unit volume} x {volume of minimal flame kernel} ~ {ρ adCp(Tad - T∞)} x {Rz3} AME 514 - Fall 2006 - Lecture 2

12

Dynamic analysis  Joulin (1985)

Radius vs. time

Minimum ignition energy vs. ignition

duration AME 514 - Fall 2006 - Lecture 2

13

Effect of spark gap & duration  Expect “optimal” ignition duration ~ ignition kernel time scale ~ RZ2/α  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 514 - Fall 2006 - Lecture 2

14

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

AME 514 - Fall 2006 - Lecture 2

15

Effect of ignition source

Minimum ignition energy (mJ)

 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?

10

1

0.1

ps laser ns laser Lewis & von Elbe Sloane & Ronney Ronney Kingdon & Weinberg

4

5

6

7

8

9

10

11

12

Mole percent CH4 in air Lim et al., 1996 AME 514 - Fall 2006 - Lecture 2

16

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. 747.9924. 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 Modelled 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.

AME 514 - Fall 2006 - Lecture 2

17