Chi Nu 21

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AME 514 - Fall 2006 - Lecture 2AME 514 - Fall 2006 - Lecture 2 11

Advanced fundamental topics Advanced fundamental topics IgnitionIgnition

Basic conceptsBasic concepts

Mathematical theoryMathematical theoryDynamics of ignitionDynamics of ignitionEffects of the state of the combustible mixtureEffects of the state of the combustible mixtureEffects of the characteristics of the ignition sourceEffects of the characteristics of the ignition sourceEffects of the flow environmentEffects of the flow environment

More detailed information:More detailed information:

http://ronney.usc.edu/Lecture2/AME514F06/AME514.ignition.review.pdfhttp://ronney.usc.edu/Lecture2/AME514F06/AME514.ignition.review.pdf

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n m u m g n o n e n e r g y m

n m u m g n o n e n e r g y m

Basic concepts Basic concepts

Experiments (Lewis & von Elbe, 1961) show that a minimum energyExperiments (Lewis & von Elbe, 1961) show that a minimum energy(E(E minmin) (not just minimum T or volume) required to ignite a flame) (not just minimum T or volume) required to ignite a flame

EE minminlowest near stoichiometric (typ. 0.2 mJ) but minimum shifts tolowest near stoichiometric (typ. 0.2 mJ) but minimum shifts toricher mixtures for higher HCs (why? Stay tuned)richer mixtures for higher HCs (why? Stay tuned)Prediction of EPrediction of E minminrelevant to energy conversion and fire safetyrelevant to energy conversion and fire safetyapplicationsapplications

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DISTANCE

T E M

P E R A T U R E Initial profile

Later

Still later

Unsuccessfulignition

DISTANCE

T E M

P E R A T U R E Initial profile

Later

Still later

SL

Successfulignition

Basic concepts Basic concepts

EE minminrelated to need to create flame kernel with dimension (related to need to create flame kernel with dimension ( ) large) largeenough that chemical reaction (enough that chemical reaction ( ) can exceed conductive loss) can exceed conductive loss

rate (rate ( // 22), thus), thus > (> ( // ))1/21/2~~ /(/( ))1/21/2~~ /S/S LL ~~ EE minmin~ energy contained in volume of gas with T T ~ energy contained in volume of gas with T T adad and radius and radius 4 4 /S/S LL E min

4 3

3 C p T ad T ( ) 0.3 4 3 3 C p T ad T ( ) 34 2 k T ad T ( )S L3

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Predictions of simple E Predictions of simple E min min formula formula

SinceSince ~ P~ P-1-1, E, E minmin ~ P~ P-2-2 if Sif S LL is independent of Pis independent of PEE

minmin100,000 times larger in a He-diluted than SF 100,000 times larger in a He-diluted than SF

66--

diluted mixture with same Sdiluted mixture with same S LL, same P (due to, same P (due to andand differences)differences)Stoichiometric CHStoichiometric CH 44-air @ 1 atm: predicted E-air @ 1 atm: predicted E minmin 0.010 mJ 0.010 mJ

30x times 30x times lowerlower than experiment (due to chemicalthan experiment (due to chemicalkinetics, heat losses, shock losses )kinetics, heat losses, shock losses ) but need something more (but need something more ( Lewis number effectsLewis number effects ):):

10% H10% H 22-air (S-air (S LL 10 cm/sec): predicted E 10 cm/sec): predicted E minmin 0.3 mJ = 2.5 times 0.3 mJ = 2.5 timeshigherhigher than experimentsthan experiments

Lean CHLean CH 44-air (S-air (S LL 5 cm/sec): E 5 cm/sec): E minmin 5 mJ compared to 5000mJ 5 mJ compared to 5000mJ for lean Cfor lean C 33HH88-air with same S-air with same S LL - but prediction is- but prediction is same for bothsame for both

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Predictions of simple E Predictions of simple E min min formula formula EE minmin~~ 33 hard to measure, but quenching distance (hard to measure, but quenching distance ( qq) (min. tube) (min. tube

diameter through which flame can propagate) should be ~diameter through which flame can propagate) should be ~ since Pesince Pe limlim= S= S L,limL,lim qq// ~~ qq// 40 constant, thus should have 40 constant, thus should have EE minmin~~ qq33PPCorrelation so-soCorrelation so-so

10 -3

10 -2

10 -1

10 0

10 1

10 2

10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0

Hydrogen (lean)Hydrogen (rich)Methane (lean)Methane (rich)

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

M i n i m u m

i g n

i t i o n e n e r g y

( m J )

Pressure * (quenching distance) 3 (atm cm 3)

Slope = 1

Slope = 0.739

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More rigorous approach More rigorous approach Assumptions: 1D spherical; ideal gases; adiabatic (except forAssumptions: 1D spherical; ideal gases; adiabatic (except forignition source Q(r,t)); 1 limiting reactant (e.g. very lean or rich);ignition source Q(r,t)); 1 limiting reactant (e.g. very lean or rich);1-step overall reaction;1-step overall reaction; D,D, , C, C

PP, etc. constant; low Mach #; no, etc. constant; low Mach #; no

body forcesbody forcesGoverning equations for mass, energy & species conservationsGoverning equations for mass, energy & species conservations(y = limiting reactant mass fraction; Q(y = limiting reactant mass fraction; Q RR = its heating value)= its heating value)

t +

1

r 2 r r

2

v( ) =0 C p

T t

+ C p1

r 2 r

r 2vT ( ) = k r 2 r

r 2 T r

+ Q R yZ exp

E T

() +Q(r , t )

y t + v

1

r 2 r r

2

y( ) = Dr 2

r r

2 y r

yZ exp

E T

()

T =

T

= co nst ant

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More rigorous approach More rigorous approach Non-dimensionalize (note TNon-dimensionalize (note T adad = T= T + Y+ Y QQ RR/C/C PP))

leads to, for mass, energy and species conservationleads to, for mass, energy and species conservation

with boundary conditionswith boundary conditions(Initial condition: T = T(Initial condition: T = T , y = y, y = y ,,

U = 0 everywhere)U = 0 everywhere)

(At infinite radius, T = T(At infinite radius, T = T , y = y, y = y ,,U = 0 for all times)U = 0 for all times)

(Symmetry condition at r = 0 for all times)(Symmetry condition at r = 0 for all times)

T

T ad ; tAe ; R r Ze

;U v

Ze

; E

T ad

T T ad

;Y y y

; Le k C p D

; Q( r , t ) C pT Ze

1/ ( ) +

1

R2

R R2

1

U

=

0

+U 1 R2

R

R2 ( ) = 1

R2

R R2

R

+ 1 ( )Yexp

1

1( )( ) + ( R, )

Y

+U 1

R2

R R2Y

( )= 1

Le

1

R2

R R2

Y

R

Yexp 1

1

( )(

( R ,0) = ;Y ( R ,0) = 1; U ( R ,0) = 0f orallR

( R , ) = ;Y ( R , ) = 1; U ( R , ) = 0asR

R

= Y R

= U R

=0at R =0andasR

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Steady (?!?) solutions Steady (?!?) solutions If reaction is confined to a thin zone near r = RIf reaction is confined to a thin zone near r = R ZZ (large(large ))

This is aThis is a flame ball flame ball solution - note for Le < > 1, Tsolution - note for Le < > 1, T ** > < T> < T adad; for Le = 1,; for Le = 1,TT** = T= T adad and Rand R ZZ == Generally unstableGenerally unstable

R < RR < R ZZ: shrinks and extinguishes: shrinks and extinguishesR > RR > R ZZ: expands and develops into steady flame: expands and develops into steady flameRR ZZ related to requirement for initiation of steady flame - expect Erelated to requirement for initiation of steady flame - expect E minmin~~RR zz33

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

R > R z : =1

Le

R z R

+ ; Y = 1 R z

R

R < R z : = * = const ant ; Y = 0

* T *

T ad = +1

Le

or T * =T +T ad T

Le

R z =

Leexp

2

1

*1

; = S L

;S L =2 Le Z

exp

2

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

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

Temperature

Fuel concentration

T ~ 1/r

Reaction zone

Interior filledwith combustion

products

Fuel & oxygendiffuse inward

Heat &products

diffuse outward

C ~ 1-1/r

T*

T

0

0.2

0.4

0.6

0.8

1

1.2

0.1 1 10 100

N

o r m a

l i z e

d t e m p e r a

t u r e

( T -

T

) / ( T

f

- T

)

Radius / Radius of flame

Propagating flame( /r

f= 1/10)

Flame ball

QuickTime and aVideo decompressor

are needed to see this pict ure.

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

0.001

0.01

0.1

1

10

100

1000

0 0.5 1 1.5 2

R z

3 / R

z 3 ( L e =

1 )

Lewis number

= 1/7 = 10

Lewis number effects Lewis number effects

Fromtherelation R z = Leexp

21

*1

From computations by TromansFrom computations by Tromansand Furzeland, 1986and Furzeland, 1986

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Lewis number effects Lewis number effects

Ok, so why does min. MIE shift to richer mixtures for higher HCs?Ok, so why does min. MIE shift to richer mixtures for higher HCs?LeLe effectiveeffective == effectiveeffective /D/DeffectiveeffectiveDDeffeff = D of stoichiometrically limiting reactant, thus for lean mixtures D= D of stoichiometrically limiting reactant, thus for lean mixtures D effeff = D= D fuelfuel ; rich mixtures D; rich mixtures D effeff = D= D O2O2Lean mixtures - LeLean mixtures - Le effectiveeffective = Le= Le fuelfuel

Mostly air, soMostly air, so effeff airair ; also D; also D effeff = D= D fuelfuelCHCH 44: D: D CH4CH4 >> airair since Msince M CH4CH4 < M< MN2&O2N2&O2 thus Lethus Le CH4CH4 < 1, thus Le< 1, thus Le effeff < 1< 1Higher HCs: DHigher HCs: D fuelfuel 1 - much higher MIE> 1 - much higher MIE

Rich mixtures - LeRich mixtures - Le effectiveeffective = Le= Le O2O2CHCH 44:: CH4CH4 >> airair since Msince M CH4CH4 < M< MN2&O2N2&O2 , so adding excess CH, so adding excess CH 44 INCREASES LeINCREASES Le effeff

Higher HCs:Higher HCs: fuelfuel M> MN2&O2N2&O2 , so adding excess fuel, so adding excess fuelDECREASES LeDECREASES Le effeffActually adding excess fuel decreases bothActually adding excess fuel decreases both and D, but decreasesand D, but decreases moremore

eff = mix ~Const 1 M mix

; DO 2 ~Const 2 M mix

+ Const 3 M O 2

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Dynamic analysis Dynamic analysis RR ZZ is related (but not equal) to an ignition requirementis related (but not equal) to an ignition requirementJoulin (1985) analyzed unsteady equations for Le < 1Joulin (1985) analyzed unsteady equations for Le < 1

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

which has the expected formwhich has the expected form

EE minmin~ {energy per unit volume} x {volume of minimal flame kernel}~ {energy per unit volume} x {volume of minimal flame kernel}~ {~ { adadCC pp(T(Tadad - T- T )} x {R)} x {R zz33}}

q

4 R zT ad *

( )2 ;

R( ) R

z

; 4 *( )21

Le

1

Le

2

t R

z

2

() ln ()( ) + q ()2 = () d ( s)d ds s0

E min

14 1

1 Le

* Le

2

ad

C p

T ad

T ( )

R z

3

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Dynamic analysis Dynamic analysis

Joulin (1985)Joulin (1985)

Radius vs. timeRadius vs. time Minimum ignition energyMinimum ignition energyvs. ignitionvs. ignition

durationduration

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Effect of spark gap & duration Effect of spark gap & duration

Expect optimal ignition duration ~ ignition kernel time scale ~ RExpect optimal ignition duration ~ ignition kernel time scale ~ R ZZ22//Duration too long - energy wasted after kernel has formed andDuration too long - energy wasted after kernel has formed and

propagated away - Epropagated away - E minmin~ t~ t 11Duration too short - larger shock losses, larger heat losses toDuration too short - larger shock losses, larger heat losses toelectrodes due to high T kernelelectrodes due to high T kernel

Expect optimal ignition kernel size ~ kernel length scale ~ RExpect optimal ignition kernel size ~ kernel length scale ~ R ZZSize too large - energy wasted in too large volume - ESize too large - energy wasted in too large volume - E minmin~ R~ R 33

Size too small - larger heat losses to electrodesSize too small - larger heat losses to electrodes

Detailed chemical modelDetailed chemical model

1-step chemical model1-step chemical model

Sloane & Ronney, 1990Sloane & Ronney, 1990 Kono et al., 1976Kono et al., 1976

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Effect of flow environment Effect of flow environment Mean flow or random flow (i.e. turbulence) (e.g. inside IC engineMean flow or random flow (i.e. turbulence) (e.g. inside IC engineor gas turbine) increases stretch, thus Eor gas turbine) increases stretch, thus E minmin

Kono et al., 1984Kono et al., 1984 DeSoete, 1984DeSoete, 1984

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Effect of ignition source Effect of ignition source Laser ignition sources higher than sparks despite lower heat losses,Laser ignition sources higher than sparks despite lower heat losses,less asymmetrical flame kernel - maybe due to higher shock losses withless asymmetrical flame kernel - maybe due to higher shock losses withshorter duration laser source?shorter duration laser source?

0.1

1

10

4 5 6 7 8 9 10 11 12

ps laserns laser

Lewis & von ElbeSloane & RonneyRonneyKingdon & Weinberg M

i n i m

u m

i g n

i t i o n e n e r g y

( m J )

Mole percent CH4

in air

Lim et al., 1996Lim et al., 1996

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17/17AME 514 Fall 2006 Lecture 2AME 514 Fall 2006 Lecture 2 1717

References 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.

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