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1

FlamePropagationLimits -1

School of Aerospace Engineering

Copyright © 2004-2005, 2008, 2012, 2014, 2016 , 2020

by Jerry M. Seitzman. All rights reserved.

AE/ME 6766 Combustion

Premixed Flames:

Propagation Limits and Stability

Jerry Seitzman

Methane Flame

0

0.05

0.1

0.15

0.2

0 0.1 0.2 0.3

Distance (cm)

Mo

le F

rac

tio

n

0

500

1000

1500

2000

2500

Te

mp

era

ture

(K

)

CH4

H2O

HCO x 1000

Temperature



Copyright © 2004-2005, 2008, 2012, 2014, 2016 , 2020



Propagation/Stability Limits: Overview

• When/how can we get a flame to propagate (or not)

in a desired/stable manner?

• flammability limits

• flame stabilization

• flashback and blowoff

• extinction

• stability of 1-d geometry

• flame quenching

• We can examine most of these issues in context of

the principles/models used for flame speed

2



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Quenching Distance

• Observation

– for given passage (e.g., cylindrical tube like Bunsen

burner), if you make diameter less than some critical

value, a flame will not propagate through the tube, even if

the velocity of the gas in the tube is well below SoL

• Quenching distance

– flame quenched for d < dq (geometry, fuel, ox., , T, p)

• Reason: flame speed essentially zero

– too much loss from flame (energy, radicals) to walls

• Importance: e.g., prevent flame propagating back into

feed system or burner

d



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Quenching Distance - Analysis

• Pick simplest geometry, semi-infinite parallel plates

d

VhmQQRfchemcond

VqQ chemchem

flame

surfA cond

Q

Tr

qsurfRf

wall

surfdAhm

dx

dTA

@

2

2

2

q

w

d

TT1

T p

o

L cTTS

112

2

2

from SoL analysis

• Thermal model - assume quenching limit caused by balance between chemical energy release and energy losses (e.g., conduction)

– conservative estimate

T2

3



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Quenching Distance - Model

• Simplifying2

1

2 8

o

Lp

q

Scd

2

28

LS

o

L

qS

d

22f

22

• So the quenching distance is on the order of (and larger than) the flame thickness

• Discussion point

– why does the flame get quenched when the walls are a few flame thicknesses away

p

o

Lq

q

cTTS

dd

TT112

2

12

222

(VII.12)



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Quenching Distance - Results

• dq : CH4, C2H6, C3H8

– 2-2.5mm @STP in air

– min. occurs near =1, but shifted from f

ref: Turns

dq 2-3f

• Discussion points

– dq(H2)~0.6 mm

– dq,cylin.>dq,plates

– diluents

• dq(He) vs. dq(Ar)

• dq(CO2) vs. dq(Ar)

4



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Flammability Limits

• Observation

– only within a range of can one

get a flame to be self-propagating

– example, will flame propagate all

the way through tall tube

(vertical, large diam., e.g., 5 cm)

• slightly different limits for other

configurations (e.g., flat flame burner)

• Essentially SL0 below some limit: SL,min

no stable flame exists below some (for other

conditions fixed)……….why?

SL

flammable

1 rich limit (UFL)

lean limit (LFL)

T1

or lower explosion

limit (LEL)

upper explosion

limit (UEL)



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Flammability Limits

• Lean and rich limits (LFL, UFL) depend on

– fuel/ox/diluents, T1, p, configuration

• Fuel dependence: simple hydrocarbon-air systems

– @STP: LFL~0.4-0.5 ; UFL~23

– also expressed in terms of %fuel by volume

CH4 C2H6 C3H8 C2H4 C3H6 C2H2 C3H4

LFL (lean) 0.50 0.52 0.52 0.40 0.53 0.30 0.41

UFL (rich) 1.7 2.4 2.5 5.7 2.7 2.7

f ,LFL (%) 5 3 2.1 2.8 2.4 2.5 2.1

f ,UFL (%) 15 12.4 9.5 28.6 11.1 ~100 12.5

5



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Flammability Limits

• Lean and rich limits (LFL, UFL) depend on

– fuel/ox/diluents, T1, p, configuration

• Pressure dependence: methane example

– rich limit varies with p

– lean limit weaker

p dependence

– surface/geometry issues

(tube size, material)

more important at lower

pressures

• Temperature dependence: limits widen with T1

CH4(%)

p[MPa]

rich limit

nearly linear w/ p

4 8 12 16

lean limit10

20

30

40



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Flammability Limits - Losses• Controlling processes

– tradeoff between losses (e.g., quenching) from flame/reaction zone (thermal conduction, radical diffusion, radiation: gas or soot) and reaction rates

• “Golden Rule” at limit

T

1

• Lower T2 reduces reaction rates

– reaction rate so low that flame moresusceptible to any losses

– often expressed that T2<Tig (but for 1d, no losses would just produce very slow and thick flame)

T

conv-diff

ph

rxn-diff

R ~O(ph/Ze)

x

T1

T2

Adiabatic

Non-

adiabatic

Zeq

q

seheat relea

losses 1

6



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Flammability Limits – 3-d Effects

• Flammability limits nominally defined for 1-d flame

– as previously noted, common approach is to use flame traveling (upward) in vertical tube

• Issues associated with size of tube and buoyancy for flame in “small” tubes

• Examine what happens for upward vs downward propagation in “small” tube



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Flammability Limits – Flame Stability

• Upward Downward

• 1-d (flat) flame can be unstable configuration

7



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Rayleigh-Taylor Instability

• Effect of buoyancy

– flame no longer 1-d and velocity field not uniform

Tube walls

Buoyancy-induced flame stretch

Direction of flame propagation

Flame front

Tube walls

Cooling combustion products near

wall cause sinking boundary layer

Direction of flame propagation

ref: Wang and Ronney (1993)

Enhanced

Losses

Upward propagation Downward propagation



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Darrieus-Landau Instability

• 1-d flame can also

be hydro-

dynamically

“unstable”

– due to gas

expansion

8



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Stability of Flame to Perturbations

• How else can flame respond to pertur-

bations (e.g., local velocity changes)

• When will perturbations grow

or decay?

• For now, consider only thermal conduction

R P R P

convex(+) concave(-)

R P

R P

– heat loss decreases SL for

convex bump (into reactants) = neg. stretch

– focused heating increases SL for

concave bump (into products) = pos. stretch

– always flattens flame,

perturbations decay



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Thermo-Diffusive Instability

• Now consider reactant diffusion

– deficient reactant will diffuse

• to convex bulgegrows perturbation

• away for concave bulgegrow perturbation

• So perturbations will grow if reactant diffusion outweighs thermal diffusion

– if Le< 1

• Flames are thermo-diffusively unstable to perturbation for

– “light” fuels + leaner mixtures

– “heavy” fuels + richer mixtures

R P R P

convex(+) concave(-)

9



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Markstein Number Criterion

• In terms of Markstein

number

• To be unstable

– SL<SoLfor negative

stretch (, Ka<0)

– SL>SoLfor positive

stretch (, Ka>0)

• So unstable when Ma<0

after Tseng et al., Combust. and Flame 95, 410 (1993)

Propane-Air

1 atm

Ma

n

0 0.5 1 1.5 2

0

-2

-4

2

4

6

Correlation

Ma = 8.8(-1.44)

Unstable

Stable

MaKaS

S

L

o

L 1



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Flame Perturbations

• Must also consider effect on flow (velocity)

– e.g., convex case - flow diverges

• centerline velocity will initially

decrease (easier for flame to propagate)

R P

10



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Cellular Flames

• N2 diluted flames of heavy hydrocarbons

– for sufficiently

rich , flames

unstable to

perturbations

– breaks into

cellular

structure

ref: G. H. Markstein, J. Aero. Sci. 18, 199 (1951)



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Flame Extinction by Stretch

• If is too large, flame temperature and SL drop

• Eventually leads to extinction at ext, “extinction strain rate” for stagnation flame

– occurs at Ka~1

Ka ~ chem/stretch

– ext may be different for curvature and flow induced stretch

ref: C.K. Law, Combustion Physics

Heat flux vectorMass Flux vector

Preheat

Zone

Streamtube

11



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Extinction Strain Rate• Roughly correlates with inverse of

flame time scale

– higher SoL ( near 1) leads to

higher ext

– H2 can withstand higher strain than methane

CH4/H2 and air Note: data not obtained at constant flame temperature

ref: G. Jackson et al., Comb. Flame 132 (2003)

=% H2 in fuel (vol)



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Strain Induced Extinction

• Example of extinction events in a bluff-body

stabilized turbulent premixed flame

100

mm

100

mm

/ blowout

1

Str

ain

, |

|

Threshold for extinction

Flow Strain on flame

from: T. LieuwenIncrease air flowrate

12



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Flame Stabilization (Flame Holding)

• Issue

– requirement for flame to remainspatially stable, i.e., stationary

– normal component of local approachvelocity must equal local flame speed

• For combustor, nonstationary behavior leads either to

– flashback ue < SL

• flame moves upstream (explosiondanger, unexpected heating)

– blowoff ue >> SL

• flame exits combustor or extinguishes

uun

SL

ue



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Flame Stabilization: Bunsen Burner

• Consider case of cylindrical tube

– focus on exit edge

– SL will tend to decrease

near wall (quenching)

– assume linear u profile

near tube

– stabilization depends on

SL vs. u variation

• So stability of flame for given flame speed depends

on burner’s velocity gradient g

u

stable

liftoffcritical

F/O

tube

wall

F/O

stable flame

SLu, SL

x

13



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Critical Gradients

• Simple model

– flame speed constant, drops to

zero within penetration depth

(dp) of wall

– linear velocity distribution near wall

• fully-developed laminar pipe (cyl.) flow,

parabolic profile

• Flashback

– occurs for u < SL anywhere at exit

wall

u

u, SL

dpr

dudrdugRr

8

SL

f

L

q

L

p

L

f

S

d

S

d

Sg

3

flashback

1 RKaf

SL

wall

u, SL

dpr

u

normal flame stabilization

u=SL



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Critical Gradients• Blowoff

– flame can not exist at exit oftube if u > SL everywhere

• flame will liftoff

– stability achieved above burner

• lifted flame can see lowerlocal u (jet expands around wall)

• flame moves farther from wall(reduced quenching, local SL)

– increasing flowrate increasesliftoff until stable configurationimpossible blowoff

• velocity and dilution

wall

u

u, SL

dp

r

SL

u

dilution

normal flame stabilization

14



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Example: Methane-Air

• For mixtures of CH4/air @ STP

gb

(s-1)

1

1000gf

(s-1)

1

1000

RRS

SSg

L

L

f

L

f

?

gb~2gf

gf,b

(s-1)

1

1000

stable



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Bunsen Flame Stabilization

• Examine stability constraints (1)

u

d

u

d

prevent flashback

2SLSL

Lf

f

L

f

Smm

du

Sdu

4

28

ffg

du

8

1cm4mm

gb~2gfbg

du

8

prevent blowoff

LSu 2

to get cone to form

jet

laminar

2000

duRe

d

5SL

size for maximum stability range

15



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Multiport Burner Stabilization

ref: Turns

• Similar stability

diagram for

multiple

premixed

fuel/air ports

(single row)

• Rich mixtures

more stable

– unburned fuel

– soot emissions



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Flame Stabilization: General

• As illustrated in the laminar Bunsen flame example

1. stationary premixed flames controlled by flame

propagation are generally stabilized by one or

more “anchor” locations

• anchoring typically occurs at

“upstream” location

• flame position downstream of

anchor (for continuous flame)

is determined by local flame

angle historytube

wall

anchor

point

16



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2. previously we considered flame stabilization anchor occurring at a location where the local flame speed matches the local flow velocity (normal flame stabilization)

– other options possible, e.g., edge flame stabilization

• divergence of oncoming reactantsaround upstream flame edgereduces local velocity

• may be important in turbulent jet flames, shear layer stabilized flames

anchor

point

tube

wall



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3. stability is improved by providing either regions

of

– sufficiently low velocity or

– sufficiently high flame speed

– or in terms of flow time and chemical time,

high Damköhler number

17



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• Common approaches to reduce local flow velocity

(or increase residence time)

1. bluff bodies: low velocity wake

2. sudden expansion (dump):

rapid expansion, recirculation

3. swirl: aerodynamically induced

recirculation zone with low velocity



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• Common approaches to increase flame speed

(or decrease chemical time)

1. optimize equivalence ratio: rich pilot for lean

mixture

2. raise reactant temperature: preheat, exhaust gas

recirculation (EGR), external

or internal

3. raise pressure: lower SL, lower chem

4. reduce heat losses: near stabilization region

5. modify fuel: e.g., add H2

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