School of Aerospace Engineering
Premixed Flames: Flame Stretch and
Flame Speed Measurements
Jerry Seitzman and
Ben Wilde
0.2
2500
Mole Fraction
1500
CH4
H2O
HCO x 1000
Temperature
0.1
1000
0.05
500
Temperature (K)
2000
0.15
Methane Flame
0
0
0
0.1
0.2
0.3
Distance (cm)
FlamePropagationLimits -1
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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AE/ME 6766 Combustion
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Idealized Premixed Flame
•
•
•
•
•
Simplest possible premixed flame configuration
– 1-dimensional, planar
– Adiabatic
Tbo=TadAdiabatic Flame Temperature
ρuuu=ρuSLo=ρbub  Mass Burning Flux
Products
What are the controlling parameters?
– Thermal and mass diffusivities
– Reaction rates
– Temperature of reactants
– Pressure
– Exothermicity of fuel/oxidizer
SLo  Fundamental property of fuel/oxidizer mixture
FlamePropagationLimits -2
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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Φ
Reactants
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Non-Ideal Premixed Flames
• Non-adiabatic
• 3-dimensional
• Non-uniform and/or unsteady
flow
• In general,
Rendering of1200K isotherm from DNS of
a turbulent Φ=0.37 H2 flame colored by
local H2 consumption rate,
– Su≠SLo
– Mass burning flux≠ρuSLo
Reactants
Day et al. Combustion and Flame (2009)
FlamePropagationLimits -3
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Stretched Flames: Basics
• Flames subject to aerodynamic non-uniformity
and/or unsteady effects are called Stretched Flames
• Two kinds of stretch effects:
– Hydrodynamic Stretch Effects: net displacement or
distortion of the flame surface due to tangential and
normal components of the flow
– Flame Stretch Effects: modification of the
temperature and/or species profiles in the transport
zone resulting in changes in the flame propagation
rate
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Stretched Flames: Physical Perspective
• Stretch causes a misalignment between convective and diffusive fluxes
near the flame
• Stretched flames are not infinitely thin (otherwise kinematic restoration
would dominate)
• Stretch effects help to explain a wide variety of interesting and important
physics not observed in premixed 1D, planar, adiabatic laminar flames:
– Flame speed
– Flame shape
– Flame stability
S L  S L0
m1D , planar ,adiabatic  m
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Tips of Bunsen Flames
• Propane (heavier than air) and methane (lighter)
Propane(C3H8)
d=10mm
=
1.38
0.53
Methane(CH4)
1.52
0.58
ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)
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Tip Opening
• Propane flames of increasing richness
Propane(C3H8)
Methane(CH4)
 = 1.07
1.17
1.32
1.41
1.43
1.47
ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)
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School of Aerospace Engineering
Bunsen Tip Flame
Temperature Data
• Curvature/stretch can cause
enhancement or reduction
in flame temperature
– comparison of measured
Ttip to Tad
– CH4 vs. C2H4 vs. C3H8
CH4-air
Tad
Tmeas
C3H8-air
C2H4-air
ref: C.K. Law, Combustion Physics
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Stretched Flames: Geometry
n
• Stretch effects exist
because of coupling
between flame surfaces
and flow fields
• Real flames are 3-D
unsteady deflagration
waves
• Assuming the flame is
thin, smooth and
continuous we can treat
the flame as a 3-D surface
n
Burned
Unburned
n
n  n  x, t 
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Stretched Flames: Mathematical Definitions
• κ  Normalized differential
change in flame surface area as
a function of time
• Flame surface moves and
deforms in space and time
• Need to define a sign
convention for stretched
flames
– Positive
– Negative
FlamePropagationLimits -10
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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
1 dA
A dt
Stretch Rate [1/s]
Unsteady Combustor Physics by T. Lieuwen
(Cambridge University Press, 2012)
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Stretched Flames: Mathematical Definitions
• Level set approach arises very naturally for the purpose of
defining the flame surface in thin, smooth, and continuous
premixed flames
• Describe the surface of the flame as,
G  x, t   0
n
G
G
• For convenience set G>0 in products and
G<0 in the reactants
• At the flame, howver,
dG G

 F G  0
dt
t
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School of Aerospace Engineering
Stretched Flames: Mathematical Analysis
• Full expression in terms of flame surface variables,
u
u
  t1  t2  (vF  n )(  n )   t  u t  (vF  n )(  n )
t1
t2
b
a
• κa-stretch due to tangential velocity gradients at the flame surface
1
• κb-stretch due to unsteady flame curvature
S    u  u T 
• Alternative expression,
n  n  x, t 
2
s  n   vF  u 
u
  nn : u    u  su (  n )  n  S  n    u  s u (  n )
S
 curv
• κS-stretch due to flow non-uniformities
• κcurv-stretch due to a curved flame in a uniform approach flow
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Stretched Flames: Mathematical Analysis
• If we consider stationary flames,
vF  0     t  u t  n    n  u 
since u t  n   u  n 
Unsteady Combustor Physics by T. Lieuwen
(Cambridge University Press, 2012)
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Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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AE/ME 6766 Combustion
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Stretched Flames
• Stretch creates an environment where convective
and diffusive fluxes do not align
• Stretch rate quantifies the intensity with which
these effects act on the flame front
• Most “real” flames are curved and/or strained
• Examples
– Bunsen flame tip
– Flat flame burner
– Unsteady Spherical flames
– Perturbations in 1-d flames (flammability limits)
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Influence of Flame Stretch

• Two basic cases
– positive stretch (flame
in tension)
– negative stretch
(flame in compression)
1 dA
A dt
related to strain,
curvature,dilatation
R
P
P
R
P
R
P Bunsen tip
•
thermal diffusion () “focuses” into reactants, enhances SL
(same for mass diffusion of radicals)
•
mass diffusion of reactants away from centerline, can
reduce [reactants], reaction rate and thus SL
•
differential diffusion can lead to less stochiometric mixture,
greater diffusional loss of deficient reactant, reduces SL
like
R
P
• Le=1, opposing effects tend to cancel
FlamePropagationLimits -15
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Flame Stretch: Lewis Number Effects
• Recall: Each reactant has different Dij in a multi-component
mixture
•
•
– “most deficient” reactant and/or the reactant with the largest gradient
is generally the controlling parameter
• fuel if lean, oxygen if rich

LeNon unity 
Three diffusivities of interest:
Di
– Thermal diffusivity, α
– Deficient reactant diffusivity, Di
D
Le preferential  i
– Abundant reactant diffusivity, Dj
Dj
Two interpretations of “Lewis Number Effects”
– Non-unity Lewis Number: Imbalance between thermal and mass
diffusivity
– Differential Diffusion: Imbalance between deficient and abundant
species diffusivities
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Stretched Flames: Non-unity Lewis Numbers
Φ=0.27
Φ=0.27
Φ=0.37
Tu=298K
P=1atm
Le>1
Le≈1
Le<1
Bell et al. Proceedings of the Combustion Institute (2007)
FlamePropagationLimits -17
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Stretch Effects in Bunsen Flames
• Stationary, axisymmetric Flame
• Curved flame with negative stretch
• Assume uniform velocity profile
exiting the tube
• Diffusive fluxes do not align with
convective fluxes
• For negative stretch case
– if thermal conduction outweighs
mass diffusion then flame speed
enhanced ( vs. D)
• so SL for Le > 1
• similarly SL for Le < 1
FlamePropagationLimits -18
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Reaction Zone
Preheat
Zone
Streamtube
P
R
P
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Non-unity Le and Negative Stretch
• Consider Bunsen flames
– tip of flame=negative stretch
• Fuel lighter than air (e.g., CH4)
R
P
– MWfuel < MWmix
– for <1, Ledeficient=mix/Dfuel
drops as 
 SL for leaner mixtures
– tip weak (open) for
sufficently lean flames
– enhanced for rich flames
Methane(CH4)
1.52
0.58
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School of Aerospace Engineering
Non-unity Le and Flame Stretch
• For fuel heavier than air
(e.g., C3H8)
– MWfuel > MWmix
– Ledeficient as 
 SL for lean mixtures
– tip enhanced for
sufficiently lean
flames
– tip weak (open)
for rich flames
Propane(C3H8)
FlamePropagationLimits -20
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R
1.38
P
0.53
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Tip Opening
• Propane flames, richer=more stretch sensitivity
Propane(C3H8)
Methane(CH4)
 = 1.07
1.17
1.32
1.41
1.43
1.47
max
stretch
location
ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)
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School of Aerospace Engineering
Stretch Effects in Opposed Flow Flames
• Flow induced stretch
– example:
stagnation flame (positively
stretched)
– diffusion not aligned with flow
• Examples
– Premixed reactants impinging
on a flat wall
– Premixed reactant impinging
on hot products
FlamePropagationLimits -22
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
rights reserved.
Preheat
Zone
Streamtube
Heat flux vector
Mass Flux vector
from: T. Lieuwen
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Stretch Effects in Unsteady Spherical Flames
• Stretch rate changes as a function of
Reactants
radius
• Curvature is present but flow
velocities align with flame surface
Products
normal
• Stationary spherical flame would be
stretchless
u
u
  t1  t2  (vF  n )(  n )   t  u t  (vF  n )(  n )
t1
t2
a
FlamePropagationLimits -23
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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b
Combustion Physics by C.K. Law
(Cambridge University Press, 2006)
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Flame Speed Corrections
• So for stretched flames, need to modify 1d flame
speed to account for curvature, flow divergence
• For small perturbations (low amounts of stretch),
asymptotic analysis (Markstein) leads to the
following for the apparent flame speed
S L  SLo    S Lo  Ma f 
Ma    f
Markstein Length
Markstein number
• Sometimes expressed in terms of Karlovitz number
Ka 
residence time for crossing unstretched flame  f S L  f 


characteri stic time for flame stretching
1
SL
SL  SLo  MaKaSL  S Lo S L  1  MaKa
FlamePropagationLimits -24
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Karlovitz Dependence
?
S Lo S L 1  MaKa
2
• Flame
o
SL SL
speeds for
propane-air
mixtures for
1
different Ka
• Ma=Ma()
0
0
0.1
0.2 Ka
0.3
0.4
after Tseng et al., Combust. and Flame 95, 410 (1993)
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Markstein Number
• Saw before Ma=Ma()
6
o
• Try simple linear correlation S L  1  MaKa
4 SL
Ma=S(n)
Propane-Air
1 atm
Ma
S
n

Kamax
2
Air/
Fuel
C3H8
-8.8
1.44 0.8-1.8 0.25
0
C2H6
-4
1.68 0.8-1.6 0.25
-2
C2H4
-2.9
1.95 0.8-1.8 0.24
H2
3.9
1.5
CH4
10.2
0.74 0.6-1.4 0.30
Correlation
Ma = 8.8(-1.44)
-4
1-4.8
0.21
0
0.5
1

n
1.5
2
after Tseng et al., Combust. and Flame 95, 410 (1993)
FlamePropagationLimits -26
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Flame Speed Measurements
• Measurements of “SL” are difficult
– hard to achieve adabatic and 1-d conditions
– usually compromise and try to correct
• Various methods
–
–
–
–
–
–
Bunsen-type burners (“simplest”)
traveling tube
spherical “bombs”
soap bubbles
flat flame burners
stagnation flames
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Bunsen (Tube) Burner Method
• Premixed fuel/air in
cylindrical tube
– laminar
– various velocity
profiles
– stationary flame
when normal
component of local
approach velocity=SL

SL
un
u
color schlieren
inner
cone
outer flame
(nonpremixed)
ref: Sébastien Ducruix
FlamePropagationLimits -28
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CH4/air
=1.05
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Bunsen (Tube) Burner Method
• Approaches

SL
particle
tracks
– measure , u (or un)
un u
• u not necessarily same as uexit
• u,  may not be constant
(depends on exit profile)
– measure flame area
  uA  S L  m exit u Aflame
m
• how to identify flame surface
– schlieren, shadow,
luminosity,…
luminousity
<1
ref: Echekki and Mungal, Phys. Fluids A 2, 1523 ( 1990)
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School of Aerospace Engineering
Bunsen Method: Flame Surface
• Flame surface
measurement
Visible
Schlieren
– luminous,
schlieren,
shadow give
different
Aflame
Shadowgraph
• Shadow closest toQ
unburned region
– but not 1-d flame
– stretch effects
SLSLo
• Luminosity corresponds
to high T rxn zone
ref: Ibarreta and Sung, 3rd Joint US Section Meeting Comb. Instit.
FlamePropagationLimits -30
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Bunsen Method: Burned Surface Area
• Measure reaction zone area (Ab)
– from flame luminosity
• Unstretched laminar flame speed (SLo )
 So  S
m Ab m  u Q
S Lo  b b  b b 


u
u
u
Ab
Ab
– flame curvature effect is small for Sb
– flame strain primarily restricted to tip
• use tall flames
CH4/C3H8 ~ 80:20 (vol.)
9 mm
H2O/Air ~ 19% (mass)
5 atm, 650 K
Chemiluminescence image
F ~ 1.0
ref: Kochar, Seitzman
31
FlamePropagationLimits -31
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School of Aerospace Engineering
Propagating Methods
• Transparent Tube
uf
ur
– fill tube with premix gases, ignite, watch flame
propagate (make sure it is sustained propagation)
– gas moves ahead of flame front (compressed)
• uf > SL, and gases may be slightly preheated
• non-1d (boundary layer), buoyancy
• Spherical Bomb
uf 
dR f
dt
– fill closed spherical chamber,
Rf
watch flame propagate
– unburned velocity (and p,Tu?) continuously increasing
– not 1-d (planar), affected by curvature and strain, must
extrapolate back to zero stretch
FlamePropagationLimits -32
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Spherical Bomb
Pressure Sensor & Gauges
Outer Chamber
Gas Releasing Holes
Quartz Window
High-Speed Video
Camera
Focus Lens
Mercury Lamp
Knife Edge
Pinhole
ref: Chen, Burke, Ju, Comb. Theory
Modelling, 13 (2009)
ref: Qin and Ju, Proc. Comb. Inst.30 (2005)
FlamePropagationLimits -33
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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Permanent
magnet
Iron Plate
Decollimating Lens
Tungsten Wire
Collimating Lens
Inner Chamber
ref: Fuller et al., AIAA-2012-167 (2012)
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Flat Flame Burner
• Construct uniform velocity profile using porous
plate, sintered metals, or small flow passages
• Burner is either water cooled or naturally cooled
• Flame can be essentially
SL
flat except at edges of burner
• Measurement of flame
Q
velocity easy (uexit)
• Nonadiabatic
– measure cooling, extrapolate to Q=0
– or T profile and compare with
computation; okay for low pressures
FlamePropagationLimits -34
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
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ref: Glassman
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Stagnation Flames
Nozzle
Stagnation plane
Stagnation plug
Stagnation plug
Flame
Nozzle
• Nearly flat flames (no curvature),
but with aerodynamic “strain” due
to deceleration caused by
stagnation plane
– extrapolate to zero-strain to
obtain SLo
2
1.6
Axial velocity (m/s)
• Opposed
jets or jet and
stagnation
plate
1.2
0.8
Plug
K=-du/dx
0.4
FlamePropagationLimits -35
X
L
D
U
Nozzle
0
1
ref: J. Natarajan PhD thesis
Copyright © 2004-2005, 2008, 2012 by Jerry M. Seitzman and Ben Wilde. All
rights reserved.
Flame
Su
3
5
7
9
Distance from stagnation plane X (mm)
11
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