premixed flames: intro. to flame methane flame ch4h2o...
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1
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AE/ME 6766 Combustion
Premixed Flames: Intro. to Flame Stretch
Effects, Flame Speed Measurements
Jerry Seitzman and
Ben Wilde
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
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Overview
• Goals of this section are:
1. examine influence of non-1D behavior on flames
2. define flame stretch and stretched flames
3. study dependence of flame properties, especially
flame speed on flame stretch, and the influence of
Lewis number(s)
4. describe various methods used to experimentally
measure flame speed
2
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AE/ME 6766 Combustion
Idealized Premixed Flame• So far we have focused on the simplest possible
premixed flame configuration– 1-dimensional, planar, adiabatic (including no
radiation), steady, no buoyancy
• product temperature Tob = Tad
• mass burning flux uuu ρuS
oL = ρbub
• Controlling processes– diffusion: thermal and mass
– reaction rates and exothermicity
• So solution, e.g., SoL, is fundamental property of
fuel/oxidizer mixture for given initial state– reactant composition
– reactant temperature and pressure
u=unburned b=burned
uu=SL ub=Sb
Premixed
ReactantsProducts
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AE/ME 6766 Combustion
• Real flames are typically– non-adiabatic
– non-uniform and 3-dimensional
– unsteady
– occur within gravity field
• In general,– uu SL ≠ So
L
– equivalently, mass burning flux ≠ ρuS
oL
– SL can depend on velocity field and flame geometry
• Following focus is non-1d(unsteady?) flames Day et al. Combustion and Flame (2009)
rendering of 1200K isotherm from DNS of
a turbulent =0.37 H2 flame colored by
local H2 consumption rate,
Reactants
Non-Ideal Premixed Flames
𝝎fuel ~ 3 1d, adiabatic result
3
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Stretched Flames: Basics
• Flames subject to aerodynamic non-uniformity and/or unsteady effects are called Stretched Flames
• Flames can be distorted, wrinkled or displaced by non-uniform or unsteady flow fields- called Hydrodynamic Stretch
• Stretched flames respond to non-uniform or unsteady flow fields they encounter by modification of the temperature and/or species profiles in the diffusive zone, changing flame propagation rate- called Flame Stretch
• Hydrodynamic stretch and flame stretch are inherently coupled concepts!
R
P
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AE/ME 6766 Combustion
• Flame stretch causes misalignment between convective
and diffusive fluxes in flame
• Can impact many
flame properties
– propagation speed,
shape, stability
and can explain
interesting
phenomena observed in non-ideal flames
Stretched Flames: Physical Perspective
flame curvature can cause stretch
Note: stretch effects would not be observed in flames that are
infinitely thin - kinematic restoration would dominate
Reactant velocity
Diffusive fluxes
ref:
Ech
ekki
an
d M
un
ga
l,
4
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Example: Bunsen Flames Tips• Non-ideal behavior observed for luminosity at tips
of Bunsen flames for different fuel-air mixtures (fuel type and equivalence ratio)
Propane(C3H8) Methane(CH4)
= 1.38 1.520.53 0.58
d=10mm
ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)
reducedenhanced
enhanced
reduced
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AE/ME 6766 Combustion
Tip Opening
• Example: propane flames with increasing rich , tip weakens until flame locally extinguished (“opens”)
Propane(C3H8) Methane(CH4)
= 1.07 1.321.17
1.41 1.43 1.47
ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984)
tip open
5
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AE/ME 6766 Combustion
Bunsen Tip Flame
Temperature Data
ref: C.K. Law, Combustion Physics
• Curvature/stretch can cause
enhancement or reduction
in flame temperature
– compares measured Ttip to
calculated Tad
– CH4 vs. C2H4 vs. C3H8
CH4-air
C3H8-air
C2H4-air
Tad
Ttip
reduced enhancedreduced“Leaner”
“Richer”enhanced reducedreduced
trend?
(Tmax) shifts rich shifts leanno shift
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AE/ME 6766 Combustion
• Stretch effects exist because of coupling between flame surfaces and flow fields
• Assuming the flame is thin, smooth and continuous we can treat the flame as a 3-D surface
– flame surface moves, deforms, and accelerates/ decelerates
Unburned
Burned
n
n
n
,n n x t
Stretched Flames: Geometry
6
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
• Consider simple case of
propagating flame
• Flame stretch rate can be defined as
normalized rate of change of flame
surface area element
– a Lagrangian quantity
– units of flame stretch are s-1,
i.e., an inverse time scale or rate
1 dA
A dt
Williams (1975)
UnburnedBurned
dA
Flame Stretch Rate Definition
(VII.14)
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AE/ME 6766 Combustion
Influence of Flame Stretch
• Two basic cases
– positive stretch (flame in tension)
– negative stretch(flame in compression)
• Diffusion for neg. stretch
– thermal diffusion () focuses heat into reactants, enhances reaction rate and thus SL
(same for mass diffusion of radicals)
– mass diffusion of reactants away from (and products to) center streamline, can reduce[reactants], and thus reaction rate and SL
PR
P
dt
dA
A
1
like
Bunsen tip
R P
R P
R P
related to strain, curvature,dilatation
7
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AE/ME 6766 Combustion
• Given previous sign convention for
– can relate sign of to direction from which heat flux vectors cross the sidewalls of a differential flame tube (control volume) immediately adjacent to flame sheet
– heat flux into sides of control volume negative stretch rate
– heat flux out of sides of control volume positive stretch rate
1 dA
A dt
Stretch Rate () Sign ConventionCurved flame
in uniform velocity flow
Flat flame in diverging
flow
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AE/ME 6766 Combustion
• So we have the following diffusivities of interest– thermal diffusivity (α) of mixture
– mass diffusivity (D) in general, but recall each species has different Dij (multi-component)
• so for reactants
– Df,j (or Df,M ) of fuel
– Dox,j (or Dox,M ) of oxygen
• Two effects arise because of non-equidiffusivities
– non-unity Le
• imbalance between thermal and mass diffusivity
– differential diffusion
• imbalance between species diffusivities, e.g., fuel and oxygen
• If all Lei=1, diffusive effects tend to counterbalance
Le Effects on Stretched Flames
and Le = /D
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AE/ME 6766 Combustion
Non-Equidiffusive Effects
• Flame response to stretch effects is strongest in flames with Lewis numbers much different from one
• Flame response in stretched flames depends on sign of stretch rate and Lewis number
– for fixed (premixed) mixture, flame response (e.g., dSL/d) will change entirely when stretch rate changes sign (e.g., positive to negative)
– for fixed stretch rate , flame response will change entirely when Le transitions from greater than to less than some critical value
• Theory predicts and experiments confirm that equi-diffusive (Le=1) stretched flames are insensitive to the magnitude of stretch
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
and Ben Wilde. All rights reserved.
AE/ME 6766 Combustion
Stretch Effects: Bunsen Flames
• Stationary, axisymmetric flame
• Stretch (negative) induced by flame curvature– assuming uniform velocity
profile exiting the tube
• Diffusive fluxes do not align with convective fluxes
• Since negative stretch here
– if thermal conduction outweighs mass diffusion then flame speed enhanced ( vs. D) SL for Le > 1
• similarly SL for Le < 1
– but also must consider differential diffusion
9
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AE/ME 6766 Combustion
0.581.52
Reexamine Bunsen Flame Tip Results• Fuel lighter than air (e.g., CH4)
– in “preheat” zoneW
f < W
mix < W
ox
– assuming molec. wt. dominates Dij
Df,M > mix > Dox,M
Lef < 1, Leox > 1
– so thermal vs “overall” mass diffusion will have some influence, but differential diffusion will tend to make mixture leaner near tip
– < crit Ttip and local SLflame weakened
– > crit Ttip and local SLflame enhanced
Methane(CH4)
negative stretch
W
mix,”lean” ~W
N2
W
mix,”rich” <W
N2
R
P
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
0.531.38
Reexamine Bunsen Flame Tip Results• Fuel heavier than air (e.g., C3H8)
– in “preheat” zoneW
f >> W
ox > W
mix
– assuming molec. wt. dominates Dij
Df,M << Dox,M ~ mix
Lef >> 1, Leox ~ 1
– now differential diffusion will tend to make reactant mixture richer near tip
– > crit Ttip and local SLflame weakened
– < crit Ttip and local SLflame enhanced
Propane(C3H8)
negative stretch
R
PW
mix,”lean” ~W
N2
W
mix,”rich” >W
N2
10
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Tip Opening Propane Flames• As we increase burner, diffusion effects at tip lead to
conditions that no longer can sustain a flame, e.g., too rich
• Richer propane mixture has more stretch sensitivity
Propane(C3H8) Methane(CH4)
= 1.07 1.321.17
1.41 1.43 1.47
max
stretch
location
at tip
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Stretch Effects: Stagnation Flames• Stretch induced by flow strain
– example: stagnation flame (positively stretched)
– no flame curvature, BUT flow (velocity) field diverging
• reacting flow is decelerating, strained=a (strain rate) near centerline
– diffusion again not aligned with flow
• Examples– premixed reactants impinging on a
(stagnation) body
– premixed reactants impinging on flow moving in opposite direction (opposed jets)
Credit S. Adusumilli
du/dx =a
dv/dr = a
x
r
11
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Stagnation Flame Example Results
S. Adusumilli, Effects of preheat temperature and vitiation on reaction kinetics of higher hydrocarbon fuels, 2019.
SL/S
o L
CH4-L
C3H8-L
C3H8-R
C2H4-L
Chemkin OPPDIF and USCII
• Tu=300 K– light and heavy fuels
have opposite sign slope (sensitivity) at =0.6
– ethene (MW=28) reduced sensitivity
– opposite sensitivity for propane at =0.6 and 1.4
• Tu=650 K– sensitivity to stretch
significantly reduced
– sign change of sensitivity for propane =1.4
1 atm 1 atm
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AE/ME 6766 Combustion
1 2
( )( ) ( )( )
ba
F F
u uv n n u v n n
t1 t2t tt t
Stretch Effects: Unsteady Spherical Flames
• In general for “thin” flame, stretch is given by
• For spherical flame– flame curved, but flow velocities align with flame
surface normal; no tangential velocities
– stationary spherical flame would be stretch-less
– for unsteady spherical flame, stretch rate changes as function of radius, r=r(t); decreases with time for outwardly expanding flame
vF=local propagation velocity of flame surfaceti =tangent to flame surfacea=stretch due to tangential velocity gradients at the flame surfaceb=stretch due to unsteady flame curvature
R
P
r
(VII.15)
12
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Flame Speed Corrections• For stretched flames, need to modify 1-d flame speed
to account for curvature, flow divergence effects
• For small perturbations (low stretch rates), asymptotic analysis (Markstein) leads to the following flame speed scaling
• Can be expressed in terms of a non-dimensional stretch rate called a Karlovitz number* (or stretch factor)
– and VII.16 becomes
f
o
L MaS
Markstein Length Markstein number
o
LLSS f
Ma
stretch
d-1
Ka
L
o
LL SKaMaSS KaMaSS L
o
L 1
*other Karlovitz number definitions used in turbulent combustion
(VII.16) (VII.17)
(VII.16a)
residence time within 1d unstretched laminar flame
characteristic time for flame stretchingo
L
f
o
Lf
S
S
1(VII.18)
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AE/ME 6766 Combustion
0 0.1 0.2 0.3 0.40
1
2
Ka
L
o
LSS
Karlovitz Number Scaling
• Flame speeds of propane-air mixtures for different Ka
nearly linearscaling
Ma=Ma()
after Tseng et al., Combust. and Flame 95, 410 (1993)
KaMaSS L
o
L 1?
=
13
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
and Ben Wilde. All rights reserved.
AE/ME 6766 Combustion
Markstein Number Dependence
Air/
Fuel
S crit Kamax
C3H8-8.8 1.44 0.8-1.8 0.25
C2H6-4 1.68 0.8-1.6 0.25
C2H4-2.9 1.95 0.8-1.8 0.24
H23.9 1.5 1-4.8 0.21
CH410.2 0.74 0.6-1.4 0.30
after Tseng et al., Combust. and Flame 95, 410 (1993)
Propane-Air
1 atm
Ma
crit
0 0.5 1 1.5 2
0
-2
-4
2
4
6
Correlation
Ma = 8.8(-1.44)
MaKaS
S
L
o
L 1
• What is Ma=Ma() relation?
• Simplest is linear correlation
Ma = S (crit)
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Flame Speed Measurements
• How does one experimentally measure flame speeds?
• Measurements of SoL are difficult
– hard to achieve adabatic and 1-d conditions
– usually compromise and try to correct
• Various methods
– Bunsen-type burners (“simplest”)
– traveling tube
– spherically expanding flames
– soap bubbles
– flat flame burners
– stagnation flames
14
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Bunsen (Tube) Burner Method
• Premixed fuel/air in cylindrical tube
– laminar
– various velocity profiles
– stationary flame when normal component of local approach velocity=SL
ref: Sébastien Ducruix
color schlieren
inner
cone
=1.05CH4/air
outer flame
(nonpremixed)
uun
SL
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Bunsen (Tube) Burner Method
• Approaches
– measure , u (or un)
• u not necessarily same as uexit
• u, may not be constant (depends on exit profile)
– measure flame area, reactant volumetric flowrate
• how to identify flame surface?
– schlieren, shadow, luminosity,…?
uun
SL
uAm flameuexitL AmS
ref: Echekki and Mungal, Phys. Fluids A 2, 1523 ( 1990)
<1
particle
tracks
luminousity
flame
uexit
A
m
reactant volumetric flowrate
15
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
and Ben Wilde. All rights reserved.
AE/ME 6766 Combustion
Bunsen Method: Flame Surface• Flame surface
measurement– luminous,
schlieren,shadow givedifferent Aflame
• Shadow closest to unburned region
– but not 1-d flame– stretch effects
• Luminosity corresponds to high T rxn zone
ref: Ibarreta and Sung, 3rd Joint US Section Meeting Comb. Instit.
SL SoL
Shadowgraph
Visible
Schlieren
Q
Shadowgraph
Visible
Schlieren
Q
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Copyright © 2004-2005, 2008, 2012,2014, 2020-2021 by Jerry M. Seitzman
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AE/ME 6766 Combustion
Bunsen Method: Burned Surface Area
• Measure reaction zone area (Ab)
– from flame luminosity
• Unstretched laminar flame speed (SLo)
– flame curvature effect is small for Sb
– flame strain primarily restricted to tip
• use tall flames9 mm
Chemiluminescence image
CH4/C3H8 ~ 80:20 (vol.)
H2O/Air ~ 19% (mass)
5 atm, 650 K
F ~ 1.0
b
u
u
b
u
bb
u
o
bbo
LA
mAmSSS
ref: Kochar, Seitzman
16
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AE/ME 6766 Combustion
Propagating Methods
• Transparent Tube
– 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 Flames
– fill closed(?) (spherical?) chamber,ignite and watch flame propagate
– unburned velocity (and p,Tu?) continuously increasing
– expanding (unsteady) flame experiences stretch ((t) ), extrapolate back to zero stretch
uf ur
dt
dRu
f
f
Rf
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AE/ME 6766 Combustion
• Construct uniform velocity profile using porous plate, sintered metals, or small flow passages
• Burner is either water cooled or naturally cooled
• Flame can be essentiallyflat except at edges of burner
• Measurement of flamevelocity easy (uexit)
• Nonadiabatic
– measure cooling, extrapolate to Q=0
– or measure T profile through flame and compare with computation (works for low pressures, thick flames)
Flat Flame Burner
ref: Glassman
SL
Q
flatflame.com
17
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AE/ME 6766 Combustion
Stagnation Flames
• Opposed
jets or jet and
stagnation
plate
• Nearly flat flames (no curvature),
but with aerodynamic “strain” due
to deceleration caused by
stagnation plane
– extrapolate to zero-strain to
obtain SLo
Flame
Stagnation plane
Flame
Stagnation planeStagnation plug
Nozzle
Stagnation plug
Nozzle
Stagnation plug
Nozzle
Stagnation plug
Nozzle
0
0.4
0.8
1.2
1.6
2
1 3 5 7 9 11
Distance from stagnation plane X (mm)
Axia
l ve
locity (
m/s
)
Su K=-du/dx
Plug
Nozzle
U
X
D
L Flame
ref: J. Natarajan PhD thesis
9 mm
Flo
w d
irec
tio
n
Stagnation plug