flame stretch, edge flames, and flame stabilization...uh ⋅∇ = −∇⋅ t ... 60 70 80 90 100...
TRANSCRIPT
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Flame Anchoring -1
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Flame Stretch, Edge Flames, and Flame Stabilization
Natarajan et al. Combustion and Flame 2007
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Course Outline A) Introduction and Outlook B) Flame Aerodynamics and Flashback C) Flame Stretch, Edge Flames, and Flame Stabilization Concepts D) Disturbance Propagation and Generation in Reacting Flows E) Flame Response to Harmonic Excitation
• Introductory Concepts • Flame Stretch • Edge Flames • Flame Stabilization in
Shear Layers • Flame Stabilization by
Stagnation Points
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Flame Anchoring -3
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Course Outline A) Introduction and Outlook B) Flame Aerodynamics and Flashback C) Flame Stretch, Edge Flames, and Flame Stabilization Concepts D) Disturbance Propagation and Generation in Reacting Flows E) Flame Response to Harmonic Excitation
• Introductory Concepts • Flame Stretch • Edge Flames • Flame Stabilization in
Shear Layers • Flame Stabilization by
Stagnation Points
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Flame Stabilization and Blowoff • Flame stabilization requires:
– A point where the local flame speed and flow velocity match:
dus u=
Figures: Natarajan et al. Combustion and Flame 2007 Petersson et al. Applied Optics 2007
• Typically found in regions with: – Low flow velocity
» Aerodynamically decelerated regions (VBB)
– High shear » Locations of flow separation
(ISL & OSL)
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Premixed Flame Stabilization: Basic Effects • Flame stabilization:
– Balance combustion wave propagation with flow velocity
• Burning velocity, edge speed, autoignition front?
• Suggests that stable flames are rare – However, flames have self-stabilizing
mechanisms • Shear layer stabilized: Upstream flame
propagation increases wall quenching • Aerodynamic stabilization – velocity
profiles
qδ
abc uds
xuFlow
()
cms
u
Lewis & Von Elbe 1987
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Flame Anchoring Locations • Complex flows can provide multiple anchor locations
I: VB
B
II: VB
B/ISR
III: ISR
IV: O
SR
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Flame Stabilization and Blowoff • Stabilization locations determine location/spatial
distribution of flame – Flame Shape – Flame Length
• Combustor operability, durability, and emissions
directly tied to these fundamental characteristics affecting: – Heat loadings to combustor hardware – Combustion instability boundaries – Blowoff limits
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Review of the Idealized Premixed Flame • Simplest possible premixed flame configuration
– 1-dimensional, planar – Adiabatic
• Tb0 = Tad →Adiabatic Flame Temperature • ρuuu = ρuSL0 = ρbub → Mass Burning Flux • What are the controlling parameters?
– Thermal and mass diffusivities – Reaction rates – Temperature of reactants – Pressure – Exothermicity of fuel/oxidizer
• SL0 → Fundamental property of fuel/oxidizer mixture
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What Happens if a Flame isn’t Flat?
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What Happens if Flow Field isn’t 1-D?
• Common theme to 2 problems: misaligned convective and diffusive fluxes
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Course Outline A) Introduction and Outlook B) Flame Aerodynamics and Flashback C) Flame Stretch, Edge Flames, and Flame Stabilization Concepts D) Disturbance Propagation and Generation in Reacting Flows E) Flame Response to Harmonic Excitation
• Introductory Concepts • Flame Stretch • Edge Flames • Flame Stabilization in
Shear Layers • Flame Stabilization by
Stagnation Points
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Overview of Flame Stretch • Consider a stationary flame; focus on
a C.V. intersection of a streamtube, and the flame.
• Steady state energy balance • (no viscous effects, no body forces)
• Constitutive relation of enthalpy flux (Fickian diffusion, no radiative heat transfer, no Soret or DuFour effects)
Enthalpy Convection EnthalpyDiffusion
Tu hρ ⋅∇ = −∇ ⋅
q
1
MassFluxHeat Flux
N
T i i ii
k T h Yρ=
= − ∇ − ∇∑
q D
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Overview of Flame Stretch • Flame stretch effects: is there a net enthalpy
loss/gain or change in composition inside the C.V. because of diffusion fluxes through its lateral surface?
• Two mechanisms:
– Lewis Number effects Le =α /D Diffusion of mass and of heat are unbalanced.
– Differential diffusion effects DFuel /Dox Lighter species diffuse faster than heavier species: equivalence ratio or diluent/reactant ratio inside the C.V. can change.
Negative stretch
Positive stretch
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Lewis number effects • If Le = 1 then α =D : no net enthalpy loss through
the lateral surface
• If Le > 1 then α >D : Heat flux > Mass flux o Positive stretch: net enthalpy flux out of the
C.V. o Negative stretch: net enthalpy flux into the C.V.
• If Le < 1 then α
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Differential diffusion effects Consider the temperature at the tip of a Bunsen Flame Ttip :
• CH4/Air: CH4 is lighter than O2, thus diffuses faster (DFuel>DOx) and its concentration inside the C.V. decreases. o If overall equivalence ratio is lean, then locally in the C.V. φ is made leaner: Ttip
is lower then Tad calculated at the overall φ. o If overall equivalence ratio is rich, then locally in the C.V. φ pulled toward
stoichiometric: Ttip is then higher then Tad calculated at the overall φ.
• C3H8/Air: C3H8 is heavier than O2, thus diffuses more slowly (DFuel
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Bunsen Tip Flame Temperature Data
From C.K. Law, “Combustion Physics”
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Example: Tips of Bunsen Flames
Propane(C3H8) Methane(CH4)
φ = 1.38 1.52 0.53 0.58 d=10mm
Ref: Mizomoto, Asaka, Ikai and Law, Proc. Combust. Inst. 20, 1933 (1984) Slide courtesy of J. Seitzman
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Stretched Flames: Non-unity Lewis Numbers
Bell et al. Proceedings of the Combustion Institute (2007)
Tu=298K P=1atm
Φ=0.27 Φ=0.27 Φ=0.37
Lei>1 Lei
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Mathematical expressions of stretch κ
• Flame stretch rate is defined as the normalized differential change with respect to time of an infinitesimal flame surface area element
• Flame stretch rate quantifies the degree of stretch imposed on a differential flame surface element – Lagrangian quantity – Units of flame stretch are 1/s – i.e. an inverse time scale
1 dAA dt
κ ≡Williams (1975)
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Mathematical expressions of stretch κ • Expression for κ in terms of flow velocity, u, and
flame sheet velocity, vF :
• Hydrodynamic stretch κa: variation of tangential
flow velocity in the tangential direction (t1, t2) or, equivalently (by continuity), variation of normal flow velocity in the direction normal (n) to the flame.
• Unsteady Curvature stretch κb: non-stationary flames
o Positive κ: divergent tangential velocities or expanding flame flame area increases
o Negative κ: convergent tangential velocity or contracting flame flame area decreases
1 dAA dt
κ =
1 2
( )( ) ( )( )ba
F Fu u
v n n u v n nκκ
κ∂ ∂
= + + ⋅ ∇ ⋅ = ∇ ⋅ + ⋅ ∇ ⋅∂ ∂
t1 t2t tt t
Unsteady curvature stretch
Hydrodynamic stretch
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Mathematical expressions of stretch κ • Stationary flames
Hydrodynamic stretch can be interpreted as a variation of the angle between flow velocity and flame normal or, equivalently, as a variation in tangential flow magnitude along the flame surface.
• Alternative flame stretch expression o κs: stretch due to flow non uniformities o κcurv: stretch of a curved flame in a uniform
approach flow
κ can be non zero also when the flow strain is zero
( )( )
0
sinceFv u n n u
u n u n
κ= → = ∇ ⋅ = − ×∇ ⋅ ×
= × ×
t t
t
( ) ( )
: ( ) ( )
1 Flow Strain ,2
S curv
u u
T uF
nn u u s n n S n u s n
S u u s n v u
κ κ
κ = − ∇ + ∇ ⋅ − ∇ ⋅ = − ⋅ ⋅ + ∇ ⋅ − ∇ ⋅
= ∇ +∇ ⋅ = −
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Unsteady Effects – Motion of Curved Flames
• Curvature is present but flow velocities align with flame surface normal
• Stationary spherical flame would be stretchless
Combustion Physics by C.K. Law (Cambridge University Press, 2006)
1 2
( )( ) ( )( )ba
F Fu u
v n n u v n nκκ
κ∂ ∂
= + + ⋅ ∇ ⋅ = ∇ ⋅ + ⋅ ∇ ⋅∂ ∂
t1 t2t tt t
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Weak stretch effects • Asymptotic analysis shows that in the linear limit of weak stretch the
effect of various type of stretch (κ, κa, κb, κS, κcurv) on flame characteristics (su, δF,…) is the same.
• For the flame speed measured in a reference frame attached to the unburned gases, su, we can write:
• Definition of Markstein length is not unique but depends on the
isosurface used to define it; e.g. for the flame speed measured in a reference frame attached to the burned gasses sb we have:
• Dimensionless quantities
– Markstein number Ma – Karlovitz number Ka
( ) ,00 0Markstein length
uu u u u u
M
uM
ss s s sκ κκ κ δ κκδ
= =
∂= + = −
∂
0
0 ,0 ,0 1u u
u uM Fu u
F
sMa Ka Ma Kas s
δ δ κδ
= = → = −
,0b b b u bM M Ms s δ κ δ δ− ≠
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Weak stretch effects
• The Markstein number contains all the stretch effects described previously
Ma= Ma(Le, DFuel/DOx, φ ,…)
• For lean mixtures of fuels lighter than air (e.g. H2, CH4) and rich mixtures of fuels heavier than air (e.g. C3H8), Ma < 0 – Conversely, for lean mixtures of heavier than air fuels and
rich mixtures of lighter than air fuels, Ma > 0
• Ma values are sensitive to the position at which flow and flame speeds are measured – For a specific mixture, measured Ma numbers in the
literature can vary widely among different investigators.
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Application – Stoichiometry Effects
C3H8/Air p = 1 atm, T u = 300 K
Tseng et al., Comb. Flame, 95(2), 1993
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Application – Fuel Effects
Ref: Tseng et al., Comb. Flame, 95(2), 1993
n-alkanes/air p =1atm, T u=300K
Ref: Halter et al. Comb and Flame, 157 (2010)
n-C8H18/air
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Application – Pressure Effects
5060708090
100110
0 25000 50000 75000
1 atm
5 atm
10 atm 15 atm
(1/s)κ 0 ,0uFKa sδ κ=
5060708090
100110
0 2 4 6 8 10
1 atm
5 atm
10 atm
15 atm
H2/CO 30/70 (by vol.) in air, T u = 300 K Counterflow twin flame φ adjusted at different p to maintain su,0 = 34 cm/s = const
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PREMIXED FLAME CONCEPTS FLAME STRETCH AND FLAME EXTINCTION
Strong Stretch Effects
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Displacement Speed sd and Consumption Speed sc • Displacement speed sd: speed at which the flame is
moving along its normal relative to the flow
• The value of sd depends on the reference surface: – Low κ : the approach flow varies weakly upstream of the flame and the
iso-surface choice is not to problematic – High κ : velocity gradients occurs on a scale comparable to the flame
thickness; sd definition becomes ambiguous
• Displacement speed can also become negative when diffusive fluxes are strong enough to contrast the bulk convection in the opposite direction
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Displacement Speed sd and Consumption Speed sc • Consumption speed sc: spatial integral of chemical rates
– Can be obtained integrating along a streamline the heat production rate and normalizing by the total change in sensible enthalpy across the flame
– Alternatively, the integrated quantity can be a reactant species consumption rate normalized by the total change in reactant species mass density
Example: 1D steady flame sensible enthalpy balance (no viscous and body forces)
( )
( ), ,
, ,
0, , , , ,
1
0
( ) ( )
Similarly
u u b bsens sens
u uc sens sensu u b bu u
Nx u u b bx sens
f i i x D i c c sens sensi
u h u hs h h
dd u h ddx qdx h Y u dx s s qdx h hdx dx dx
ρ ρ
ρ ρρ
ρρ ρ ρ
∞ −∞
∞ −∞=
∞ ∞ ∞ ∞
∞ −∞=−∞ −∞ −∞ −∞
=−= −
= − + → = = −
∑∫ ∫ ∫ ∫
q
( ), ,from species eq. c i i is w dx Y Yρ∞
∞ −∞−∞
= −∫
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Displacement Speed sd and Consumption Speed sc
0
20
40
60
80
100
120
0 10000 20000 30000
su(c
m/s
)
(1/s)κ
uds
( )2Hucsucs
(enthalpy )
sc0=sd0 but their values differ at non-zero κ values
H2/CO 30/70 (by vol.) in air φ = 0.75, T u = 300 K, p = 5 atm
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Extinction stretch rate κext κext: maximum stretch that a flame can sustain
before extinguishing
0 ,0uFKa sδ κ=
5060708090
100110
0 2 4 6 8 10
1 atm
5 atm
10 atm
15 atm
H2/CO 30/70 (by vol.) in air φ = 0.75, T u = 300K
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Example: Pressure Effects
• Most of the available data are for steady symmetric opposed flow flames : o κext depends on flame chemical time τchem=δF/su,0 (eg. p effects at fixed su,0)
H2/CO 30/70 (by vol.) in air T u = 300 K φ adjusted at different p to maintain su,0 = 34 cm/s = const
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Example: Fuel and Stoichiometry Effects
Ref: Jackson et al., Comb. Fl., 1994, 25(1)
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Example: Preheat Effects • At high dilution/preheating levels, the flame does not
"extinguish“ – increases in reactant temperature are equivalent to a
reduction in dimensionless activation energy – Example: calculation of CH4/air flame stagnating against
hot products, whose temperature is indicated on the plot
0
5
10
15
20
25
0 200 400 600
[cm
/s]
Strain Rate [1/s]
1450 K1400 K
1350 K
-5
0
5
10
15
20
0 200 400 600
[cm
/s]
Strain Rate [1/s]
1450 K1400 K
1350 K
(cm
/s)u cs
(cm/s)
u ds
Strain rate (1/s) Strain rate (1/s)
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Caveats on Stretch Sensitivity of Highly Stretched flames Stretch sensitivities and κext values are not intrinsic to mixture but also depend on manner in which stretch is applied – Example: it depends also on flame
geometry and configuration: o Velocity profile across the flame
thickness (eg. κext for opposed flow flames depends on jets distance)
o Type of stretch (κ, κa, κb, κS, κcurv) o Length and time scale of
flame/stretch interaction
H2/air, φ = 0.37, Tu = 298 K, p = 1 atm
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Course Outline A) Introduction and Outlook B) Flame Aerodynamics and Flashback C) Flame Stretch, Edge Flames, and Flame Stabilization Concepts D) Disturbance Propagation and Generation in Reacting Flows E) Flame Response to Harmonic Excitation
• Introductory Concepts • Flame Stretch • Edge Flames • Flame Stabilization in
Shear Layers • Flame Stabilization by
Stagnation Points
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Overview • Real flames have edges • structure is different than “continuous” flames previously considered:
– Non-premixed flames do not propagate, but their edges do; – Premixed flame edge velocity is different from the laminar burning rate
(e.g., can be negative) • Applications
– Stabilization of non-premixed (a) and premixed flames (b) – Propagation of an ignition front (c) – Flame propagation after local extinction (d)
• Edge flame can be advancing, retreating or stationary – Attention has to be paid to the observer reference frame.
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Edge flame examples • Piloted Bunsen flame
– A retreating flame edge that is stationary in lab coordinate
Rajaram et al., Comb. Sci.Tech ,(175) 2003
vF
vflow
High φ Low φ
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Edge flame examples • Premixed bluff body stabilized flame near blow-off
vF vflow
Chaudhury et al., Comb. Flame (158), 2011
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Edge flame examples • Cabra burner
Dunn et. al, Comb. Flame ,(151) 2007
Vitiated coflow 1500K, 0.8m/s
Natural gas/Air
Cen
tral j
et v
eloc
ity,
(m
/s)
Equivalence Ratio,φ
Downstream extinction observed
Continuous flame
0.80.2 0.3 0.4 0.5 0.6 0.7
200
150
100
50
0
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Edge Flame Concepts Illustrative Model Problem
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Buckmaster’s Edge flame model problem • Generalize the one dimensional non-
premixed chambered flame (z→+∞).
Fuel
L
Flameedge
Oxidizer
Ta
z
x Non-premixed
flame
,Ox aY ,Fuel bYTb
Fv0zu =
2 2
2 2
TransversefluxesE TFuel a u
OxFuel
p T T p x FuelY Y e
MW
T T T Tc k k c u Q wt z x x
ρ
ρ ρ−=−
∂ ∂ ∂ ∂− = − − ∂ ∂ ∂ ∂
B R
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Buckmaster’s Edge flame model problem • Generalize the one dimensional non-
premixed chambered flame (z→+∞).
Fuel
L
Flameedge
Oxidizer
Ta
z
x Non-premixed
flame
,Ox aY ,Fuel bYTb
Fv
( )
2
2 2
2 2
E TFuel a uOx
FuelbT
p T T p x FuelY Y e
MWT Tapproximate as k
L
T T T Tc k k c u Q wt z x x
ρ
ρ ρ−=−
−
∂ ∂ ∂ ∂− = − − ∂ ∂ ∂ ∂
B R
0zu =
-Approximate transverse flux terms by convective loss-like term -L characterizes the scale of gradients normal to the flame, such as due to strain.
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Edge flame model problem
• Dimensionless equation (Le=1)
Fuel
L
Flameedge
Oxidizer
Ta
z
x Non-premixed
flame
,Ox aY ,Fuel bYTb
Fv0zu =
2,, , , ,
1flow p TFuel ba
u b b p b chem
c L kY QE z TE z T Q DaT L T c T
τ ρτ
= = = = = = BR
2
,(1 )where ( , ) 1 exp and F pFuel b F
T
v c LT Q EF T Da T Y Da vT kQ
ρ − += − + − =
2
2 ( , )FdT d Tv F T Dadz dz
− =
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Solution Limit for Edge-less Flame • Steady state solution with no z-
direction variation: – the problem becomes the same as
the steady well stirred reactor; – recover the same S-curve
behavior.
• We will focus on DaI
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• Edge flame
velocity
Edge flame model problem
2
( , )high
low
T
FT
dTv F T Da dT dzdz
∞
−∞
=
∫ ∫
14, 3E Q= =
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• Edge flame velocity
• vF sign depends on the numerator: vF>0
for Da>DaV and vF
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Edge Flame Concepts Edge Structure and Velocity
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Edge flames structure • Non-premixed flames:
Advancing (ignition front, vF>0) have often a triple flame structure; Retreating (extinction front, vF0 vF ~ 0 vF < 0 Computed Reaction rate contours Daou et al., Proc. Comb. Inst.,(29) 2002
Computed Reaction rate contours Verdarajan et al., Comb. Flame,(114) 1998
Image counterflow burner Liu et al., Comb. Sci. Tech.,(144) 1999
Low Stretch
High Stretch
False color images Cha et al., Comb. Flame,(146) 2006
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• Velocity of edge flames vF depends on density ratio σρ (=ρb/ρu) across the flame, Damkohler number Da, heat losses, Le, DFuel/DOx and Zst.
• Dependence on σρ: for a convex flame the deceleration ∆u of the approach flow in front of the flame monotonically increases with σρ (to be discussed later)
• Reutsch et al.’s nonpremixed flame scaling for Da→∞
Flame edge velocity Gas Expansion Effects
uF Dav s ρσ→∞ ∝
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Flame edge velocity Heat Loss Effects
• Heat losses may be important process in edge flames stabilized near metal surfaces
• Heat losses can cause vF
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Conditions at the flame edge • Consider a premixed flame subject
to a spatially varying stretch rate κ at t=0. – Hole will form at points where κ
>κext – edges will retreat to points where
κ=κ(vF=0)=κedge
κextκedge
time
Spatial coordinate
κ
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Conditions at the flame edge
• From edge flame model problem
– For T0/Tad=0.2 and Ea/R uTad=10-20 – 0.5
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Conditions at the flame edge • Experiments show additional
physics: – Tangential flows of hot gases
(e.g., in a lab stationary, retreating edge flame) can increase vF and cause κedge>κext
– When a hole forms in a premixed flames, reactants and products can mix:
• Mass burning rate increases because of presence of radicals and increased initial temperature. Peak heat release rate changes little across different dilution levels;
• The flame looses its S-curve character.
4 , 0.58 equilibrium products
( 450 1 )uCH Air
T K p atmφ = +
= =
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Course Outline A) Introduction and Outlook B) Flame Aerodynamics and Flashback C) Flame Stretch, Edge Flames, and Flame Stabilization Concepts D) Disturbance Propagation and Generation in Reacting Flows E) Flame Response to Harmonic Excitation
• Introductory Concepts • Flame Stretch • Edge Flames • Flame Stabilization in
Shear Layers • Flame Stabilization by
Stagnation Points
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Flame Anchoring -57
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Stretch Effects on Shear Layer Flames • Flame will extinguish
when flame stretch rate exceeds κext – As expected, higher
flow velocities result in flame extinction occurring at higher values of κext
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Flame Anchoring -58
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Shear Layer Stabilized Flames
• In high speed flows, although locally low velocities exist within the shear layer, flame extinction typically leads to liftoff/blowoff – Limited by the amount of flame stretch which they
can withstand before extinction – e.g, 50 m/s jet with 1 mm shear layer thickness
shear~duz/dx ~ 50×103 s-1
• Much greater than typical extinction strain rates, κext
• How is flame stretch related to flow strain in a shear layer?
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Flame Anchoring -59
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Sources of Flame Stretch 1. Flame curvature 2. Unsteadiness in flame and
flow 3. Hydrodynamic strain:
– For reference, fluid strain rate
given by tensor:
Q. Zhang et al. J. Eng. for Gas Turbines & Power 2010
12
jiij
j i
uuSx x
∂∂= + ∂ ∂
( ), is strain ij i jj
un nx
κ δ ∂= −∂
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Flame Anchoring -60
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Flame Stretch Due to Fluid Strain
• General expression can be reduced by assuming 2-D flow and incompressibility (upstream of flame):
2 2( )
uu uxz z
s x z x zuu un n n n
z z xκ
∂∂ ∂= − − + ∂ ∂ ∂
Normal Strain Contribution
Shear Strain Contribution
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Flame Anchoring -61
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Shear Strain Contribution
,
u ux z
s shear x zu un nz x
κ ∂ ∂
= − + ∂ ∂
• Flame strain occurs due to variations in tangential velocity • Leads to positive stretch
Flame Stretch Due to Fluid Strain
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Flame Anchoring -62
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Flame Stretch Due to Fluid Strain
( )2 2,
uz
s normal x zun nz
κ ∂= −∂
Normal Strain Contribution
• Jet flows typically decelerate producing normal strain • Leads to negative stretch
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Flame Anchoring -63
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( )2 2,
uz
s normal x zun nz
κ ∂= −∂
,
u ux z
s shear x zu un nz x
κ ∂ ∂
= − + ∂ ∂
θ
nzn
xn
For high speed flows:
21 ( )xn O θ= − + ( )3zn Oθ θ= +
xu
zu uz
ux
∂∂
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Flame Anchoring -64
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Stretch from Shear Strain •
• If then
,
uz
s shearux
κ θ ∂≈∂
uduz
su
θ ≈,
u ud z
s shear uz
s uu x
κ ∂≈∂
shudshears s δκ ~,→
⇒ Stretch rate due to shear ~indep. of u ? increasing u ⇒ shear ↑ but θ ↓
but u can influence shear layer: δsh∝ u-1/2
Shearing flow velocity profile
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Flame Anchoring -65
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Stretch from Normal Strain
• Obtain traditional flow time scaling approach
Decelerating flow velocity profile
zuuz
normals ∂∂~,κ
char
uz
Lu~
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Flame Anchoring -66
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Total Stretch from Strain • Total stretch due to strain
⇒ Opposite signs if decelerating flow
which term dominates - θ small ?
xu
zu uz
uz
s ∂∂
+∂
∂≈ θκ
xu
zu uz
ux
∂∂
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Flame Anchoring -67
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Flame Stretch Distribution in Swirl Flame • Dimensionless value
of 1= 4,125 1/s
Zhang, Q., Shanbogue, S., Shreekrishna,O’Connor, J., Lieuwen, T., “Strain Characteristics Near the Flame Attachment Point in a Swirling Flow”, Combustion Science and Technology, Vol. 83, 2011, 665-685.
• Shows dominance of deceleration term in first 10 mm
• Shear term dominates farther downstream
0 5 10 15 20-0.8-0.6-0.4-0.2
00.20.40.60.8
1
Axial Location (mm)
Nor
mal
ized
Str
ain
Rat
e (1
/s)
-nr2*∂u/∂r
-nz2*∂v/∂z
-nr*nz*∂u/∂z
-nr*nz*∂v/∂r
κs
2
2
x x
z z
x z x
x z z
s
n u x
n u zn n u zn n u x
κ
− ∗∂ ∂
− ∗∂ ∂
− ∗ ∗∂ ∂
− ∗ ∗∂ ∂
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Flame Anchoring -68
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Piloting or Flow Recirculation Effects
• Flame stabilization can be enhanced through: – Pilot flames – Recirculation zones
• Transport hot products to the attachment point of a flame
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Flame Anchoring -69
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Dilution/Liftoff Effects • At high dilution/preheating levels, the flame does not
"extinguish" – Increases in reactant temperature are equivalent to a reduction in
dimensionless activation energy – Example: calculation of CH4/air flame stagnating against hot
products with indicated temperature
0
5
10
15
20
25
0 200 400 600
[cm
/s]
Strain Rate [1/s]
1450 K1400 K
1350 K
-5
0
5
10
15
20
0 200 400 600
[cm
/s]
Strain Rate [1/s]
1450 K1400 K
1350 K
(cm
/s)u cs
(cm/s)
u ds
Strain rate (1/s) Strain rate (1/s)
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Flame Anchoring -70
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Blowoff of Bluff Body Stabilized Flames • Stages of blowoff
– Stage 1: Flame is continuous but marked by local extinction events
– Stage 2: Changes in wake dynamics as large scale structures become visible
– Stage 3: Blowoff of flame
• Da Approach: – Scaling captures onset of flame
extinction events – Ability to capture blowoff dependent
on link between extinction events and blowoff physics
Nair J. Prop. Power 2007
Images courtesy of D. R. Noble
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Flame Anchoring -71
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Course Outline A) Introduction and Outlook B) Flame Aerodynamics and Flashback C) Flame Stretch, Edge Flames, and Flame Stabilization Concepts D) Disturbance Propagation and Generation in Reacting Flows E) Flame Response to Harmonic Excitation
• Introductory Concepts • Flame Stretch • Edge Flames • Flame Stabilization in
Shear Layers • Flame Stabilization by
Stagnation Points
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Flame Anchoring -72
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Flame Anchoring Locations and Flame Shapes in Swirling Flows
(d) Centerbody & Outer Nozzle (c) IRZ & Outer Nozzle
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Flame Anchoring -73
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Flame Anchoring Locations and Flame Shapes in Annular Nozzle Geometries
From Kumar and Lieuwen
• Flame stabilizes in front of stagnation point of vortex breakdown bubble – Stagnation point apparently precesses,
probably also moves up and down – i.e., flame anchoring position highly
unsteady, in contrast to stabilization at edges/corners
• Under what circumstances can such flames exist? – Not always observed; flames may
blowoff directly without reverting to a “free floating” configuration
– Flow must have interior stagnation point
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Flame Anchoring -74
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Flame Anchoring -75
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Vortex Breakdown in Annular Geometries • Nature of centerbody wake/ VBB changes with geometry, swirl #,
and Reynolds #
Swirl number/ Centerbody Diameter
Recirculation zone with vortex tube
Recirculation zone with bubble-like breakdown above
Merged recirculation zones
Sheen et al., Phys. Fluids, 1996
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Flame Anchoring -76
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• Nature of centerbody wake/ VBB changes with geometry, swirl #, heat release parameter, and Reynolds #
Vortex Breakdown in Annular Geometries
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Flame Anchoring -77
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• Nature of centerbody wake/ VBB changes with geometry, swirl #, and Reynolds #
Vortex Breakdown in Annular Geometries
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Flame Anchoring -78
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Flame Stabilization Influenced by Downstream Boundary Conditions
• Fluid rotation introduces inertial wave propagation mechanism – “sub-” and “supercritical”
flow distinction
• Exit boundary condition has significant influence on vortex breakdown bubble topology
Emara et. al 2009
Flame Stretch, Edge Flames, and Flame StabilizationCourse OutlineCourse OutlineFlame Stabilization and BlowoffPremixed Flame Stabilization: Basic EffectsFlame Anchoring LocationsFlame Stabilization and BlowoffReview of the Idealized Premixed FlameWhat Happens if a Flame isn’t Flat?What Happens if Flow Field isn’t 1-D?Course OutlineOverview of Flame StretchOverview of Flame StretchLewis number effectsDifferential diffusion effectsBunsen Tip Flame Temperature DataExample: Tips of Bunsen FlamesStretched Flames: Non-unity Lewis NumbersMathematical expressions of stretch k Mathematical expressions of stretch k Mathematical expressions of stretch k Unsteady Effects – Motion of Curved FlamesWeak stretch effectsWeak stretch effectsApplication – Stoichiometry EffectsApplication – Fuel EffectsApplication – Pressure EffectsPremixed Flame Concepts�Flame Stretch and Flame ExtinctionDisplacement Speed sd and Consumption Speed scDisplacement Speed sd and Consumption Speed scDisplacement Speed sd and Consumption Speed scExtinction stretch rate kextExample: Pressure EffectsExample: Fuel and Stoichiometry EffectsExample: Preheat EffectsCaveats on Stretch Sensitivity of Highly Stretched flamesCourse OutlineOverviewEdge flame examplesEdge flame examplesEdge flame examplesEdge Flame Concepts� Illustrative Model ProblemBuckmaster’s Edge flame model problemBuckmaster’s Edge flame model problemEdge flame model problemSolution Limit for Edge-less FlameEdge flame model problemEdge flame model problemEdge Flame Concepts�Edge Structure and VelocityEdge flames structureFlame edge velocity�Gas Expansion EffectsFlame edge velocity�Heat Loss EffectsConditions at the flame edgeConditions at the flame edgeConditions at the flame edgeCourse OutlineStretch Effects on Shear Layer FlamesShear Layer Stabilized FlamesSources of Flame Stretch Flame Stretch Due to Fluid StrainFlame Stretch Due to Fluid StrainFlame Stretch Due to Fluid StrainFlame Stretch Due to Fluid StrainStretch from Shear StrainStretch from Normal StrainTotal Stretch from StrainFlame Stretch Distribution in Swirl FlamePiloting or Flow Recirculation EffectsDilution/Liftoff EffectsBlowoff of Bluff Body Stabilized FlamesCourse OutlineFlame Anchoring Locations and Flame Shapes in Swirling FlowsFlame Anchoring Locations and Flame Shapes in Annular Nozzle GeometriesSlide Number 74Vortex Breakdown in Annular GeometriesVortex Breakdown in Annular GeometriesVortex Breakdown in Annular GeometriesFlame Stabilization Influenced by Downstream Boundary Conditions