flame stretch, edge flames, and flame stabilization...uh ⋅∇ = −∇⋅ t ... 60 70 80 90 100...

Flame Anchoring -1

School of Aerospace Engineering

Copyright © T. Lieuwen 2013 Unauthorized Reproduction Prohibited

Flame Stretch, Edge Flames, and Flame Stabilization

Natarajan et al. Combustion and Flame 2007

Flame Anchoring -2



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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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

Flame Anchoring -6



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

Flame Anchoring -8



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

Flame Anchoring -9



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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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

Flame Anchoring -13



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

Flame Anchoring -23



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

Flame Anchoring -30



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∞

∞ −∞−∞

= −∫

Flame Anchoring -31



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

Flame Anchoring -32



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

Flame Anchoring -33



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

Flame Anchoring -34



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)

Flame Anchoring -36



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

Flame Anchoring -37






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.

Flame Anchoring -39



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

Flame Anchoring -42



Edge Flame Concepts Illustrative Model Problem

Flame Anchoring -43



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

Flame Anchoring -44



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.

Flame Anchoring -45



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

− =

Flame Anchoring -46



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

Flame Anchoring -47



• Edge flame

velocity

Edge flame model problem

2

( , )high

low

T

FT

dTv F T Da dT dzdz

∞

−∞

=

∫ ∫

14, 3E Q= =

Flame Anchoring -48



• Edge flame velocity

• vF sign depends on the numerator: vF>0

for Da>DaV and vF

Flame Anchoring -49



Edge Flame Concepts Edge Structure and Velocity

Flame Anchoring -50



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

Flame Anchoring -51



• 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→∞ ∝

Flame Anchoring -52



Flame edge velocity Heat Loss Effects

• Heat losses may be important process in edge flames stabilized near metal surfaces

• Heat losses can cause vF

Flame Anchoring -53



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

Flame Anchoring -54



Conditions at the flame edge

• From edge flame model problem

– For T0/Tad=0.2 and Ea/R uTad=10-20 – 0.5

Flame Anchoring -55



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 = +

= =

Flame Anchoring -56






Stagnation Points

Flame Anchoring -57



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

Flame Anchoring -58



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?

Flame Anchoring -59



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 ∂= −∂

Flame Anchoring -60



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

Flame Anchoring -61



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 Anchoring -62




( )2 2,

uz

s normal x zun nz

κ ∂= −∂

Normal Strain Contribution

• Jet flows typically decelerate producing normal strain • Leads to negative stretch

Flame Anchoring -63



( )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

∂∂

Flame Anchoring -64



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

Flame Anchoring -65



Stretch from Normal Strain

• Obtain traditional flow time scaling approach

Decelerating flow velocity profile

zuuz

normals ∂∂~,κ

char

uz

Lu~

Flame Anchoring -66



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

∂∂

Flame Anchoring -67



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

− ∗∂ ∂

− ∗∂ ∂

− ∗ ∗∂ ∂

− ∗ ∗∂ ∂

Flame Anchoring -68



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

Flame Anchoring -69



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)

Flame Anchoring -70



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

Flame Anchoring -71






Stagnation Points

Flame Anchoring -72



Flame Anchoring Locations and Flame Shapes in Swirling Flows

(d) Centerbody & Outer Nozzle (c) IRZ & Outer Nozzle

Flame Anchoring -73



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

Flame Anchoring -74



Flame Anchoring -75



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

Flame Anchoring -76



• Nature of centerbody wake/ VBB changes with geometry, swirl #, heat release parameter, and Reynolds #

Vortex Breakdown in Annular Geometries

Flame Anchoring -77



• Nature of centerbody wake/ VBB changes with geometry, swirl #, and Reynolds #

Vortex Breakdown in Annular Geometries

Flame Anchoring -78



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

flame stretch, edge flames, and flame stabilization...uh ⋅∇ = −∇⋅ t ... 60 70 80 90 100...

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