Lecture 8. Turbulent Premixed Flames
X.S. Bai
Turbulent premixed Flames
Content
•
•
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•
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Feastures of turbulent premixed flames
Mechanisms of flame wrinkling
Regimes of turbulent premixed flames
Turbulent burning velocity
Propagation of turbulent flames in flow field
Turbulent premixed flame stabilization
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Turbulent premixed Flames
Experimental setup: Low swirl burner
Filtered Rayleigh Scattering setup
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Turbulent premixed Flames
Results - simultaneous PIV / PLIF
The combined PIV / OH-PLIF results
showing the flame front structure and
its position in the flow field.
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Turbulent premixed Flames
PLIF of fuel
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Turbulent premixed Flames
PLIF of fuel and OH
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Turbulent premixed Flames
Premixed jet flames
D outer
ceramic
holder
Do=22mm
Di=2.2mm
D inner
methane/air
(outer)
methane/air
(inner)
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Turbulent premixed Flames
Laminar flame
photo
CH2O
CH
Vo=0.45 m/s, phi=1.17; Vin=11m/s, phi=1.1
X.S. Bai
Turbulent premixed Flames
Turbulent jet flame
photo
CH2O
CH
Vo=0.45 m/s, phi=1.17; Vin=120m/s, phi=1.0
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Turbulent premixed Flames
The shape of a turbulent premixed flame: a closer look
•
Planar single pulse OH radical
concentration, 50mm above the
burner. Field size: 150x110 mm
•
natural gas/air premixed flame
measured by Buschmann et al (26th
symp. Comb., pp.437, 1996)
•
OH peak denotes the flame zone. Why
flame zone is wrinkled? See next slide
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Turbulent premixed Flames
Lean H2/air premixed flame in a room
door
Lean
H2/air mixture
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Turbulent premixed Flames
Lean H2/air premixed flame in a room
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Turbulent premixed Flames
Basic features of TPF
• TPF can be divided to three zones
– Preheat zone
– Reaction zone
– Postflame zone
• The reaction zone in typical TPF is thin
– CH layer;
– fuel consumption layer
• The reaction zone is highly wrinkled
– Due to turbulence eddies
– Due to self-instability
• Hydrodynamic instability (Landau-Darrieus)
• Diffusion-thermal instability
• Bouyancy effect (Rayleigh-Taylor)
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Turbulent premixed Flames
Wrinking by turbulence eddies
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Turbulent premixed Flames
Flame – turbulence interaction and
regimes turbulent premixed flames
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Turbulent premixed Flames
Different scales in turbulent premixed flames
• Flow scales
– Mean flow scales
• Length (L), velocity (U), time (t=L/U)
– integral scales
• length (l0), velocity (v0=u(l0)), time (τ0= l0 /v0),
– Kolmogrov scales
• length (η), velocity (vη=u(η)), time (τη= η /vη),
• Flame scales
– flame speed (SL)
– flame thickness (δL)
– time scale (tc)
• flame thickness/flame speed
• chemical reaction time
– the flame structure may not be laminar
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Turbulent premixed Flames
Physical interpretation of length, time and velocity scales
Chemical reaction and flame scales
oxidation layer
mole fraction
0.2
2000
1800
T
1600
inner layer
0.15
1400
0.1
O2
0.05
CO2
1200
1000
800
C3H8
CO
600
0
−2
temperature (K)
preheat zone
−1
0
1
2
flame coordinate (mm)
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Turbulent premixed Flames
Physical interpretation of length, time and velocity scales
Mean flow scales
U
alpha
SL = U sin(alpha)
SL
Flow time >> molecularmixing time
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Turbulent premixed Flames
Physical interpretation of length, time and velocity scales
Turbulence eddy scales
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Turbulent premixed Flames
Physical interpretation of length, time and velocity
scales
Turbulence eddy scales
Eddy size –
Eddy velocity –
Eddy turn over time –
l
ul
teddy=l/ul
Molecular mixing time of
Material of size lk –
tmixing=lk2/D=lk/uk
teddy
ul
l
tmixing
l uk
=
= Rel 1 / 2
ul l k
note : lk = η, uk = u η
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Turbulent premixed Flames
Physical interpretation of length, time and velocity
scales
inlet, other
boundaries
Energy transfer at a
‘constant’ rate ε
heat
δL
ul
l
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Turbulent premixed Flames
Turbulent jet flame
photo
CH2O
CH
Vo=0.45 m/s, phi=1.17; Vin=120m/s, phi=1.0
X.S. Bai
Turbulent premixed Flames
Turbulent jet flame
PLIF images of
formaldehyde (green)
and CH (red) in
laminar (a) and
turbulent (b-f) flames
with different gas
supply speeds in the
inner tube.
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Turbulent premixed Flames
Scale relationship
Energy transfer at a
‘constant’ rate ε
inlet, other
boundaries
heat
⎛ l 0 ⎞⎟
v η3
v0
l0 vη
τ0
ε∝
∝
⇒
∝
∝ ⎜⎜ ⎟⎟
⎜⎝ η ⎠⎟
η
τη
l0
v0 η
vη η
vl
∝ 1 ⇒ 0 0 ∝ Rel 0
ν
vη η
2/3
3
l0
l0 v0 vη
l 0v 0 ⎛⎜ η ⎞⎟
∝
∝
⎜⎜ ⎟⎟
η
η vη v0
ν ⎝ l 0 ⎠⎟
1/ 3
⇒
τ
l0
v
∝ Rel 0 3 / 4 ; 0 ∝ Rel 01/ 4 ; 0 ∝ Rel 01/ 2 ;
η
τη
vη
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Turbulent premixed Flames
Non-dimensional numbers
in turbulent premixed flames
Reynolds number
Damköhler number
Karlovitz number
v 0l 0
Rel 0 =
ν
τ0
l0 S L
Da =
=
τc
v 0 δL
τc
δL v η
δL δL D v η η ⎛⎜ δL ⎞⎟
Ka =
=
=
= ⎜ ⎟⎟
⎜⎝ η ⎠⎟
SL η
S L δL ν ηη
τη
Turbulent intensity
v0
TI =
SL
2
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Turbulent premixed Flames
Non-dimensional numbers
Reynolds number
Re l =
v0 l0
ν
∴ S L ∝ (D ⋅ rr ) , δ L ∝ (D / rr ) , S Lδ L ∝ D ∝ ν
1/ 2
1/ 2
v0 l0
v0 l0
v0 l0
∝
∝
Re l =
D
S Lδ L
ν
⎛ v0 ⎞
⎛ l0 ⎞
⇒ log ⎜⎜ ⎟⎟ = log (Re l ) − log ⎜⎜ ⎟⎟
⎝ SL ⎠
⎝δL ⎠
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Constant Rel lines in the
Borghi-diagram
Turbulent premixed Flames
Borghi-diagram
Rel=104
Constant Rel lines
Rel=100
⎛ v0 ⎞⎟
⎛ l0 ⎞⎟
⎜
log ⎜ ⎟⎟ = log (Rel ) − log ⎜⎜ ⎟⎟
⎜⎝S ⎠⎟
⎝⎜ δ ⎠⎟
L
Rel=1
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Turbulent premixed Flames
L
Non-dimensional numbers
Damköhler number
τ0
l0 S L
Da =
=
τc
v 0 δL
l0
v0
log(Da ) = log( ) − log( )
δL
SL
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Turbulent premixed Flames
Da=0.01
Borghi-diagram
Constant Da lines
Da=1
Da=100
l
v
log(Da ) = log( 0 ) − log( 0 )
δL
SL
Rel=1
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Turbulent premixed Flames
Non-dimensional numbers
Karlovitz number
τc
δL v η
δL l 0 v η u ′
δL u ′ l 0 v η
=
=
=
Ka =
SL η
S L l0 η u ′
l0 S L η u ′
τη
δL u ′
δL 1/ 2 u ′ 3 / 2
1/ 2
=
Rel 0 = ( ) ( )
l0 S L
l0
SL
1
2
u′
l0
log( ) = log( ) + log(Ka )
3
3
SL
δL
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Turbulent premixed Flames
Borghi-diagram
Ka=100
Constant Ka lines
Ka=1
u′
1
l
2
log( ) = log( 0 ) + log(Ka )
SL
3
δL
3
Rel=1
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Ka=0.01
Turbulent premixed Flames
Borghi-diagram
Ka=100
dark region: GT engines
small circle: GE LM6000
squares: VR-1
I: laminar flames
II: wrinkled flamelet
III: corrugated flamelet
IV: thin reaction zone
V: distributed reactions
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Turbulent premixed Flames
Flamelet regimes
τc
δL v η
δL δL D v η η ⎛⎜ δL ⎞⎟
Ka =
=
=
= ⎜ ⎟⎟ < 1
⎜⎝ η ⎠⎟
SL η
S L δL ν ηη
τη
2
• The thickness of reaction zone + preheat zone is thinner than the Kolmogrov
scale, i.e. δL<η
– Tranport of mass and heat between the reaction zone and preheat zone is
by molecular mixing
– As a good approximation the local flame propagates at laminar flame
speed and the thickness of the flame is laminar
burned
Unburned
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mKolmogrov
mreaction ,all _ layers
∼
u(η) D
δ u(η)η
/ 2 ∼ L
δL
δL
η D
∼
δL
<1
η
Turbulent premixed Flames
Turbulent jet flame
PLIF images of
formaldehyde (green)
and CH (red) in
laminar (a) and
turbulent (b-f) flames
with different gas
supply speeds in the
inner tube.
X.S. Bai
Turbulent premixed Flames
Thin reaction zone regime
τ
δ v
δ δ D v η η ⎛⎜ δL ⎞⎟
= ⎜ ⎟⎟ ,1 < Ka < 100
Ka = c = L η = L L
⎜⎝ η ⎠⎟
τη
SL η
S L δL ν ηη
2
burned
Reactant pockets
May not pass the
Inner layer of
The reaction zone
Unburned
mKolmogrov
mreaction ,all −layers
δ u(η)η
u(η)
u(η) D
/Ω ∼
/ 2 ∼ L
∼
δL
δL
δL
η D
∼
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δL
>1
η
mkolmogrov
mreaction ,inner _ layer
∼
u(η) S L
δ u(η)η
/
∼ inn
δL
δin
η D
∼
δinn
δ
∼ 0.1 L ∼ 0.1Ka 1 / 2 < 1
η
η
Turbulent premixed Flames
Turbulent jet flame
PLIF images of
formaldehyde (green)
and CH (red) in
laminar (a) and
turbulent (b-f) flames
with different gas
supply speeds in the
inner tube.
X.S. Bai
Turbulent premixed Flames
Distributed reaction zone regime
τ
δ v
δ δ D v η η ⎛⎜ δL ⎞⎟
Ka = c = L η = L L
= ⎜ ⎟⎟ , Ka > 100
⎜⎝ η ⎠⎟
τη
SL η
S L δL ν ηη
2
Reactant pockets
May pass the
Reaction zone
Without full
consumption
burned
Unburned
mKolmogrov
mreaction ,all _ layers
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∼
u(η) D
δ u(η)η
/ 2 ∼ L
δL
δL
η D
∼
δL
>1
η
mkolmogrov
mreaction ,inner _ layer
∼
u(η) S L
δ u(η)η
/
∼ inn
δL
δin
η D
∼
δinn
δ
∼ 0.1 L ∼ 0.1Ka 1 / 2 > 1
η
η
Turbulent premixed Flames
How does TPF propagate
• TPF propagates due to
– Heat transfer to preheat zone to heat up the fuel/air to above
’cross-over’ temperature
– Fuel/air mass transfer to the reaction zone to provide fuel/air
for combustion and releasing heat
• Transport of mass and heat between the reaction zone and the
preheat zone
– can be different from laminar premixed flames
– Depending on the thickness of the zones
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Turbulent premixed Flames
Turbulent burning velocity
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Turbulent premixed Flames
Turbulent burning velocity
• Also called turbulent flame speed
• Defined as the propagation speed of the mean flame front, relative
to the unburned mixture
• Is equal to the consumption rate of the unburned mixture (volume
flow per unit area of the mean flame front)
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Turbulent premixed Flames
Turbulent burning velocity: flamelet regime
• Also called turbulent flame speed
• Defined as the propagation speed of the mean flame front, relative
to the unburned mixture
• Is equal to the consumption rate of the unburned mixture (volume
flow per unit area of the mean flame front)
AL
sT
unburned
side
AM
burned
side
sL
η
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low-intensity, large
scale
Turbulent premixed Flames
Turbulent burning velocity: flamelet regime
ST / S L = 1 + u ′ / S L
ST / S L
Flamelet
theory
Fall-off
1
∼ 10 − 100
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u′ / S L
Turbulent premixed Flames
Turbulent burning velocity: thin reaction zone regime
ST / S L ∼ Dt / D ∼ u '
0 / ν = Re
ST / S L
Flamelet
theory
Fall-off
1
∼ 10 − 100
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u′ / S L
Turbulent premixed Flames
1/ 2
0
Burning velocities
• Laminar burning velocity
– Depending on Molecular diffusion
– Depending on Chemical reactions
– Independent of flow
• Turbulent burning velocity
– Depending on Molecular diffusion
– Depending on Chemical reactions
– Depending on flow
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Turbulent premixed Flames
Propagation of turbulent premixed flames
Propagation of the instantaneous flame front
∂G
+ v ⋅ ∇G = S L ∇ G
∂t
Propagation of the mean flame front
ST
SL
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∂G
+ v ⋅ ∇G = ST ∇G
∂t
Turbulent premixed Flames
Mean planar flame in a tube
Unburned
x< 0
ST
U
x= 0 (at t=0)
•
•
•
•
Stable flame
Flashback
Blowoff
Quenching distance
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burned
x> 0
x
Flame position
x = (U − ST )t
Turbulent premixed Flames
Mean conical flame
G(x,r,t)=0
U
x
R
r
ST
U 2 − ST 2
x = (R − r)
ST 2
U
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Rim stablization
Liftoff
Blowoff
flashback
Turbulent premixed Flames
Flame stabilization
Zst
x
Ssgs
v
Temperature field
and streamlines
(white) from LES
Schematic of the conical burner
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Turbulent premixed Flames
Flame stabilization
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Turbulent premixed Flames
AEV burner
Between 1990 and 2005, all new gas turbines of ABB (later Alstom/Siemens) have
Implemented EV burners.
ABB/Alstom EV burner
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Turbulent premixed Flames
AEV burner: flame stabilization by swirling flow
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Turbulent premixed Flames
Swirl combustor, dump combustor, bluff-body stabilization
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Turbulent premixed Flames