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25/05/2019
1
Combustion dynamics Lecture 5c
S. Candel, D. Durox , T. Schuller!
Princeton summer school, June 2019 DD TS SC
Copyright ©2019 by [Sébastien Candel]. This material is not to be sold, reproduced or distributed without prior written permission of the owner, [Sébastien Candel].
CentraleSupélec Université Paris-Saclay, EM2C lab, CNRS
Combustion dynamics of inverted conical flames
Confined flames
Radiant burners
Domestic burners
Unconfined flames
Combustion chambers Gas turbine combustors
Low emission systems operating in premixed lean modes. Flames are less well stabilized and more susceptibleto external perturbations
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Experimental set-up
Diameter 22 mm CH4 - air Eq. Ratio : 0.92 Flow velocity : 2.05 m/s
Steady flame mixture of
gases
CH*filter
MicroPM
LDVFlame
Rod
(431 nm)
Inverted conical flame (ICF)
©Sebastien Candel, June 2019
Microphone
Gas mixture
CH* Filter (431nm)
Flame
Rod
4
Self-induced Instability
Self-excited flame at f = 172 Hz Eq. Ratio : 0.92 Flow velocity : 2.05 m/s v' = 0.14 m/s
mixture ofgases
CH*filter
MicroPM
LDVFlame
Rod
For certain flow conditions, equivalence ratios and geometry
©Sebastien Candel, June 2019
Microphone
CH* Filter (431nm)
Rod Rod
Gas mixture
Flame
�Q�Q
�p
�p�v
�v
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5
Transfer function
Self-excited flame at f = 100 Hz Eq. ratio : 0.92 Flow velocity : 2.05 m/s v’1 = 0.14 m/s
mixture ofgases
loudspeaker
CH*filter
MicroPM
LDVFlame
Rod
I’(t) (r = 7 mm, z = 0.8 mm)
€
I ∝Qv0
�Q
Q= f(
�v
v)
©Sebastien Candel, June 2019
CH* Filter (431nm)
Rod Rod
Gas mixture
Flame
Driver unit
Describing function
0
0.5
1
1.5
2v' = 0.14 m/sv' = 0.20 m/sv' = 0.30 m/sv' = 0.38 m/s
0 100 200 300 400
Gai
n
1
1
1
1
Freq (Hz)
0
2
4
6
0 100 200 300 400
Phas
e D
iffer
ence
(rad
)
Freq (Hz)
π
π
π
0
ϕ is nearly linear convective lag = 8.6 ms
Φ=0.92Vd=2.05m/s
I 0CH⇤(t) = G[v01]t�⌧c
©Sebastien Candel, June 2019
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7
Φ =0.8Vd=1.87m/sv'1=0.15m/s
Flame dynamics Laser tomography of fresh stream seeded with oil droplets.
f=70Hz
©Sebastien Candel, June 2019
8
Φ =0.8Vd=1.87m/sv'1=0.15m/s
Flame dynamics
f=150Hz
©Sebastien Candel, June 2015
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Φ =0.8Vd=1.87m/s,v'1=0.15m/sf=150Hz
Unsteady vorticity field
The vortices are convected at a velocity
0
1
2
3
4Eq. R. : 0.92 -- Vd = 2.05 m/s -- z = 0.7 mm
Steady v' = 0.16 v' = 0.38
-15 -10 -5 0 5 10 15
V (m
/s)
1 1
r (mm)
©Sebastien Candel, June 2019
Uc
' 0.5vmax
10
Helmholtz resonator Bulk oscillation inside the burner
fo = 163 Hz
S z( ) z
δend
V
Mechanism of instability
Micro MO
S1 1
L=164mm
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400Am
p. o
f Pre
s. O
sc. (
a.u.
)
Freq (Hz)
L!20 = (c2S1)/(V Leff )
Leff
=
Zout
in
S1
S(z)dz + �
e
©Sebastien Candel, June 2019
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Effective mass of gases
System damping
Stiffness of the gas volume
The resonator is driven by external fluctuations
Helmholtz resonator with driving
Mechanism of instability
Md2v01dt2
+Rdv01dt
+ kv01 = �S1dp01dt
M = ⇢S1Leff
R = ⇢S1v1
k = ⇢c2S21/V
Φ=0.92Vd=2.05m/sv'1=0.14m/sf=172Hz
Signals measured in self-sustained instability case
0
1
2
3
4
-50
0
50
100
150
0 5 10 15 20 25LDV
(m/s
) - C
H*
(arb
.uni
t)
Time (ms)
LDV
CH*
Micro
Pressure (Pa) --- Micro (a.u.)
Pressure p'0
mixture ofgases
CH*filter
MicroPM
LDVFlame
Rod
1
€
p'1 t( ) ≈ E dQ' dt[ ]t−τ a
0
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Time lag model
Mechanism of instability
v 1v'1
p’(t)
1
I 0CH⇤(t) = G[v01]t�⌧c p01(t) = B[I 0CH⇤]t�⌧a
Steady flow streamlines
Average location of the flame front in the absence of perturbation
Averaged image of the flame
front positions with a perturbation
at 70 Hz
Φ =0.8Vd=1.87m/s
v'1=0.15m/sf=70Hz
The dot corresponds to
©Sebastien Candel, June 2019
h = ⌧c
Uc
' ⌧c
(0.5vmax
)
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Mechanism of instability
I 0CH⇤(t) = G[v01]t�⌧c
p01(t) = B[I 0CH⇤]t�⌧a
Md2v01dt2
+Rdv01dt
+ kv01 = �S1dp01dt
!20 =
S1c2
V Le
2�!0 = R/M
⌦ = GBS1/M
If δ and Ω are small, a linear analysis indicates that a necessary condition to have an instability is:
belongs to modulo 2π
Mechanism of instability
d2v01dt2
+ 2�!0dv01dt
+ !20v
01 = �⌦
⇥dv01dt
⇤t�⌧a�⌧c
⌧a << ⌧c ⌧ ' ⌧c
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0
0.5
1
1.5
2v' = 0.14 m/sv' = 0.20 m/sv' = 0.30 m/sv' = 0.38 m/s
0 100 200 300 400
Gai
n
1
1
1
1
Freq (Hz)0
2
4
6
0 100 200 300 400
Phas
e D
iffer
ence
(rad
)
Freq (Hz)
π
π
π
0
unstable
unstable
unstable
Mechanism of instability
Φ=0.92Vd=2.05m/s
fo = 163 Hz f = 172 Hz Frequency peak at the resonance
Instability frequency
Conclusions
ICF's are sensitive to low frequency acoustic excitations. They behave like an amplifier in a broad frequency range. The transfer function phase grows linearly : the process involves a convective delay. The main wrinkling of the flame front is due to vortex structures created in the shear layer.
The strong rolling-up of the flame induces a mutual annihilation of neighboring reactive elements
Rapid variation of flame surface area Important source of pressure wave.
With ICF's, at low amplitude modulation, entrainement of air modifies the equivalence ratio near the flame tip and the light emission ceases to be proportional to the heat release.