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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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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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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

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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.