Considerable research and development efforts are required to meet the targets of future gas turbine technologies in terms of performance, emissions, and operational flexibility. One of the recurring problems is the constructive coupling between flames and combustor's acoustics. These thermoacoustic interactions can cause high-amplitude dynamic pressure limit cycles, which reduce the lifetime of the hot gas path parts or in the worst-case scenario destroy these mechanical components as a result of a sudden catastrophic event. It is shown in this paper that the dynamics and the statistics of the acoustic signal envelope can be used to identify the linear growth rates hidden behind the observed pulsations, and the results are validated against numerical simulations. This is a major step forward and it will contribute to the development of future gas turbine combustors, because the knowledge of these linear growth rates is essential to develop robust active and passive systems to control these combustion instabilities.

References

References
1.
Lieuwen
,
T.
,
2012
,
Unsteady Combustor Physics
,
Cambridge University Press
,
New York
.
2.
Noiray
,
N.
, and
Schuermans
,
B.
,
2013
, “
Deterministic Quantities Characterizing Noise Driven Hopf Bifurcations in Gas Turbine Combustor
,”
Int. J. Non-Linear Mech.
,
50
, pp.
152
163
.
3.
Lieuwen
,
T. C.
,
2003
, “
Statistical Characteristics of Pressure Oscillations in a Premixed Combustor
,”
J. Sound Vib.
,
260
(
1
), pp.
3
17
.
4.
Seume
,
J. R.
,
Vortmeyer
,
N.
,
Krause
,
W.
,
Hermann
,
J.
,
Hantschk
,
C.
,
Zangl
,
P.
,
Gleis
,
S.
,
Vortmeyer
,
D.
, and
Orthmann
,
A.
,
1998
, “
Application of Active Combustion Instability Control to a Heavy Duty Gas Turbine
,”
ASME J. Eng. Gas Turbines Power
,
120
(
4
), pp.
721
726
.
5.
Noiray
,
N.
, and
Schuermans
,
B.
,
2012
, “
Theoretical and Experimental Investigations on Damper Performance for Suppression of Thermoacoustic Oscillations
,”
J. Sound Vib.
,
331
(
12
), pp.
2753
2763
.
6.
Bothien
,
M.
,
Moeck
,
J.
, and
Paschereit
,
C. O.
,
2010
, “
Comparison of Linear Stability Analysis With Experiments by Actively Tuning the Acoustic Boundary Conditions of a Premixed Combustor
,”
ASME J. Eng. Gas Turbines Power
,
132
(
12
), p.
121502
.
7.
Noiray
,
N.
, and
Schuermans
,
B.
,
2013
, “
On the Dynamic Nature of Azimuthal Thermoacoustic Modes in Annular Gas Turbine Combustion Chambers
,”
Proc. R. Soc. A
,
469
(
2151
), p.
20120535
.
8.
Ghirardo
,
G.
, and
Juniper
,
M. P.
,
2013
, “
Azimuthal Instabilities in Annular Combustors: Standing and Spinning Modes
,”
Proc. R. Soc. A
,
469
(
2157
), p.
20130232
.
9.
Nicoud
,
F.
,
Benoit
,
L.
,
Sensiau
,
C.
, and
Poinsot
,
T.
,
2007
, “
Acoustic Modes in Combustors With Complex Impedances and Multidimensional Active Flames
,”
AIAA J.
,
45
(
2
), pp.
426
441
.
10.
Morse
,
P. M.
, and
Ingard
,
K. U.
,
1968
,
Theoretical Acoustics
,
McGraw-Hill
,
New York
.
11.
Culick
,
F. E. C.
,
2006
, “
Unsteady Motions in Combustion Chambers for Propulsion Systems (AGARDograph)
,” OrganisationNorth Atlantic Treaty OrganisationNeuilly-sur-Seine Cedex, France Report No. NATO/RTO-AG-AVT-039.
12.
Ghirardo
,
G.
,
Juniper
,
M.
, and
Moeck
,
J.
,
2015
, “
Stability Criteria for Standing and Spinning Waves in Annular Combustors
,”
ASME
Paper No. GT2015-43127.
13.
Poinsot
,
T.
, and
Veynante
,
D.
,
2001
,
Theoretical and Numerical Combustion
,
Edwards
,
Philadelphia, PA
.
14.
Clavin
,
P.
,
Kim
,
J. S.
, and
Williams
,
F. A.
,
1994
, “
Turbulence-Induced Noise Effects on High-Frequency Combustion Instabilities
,”
Combust. Sci. Technol.
,
96
, pp.
61
84
.
15.
Lieuwen
,
T.
, and
Banaszuk
,
A.
,
2005
, “
Background Noise Effects on Combustor Stability
,”
J. Propul. Power
,
21
(
1
), pp.
25
31
.
16.
Balachandran
,
R.
,
Ayoola
,
B. O.
,
Kaminski
,
C. F.
,
Dowling
,
A. P.
, and
Mastorakos
,
E.
,
2005
, “
Experimental Investigation of the Nonlinear Response of Turbulent Premixed Flames to Imposed Inlet Velocity Oscillations
,”
Combust. Flame
,
143
, pp.
37
55
.
17.
Krylov
,
N.
, and
Bogoliubov
,
N.
,
1949
,
Introduction to Nonlinear Mechanics
,
Princeton University Press
,
London, UK
.
18.
Lieuwen
,
T.
,
2005
, “
Online Combustor Stability Margin Assessment Using Dynamic Pressure Data
,”
ASME J. Eng. Gas Turbines Power
,
127
(
3
), pp.
478
482
.
19.
Yi
,
T.
, and
Gutmark
,
E. J.
,
2008
, “
Online Prediction of the Onset of Combustion Instability Based on the Computation of Damping Ratios
,”
J. Sound Vib.
,
310
, pp.
442
447
.
20.
Schulze
,
M.
,
Kathan
,
R.
, and
Sattelmayer
,
T.
,
2015
, “
Impact of Absorber Ring Position and Cavity Length on Acoustic Damping
,”
J. Spacecr. Rockets
,
52
(
3
), pp.
917
927
.
21.
Hagen
,
G.
,
2011
, “
Stochastic Averaging for Identification of Feedback Nonlinearities in Thermoacoustic Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
133
(
6
), p.
061017
.
22.
Meija
,
D.
,
Miguel-Brebion
,
M.
, and
Selle
,
L.
,
2016
, “
On the Experimental Determination of Growth and Damping Rates for Combustion Instabilities
,”
Combust. Flame
,
169
, pp.
287
296
.
23.
Lax
,
M.
,
1967
, “
Classical Noise. V. Noise in Self-Sustained Oscillators
,”
Phys. Rev.
,
160
(
2
), pp.
290
307
.
24.
Lax
,
M.
,
Cai
,
W.
, and
Xu
,
M.
,
2006
,
Random Processes in Physics and Finance
,
Oxford University Press
,
New York
.
25.
Friedrich
,
R.
,
Siegert
,
S.
,
Peinke
,
J.
,
Lück
,
S.
,
Siefert
,
M.
,
Lindemann
,
M.
,
Raethjen
,
J.
,
Deuschl
,
G.
, and
Pfister
,
G.
,
2000
, “
Extracting Model Equations From Experimental Data
,”
Phys. Lett. A
,
271
(
3
), pp.
217
222
.
26.
Gradisek
,
J.
,
Siegert
,
S.
,
Friedrich
,
R.
, and
Grabec
,
I.
,
2000
, “
Analysis of Time Series From Stochastic Processes
,”
Phys. Rev. E
,
62
(
3146–3155
), pp.
217
222
.
27.
Kolmogorov
,
A. N.
,
1931
, “
Über die Analytischen Methoden in der Wahrscheinlichkeitsrechnung
,”
Math. Ann.
,
140
, pp.
415
458
.
28.
Friedrich
,
R.
,
Peinke
,
J.
,
Sahimi
,
M.
, and
Tabar
,
M. R. R.
,
2011
, “
Approaching Complexity by Stochastic Methods: From Biological Systems to Turbulence
,”
Phys. Rep.
,
506
(
5
), pp.
87
162
.
29.
Siegert
,
S.
,
Friedrich
,
R.
, and
Peinke
,
J.
,
1998
, “
Analysis of Data Sets of Stochastic Systems
,”
Phys. Lett. A
,
243
, pp.
275
280
.
30.
Stratonovich
,
R. C.
,
1963
,
Topics in the Theory of Random Noise
, Vol.
2
,
Gordon & Breach
,
New York
.
31.
Roberts
,
J. B.
, and
Spanos
,
P. D.
,
1986
, “
Invited Review No. 1: Stochastic Averaging: An Approximate Method of Solving Random Vibration Problems
,”
Int. J. Non-Linear Mech.
,
21
(
2
), pp.
111
134
.
32.
Kim
,
K.
, and
Hochgreb
,
S.
,
2012
, “
Measurements of Triggering and Transient Growth in a Model Lean-Premixed Gas Turbine Combustor
,”
Combust. Flame
,
159
(
3
), pp.
1215
1227
.
33.
Moeck
,
J.
,
Bothien
,
M.
,
Schimek
,
S.
,
Lacarelle
,
A.
, and
Paschereit
,
C. O.
,
2008
, “
Subcritical Thermoacoustic Instabilities in a Premixed Combustor
,”
AIAA
Paper No. 2008-2946.
34.
Ushakov
,
O. V.
,
Wunsche
,
H.-J.
,
Henneberger
,
F.
,
Khovanov
,
I. A.
,
Schimansky-Geier
,
L.
, and
Zaks
,
M. A.
,
2005
, “
Coherence Resonance Near a Hopf Bifurcation
,”
Phys. Rev. Lett.
,
95
(
12
), p.
123903
.
35.
Zakharova
,
A.
,
Vadivasova
,
T.
,
Anishchenko
,
V.
,
Koseska
,
A.
, and
Kurths
,
J.
,
2010
, “
Stochastic Bifurcations and Coherencelike Resonance in a Self-Sustained Bistable Noisy Oscillator
,”
Phys. Rev. E
,
81
(
1
), p.
011106
.
36.
Kabiraj
,
L.
,
Steinert
,
R.
,
Saurahb
,
A.
, and
Paschereit
,
C. O.
,
2015
, “
Coherence Resonance in a Thermoacoustic System
,”
Phys. Rev. E
,
92
(
4
), p.
042909
.
37.
Waugh
,
I. C.
, and
Juniper
,
M. P.
,
2011
, “
Triggering in a Thermoacoustic System With Stochastic Noise
,”
Int. J. Spray Combust. Dyn.
,
3
(
3–4
), pp.
225
242
.
38.
Gotoda
,
H.
,
Shinoda
,
Y.
,
Kobayashi
,
M.
,
Okuno
,
Y.
, and
Tachibana
,
S.
,
2014
, “
Detection and Control of Combustion Instability Based on the Concept of Dynamical System Theory
,”
Phys. Rev. E
,
89
(
2
), p.
022910
.
39.
Gopalakrishnan
,
E. A.
, and
Sujith
,
R. I.
,
2015
, “
Effect of External Noise on the Hysteresis Characteristics of a Thermoacoustic System
,”
J. Fluid Mech.
,
776
, pp.
334
353
.
You do not currently have access to this content.