Indirect combustion noise originates from the acceleration of nonuniform temperature or high vorticity regions when convected through a nozzle or a turbine. In a recent contribution (Giauque et al., 2012, “Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles,” ASME J. Eng. Gas Turbies Power, 134(11), p. 111202) the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrarily shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in detail. The evolution of the cross-section changes are introduced using Bezier's splines, which provide the necessary freedom to actually achieve arbitrary shapes. Bezier's polar coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (Bloy, 1979, “The Pressure Waves Produced by the Convection of Temperature Disturbances in High Subsonic Nozzle Flows,” J. Fluid Mech., 94(3), pp. 465–475), the results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections, leading to a square evolution of the cross-section area. Providing insight into the underlying physical reason leading to the difference in the noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an acoustic emission factor, which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This acoustic emission factor, which is much faster to compute, only involves the knowledge of the evolution of the cross-section area and the inlet thermodynamic and velocity characteristics to be computed.

References

References
1.
Candel
,
S. M.
,
1972
, “
Analytical Studies of Some Acoustic Problems of Jet Engines
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
2.
Marble
,
F. E.
,
1973
, “
Acoustic Disturbance From Gas Non-Uniformities Convecting Through a Nozzle
,”
Interagency Symposium on University Research in Transportation Noise, Stanford, CA, March 28–30
.
3.
Morfey
,
C. L.
,
1973
, “
Amplification of Aerodynamic Noise by Convected Flow Inhomogeneities
,”
J. Sound Vib.
,
31
, pp.
391
397
.10.1016/S0022-460X(73)80255-X
4.
Marble
,
F. E.
, and
Candel
,
S. M.
,
1977
, “
Acoustic Disturbance From Gas Non-Uniformities Convecting Through a Nozzle
,”
J. Sound Vib.
,
55
(
2
), pp.
225
243
.10.1016/0022-460X(77)90596-X
5.
Cumpsty
,
N. A.
, and
Marble
,
F. E.
,
1977
, “
Core Noise From Gas Turbine Exhausts
,”
J. Sound Vib.
,
54
, pp.
297
309
.10.1016/0022-460X(77)90031-1
6.
Blacodon
,
D.
,
2009
, “
Combustion-Noise Characterization of a Turbofan Engine With Spectral Estimation Method
,”
J. Propul. Power
,
25
(
2
), pp.
374
379
.10.2514/1.37013
7.
Poinsot
,
T.
, and
Veynante
,
D.
,
2012
,
Theoretical and Numerical Combustion
,
3rd ed.
,
R. T. Edwards
,
Flourtown
, PA.
8.
Culick
,
F.
, and Kuentzmann, P.,
2006
, “Unsteady Motions in Combustion Chambers for Propulsion Systems,” NATO Research and Technology Organization Neuilly-Sur-Seine, France, Paper No. AC/323 (AVT-039) TP/103.
9.
Hochgreb
,
S.
,
Dennis
,
D.
,
Ayranci
,
I.
,
Bainbridge
,
W.
, and
Cant
,
S.
,
2013
, “
Forced and Self-Excited Instabilities From Lean Premixed, Liquid-Fuelled Aeroengine Injectors at High Pressures and Temperatures
,” ASME Turbo Expo, San Antonio, TX, June 3–7, ASME Paper No. GT2013-95311.
10.
Motheau
,
E.
,
Nicoud
,
F.
,
Mery
,
Y.
, and
Poinsot
,
T.
,
2013
, “
Analysis and Modelling of Entropy Modes in a Realistic Aeronautical Gas Turbine
,” ASME Turbo Expo, San Antonio, TX, June 3–7, ASME Paper No. GT2013-94224.
11.
Moase
,
W.
,
Brear
,
M. J.
, and
Manzie
,
C.
,
2007
, “
The Forced Response of Choked Nozzles and Supersonic Diffusers
,”
J. Fluid Mech.
,
585
, pp.
281
304
.10.1017/S0022112007006647
12.
Giauque
,
A.
,
Huet
,
M.
, and
Clero
,
F.
,
2012
, “
Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles
,”
ASME J. Eng. Gas Turbines Power
,
134
(
11
), p.
111202
.10.1115/1.4007318
13.
Mishra
,
A.
, and
Bodony
,
D.
,
2013
, “
Evaluation of Actuator Disk Theory for Predicting Indirect Combustion Noise
,”
J. Sound Vib.
,
332
(
4
), pp.
821
838
.10.1016/j.jsv.2012.09.025
14.
Leyko
,
M.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2009
, “
Numerical and Analytical Investigation of the Indirect Noise in a Nozzle
,”
C. R. Mec.
,
337
, pp.
415
425
.10.1016/j.crme.2009.06.025
15.
Bake
,
F.
,
Richter
,
C.
,
Mühlbauer
,
B.
,
Kings
,
N.
,
Rohle
,
I.
,
Thiele
,
F.
, and
Noll
,
B.
,
2009
, “
The Entropy Wave Generator (EWG): A Reference Case on Entropy Noise
,”
J. Sound Vib.
,
326
, pp.
574
598
.10.1016/j.jsv.2009.05.018
16.
Hield
,
P. A.
,
Brear
,
M. J.
, and
Jin
,
S. H.
,
2009
, “
Thermoacoustic Limit Cycles in a Premixed Laboratory Combustor With Open and Choked Exits
,”
Combust. Flame
,
156
(
9
), pp.
1683
1697
.10.1016/j.combustflame.2009.05.011
17.
Howe
,
M. S.
,
2010
, “
Indirect Combustion Noise
,”
J. Fluid Mech.
,
659
, pp.
267
288
.10.1017/S0022112010002466
18.
Strahle
,
W. C.
,
1978
, “
Combustion Noise
,”
Prog. Energy Combust. Sci.
,
4
(
3
), pp.
157
176
.10.1016/0360-1285(78)90002-3
19.
Muthukrishnan
,
M.
,
Strahle
,
W. C.
, and
Neale
,
D. H.
,
1978
, “
Separation of Hydrodynamic, Entropy, and Combustion Noise in a Gas Turbine Combustor
,”
AIAA J.
,
16
(
4
), pp.
320
327
.10.2514/3.60895
20.
Bohn
,
M. S.
,
1976
, “
Noise Produced by the Interaction of Acoustic Waves and Entropy Waves With High-Speed Nozzle Flows
,” PhD thesis, California Institute of Technology, Pasadena, CA.
21.
Zukoski
,
E. E.
, and
Auerbach
,
J. M.
,
1976
, “
Experiments Concerning the Response of Supersonic Nozzles to Fluctuating Inlet Conditions
,”
ASME J. Eng. Power
,
98
(
1
), pp.
60
64
.10.1115/1.3446114
22.
Durán
,
I.
, and
Moreau
,
S.
,
2011
, “
Analytical and Numerical Study of the Entropy Wave Generator Experiment on Indirect Combustion Noise
,
17th AIAA/CEAS Aeroacoustics Conference
,
Portland, OR
, June 5–8,
AIAA
Paper No. 2011–2829.10.2514/6.2011-2829
23.
Tran
,
N.
,
Ducruix
,
S.
, and
Schuller
,
T.
,
2009
, “
Damping Combustion Instabilities With Perforates at the Premixer Inlet of a Swirled Burner
,”
Proc. Combust. Inst.
,
32
(
2
), pp.
2917
2924
.10.1016/j.proci.2008.06.123
24.
Goldberg
,
D.
,
1989
,
Genetic Algorithms in Search, Optimization, and Machine Learning
,
Addison-Wesley
,
Reading, MA
.
25.
Ihme
,
M.
, and
Pitsch
,
H.
,
2012
, “
On the Generation of Direct Combustion Noise in Turbulent Non-Premixed Flames
,”
Int. J. Aeroacoust.
,
11
(
1
), pp.
25–78
.10.1260/1475-472X.11.1.25
26.
Bogey
,
C.
, and
Bailly
,
C.
,
2004
, “
A Family of Low Dispersive and Low Dissipative Explicit Schemes for Flow and Noise Computations
,”
J. Comput. Phys.
,
194
(
1
), pp.
194
214
.10.1016/j.jcp.2003.09.003
27.
Cacqueray
,
N. D.
,
2010
, “
Méthodes Numériques Pour les Écoulements Supersoniques Avec Application au Calcul du Bruit Rayonné par un jet Sur-détendu
,” Ph.D. thesis, École Centrale de Lyon, Lyon, France.
28.
Thompson
,
K. W.
,
1987
, “
Time Dependent Boundary Conditions for Hyperbolic Systems
,”
J. Comput. Phys.
,
68
(
1
), pp.
1
24
.10.1016/0021-9991(87)90041-6
29.
Poinsot
,
T. J.
and
Lele
,
S. K.
,
1992
, “
Boundary Conditions for Direct Simulations of Compressible Viscous Flows
,”
J. Comput. Phys.
,
101
(
1
), pp.
104
129
.10.1016/0021-9991(92)90046-2
30.
Kaufmann
,
A.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2002
, “
Flow Forcing Techniques for Numerical Simulation of Combustion Instabilities
,”
Combust. Flame
,
131
(
4
), pp.
371
385
.10.1016/S0010-2180(02)00419-4
31.
Crighton
,
D. G.
,
Dowling
,
A. P.
,
Ffowcs Williams
,
J. E.
,
Heckl
,
M.
, and
Leppington
,
F. G.
,
1996
,
Modern Methods in Analytical Acoustics
,
Springer
,
New York
.
32.
Bloy
,
A. W.
,
1979
, “
The Pressure Waves Produced by the Convection of Temperature Disturbances in High Subsonic Nozzle Flows
,”
J. Fluid Mech.
,
94
(
3
), pp.
465
475
.10.1017/S0022112079001130
You do not currently have access to this content.