Abstract

The ability of acoustic network models to model combustion instabilities is dependent on the accuracy of acoustic two-port models. While several forms of two-ports are available, the most common for these types of analyses is the scattering matrix. To facilitate the modeling of industrial-type components in these models, two industrial components, a perforated plate and an axial swirler with vane-based fuel injection, are tested in an impedance tube. Both elements were tested from 100 Hz to 1000 Hz and with bias flow; the perforated plate was tested with a 1–4% differential pressure across the plate and the axial swirler was tested with a bias flow of 0–50 m/s. The experimental results are then used to generate the scattering matrix, and the swirler experimental results are compared to previously published numerical and analytical results.

References

1.
Lefebvre
,
A. H.
, and
Ballal
,
D. R.
,
2010
,
Gas Turbine Combustion: Alternative Fuels and Emissions
, 3rd ed.,
CRC Press
, Boca Rotan, FL.
2.
Paschereit
,
C. O.
,
Schuermans
,
B.
,
Polifke
,
W.
, and
Mattson
,
O.
,
2002
, “
Measurement of Transfer Matrices and Source Terms of Premixed Flames
,”
ASME J. Eng. Gas Turbines Power
,
124
(
2
), pp.
239
247
.10.1115/1.1383255
3.
Fischer
,
A.
,
Hirsch
,
C.
, and
Sattelmayer
,
T.
,
2006
, “
Comparison of Multi-Microphone Transfer Matrix Measurements With Acoustic Network Models of Swirl Burners
,”
J. Sound Vib.
,
298
(
1–2
), pp.
73
83
.10.1016/j.jsv.2006.04.040
4.
Gaudron
,
R.
,
Gatti
,
M.
,
Mirat
,
C.
, and
Schuller
,
T.
,
2019
, “
Impact of the Acoustic Forcing Level on the Transfer Matrix of a Turbulent Swirling Combustor With and Without Flame
,”
Flow, Turbul. Combust.
,
103
(
3
), pp.
751
771
.10.1007/s10494-019-00033-z
5.
Yang
,
F.
,
Guo
,
Z.
,
Fu
,
X.
, and
Yu
,
D.
,
2015
, “
Computation of Acoustic Transfer Matrices of Swirl Burner With Finite Element and Acoustic Network Method
,”
J. Low Freq. Noise, Vib. Act. Control
,
34
(
2
), pp.
169
184
.10.1260/0263-0923.34.2.169
6.
Gentemann
,
A.
,
Fischer
,
A.
,
Evesque
,
S.
, and
Polifke
,
W.
,
2003
, “
Acoustic Transfer Matrix Reconstruction and Analysis for Ducts With Sudden Change of Area
,”
AIAA
Paper No. 2003-3142.10.2514/6.2003-3142
7.
Su
,
J.
,
Rupp
,
J.
,
Garmory
,
A.
, and
Carrotte
,
J. F.
,
2015
, “
Measurements and Computational Fluid Dynamics Predictions of the Acoustic Impedance of Orifices
,”
J. Sound Vib.
,
352
, pp.
174
191
.10.1016/j.jsv.2015.05.009
8.
Tran
,
N.
,
Ducruix
,
S.
, and
Schuller
,
T.
,
2009
, “
Passive Control of the Inlet Acoustic Boundary of a Swirled Burner at High Amplitude Combustion Instabilities
,”
ASME J. Eng. Gas Turbines Power
,
131
(
5
), p.
051502
.10.1115/1.3078206
9.
Meng
,
S.
,
Zhou
,
H.
, and
Cen
,
K.
,
2019
, “
Application of the Perforated Plate in Passive Control of the Nonpremixed Swirl Combustion Instability Under Acoustic Excitation
,”
ASME J. Eng. Gas Turbines Power
,
141
(
9
), p.
091007
.10.1115/1.4043848
10.
Howe
,
M. S.
,
1979
, “
On the Theory of Unsteady High Reynolds Number Flow Through a Circular Aperture
,”
Proc. R. Soc. London, Ser. A
,
366
(
1725
), pp.
205
223
.10.1098/rspa.1979.0048
11.
Cummings
,
A.
, and
Chang
,
I.-J.
,
1986
, “
The Transmission of Intense Transient and Multiple Frequency Sound Waves Through Orifice Plates With Mean Fluid Flow
,”
Rev. Phys. Appl.
,
21
(
2
), pp.
151
161
.10.1051/rphysap:01986002102015100
12.
Jing
,
X.
, and
Sun
,
X.
,
1999
, “
Experimental Investigations of Perforated Liners With Bias Flow
,”
J. Acoust. Soc. Am.
,
106
(
5
), pp.
2436
2441
.10.1121/1.428128
13.
Jing
,
X.
, and
Sun
,
X.
,
2000
, “
Effect of Plate Thickness on Impedance of Perforated Plates With Bias Flow
,”
AIAA J.
,
38
(
9
), pp.
1573
1578
.10.2514/2.1139
14.
Luong
,
T.
,
Howe
,
M. S.
, and
McGowan
,
R. S.
,
2005
, “
On the Rayleigh Conductivity of a Bias-Flow Aperture
,”
J. Fluids Struct.
,
21
(
8
), pp.
769
778
.10.1016/j.jfluidstructs.2005.09.010
15.
Bellucci
,
V.
,
Flohr
,
P.
, and
Paschereit
,
C. O.
,
2004
, “
Numerical and Experimental Study of Acoustic Damping Generated by Perforated Screens
,”
AIAA J.
,
42
(
8
), pp.
1543
1549
.10.2514/1.9841
16.
Zhou
,
L.
, and
Bodén
,
H.
,
2013
, “
The Effect of Combined High Level Acoustic Excitation and Bias Flow on the Acoustic Properties of an In-Duct Orifice
,”
AIAA
Paper No. 2013-2128.10.2514/6.2013-2128
17.
Jing
,
X.
, and
Sun
,
X.
,
2000
, “
Discrete Vortex Simulation on the Acoustic Nonlinearity of an Orifice
,”
AIAA J.
,
38
(
9
), pp.
1565
1572
.10.2514/2.1178
18.
Palies
,
P.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2010
, “
The Combined Dynamics of Swirler and Turbulent Premixed Swirling Flames
,”
Combust. Flame
,
157
(
9
), pp.
1698
1717
.10.1016/j.combustflame.2010.02.011
19.
Palies
,
P.
,
Durox
,
D.
,
Schuller
,
T.
, and
Candel
,
S.
,
2011
, “
Acoustic-Convective Mode Conversion in an Aerofoil Cascade
,”
J. Fluid Mech.
,
672
, pp.
545
569
.10.1017/S0022112010006142
20.
Candel
,
S.
,
Durox
,
D.
,
Schuller
,
T.
,
Bourgouin
,
J.-F.
, and
Moeck
,
J. P.
,
2014
, “
Dynamics of Swirling Flames
,”
Annu. Rev. Fluid Mech.
,
46
(
1
), pp.
147
173
.10.1146/annurev-fluid-010313-141300
21.
Merk
,
M.
,
Silva
,
C.
,
Polifke
,
W.
,
Gaudron
,
R.
,
Gatti
,
M.
,
Mirat
,
C.
, and
Schuller
,
T.
,
2019
, “
Direct Assessment of the Acoustic Scattering Matrix of a Turbulent Swirl Combustor by Combining System Identification, Large Eddy Simulation and Analytical Approaches
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), p.
021035
.10.1115/1.4040731
22.
Ni
,
F.
,
Miguel-Brebion
,
M.
,
Nicoud
,
F.
, and
Poinsot
,
T.
,
2017
, “
Accounting for Acoustic Damping in a Helmholtz Solver
,”
AIAA J.
,
55
(
4
), pp.
1205
1220
.10.2514/1.J055248
23.
Meindl
,
M.
,
Merk
,
M.
,
Fritz
,
F.
, and
Polifke
,
W.
,
2019
, “
Determination of Acoustic Scattering Matrices From Linearized Compressible Flow Equations With Application to Thermoacoustic Stability Analysis
,”
J. Theor. Comput. Acoust.
,
27
(
03
), p.
1850027
.10.1142/S2591728518500275
24.
Su
,
J.
,
Garmory
,
A.
, and
Carrotte
,
J. F.
,
2019
, “
On the Acoustic Response of a Generic Gas Turbine Fuel Injector Passage
,”
J. Sound Vib.
,
446
, pp.
343
373
.10.1016/j.jsv.2019.01.043
25.
Fujimori
,
T.
,
Sato
,
S.
, and
Miura
,
H.
,
1984
, “
An Automated Measurement System of Complex Sound Pressure Reflection Coefficients
,”
INTER-NOISE and NOISE-CON Congress and Conference Proceedings
, Honolulu, HI, Dec. 3–5, pp.
1009
1014
.https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=200902023998812587
26.
Rienstra
,
S. W.
, and
Hirschberg
,
A.
,
2004
,
An Introduction to Acoustics
,
Eindhoven University of Technology
, Eindhoven, The Netherlands.
27.
ASTM
,
2019
, “
Standard Test Method for Normal Incidence Determination of Porous Material Acoustical Properties Based on the Transfer Matrix Method
,”
ASTM
, West Conshohocken, PA, Standard No. E2611-19.https://www.astm.org/e2611-19.html
28.
Munjal
,
M. L.
, and
Doige
,
A. G.
,
1990
, “
Theory of a Two Source-Location Method for Direct Experimental Evaluation of the Four-Pole Parameters of an Aeroacoustic Element
,”
J. Sound Vib.
,
141
(
2
), pp.
323
333
.10.1016/0022-460X(90)90843-O
29.
Bendat
,
J. S.
, and
Piersol
,
A. G.
,
2010
,
Random Data: Analysis and Measurement Procedures
(Wiley Series in Probability and Statistics), 4th ed.,
Wiley
, New York.
30.
Richter
,
P. H.
,
1995
, “
Estimating Errors in Least-Squares Fitting
,”
Telecommun. Data Acquis. Prog. Rep.
,
42
(
122
), pp.
107
137
.https://ipnpr.jpl.nasa.gov/progress_report/42-122/122E.pdf
31.
Fischer
,
A.
, and
Sattelmayer
,
T.
,
2005
, “
Random Error Propagation in Multi-Microphone Transfer Matrix Measurements
,”
Technical University of Munich
, Munich, DE.https://www.researchgate.net/publication/263199026_Random_Error_Propagation_in_Multi-Microphone_Transfer_Matrix_Measurements
32.
Dieck
,
R.
,
2007
,
Measurement Uncertainty: Methods and Applications
, 4th ed.,
ISA
,
Research Triangle Park, NC
.
33.
Chung
,
J. Y.
, and
Blaser
,
D. A.
,
1980
, “
Transfer Function Method of Measuring In-Duct Acoustic Properties. I. Theory
,”
J. Acoust. Soc. Am.
,
68
(
3
), pp.
907
913
.10.1121/1.384778
34.
Teasley
,
T. W.
,
2017
, “
A Study of the Nonlinear Acoustic Response of Area-Contractions and Sense-Lines
,” MS thesis,
Auburn University
, Auburn, AL.
35.
Ingård
,
U.
, and
Labate
,
S.
,
1950
, “
Acoustic Circulation Effects and the Nonlinear Impedance of Orifices
,”
J. Acoust. Soc. Am.
,
22
(
2
), pp.
211
218
.10.1121/1.1906591
36.
Rupp
,
J.
,
2013
, “Acoustic Absorption and the Unsteady Flow Associated With Circular Apertures in a Gas Turbine Environment,” Ph.D. thesis,
Loughborough University
, Loughborough, UK.
37.
Ingård
,
U.
, and
Ising
,
H.
,
1967
, “
Acoustic Nonlinearity of an Orifice
,”
J. Acoust. Soc. Am.
,
42
(
1
), pp.
6
17
.10.1121/1.1910576
38.
Kawell
,
S. T.
,
Humphreys
,
L. H.
,
Stubbs
,
D. C.
, and
Scarborough
,
D. E.
,
2020
, “
A Theoretical Investigation of the Nonlinear Acoustic Response of Abrupt Area Contractions
,”
J. Acoust. Soc. Am.
,
147
(
1
), pp.
500
507
.10.1121/10.0000607
39.
Åbom
,
M.
,
1991
, “
Measurement of the Scattering-Matrix of Acoustical Two-Ports
,”
Mech. Syst. Signal Process.
,
5
(
2
), pp.
89
104
.10.1016/0888-3270(91)90017-Y
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