Abstract

This paper presents a methodology to compute acoustic damping rates of transversal, high-frequency modes induced by vortex-shedding. The acoustic damping rate presents one key quantity for the assessment of the linear thermoacoustic stability of gas turbine combustors. State-of-the-art network models—as employed to calculate damping rates in low-frequency, longitudinal systems—cannot fulfill this task due to the acoustic noncompactness encountered in the high-frequency regime. Furthermore, it is yet unclear, whether direct eigensolutions of the linearized Euler equations (LEE), which capture the mechanism of vortex shedding, yield correct damping rate results constituted by the implicit presence of acoustic as well as hydrodynamic contributions in these solutions. The methodology's applicability to technically relevant systems is demonstrated by a validation test case using a lab-scale, swirl-stabilized combustion system.

References

1.
Sattelmayer
,
T.
,
2010
, “
Grundlagen der Verbrennung in Stationären Gasturbinen
,”
Stationäre Gasturbinen
,
C.
Lechner
and
J.
Seume
, eds.,
Springer
,
Berlin
, pp.
397
452
.
2.
Culick
,
F.
E. C.,
2006
, “
Unsteady Motions in Combustion Chambers for Propulsion Systems
,” NATO RTO AGARDograph, Report No. RTO AG-AVT-039.
3.
Lieuwen
,
T. C.
,
2013
,
Unsteady Combustor Physics
,
Cambridge University Press
, New York.
4.
Schulze
,
M.
,
Hummel
,
T.
,
Klarmann
,
N.
,
Berger
,
F.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2017
, “
Linearized Euler Equations for the Prediction of Linear High-Frequency Stability in Gas Turbine Combustors
,”
ASME J. Eng. Gas Turbines Power
,
139
(
3
), p.
031510
.10.1115/1.4034453
5.
Hummel
,
T.
,
2019
, “
Modeling and Analysis of High-Frequency Thermoacoustic Oscillations in Gas Turbine Combustion Chambers
,” Dissertation, Technical University of Munich, Munich, Germany.
6.
Howe
,
M. S.
,
1979
, “
Attenuation of Sound in a Low Mach Number Nozzle Flow
,”
J. Fluid Mech.
,
91
(
2
), pp.
209
229
.10.1017/S0022112079000124
7.
Howe
,
M. S.
,
1979
, “
On the Theory of Unsteady High Reynolds Number Flow Through a Circular Aperture
,”
Proc. R. Soc. A
,
366
(
1725
), pp.
205
223
.10.1098/rspa.1979.0048
8.
Bechert
,
D. W.
,
1980
, “
Sound Absorption Caused by Vorticity Shedding, Demonstrated With a Jet Flow
,”
J. Sound Vib.
,
70
(
3
), pp.
389
405
.10.1016/0022-460X(80)90307-7
9.
Schwing
,
J.
,
Sattelmayer
,
T.
, and
Noiray
,
N.
,
2011
, “
Interaction of Vortex Shedding and Transverse High-Frequency Pressure Oscillations in a Tubular Combustion Chamber
,”
ASME
Paper No. GT2011-45246.10.1115/GT2011-45246
10.
Howe
,
M. S.
,
1980
, “
The Dissipation of Sound at an Edge
,”
J. Sound Vib.
,
70
(
3
), pp.
407
411
.10.1016/0022-460X(80)90308-9
11.
Hummel
,
T.
,
Berger
,
F.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2016
, “
Theory and Modeling of Non-Degenerate Transversal Thermoacoustic Limit Cycle Oscillations
,”
International Symposium on Thermoacoustic Instabilities in Gas Turbines and Rocket Engines: Industry Meets Academia
, TUM, LS Für Thermodynamik/IAS, Munich, Germany, Paper No. GTRE-038.
12.
Rienstra
,
S.
, and
Hirschberg
,
A.
,
2016
,
An Introduction to Acoustics
, Revised Edition of IWDE 92-06, Eindhoven University of Technology, Eindhoven, The Netherlands.
13.
Hummel
,
T.
,
Berger
,
F.
,
Hertweck
,
M.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2017
, “
High-Frequency Thermoacoustic Modulation Mechanisms in Swirl-Stabilized Gas Turbine Combustors—Part II: Modeling and Analysis
,”
ASME J. Eng. Gas Turbines Power
,
139
(
7
), p.
071502
.10.1115/1.4035592
14.
Romero
,
P.
,
Hummel
,
T.
,
Berger
,
F.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2017
, “
Damping Due to Acoustic Boundary Layer in High-Frequency Transverse Modes
,”
24th International Congress on Sound and Vibration (ICSV24)
, London.
15.
Hummel
,
T.
,
Hofmeister
,
T.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2017
, “
Modeling and Quantification of Acoustic Damping Induced by Vortex Shedding in Non-Compact Thermoacoustic Systems
,”
24th International Congress on Sound and Vibration (ICSV24)
, London.
16.
Hofmeister
,
T.
,
Hummel
,
T.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2019
, “
Theory and Quantification of Energy Transformation Processes Between Acoustic and Hydrodynamic Perturbation Modes in Non-Compact Thermoacoustic Systems Via a Helmholtz-Hodge Decomposition Approach
,” ASME Paper No. GT2019-90240.
17.
Schulze
,
M.
,
2016
, “
Linear Stability Assessment of Cryogenic Rocket Engines
,” Dissertation, Technical University of Munich, Munich, Germany.
18.
Donéa
,
J.
, and
Huerta
,
A.
,
2003
,
Finite Element Methods for Flow Problems
,
Wiley
,
Chichester, UK
.
19.
Hummel
,
T.
,
Berger
,
F.
,
Stadlmair
,
N.
,
Schuermans
,
B.
, and
Sattelmayer
,
T.
,
2017
, “
Extraction of Linear Growth and Damping Rates of High-Frequency Thermoacoustic Oscillations From Time Domain Data
,”
ASME
Paper No. GT2017-64233.10.1115/GT2017-64233
20.
Schuermans
,
B.
,
Bellucci
,
V.
, and
Paschereit
,
C. O.
,
2003
, “
Thermoacoustic Modeling and Control of Multi Burner Combustion Systems
,”
ASME
Paper No. GT2003-38688.10.1115/GT2003-38688
21.
Ewert
,
R.
, and
Schröder
,
W.
,
2003
, “
Acoustic Perturbation Equations Based on Flow Decomposition Via Source Filtering
,”
J. Comput. Phys.
,
188
(
2
), pp.
365
398
.10.1016/S0021-9991(03)00168-2
22.
Myers
,
M. K.
,
1986
, “
An Exact Energy Corollary for Homentropic Flow
,”
J. Sound Vib.
,
109
(
2
), pp.
277
284
.10.1016/S0022-460X(86)80008-6
23.
Truesdell
,
C.
,
1960
, “
Fluid Dynamics
,”
Encyclopedia of Physics/Handbuch der Physik
,
Springer
,
Berlin
.
24.
Ronneberger
,
D.
,
1987
, “
Theoretische und Experimentelle Untersuchung der Schallausbreitung Durch Querschnittssprünge und Lochplatten in Strömungskanälen
,” Technical Report, DFG-Abschlussbericht, Drittes Physikalisches Institut der Universität Göttingen, Göttingen, Germany.
You do not currently have access to this content.