The present study is devoted to the modeling of mean flow effects while computing thermoacoustic modes under the zero Mach number assumption. It is first recalled that the acoustic impedance modeling of a compressor or a turbine must be prescribed under an energetical form instead of the classical acoustic variables. Then we demonstrate the feasibility to take into account the coupling between acoustic and entropy waves in a zero Mach number framework to capture a family of low frequency entropic modes. The proposed approach relies on a new delayed entropy coupled boundary condition (DECBC) and proves able to capture a family of low frequency entropic mode even though no mean flow term is included in the fluctuating pressure equation.
Issue Section:
Gas Turbines: Combustion, Fuels, and Emissions
References
1.
Lieuwen
, T.
, and Yang
, V.
, 2005, “Combustion Instabilities in Gas Turbine Engines. Operational Experience, Fundamental Mechanisms and Modeling
,” Progress in Astronautics and Aeronautics
, Vol. 210
, AIAA
, Reston, VA
.2.
Dowling
, A. P.
, 1995, “The Calculation of Thermoacoustic Oscillations
,” J. Sound Vib.
, 180
(4
), pp. 557
–581
.3.
Polifke
, W.
, Poncet
, A.
, Paschereit
, C. O.
, and Doebbeling
, K.
, 2001. “Reconstruction of Acoustic Transfer Matrices by Stationary Computational Fluid Dynamics
,” J. Sound Vib.
, 245
(3
), pp. 483
–510
.4.
Selle
, L.
, Benoit
, L.
, Poinsot
, T.
, Nicoud
, F.
, and Krebs
, W.
, 2006, “Joint Use of Compressible Large-Eddy Simulation and Helmoltz Solvers for the Analysis of Rotating Modes in an Industrial Swirled Burner
,” Combust. Flame
, 145
(1–2
), pp. 194
–205
.5.
Lieuwen
, T.
, 2003, “Modeling Premixed Combustion-Acoustic Wave Interactions: A Review
,” J. Propul. Power
, 19
(5
), pp. 765
–781
.6.
Morfey
, C. L.
, 1973, “Amplification of Aerodynamic Noise by Convected Flow Inhomogeneities
,” J. Sound Vib.
, 31
, pp. 391
–397
.7.
Williams
, J. E. F.
, and Howe
, M. S.
, 1975, “The Generation of Sound by Density Inhomogeneities in Low Mach Number Nozzle Flows
,” J. Fluid Mech.
, 70
(03
), pp. 605
–622
.8.
Howe
, M.
, 1975, “Contributions to the Theory of Aerodynamic Sound, With Application to Excess Jet Noise and the Theory of the Flute
,” J. Fluid Mech.
, 71
(04
), pp. 625
–673
.9.
Candel
, S.
, 1975. “Acoustic Conservation Principles, Application to Plane and Modal Propagation in Nozzles and Diffusers
,” J. Sound Vib.
, 41
, pp. 207
–232
.10.
Polifke
, W.
, Paschereit
, C. O.
, and Döbbeling
, K.
, 2001, “Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor With a Choked Exit
,” Int. J. Acoust. Vib.
, 6
(3
), pp. 135
–146
.http://www.iiav.org/ijav/content/volumes/6_2001_1107531272264886/vol_3/317_firstpage_1468481287056113.pdfhttp://www.iiav.org/ijav/content/volumes/6_2001_1107531272264886/vol_3/317_firstpage_1468481287056113.pdf11.
Bloxsidge
, G.
, Dowling
, A.
, Hooper
, N.
, and Langhorne
, P.
, 1988, “Active Control of Reheat Buzz
,” AIAA J.
, 26
, pp. 783
–790
.12.
Nicoud
, F.
, and Wieczorek
, K.
, 2009, “About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities
,” Int. J. Spray Combust. Dyn.
, 1
, pp. 67
–112
.13.
Rao
, P.
, and Morris
, P.
, 2006, “Use of Finite Element Methods in Frequency Domain Aeroacoustics
,” AIAA J.
, 44
, pp. 1643
–1652
.14.
Davies
, P. O. A. L.
, 1988, “Practical Flow Duct Acoustics
,” J. Sound Vib.
, 124
(1
), pp. 91
–115
.15.
Sattelmayer
, T.
, 2003, “Influence of the Combustor Aerodynamics on Combustion Instabilities From Equivalence Ratio Fluctuations
,” J. Eng. Gas Turbine Power
, 125
, pp. 11
–19
.16.
Marble
, F. E.
, and Candel
, S.
, 1977, “Acoustic Disturbances From Gas Nonuniformities Convected Through a Nozzle
,” J. Sound Vib.
, 55
, pp. 225
–243
.17.
Lamarque
, N.
, and Poinsot
, T.
, 2008, “Boundary Conditions for Acoustic Eigenmodes Computation in Gas Turbine Combustion Chambers
,” AIAA J.
, 46
(9
), pp. 2282
–2292
.18.
Peters
, M.
, Hirschberg
, A.
, Reijnen
, A.
, and Wijnands
, A.
, 1993, “Damping and Reflection Coefficient Measurements for an Open Pipe at Low Mach and Low Helmholtz Numbers
,” J. Fluid Mech.
, 256
, pp. 499
–499
.19.
Cantrell
, R.
, and Hart
, R.
, 1964, “Interaction Between Sound and Flow in Acoustic Cavities: Mass, Momentum, and Energy Considerations
,” J. Acoust. Soc.
, 36
, p. 697
.20.
Doak
, P.
, 1998, “Fluctuating Total Enthalpy as the Basic Generalized Acoustic Field
,” Theor. Comput. Fluid Dyn.
, 10
(1
), pp. 115
–133
.21.
Leyko
, M.
, Moreau
, S.
, Nicoud
, F.
, and Poinsot
, T.
, 2011, “Numerical and Analytical Modelling of Entropy Noise in a Supersonic Nozzle With a Shock
,” J. Sound Vib.
, 330
(16, 1
), pp. 3944
–3958
.22.
Hield
, P.
, Brear
, M.
, and Jin
, S.
, 2009, “Thermoacoustic Limit Cycles in a Premixed Laboratory Combustor With Open and Choked Exits
,” Combust. Flame
, 156
(9
), pp. 1683
–1697
.23.
Macquisten
, M. A.
, and Dowling
, A. P.
, 1994, “Low-Frequency Combustion Oscillations in a Model Afterburner
,” Combust. Flame
, 94
(4
), pp. 253
–264
.24.
Goh
, C.
, and Morgans
, A.
, 2011, “Phase Prediction of the Response of Choked Nozzles to Entropy and Acoustic Disturbances
,” J. Sound Vib.
, 330
(21
), pp. 5184
–5198
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.