A novel method for the simulation of combustion instabilities in annular combustors is presented. It is based on the idea to solve the equations governing the acoustics in the time domain and couple them to a model for the heat release in the flames. The linear wave equation describing the temporal and spatial evolution of the pressure fluctuations is implemented in a finite element code. Providing high flexibility, this code in principle allows both the computational domain to be of arbitrary shape and the mean flow to be included. This yields applicability to realistic technical combustors. The fluctuating heat release acting as a volume source appears as a source term in the equation to be solved. Employing a time-lag model, the heat release rate at each individual burner is related to the velocity in the corresponding burner at an earlier time. As saturation also is considered, a nonlinearity is introduced into the system. Starting the simulation from a random initial perturbation with suitable values for the parameters of the heat release model, a self-excited instability is induced, leading to a finite-amplitude limit cycle oscillation. The feasibility of the approach is demonstrated with three-dimensional simulations of a simple model annular combustor. The effect of the model parameters and of axial mean flow on the stability and the shape of the excited modes is shown.

Issue Section:
Gas Turbines: Combustion and Fuel
Keywords:
combustion, time-domain analysis, flames, finite element analysis, wave equations, flow instability, chemically reactive flow
Topics:
Combustion, Combustion chambers, Flames, Flow (Dynamics), Heat, Limit cycles, Oscillations, Pressure, Simulation, Acoustics, Fluctuations (Physics), Stability, Wave equations
1.
Crocco, L., and Cheng, S. I., 1956, “Theory of Combustion Instability in Liquid Propellant Rocket Motors,” AGARD Monograph No. 8.
2.
Sattelmayer
,
T.
,
2003
, “
Influence of the Combustor Aerodynamics on Combustion Instabilities From Equivalence Ratio Fluctuations
,”
ASME J. Eng. Gas Turbines Power
,
125
, pp.
11
–
19
.
3.
Culick
,
F. E. C.
,
1971
, “
Non-Linear Growth and Limiting Amplitude of Acoustic Oscillations in Combustion Chambers
,”
Combust. Sci. Technol.
,
3
, pp.
1
–
16
.
4.
Culick
,
F. E. C.
,
1994
, “
Some Recent Results for Nonlinear Acoustics in Combustion Chambers
,”
AIAA J.
,
32
(
1
), pp.
146
–
169
.
5.
Peracchio, A. A., and Proscia, W. M., 1998, “Nonlinear Heat-Release/Acoustic Model for Thermoacoustic Instability in Lean Premix Combustors,” ASME Paper No. 98-GT-269.
6.
Akamatsu, S., and Dowling, A. P., 2001, “Three Dimensional Thermoacoustic Oscillation in a Premix Combustor,” ASME Paper No. 2001-GT-0034.
7.
Murota, T., and Ohtsuka, M., 1999, “Large-Eddy Simulation of Combustion Oscillation in the Premixed Combustor,” ASME Paper No. 99-GT-274.
8.
Brookes, S. J., Cant, R. S., and Dowling, A. P., 1999, “Modelling Combustion Instabilities Using Computational Fluid Dynamics,” ASME Paper No. 99-GT-112.
9.
Hantschk
,
C.-C.
, and
Vortmeyer
,
D.
,
2002
, “
Numerical Simulation of Self-Excited Combustion Oscillations in a Non-Premixed Burner
,”
Combust. Sci. Technol.
,
174
, pp.
189
–
204
.
10.
Wake, B. E., Choi, D., and Hendricks, G. J., 1996, “Numerical Investigation of Pre-Mixed Step-Combustor Instabilities,” AIAA Paper No. AIAA 96-0816.
11.
Dowling
,
A. P.
,
1997
, “
Nonlinear Self-Excited Oscillations of a Ducted Flame
,”
J. Fluid Mech.
,
346
, pp.
271
–
290
.
12.
Walz, G., Krebs, W., Hoffmann, S., and Judith, H., 1999, “Detailed Analysis of the Acoustic Mode Shapes of an Annular Combustion Chamber,” ASME Paper No. 99-GT-113.
13.
Walz, G., Krebs, W., Flohr, P., and Hoffmann, S., 2001, “Modal Analysis of Annular Combustors: Effect of Burner Impedance,” ASME Paper No. 2001-GT-0042.
14.
Kru¨ger, U., Hu¨ren, J., Hoffmann, S., Krebs, W., and Bohn, D., 1999, “Prediction of Thermoacoustic Instabilities With Focus on the Dynamic Flame Behavior of the 3A-Series Gas Turbine of Siemens KWU,” ASME Paper No. 99-GT-111.
15.
Kru¨ger
,
U.
,
Hu¨ren
,
J.
,
Hoffmann
,
S.
,
Krebs
,
W.
,
Flohr
,
P.
, and
Bohn
,
D.
,
2001
, “
Prediction and Measurement of Thermoacoustic Improvements in Gas Turbines With Annular Combustion Systems
,”
ASME J. Eng. Gas Turbines Power
,
123
, pp.
557
–
566
.
16.
Krebs, W., Walz, G., and Hoffmann, S., 1999, “Thermoacoustic Analysis of Annular Combustor,” AIAA Paper No. AIAA 99-1971.
17.
Stow, S. R., and Dowling, A. P., 2001, “Thermoacoustic Oscillations in an Annular Combustor,” ASME Paper No. 2001-GT-0037.
18.
Evesque, S., and Polifke, W., 2002, “Validation of Low-Order Acoustic Modelling for Annular Combustors,” ASME Paper No. GT-2002-30064.
19.
Ffowcs Williams
,
J. E.
,
1982
, “
Sound Sources in Aerodynamics—Fact and Fiction
,”
AIAA J.
,
20
(
3
), pp.
307
–
315
.
20.
Polifke
,
W.
,
Paschereit
,
C. O.
, and
Do¨bbeling
,
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.
21.
Flohr, P., Paschereit, O. C., van Roon, B., and Schuermans, B., 2001, “Using CFD for Time-Delay Modeling of Premix Flames,” ASME Paper No. 2001-GT-0376.
22.
COMSOL AB, “FEMLAB Reference Manual,” 2000.
23.
Harper, J., Johnson, C., Neumeier, Y., Lieuwen, T. C., and Zinn, B. T., 2001, “Experimental Investigation of the Nonlinear Flame Response to Flow Disturbances in a Gas Turbine Combustor,” AIAA Paper No. AIAA-01-0486.
24.
Chu, B.-T., 1956, “Stability of Systems Containing a Heat Source—The Rayleigh Criterion,” NACA Research Memorandum NACA RM 56D27.
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