Numerical Simulation of the Dynamics of Turbulent Swirling Flames

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Introduction fluctuations of the heat release . Flame transfer functions may be obtained experimentally, using velocity or pressure sensors in combination with chemiluminescence as an indicator of heat release in the flame (see e.g. [9,78,96,137]). Unfortunately, the experimental determination of FTFs for configurations of technical interest is very difficult and costly. (Semi-)analytical models for the FTF have been also proposed (see e.g. [78, 85, 116, 181]). However, it is in general difficult to predict flame responses from first principles. Alternatively, it is possible to determine the FTF with CFD: First an unsteady CFD simulation is performed to generate time series of fluctuating velocity and heat release rate. Then the FTF is reconstructed from the data using methods from system identification (SI) [66, 85, 158, 160, 199]. These methods should provide information about the flame dynamics with a reasonable accuracy to proceed to the stability analysis. Having an incorrect description of the flame dynamics can lead to a wrong prediction of the stability behavior [198]. Thus, it is important to validate the modeling approaches used to obtain the flame transfer function. A strategy of “Divide and Conquer” [106,154,156] is applied in this work, using a hybrid methodology for the stability analysis. The methodology is based on the description of the different elements of the system in an acoustic network model, providing the information about the flame response from LES or experiments. In this way, the system and boundary conditions are described in a suitable way, including an appropriate description of the flame dynamics, and reducing the demand of resources for the analysis. Furthermore, as experimental investigations on multi-burner industrial gas turbines at operating conditions are very costly, they are often carried out in a single burner configuration. However, for annular combustors, single burner experiments are in general not representative of machine conditions due to variations in combustor wall temperatures, combustor cross section size, operating pressure, flame-flame interaction between adjacent burners, etc. Such variations in general influence both flow field and flame shape, changing the flame dynamics, and under certain conditions the stability behavior of the system. 6
1.2 Overview of the Thesis 1.2 Overview of the Thesis In this study, the flame dynamics in a perfectly premixed axial swirl burner is investigated. LES in combination with system identification methods is applied to obtain the flame transfer function. The validation of the method with experimental data is carried out in a first step. Then the potential of the LES/SI approach to detect the impact of different conditions interacting with the flame on the FTF is investigated and compared with the reference case. The influence of the differences in the flame transfer functions on stability limits is analyzed with a low-order thermoacoustic model. In Chapter 2, an overview of concepts in turbulent combustion, as the energy spectrum and combustion regimes, is presented. This is followed by the fundamental governing equations for reacting flow LES used in the code AVBP. Finally, the Thickened Flame and Dynamically Thickened Flame combustion models used in this study are presented. In Chapter 3, the flame dynamics of premixed flames submitted to velocity disturbances is reviewed, presenting the definition of the flame transfer function and the different methods to obtain it. The influences of various parameters on the flame transfer function are shown. At the end of the chapter, the model of the flame transfer function produced by axial velocity and swirl fluctuations from Komarek and Polifke [103] is shown to describe the flame dynamics by the unit impulse responses of the different perturbations. In Chapter 4, background about system identification for linear-time invariant systems is presented, followed by the description and derivation of the Wiener Filter. Finally, the LES/SI method for the identification of the flame transfer function is described. In Chapter 5, results from the identification of the flame transfer functions obtained using the LES/SI method for different conditions are presented. First, the experimental set-up developed by Komarek [103] is introduced; followed by the validation of the method with experiments. After that, the geometrical and operating conditions in the combustor and burner are varied by changing the level of heat transfer in thermal boundary conditions at the combus- 7
Page 1: Technische Universität München In
Page 4 and 5: gas turbine combustion during my in
Page 6 and 7: Zusammenfassung Die Dynamik von per
Page 8 and 9: CONTENTS 3.3.3 Influence of Swirler
Page 10 and 11: CONTENTS A.7.4 Inlet . . . . . . .
Page 12 and 13: LIST OF FIGURES 3.2 Scheme of deter
Page 14 and 15: LIST OF FIGURES 5.21 Instantaneous
Page 16 and 17: LIST OF FIGURES 5.47 FTFs from expe
Page 18 and 19: List of Tables 2.1 LES Combustion M
Page 20 and 21: Nomenclature R i j Two-point veloci
Page 22 and 23: Nomenclature M MF O prop r stoich S
Page 24 and 25: xxiv Nomenclature
Page 26 and 27: Introduction Figure 1.1: Left: Worl
Page 28 and 29: Introduction Figure 1.4: Illustrati
Page 32 and 33: Introduction tor walls, increasing
Page 34 and 35: Turbulent Reacting Flows Figure 2.1
Page 38 and 39: Turbulent Reacting Flows time scale
Page 40 and 41: Turbulent Reacting Flows instantane
Page 42 and 43: Turbulent Reacting Flows as the pro
Page 44 and 45: Turbulent Reacting Flows where s L
Page 48 and 49: Turbulent Reacting Flows 2.4.2 Fund
Page 50 and 51: Turbulent Reacting Flows 2.4.2.1 Mo
Page 52 and 53: Turbulent Reacting Flows Some of th
Page 54 and 55: Turbulent Reacting Flows Table 2.1:
Page 56 and 57: Turbulent Reacting Flows port equat
Page 58 and 59: 3 Response of Premixed Flames to Ve
Page 60 and 61: Response of Premixed Flames to Velo
Page 76 and 77: System Identification put, the heat
Page 78 and 79: System Identification Figure 4.2: U
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System Identification 4.2 The Wiene
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System Identification Figure 4.3: S
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System Identification 4.3 The LES/S
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System Identification A flow chart
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Identification of Flame Transfer Fu
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6 Stability Analysis with Low-Order
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Stability Analysis with Low-Order N
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Summary and Conclusions series gene
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Summary and Conclusions • The ide
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Outlook tion. The system identifica
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BIBLIOGRAPHY [8] H. Büchner, C. Hi
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BIBLIOGRAPHY [28] P.J. Colucci, F.A
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BIBLIOGRAPHY [48] D. Fanaca. Influe
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BIBLIOGRAPHY [65] M. Germano, U. Pi
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BIBLIOGRAPHY [83] A. Huber. Impact
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BIBLIOGRAPHY [102] T. Komarek. Priv
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BIBLIOGRAPHY [122] L. Ljung. System
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BIBLIOGRAPHY [141] P. Palies, T. Sc
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BIBLIOGRAPHY [163] S.B. Pope. Compu
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BIBLIOGRAPHY [183] F. Selimefendigi
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BIBLIOGRAPHY [200] L. Tay Wo Chong,
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BIBLIOGRAPHY [223] B.T. Zinn and T.
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Appendices Figure A.1: Evaluation o
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Appendices Table A.1: One Step Reac
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Appendices and isotropic, the energ
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Appendices Figure A.2: DRBS Input s
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Appendices (a) The flow is homentro
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Appendices ends of the duct, the fo
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Appendices Figure A.6: Scheme for f
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Appendices Expressing Eqs. (A.59) a
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Appendices Figure A.7: Scattering M
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Appendices ping [45] is used. The i
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Appendices 4. Load in TECPLOT only
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Numerical Simulation of the Dynamics of Turbulent Swirling Flames

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