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Validation of a Physics‐Based Low‐Order Thermo‐Acoustic Model of a Liquid‐Fueled Gas

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Validation of a Physics‐Based Low‐Order Thermo‐Acoustic Model of a Liquid‐Fueled Gas Validation of a Physics Based Low Order Thermo Acoustic Model of a Liquid Fueled‐‐‐ Gas Turbine‐‐‐ Combustor‐‐‐ and its Application for Predicting‐‐‐ Combustion Driven Oscillations A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfilment of the requirements for the degree of Doctor of Philosophy (Ph.D.) In the Department of Aerospace Engineering and Engineering Mechanics of the College of Engineering and Applied Sciences By Michael Knadler B.S., Aerospace Engineering, University of Cincinnati, 2011 November 2017 Committee Chair: Dr. Jongguen Lee, Ph.D. Abstract This research validates a physics based model for the thermo-acoustic behavior of a liquid-fueled gas turbine combustor as a tool for diagnosing the cause of combustion oscillations. A single nozzle, acoustically tunable gas turbine combustion rig fueled with Jet-A was built capable of operating in the unsteady combustion regime. A parametric study was performed with the experimental rig to determine the operating conditions resulting in thermoacoustic instabilities. The flame transfer function has been determined for varying fuel injection and flame stabilization arrangements to better understand the feedback loop concerning the heat release and acoustics. The acoustic impedance of the boundaries of the combustion system was experimentally determined. The results were implemented in a COMSOL Multiphysics model as complex impedance boundary conditions at the inlet and exit and a source term to model the flame and heat release. The validity of that model was determined based on an eigenvalue study comparing both the frequency and growth rate of the eigenvalues with the experimentally measured frequencies and pressures of the stable and unstable operating conditions. The model demonstrated that it can accurately predict the instability of the examined operating conditions. The model also closely predicted the frequency of instability and demonstrated the usefulness of including the experimentally determined acoustic boundary conditions over idealized sound hard boundaries. i © Copyright by Michael Knadler 2017 All Rights Reserved ii Acknowledgments: I would first like to thank my advisor, Dr. Jongguen Lee, for his year of guidance and patience in leading me through my research. I would also like to thank my committee members, Dr. Jay Kim, Dr. Kwanwoo Kim, and Dr. Mark Turner for their insight and advice throughout my dissertation research and studies. Also in need of recognition are my fellow graduate students who help me both in completing my research, Arda Cakmakci and Thomas Caley, and keeping me sane in and out of the lab, Jun Hee Han. Of course nothing would get done in the lab without Curt Fox who has helped me with most every piece of technical equipment I have needed. And finally, Kiev, for always reminding me to never work too hard. iii TABLE OF CONTENTS 1. Introduction ........................................................................................................................... 1 1.1. The Thermoacoustic Problem ....................................................................................... 1 1.2. Objectives ........................................................................................................................ 1 2. Theory of Thermoacoustic Instability ................................................................................. 3 2.1. The Rayleigh Criterion for Thermoacoustic Instability ............................................. 3 2.2. Mathematical Model for Thermoacoustic Instability ................................................. 8 2.3. One Dimensional Wave Theory for Acoustic Perturbations .................................... 11 3. Previous Approaches to Thermoacoustic Modeling ........................................................ 16 3.1. Computational Fluid Dynamics (CFD) ...................................................................... 16 3.2. Thermoacoustic Network Model................................................................................. 17 4. Finite Element Modeling for Thermoacoustic Instabilities ............................................ 26 4.1. Acoustic Wave Coefficients ......................................................................................... 26 4.1.1. Determining Acoustic Wave Coefficients ........................................................... 26 4.1.2. Acoustic Wave Coefficient Error Analysis ......................................................... 28 4.2. Acoustic Impedance Measurements and Boundary Conditions .............................. 29 4.3. Flame Modelling ........................................................................................................... 39 5. Experimental Details .......................................................................................................... 54 5.1. Single Nozzle Acoustically Tunable Gas Turbine Combustion Rig Setup .............. 54 5.1.1. Inline Heater .......................................................................................................... 55 5.1.2. Air Siren ................................................................................................................. 55 5.1.3. Inlet Plenum .......................................................................................................... 57 5.1.4. Fuel Nozzle and Swirler ........................................................................................ 57 5.1.5. Combustion Chamber and Pressure Vessel ....................................................... 61 5.1.6. Transition Tube ..................................................................................................... 62 5.1.7. Pressure Screws ..................................................................................................... 62 5.2. Dynamic Pressure Sensor Setup ................................................................................. 63 5.3. Flame Transfer Function Setup .................................................................................. 67 5.4. High Speed Camera Setup ........................................................................................... 72 5.5. COMSOL Model Development ................................................................................... 72 6. Results .................................................................................................................................. 78 6.1. Stability Map ................................................................................................................ 78 6.2. Flame Transfer Function Measurement .................................................................... 83 iv 6.3. High Speed Flame Imaging ......................................................................................... 86 6.3.1. High Speed Color Imaging ................................................................................... 87 6.3.2. OH* ICCD Imaging .............................................................................................. 89 6.4. Time Delay Determination .......................................................................................... 94 6.5. Acoustic Boundary Condition Measurement ............................................................ 98 6.6. Combustor Temperature Profile .............................................................................. 101 6.7. Eigenfrequency Study ................................................................................................ 102 7. Conclusion ......................................................................................................................... 110 8. Bibliography ...................................................................................................................... 112 A. APPENDIX A: Flush to Recess Mounting Calibration and MATLAB Code ............. 116 B. APPENDIX B: Flame Transfer Function MATLAB Code .......................................... 125 C. APPENDIX C: Three-line Pyrometry Theory and Calibration ................................... 131 D. APPENDIX D: Impedance Calculation MATLAB Code.............................................. 134 v LIST OF FIGURES Figure 2.1: Thermodynamic interpretation of the Rayleigh criterion. Heat addition in phase with pressure (red) and out of phase with pressure (green) .................................................................... 6 Figure 2.2: Block diagram representation of feedback loop between acoustic fluctuations and heat release ...................................................................................................................................... 8 Figure 2.3: Acoustic wave propagation in a duct ......................................................................... 13 Figure 3.1: (a) Schematic of a model gas turbine combustor with acoustic waves A and B upstream and downstream of the flame (b) Block diagram of thermoacoustic network model ... 18 Figure 3.2: (left) Upstream and downstream acoustic variables with relation to thermoacoustic network element (right) Reimann invariants upstream and downstream with respective directions of flow ........................................................................................................................................... 19 Figure 3.3: Converging-diverging nozzle ..................................................................................... 20 Figure 3.4: Combustor with premix duct used to develop transfer matrices presented in
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