Impact of fuel supply impedance and fuel staging on gas turbine ...

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Acoustics 68
4 Modeling <strong>of</strong> turbulent reactive flows using CFD In the present work transient Computational Fluid Dynamics simulations are used to analyze quantitatively the response <strong>of</strong> a practical premixed flame to acoustic fluctuations at the flame holder <strong>and</strong> in the vicinity <strong>of</strong> the <strong>fuel</strong> injection. The dynamics <strong>of</strong> the flame is determined in a post-processing step using the exported transient CFD data <strong>and</strong> the system identification method presented in chapter 5. This section describes the basic concepts <strong>of</strong> the numerical methods used in this work to model the turbulent reactive flow. For a more detailed information the reader is referred to Pope [104], Friedrich [33] or Tennekes <strong>and</strong> Lumley [126] regarding the description <strong>of</strong> turbulence <strong>and</strong> to Poinsot <strong>and</strong> Veynante [94], Turns [128], Peters [92], Fox [32] <strong>and</strong> Williams [132] in terms <strong>of</strong> turbulent reacting flows. As the CFD simulations are performed using the commercial s<strong>of</strong>tware package ANSYS CFX, the equations presented below are similar to those described in [5]. 4.1 Theory <strong>and</strong> numerical modeling <strong>of</strong> turbulence 4.1.1 Basic equations <strong>of</strong> turbulent flows The numerical simulation <strong>of</strong> a turbulent reacting flow is based on the conservation <strong>of</strong> mass, momentum <strong>and</strong> energy. As the conservation equations contain more unknowns than equations, further simplifications have to be made to obtain a closed system <strong>of</strong> equations. These simplifications include the introduction <strong>of</strong> the equation <strong>of</strong> state for an ideal gas (Eqn. (3.7)), the caloric constitutive equation d e= c v d T <strong>and</strong> a relation for the stress tensor. The resulting system <strong>of</strong> equations is called the unsteady Navier-Stokes equations, which can 69
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Technische Universität München In
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und ihre Geduld besonders für die
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Contents 1 Introduction 1 1.1 Techn
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CONTENTS 7.2.2 Impact</stro
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Nomenclature G stretch factor [-] h
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Nomenclature λ air-fuel</s
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1 Introduction 1.1 Technology backg
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1.2 Thermo-acoustic instabilities 1
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1.2 Thermo-acoustic instabilities d
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1.3 Control of the
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1.3 Control of the
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1.4 Intention and
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1.5 Terminology and</strong
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1.5 Terminology and</strong
Page 31 and 32: 2 Numerical analysis of</st
Page 33 and 34: 2.1 Overview of me
Page 39 and 40: 2.2 Flame dynamics of</stro
Page 47 and 48: 2.3 Identification of</stro
Page 57 and 58: 3 Acoustics Before analyzing the ac
Page 59 and 60: 3.1 Basic acoustic equations as a f
Page 61 and 62: 3.2 Linear acoustic equations Here,
Page 63 and 64: 3.2 Linear acoustic equations p ′
Page 65 and 66: 3.3 Acoustic network model p ′ (x
Page 67 and 68: 3.3 Acoustic network model matrix e
Page 69 and 70: 3.3 Acoustic network model The <str
Page 71 and 72: 3.3 Acoustic network model where A
Page 73 and 74: 3.3 Acoustic network model coming c
Page 75 and 76: 3.3 Acoustic network model Z i Air
Page 77 and 78: 3.3 Acoustic network model pressure
Page 79 and 80: 3.3 Acoustic network model The eige
Page 81: 3.3 Acoustic network model tine. To
Page 85 and 86: 4.1 Theory and num
Page 87 and 88: 4.1 Theory and num
Page 89 and 90: 4.2 Theoretical and</strong
Page 95 and 96: 5 System Identification Flame trans
Page 97 and 98: 5.1 Model structures and</s
Page 99 and 100: 5.2 System Identification 5.2 Syste
Page 101 and 102: 5.3 Excitation signals the zero mea
Page 103 and 104: 5.4 A posteriori validation <strong
Page 105 and 106: 5.4 A posteriori validation <strong
Page 107 and 108: 5.5 Proof
Page 119 and 120: 6 Numerical simulation MISO model i
Page 121 and 122: 6.1 Practical premixed combustor co
Page 129 and 130: 6.2 Steady-state simulations <stron
Page 131 and 132: 6.2 Steady-state simulations <stron
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6.3 Identifiction of</stron
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6.4 Identification of</stro
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6.4 Identification of</stro
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7 Acoustic analysis Once the acoust
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7.1 Setup of the a
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7.2 Acoustic network model results
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8 Summary and Conc
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The flame element of</stron
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Bibliography [1] Verband</s
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BIBLIOGRAPHY [18] L. Crocco. Theore
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BIBLIOGRAPHY [36] A. Giauque, L. Se
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BIBLIOGRAPHY [54] J.J. Keller, W. E
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BIBLIOGRAPHY [72] T. Lieuwen <stron
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BIBLIOGRAPHY Number 98-GT-269 in In
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BIBLIOGRAPHY [112] T. Sattelmayer.
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BIBLIOGRAPHY [130] A. Widenhorn. pr
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A.2 Estimation of
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A.3 Main flow parameters an
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