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

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Numerical analysis <strong>of</strong> thermo-acoustic instabilities lated to an equivalent element in the acoustic network model. The identification <strong>of</strong> flame transfer functions by CFD/SI requires an excitation <strong>of</strong> the flow variables to cause a system response. As the flame responds to mass flow <strong>and</strong> equivalence ratio fluctuations two independent excitation signals are required to discern the individual effects in the post-processing identification step. The excitation in such a simulation should be provided by the boundary conditions or adequate sources inside the CFD domain. A meaningful coupling between CFD/SI <strong>and</strong> acoustic network model has to take into account that the network model describes the system characteristics in terms <strong>of</strong> acoustic variables. Therefore equivalence ratio fluctuations have to be expressed in a suitable way as, e.g. described in Eqn. (2.10). The excitation, the signal <strong>and</strong> its location, which will be used as the input to identify F φ,i , determine the size <strong>of</strong> the simulated domain <strong>and</strong> therefore the computational effort. It also affects the interface between CFD/SI <strong>and</strong> network model <strong>and</strong> the corresponding network flame element. The kinematic flame response F u , on the other h<strong>and</strong>, can be included in a straightforward manner extracting the acoustic velocity fluctuations at the burner exit. Its identification only requires the simulation <strong>of</strong> the combustion chamber if a proper inlet boundary condition is set, which takes the flow conditions upstream into account (e.g. swirling flow). In the following different possibilities are discussed, which are denoted as A, B, C <strong>and</strong> D. The comparison between the possibilities is shown in Fig. 2.7. The columns present the computational domain required, the excitation <strong>and</strong> signals extracted <strong>and</strong> their locations <strong>and</strong> the corresponding network flame element. In case A the combustor, including swirler vanes, mixing section <strong>and</strong> part <strong>of</strong> the <strong>fuel</strong> injectors is resolved as shown in the first row <strong>and</strong> first column. The length <strong>of</strong> the <strong>fuel</strong> injectors, which have to be modeled, should be long enough to ensure a well developed velocity pr<strong>of</strong>ile at the entry to the mixing section. For this option, the <strong>fuel</strong> mass flow <strong>and</strong> the air mass flow are excited at the inlet boundary condition <strong>of</strong> the <strong>fuel</strong> line <strong>and</strong> <strong>of</strong> the mixing section, respectively. Here, the mass flow averaged velocity fluctuations upstream the <strong>fuel</strong> injec- 38
2.3 Identification <strong>of</strong> flame transfer functions CFD simulation Excitation & Extraction Flame element Inlet boundaries . m' m' F,i Excitation A CFD domain u' F,i u' b . m' u' A,i A,i Measurement planes u' b . u' A,i φ' u' i F,i Q' Inlet boundary Excitation B CFD domain Y' . m' Y' <strong>fuel</strong> φ' u' b Measurement planes - only valid if C Inlet boundary u' Y' b <strong>fuel</strong> m' . φ' Excitation - additional information required D CFD domain . m' m' A,i Measurement planes Excitation . m' u' b m' F,i φ' Measurement planes u' b . u' A,i φ' u' F,i Q' Figure 2.7: Comparison <strong>of</strong> possibilities to identify the flame transfer functions <strong>and</strong> to couple the transfer functions to the acoustic network model 39
Page 1: Technische Universität München In
Page 4 and 5: und ihre Geduld besonders für die
Page 7 and 8: Contents 1 Introduction 1 1.1 Techn
Page 9 and 10: CONTENTS 7.2.2 Impact</stro
Page 11 and 12: Nomenclature G stretch factor [-] h
Page 13 and 14: Nomenclature λ air-fuel</s
Page 15 and 16: 1 Introduction 1.1 Technology backg
Page 17 and 18: 1.2 Thermo-acoustic instabilities 1
Page 19 and 20: 1.2 Thermo-acoustic instabilities d
Page 21 and 22: 1.3 Control of the
Page 23 and 24: 1.3 Control of the
Page 25 and 26: 1.4 Intention and
Page 27 and 28: 1.5 Terminology and</strong
Page 29 and 30: 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 51: 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 and 82: 3.3 Acoustic network model tine. To
Page 83 and 84: 4 Modeling of turb
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
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5.4 A posteriori validation <strong
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5.4 A posteriori validation <strong
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5.5 Proof
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5.5 Proof
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5.5 Proof
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5.5 Proof
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5.5 Proof
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5.5 Proof
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6 Numerical simulation MISO model i
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6.1 Practical premixed combustor co
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6.2 Steady-state simulations <stron
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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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