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

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Numerical analysis <strong>of</strong> thermo-acoustic instabilities tion <strong>and</strong> in the mixing section upstream <strong>of</strong> the burner exit are taken as the input signals for the post-processor. They are extracted at the ”measurement” planes, which are shown in the second column. The heat release fluctuations due to equivalence ratio fluctuations can thus be determined by combining Eqn. (2.10) <strong>and</strong> (2.5). The total heat release rate fluctuations can be obtained by the summation <strong>of</strong> the two flame transfer functions: ˙Q ′ ¯˙Q ( ) u ′ F,i = F φ,i − u′ A,k ū F,i ū A,k ¯ṁ F,i ∑ N i=1 ¯ṁ F,i + F u u ′ b ū b . (2.14) This flame model structure can be directly transferred to the acoustic network model environment as the input for both models are the velocity fluctuations u ′ F,i , u′ A,i <strong>and</strong> u′ b . A sketch <strong>of</strong> the flame element is shown in the third column3 . Alternatively, the <strong>fuel</strong> mass flow can be excited downstream the <strong>fuel</strong> injector in applying <strong>fuel</strong> mass fraction fluctuations at the inlet boundary. The mass fraction Y is defined as the ratio <strong>of</strong> the mass m k <strong>of</strong> a particular species k <strong>and</strong> the total mass <strong>of</strong> the fluid m: Y = m k m . (2.15) To obtain the flame response to velocity fluctuations at the burner exit the total mass flow rate is in addition excited at the inlet. This is shown in the second row (case B). Here, the CFD domain contains a part <strong>of</strong> the mixing section, the swirler <strong>and</strong> the combustion chamber. The input signal for the identification <strong>of</strong> F φ,i would be the equivalence ratio fluctuations φ ′ at the inlet, which can be calculated using (see also Eqn. (2.6)) φ ′ Y ′ F = s st Y ′ , (2.16) O where Y F <strong>and</strong> Y O denote the <strong>fuel</strong> mass fraction <strong>of</strong> <strong>fuel</strong> <strong>and</strong> oxidizer mass fraction, respectively. However, this possibility is based, as discussed in chapter 2.2.2, on the assumption that the spatial distribution <strong>of</strong> equivalence ratio fluctuations does not vary with injection momentum. This is not the case for all 3 The response ˙Q ′ <strong>of</strong> the network flame element has still to be expressed as a function the acoustic variables downstream <strong>of</strong> the flame, which can be done using e.g. the Rankine-Hugoniot relations. 40
2.3 Identification <strong>of</strong> flame transfer functions injection systems. Examples are jet-in-cross flow injector configurations, in which a strong dependence on momentum ratio between air <strong>and</strong> <strong>fuel</strong> stream is observed. In this case, an increased <strong>fuel</strong> velocity results in increased penetration <strong>of</strong> the <strong>fuel</strong> stream into the air stream <strong>and</strong> thus in a different <strong>fuel</strong> distribution, which may influence the heat release rate. As the equivalence ratio fluctuations are generated at the location <strong>of</strong> injection, a transfer function T has to be defined in the network model environment, which connects the acoustic velocities at this location to the equivalence ratio fluctuations at the ”measurement” plane in the CFD simulation. Here, the equivalence ratio fluctuations do not have to be extracted. They can be directly calculated using the excitation signals at the inlet boundary. The corresponding network elements are shown in the third column. In simple configurations a constant time delay model can be chosen, which accounts for the convective transport <strong>of</strong> the <strong>fuel</strong> between both locations. If the inlet boundary <strong>and</strong> the ”measurement” plane is taken very close to the injection point, the same relation for the flame transfer function <strong>and</strong> the same network flame element can be used as in case A. The CFD domain could be further reduced in considering the combustor downstream <strong>of</strong> the <strong>fuel</strong> injection <strong>and</strong> swirler vanes, which is shown in the third <strong>and</strong> fourth row <strong>of</strong> Table 2.7. Here, the swirler <strong>and</strong> <strong>fuel</strong> injection are not modeled. The excitation can be provided by • C) a <strong>fuel</strong> mass fraction fluctuation <strong>and</strong> a fluctuation <strong>of</strong> the total mass flow rate, which are applied at the inlet boundary • D) introducing a fluctuating mass source function inside the computational domain <strong>and</strong> a fluctuation <strong>of</strong> the air mass flow rate at the inlet boundary In both cases the equivalence ratio fluctuations can be calculated using Eqn. (2.16). In case C the excitation signals can be used directly for the calculation. In case D only one ”measurement” plane at the burner exit is necessary to extract the <strong>fuel</strong> <strong>and</strong> oxidizer mass fractions as well as velocity fluctuations. The network flame model for both cases require again a transfer function T to express the equivalence ratio in terms <strong>of</strong> the acoustic fluctuations at the location <strong>of</strong> <strong>fuel</strong> injection. In contrast to case B such a transfer function should 41
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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 53: 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
Page 103 and 104: 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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