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

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Acoustic analysis Amplitude 0.01 0.005 0 1.1 1.2 1.3 1.4 1.5 Phase 3.14 1.57 0 −1.57 −3.14 1.1 1.2 1.3 1.4 1.5 Strouhal number Figure 7.11: Amplitude <strong>and</strong> phase <strong>of</strong> heat release rate contributions <strong>of</strong> the baseline configuration (ζ≫1) (-· F φ,2 φ ′ 2 / ¯φ, -- F u u ′ b / u¯ b) <strong>and</strong> configuration with resonator length L R,2 = 0.12 m (-◦ F φ,2 φ ′ 2 / ¯φ, −− F u u ′ b / u¯ b) rate fluctuations is also increased as the heat release rate contributions are almost in phase, which is presented in Fig. 7.11. As the heat release rate fluctuations <strong>and</strong> the pressure fluctuations are certainly out <strong>of</strong> phase, the increase could even strengthen the stabilizing effect. The observations confirm the fact that the main driving parameter is the phase <strong>of</strong> the equivalence ratio fluctuations, which influences the phase <strong>of</strong> the heat release rate fluctuations <strong>and</strong> thus the stability <strong>of</strong> the system. The amplitude <strong>of</strong> the equivalence ratio fluctuations, however, determines the absolute value <strong>of</strong> the cycle increment. A length <strong>of</strong> the resonator tube <strong>of</strong> L R,2 = 0.42 m results in a reduction <strong>of</strong> equivalence ratio fluctuations φ ′ 2 at a Strouhal number <strong>of</strong> about Sr = 0.51. At this frequency the amplitude <strong>of</strong> the <strong>fuel</strong> velocity fluctuation u ′ F,2 is increased. Compared to the last case the phase difference between u ′ F,2 <strong>and</strong> the velocity fluctuation <strong>of</strong> the main stream u ′ A,2 is now roughly zero as it is demonstrated in Fig. 7.12. As both velocity fluctuations have almost the same amplitude at this fre- 152
7.2 Acoustic network model results 0.05 Amplitude 0 0.4 0.5 0.6 Phase 3.14 1.57 0 −1.57 −3.14 0.4 0.5 0.6 Strouhal number Figure 7.12: Velocity fluctuations at the <strong>fuel</strong> injection location <strong>of</strong> the baseline configuration (ζ≫1) (-· u ′ A,2 , -- u′ F,2 ) <strong>and</strong> configuration with resonator length L R,2 = 0.42 m (-◦ u ′ A,2 ,−− u′ F,2 ) 0.04 0.03 Amplitude 0.02 0.01 0 0.4 0.5 0.6 Strouhal number Figure 7.13: Heat release rate fluctuations caused by equivalence ratio fluctuations (F φ,2 φ ′ 2 / ¯φ) <strong>of</strong> the baseline configuration (ζ ≫ 1) (--) <strong>and</strong> configuration with resonator length L R,2 = 0.42 m (−−) 153
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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
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2 Numerical analysis of</st
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2.1 Overview of me
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2.1 Overview of me
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2.1 Overview of me
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2.2 Flame dynamics of</stro
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2.3 Identification of</stro
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3 Acoustics Before analyzing the ac
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3.1 Basic acoustic equations as a f
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3.2 Linear acoustic equations Here,
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3.2 Linear acoustic equations p ′
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3.3 Acoustic network model p ′ (x
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3.3 Acoustic network model matrix e
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3.3 Acoustic network model The <str
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3.3 Acoustic network model where A
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3.3 Acoustic network model coming c
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3.3 Acoustic network model Z i Air
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3.3 Acoustic network model pressure
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3.3 Acoustic network model The eige
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3.3 Acoustic network model tine. To
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4 Modeling of turb
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4.1 Theory and num
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4.1 Theory and num
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4.2 Theoretical and</strong
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5 System Identification Flame trans
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5.1 Model structures and</s
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5.2 System Identification 5.2 Syste
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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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Page 119 and 120: 6 Numerical simulation MISO model i
Page 121 and 122: 6.1 Practical premixed combustor co
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Page 133 and 134: 6.3 Identifiction of</stron
Page 149 and 150: 6.4 Identification of</stro
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Page 153 and 154: 7 Acoustic analysis Once the acoust
Page 155 and 156: 7.1 Setup of the a
Page 157 and 158: 7.2 Acoustic network model results
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Page 181 and 182: 8 Summary and Conc
Page 183 and 184: The flame element of</stron
Page 185 and 186: Bibliography [1] Verband</s
Page 187 and 188: BIBLIOGRAPHY [18] L. Crocco. Theore
Page 189 and 190: BIBLIOGRAPHY [36] A. Giauque, L. Se
Page 191 and 192: BIBLIOGRAPHY [54] J.J. Keller, W. E
Page 193 and 194: BIBLIOGRAPHY [72] T. Lieuwen <stron
Page 195 and 196: BIBLIOGRAPHY Number 98-GT-269 in In
Page 197 and 198: BIBLIOGRAPHY [112] T. Sattelmayer.
Page 199 and 200: BIBLIOGRAPHY [130] A. Widenhorn. pr
Page 201 and 202: A.2 Estimation of
Page 203 and 204: A.3 Main flow parameters an
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