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

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Acoustic analysis 1.5 100 10 (CI − 1) 1 0.5 0 1 0.1 0.01 0.001 −0.5 0.5 1 1.5 2 Strouhal number 0.0001 Figure 7.5: Stability map <strong>of</strong> the baseline configuration, case A with acoustically decoupled <strong>fuel</strong> <strong>supply</strong> (ζ≫ 1) In the following three eigenfrequencies <strong>of</strong> the baseline configuration are exemplarily analyzed in more detail: two unstable eigenmodes around Sr = 1.13 <strong>and</strong> Sr = 1.32 <strong>and</strong> one stable eigenmode at Sr = 0.51. The eigenfrequencies <strong>and</strong> their corresponding cycle increments can be found in Fig. 7.6. In tuning the <strong>impedance</strong> <strong>of</strong> the <strong>fuel</strong> injector it is demonstrated how the three eigenfrequencies can be influenced in applying the different approaches presented above. To acoustically couple the <strong>fuel</strong> injection stage to the combustion system the pressure loss coefficients are set in the following to zero between the <strong>fuel</strong> plenum <strong>and</strong> the injection tube <strong>and</strong> to 0.2 between the injection tube <strong>and</strong> the mixing section. The values are lower than the ones obtained by steady state CFD simulations. They are chosen to enhance the demonstration <strong>of</strong> the stabilizing potential <strong>of</strong> the tuned <strong>fuel</strong> injector <strong>impedance</strong>s 1 . In the first example the combined length <strong>of</strong> the resonator tube <strong>and</strong> the <strong>fuel</strong> 1 The values obtained by CFD are in some demonstration cases too high to realize a stable combustion system. A reduction <strong>of</strong> the pressure loss can be realized, for example, in using injection holes with a higher diameter. The resulting lower <strong>fuel</strong> velocity leads to a lower impulse <strong>of</strong> the <strong>fuel</strong>, which can lead to lower mixing qualities. To obtain similar mixing qualities the <strong>fuel</strong> has to be injected closer to the middle <strong>of</strong> the mixing section, e.g. by extending the injection tubes into the mixing section. 148
7.2 Acoustic network model results 0.5 (CI − 1) 0 −0.5 0.5 1 1.5 Strouhal number Figure 7.6: Influence <strong>of</strong> the injector <strong>impedance</strong> on the eigenfrequencies <strong>and</strong> cycle increments – comparison between baseline configuration (ζ ≫ 1) (□) <strong>and</strong> configurations with resonator length L R,2 = 0.12 m (◦), L R,2 = 0.42 m (⊳), <strong>and</strong> L R,2 = 0.18 m (⋄) plenum is set to L R,2 = 0.12 m. The corresponding eigenfrequency <strong>of</strong> this <strong>fuel</strong> injection stage affects mainly the eigenfrequency at Sr = 1.32 <strong>of</strong> the baseline configuration. Here, the phase <strong>of</strong> the equivalence ratio fluctuations φ ′ 2 at the <strong>fuel</strong> injection stage is shifted by nearly π. In addition also the phase <strong>of</strong> the velocity fluctuations at the burner mouth u ′ is changed. Both are b shown in Fig. 7.7. In consequence the phase <strong>of</strong> the heat release rate contributions F φ,2 φ ′ 2 / ¯φ <strong>and</strong> F u u ′ b / u¯ b <strong>and</strong> thus <strong>of</strong> the heat release rate fluctuations are changed by about 1.1 π, see Fig. 7.8. This change leads to a favorable phase relationship between pressure fluctuations <strong>and</strong> heat release rate fluctuations <strong>and</strong> turns finally the unstable eigenfrequency (C I − 1=0.19) into a stable one (C I − 1=−0.1). The amplitude <strong>of</strong> the equivalence ratio fluctuation, however, is increased by the increase <strong>of</strong> the <strong>fuel</strong> velocity fluctuation u ′ F,2 <strong>and</strong> the fact that u ′ F,2 <strong>and</strong> the velocity <strong>of</strong> the main stream u′ A,2 are out <strong>of</strong> phase, see Fig. 7.9 <strong>and</strong> Fig. 7.10. Here <strong>and</strong> in the following all amplitudes are normalized with their mean values. Higher equivalence ratio fluctuations increase the amplitude <strong>of</strong> the heat release rate contribution F φ,2 φ ′ 2 / ¯φ. The amplitude <strong>of</strong> the heat release 149
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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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Page 153 and 154: 7 Acoustic analysis Once the acoust
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Page 157 and 158: 7.2 Acoustic network model results
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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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Impact of fuel supply impedance and fuel staging on gas turbine ...

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