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

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Numerical simulation Phase Amplitude 2 1 3.14 1.57 −1.57 0 0 0.5 1 1.5 2 0 −3.14 0 0.5 1 1.5 2 Strouhal number Figure 6.18: Flame transfer function, case B (−− F φ,2 , -- F φ,3 , -· F u ) consumed in this region. This influence can also be observed in the flame response to velocity fluctuations. As the velocity increases with increasing radial distance <strong>and</strong> taking into account the slightly changed flow field, the impact <strong>of</strong> the velocity fluctuations at the burner exit results in a strong response <strong>of</strong> the outer flame region, see again Fig. 6.17. In contrast to the two <strong>fuel</strong> injection stage configuration the first peak <strong>of</strong> the UIR u has a higher amplitude than the second one, indicating that the flame in this case responds stronger to velocity fluctuations at the burner exit than to those at the swirler. The response UIR φ,3 starts about 170 time steps <strong>and</strong> reaches its positive maximum at 220 time steps. It exhibits a time-shifted, but comparable time delay distribution as UIR φ,2 in the first configuration. The mean time delay <strong>of</strong> the different impacts is τ ≈ 6.2 ms for the upstream <strong>fuel</strong> injection, τ ≈ 4.5 ms for the downstream <strong>fuel</strong> injection <strong>and</strong> τ≈2 ms for the velocity fluctuations at the burner exit. Compared to case A, the shortened time delays are mainly due to the slightly changed heat release rate distribution <strong>and</strong> to the fact that the mean inlet velocity <strong>of</strong> case B is about 0.5 m/s less than in case A. Similar to the first 126
6.3 Identifiction <strong>of</strong> the flame transfer functions Amplitude Amplitude Amplitude Amplitude 1 0 −1 0 200 400 600 800 0.1 0 −0.1 0 200 400 600 800 0.1 0 −0.1 0.1 0 0 200 400 600 800 −0.1 0 200 400 Time steps 600 800 Figure 6.19: Auto- <strong>and</strong> cross-correlation <strong>of</strong> error <strong>and</strong> signals, case B. (From top to bottom: Γ ǫ , C ǫφ ′ 2 , C ǫφ ′ 3 , C ǫu ′ b ) configuration, the deviations between the predicted <strong>and</strong> measured heat release rate signal is rather low. The quality parameter Q equals 90.4%. Fig. 6.19 shows the auto- <strong>and</strong> cross-correlation analysis <strong>of</strong> the prediction error <strong>and</strong> the input signals φ ′ 2 , φ′ 3 <strong>and</strong> u′ . Again the cross-correlation values stay for nearly b all considered time delays within the 99% confidence interval. Only a few values are located slightly at or outside the border. The auto-correlation shows unexpected deviations at large delay times, which are again probably due to non-linearities. 127
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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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Page 95 and 96: 5 System Identification Flame trans
Page 97 and 98: 5.1 Model structures and</s
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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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Page 107 and 108: 5.5 Proof
Page 119 and 120: 6 Numerical simulation MISO model i
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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
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
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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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