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

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Acoustic analysis ply could change the phase <strong>and</strong> amplitude <strong>of</strong> the equivalence ratio fluctuations. In their study the phase <strong>of</strong> the equivalence ratio fluctuations modified the phase relationship between pressure <strong>and</strong> heat release rate fluctuations <strong>and</strong> led finally to a significant reduction <strong>of</strong> pressure oscillations. This can also be confirmed by the considerations derived above: As the the amplitude <strong>and</strong> phase <strong>of</strong> the velocity fluctuations in the <strong>fuel</strong> line u ′ F,i is directly driven by the <strong>impedance</strong> <strong>of</strong> the <strong>fuel</strong> injection stage i , it follows from φ ′ i (ω) ( u ′ ¯φ ∼ F,i (ω) − u′ A,i (ω) ) , (7.3) ū F,i ū A,i that the amplitude <strong>and</strong> phase <strong>of</strong> the equivalence ratio is also modified. If now the phase change is sufficient to influence the phase <strong>of</strong> the heat release rate fluctuations (see Eqn. (7.2)) in such a way that the heat release rate fluctuations <strong>and</strong> the acoustic pressure at the flame are out <strong>of</strong> phase, the system becomes stable. Scarinci et. al. [116] suggested that minimizing the overall amplitude <strong>of</strong> equivalence ratio fluctuations can be useful to reduce the heat release rate fluctuations <strong>and</strong> thus to realize a low-oscillation combustion chamber. They developed a new mixing strategy, which is based on multiple injection stages injecting air instead <strong>of</strong> <strong>fuel</strong>. In this way the <strong>fuel</strong>-air mixing process is decoupled from pressure pulsations in the combustion chamber as the local equivalence ratio fluctuations are damped on the way through the premixer. In the present context using <strong>fuel</strong> injection stages a reduction <strong>of</strong> heat release rate fluctuations can be achieved in changing the velocity fluctuation u ′ F,i such that it is in phase with u ′ A,i . If both fluctuations have the same amplitude the resulting equivalence ratio fluctuations are reduced to zero: φ ′ i (ω) ( u ′ ¯φ ∼ F,i (ω) − u′ A,i (ω) ) → 0. (7.4) ū F,i ū A,i The consequence is a reduction <strong>of</strong> heat release rate fluctuations. The reduction leads to a decrease in growth rate <strong>and</strong> results therefore in a more stable system. Both studies mentioned have shown that influencing the equivalence ratio 146
7.2 Acoustic network model results fluctuations can lead to lower thermo-acoustic oscillations in combustion systems. However, the models derived only account for the impact <strong>of</strong> equivalence fluctuations on the heat release rate. As the heat release rate fluctuation in a practical premixed system is also driven by the kinematic response <strong>of</strong> the flame, tuning <strong>of</strong> the amplitude <strong>and</strong> phase <strong>of</strong> equivalence ratio fluctuations alone will in general not be sufficient to achieve a stable system. In the worst case it may lead also to a more unstable system, which is explained in the following. Taking into account both contributions (F u u ′ b /ū b, F φ,i φ ′ i / ¯φ) to fluctuations <strong>of</strong> heat release rate, a reduction <strong>of</strong> the heat release rate fluctuation can also be achieved if the phase difference between both equals π. This implies that both contributions are out <strong>of</strong> phase with respect to each other <strong>and</strong> lead to a destructive interference: F u (ω) u′ b (ω) ū b + F φ,i (ω) φ′ i (ω) ¯φ → 0. (7.5) The superposition <strong>of</strong> both contributions equals zero if the corresponding amplitudes have the same order <strong>of</strong> magnitude. Returning to the argument above, such a constellation would be affected in a negative way if the amplitude <strong>of</strong> the equivalence ratio fluctuations is reduced. The result would be an undesired increase <strong>of</strong> the heat release rate fluctuations. To analyze the conceptual considerations the combustion configuration A is used in the following, in which the <strong>fuel</strong> <strong>supply</strong> is located, as in the CFD simulation, 0.125 m upstream the burner exit. In the baseline configuration the pressure loss coefficient between <strong>fuel</strong> injection tube <strong>and</strong> mixing section is set to a large value (ζ≫1) to decouple the acoustic field <strong>of</strong> the <strong>fuel</strong> <strong>supply</strong> from the remaining system. The stability map (det(S(ω))) <strong>of</strong> the baseline configuration is shown in Fig. 7.5 in the range <strong>of</strong> Sr = [0 2]. The ordinate is plotted using the cycle increment C I−1. The figure includes all possible stable or unstable eigenfrequencies <strong>of</strong> the system in the frequency range considered. The stability border is marked as a solid line with C I− 1=0. As discussed in chapter 3.3.2 a value below zero corresponds to a stable eigenfrequency, whereas a value greater zero indicates an acoustically unstable system. 147
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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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Page 119 and 120: 6 Numerical simulation MISO model i
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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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