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

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Acoustic analysis Figure 7.2: Finite element analysis <strong>of</strong> the <strong>fuel</strong> injection system (left: first eigenmode, right: second eigenmode work model represents the acoustic behavior <strong>of</strong> the <strong>fuel</strong> injector quite well. However, the impact <strong>of</strong> the acoustic <strong>impedance</strong> should be shown in general. Therefore, small deviations, like the ones presented, can be neglected. In the following L R , as the length <strong>of</strong> the resonator tube, is exclusively taken as the length <strong>of</strong> the combined tube in the simplified network model. The termination <strong>of</strong> the combustion chamber through which the hot products Eigenfrequencies: 1st 2nd 3rd Finite element-based model 0.61 1.71 2.62 Simplified network model w/o mean flow <strong>and</strong> pressure loss 0.59 1.79 2.99 Simplified network model with mean flow <strong>and</strong> pressure loss 0.57 1.75 2.98 Table 7.1: Eigenfrequencies <strong>of</strong> the finite element-based model <strong>and</strong> simplified network model <strong>of</strong> the <strong>fuel</strong> <strong>supply</strong> 142
7.2 Acoustic network model results leave the chamber into the atmosphere is acoustically described by a partly reflecting open end with a reflection coefficient <strong>of</strong> R f = 0.5 [55]. The further combustion test rig elements are modeled according to their dimensions described in chapter 6.1 <strong>and</strong> Fig. 6.3. The acoustic behavior <strong>of</strong> the flame <strong>and</strong> the axial swirler are implemented using the identified time domain information in form <strong>of</strong> the unit impulse response. The UIR can be transformed in the real or complex frequency domain using Eqn. (5.5), which is repeated here for completeness: M∑ F (ω real ,ω im )= h k e −i (ω real+i ω im )k△t . (7.1) k=0 In this way it is possible to use the eigenfrequency search method described in chapter 3.3.2. The main flow parameters <strong>of</strong> the acoustic network models, case A <strong>and</strong> case B, can be found in appendix A.3. 7.2 Acoustic network model results With the acoustic network models <strong>of</strong> the two combustion configurations, the impact <strong>of</strong> acoustic <strong>impedance</strong>, <strong>fuel</strong> injection location <strong>and</strong> <strong>fuel</strong> <strong>staging</strong> on the thermo-acoustic stability <strong>of</strong> the entire combustion system can be analyzed in detail. The eigenfrequencies <strong>and</strong> thereby the linear stability <strong>of</strong> the eigenmodes are determined as the roots <strong>of</strong> the determinant <strong>of</strong> the system matrix. To gain further insight into the complex system, frequency responses <strong>of</strong> the acoustic variables to a velocity excitation (loudspeaker) at the plenum are calculated in solving the inhomogeneous matrix equation. The excitation amplitude was set to 10%. Both methods are described in more detail in chapter 3.3.2. The three different design options influence predominantly the amplitude <strong>of</strong> the heat release rate fluctuations <strong>and</strong> the phase relationship between fluctuations <strong>of</strong> pressure <strong>and</strong> heat release rate (see also the discussion in chapter 1.2). The parameters, which are affected, can therefore be found in the relation, which describes the heat release rate fluctuations (see also Eqn. (2.11)): ˙Q ′ (ω) ¯˙Q = F u (ω) u′ b (ω) N∑ + ū b k=1 F φ,i φ ′ i (ω) ¯φ 143
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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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Page 133 and 134: 6.3 Identifiction of</stron
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Page 153 and 154: 7 Acoustic analysis Once the acoust
Page 155: 7.1 Setup of the a
Page 159 and 160: 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
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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