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

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A Appendix A.1 Transformation <strong>of</strong> pu, f g transfer matrix <strong>and</strong> scattering (sr ) matrix notation The following relations show the necessary operations to transform a transfer or scattering matrix from one notation into another: T pu = Z T fg Z −1 T fg = Z −1 T pu Z (A.1) (A.2) where ⎛ ⎜ Z ≡ ⎝ 1 1 −1 1 ⎞ ⎟ ⎠. (A.3) With ⎛ ⎜ T fg ≡ ⎝ A C B D ⎞ ⎟ ⎠ (A.4) the scattering matrix can be obtained: ⎛ ⎜ S sr = ⎝ A− B C D − C D B D 1 D ⎞ ⎟ ⎠. (A.5) 186
A.2 Estimation <strong>of</strong> the optimum number <strong>of</strong> circumferential injection holes A.2 Estimation <strong>of</strong> the optimum number <strong>of</strong> circumferential injection holes The optimum number <strong>of</strong> circumferential holes was estimated according to Holdeman et al. [45] using the relation C = S H √ J, (A.6) where S denotes the spacing <strong>of</strong> the holes <strong>and</strong> H corresponds to the height <strong>of</strong> rectangular duct. C represents a constant with an optimum value <strong>of</strong> 2.5. For a cylindrical duct the spacing amounts to S = 2πR/n with n being the number <strong>of</strong> holes. Therefore the number <strong>of</strong> holes can be calculated by the following equation: n= 2πR √ J. H (A.7) In case <strong>of</strong> a cylindrical duct the height can be substituted by the radius using the relation R = H/ 2. For the analyzed case the radius can be determined by the outer radius or the difference between the outer radius <strong>and</strong> the inner radius <strong>of</strong> the mixing section. The optimum number <strong>of</strong> injection holes can then be calculated <strong>and</strong> lies in the range between 6.1 <strong>and</strong> 10.2. A.3 Main flow parameters <strong>and</strong> structure <strong>of</strong> the acoustic network models The following tables represent the basic flow parameters which are required as an input for the acoustic network models used in the present work. In addition Fig. A.1 shows the network structure <strong>of</strong> the combustion configuration with three <strong>fuel</strong> injection systems (configuration B). 187
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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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5.5 Proof
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5.5 Proof
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6 Numerical simulation MISO model i
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6.1 Practical premixed combustor co
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6.2 Steady-state simulations <stron
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6.2 Steady-state simulations <stron
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6.3 Identifiction of</stron
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Page 149 and 150: 6.4 Identification of</stro
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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 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: BIBLIOGRAPHY [130] A. Widenhorn. pr
Page 203 and 204: A.3 Main flow parameters an
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