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

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Nomenclature Latin letters A area [m 2 ] aCFL acoustic Courant-Friedrichs-Lewy number [-] c speed <strong>of</strong> sound [m/s] c reaction progress variable [-] ci confidence intervall [-] c p specific heat capacity (constant pressure) [J/kg-K] c v specific heat capacity (constant volume) [J/kg-K] C cross-correlation vector [-] C r crest factor [-] C I cycle increment [-] CFL Courant-Friedrichs-Lewy number [-] d diameter <strong>of</strong> burner mouth [m] d j diameter <strong>of</strong> <strong>fuel</strong> injection tube [m] D diffusion coefficient [m 2 /s] Da Damköhler number [-] e internal energy per unit mass [J/kg] e n noise term [-] f Riemann invariant (in positive direction) [m/s] f frequency [1/s] f c cut-<strong>of</strong>f frequency [1/s] f N Nyquist frequency [1/s] F w weighted reaction progress [-] F flame transfer function [-] g Riemann invariant (in negative direction) [m/s] x
Nomenclature G stretch factor [-] h unit impulse response vector [-] h s specific enthalpy per unit mass [J/kg] h t total enthalpy per unit mass [J/kg] He Helmholtz number [-] △H enthalpy per unit mass [J/kg] J impulse ratio <strong>of</strong> the <strong>fuel</strong> <strong>and</strong> main stream [-] k turbulent kinetic energy [m 2 /s 2 ] k b Boltzmann constant [J/K] k x wave number (in x-direction) [1/m] Ka Karlowitz number [-] l f laminar flame thickness [m] L length [m] L f axial distance between <strong>fuel</strong> injection <strong>and</strong> burner mouth [m] L R length <strong>of</strong> resonator tube [m] l t turbulent integral length scale [m] Le Lewis number [-] m mass [kg] M molar mass [kg/kmol] n interaction index [-] N A Avogadro number [-] p static pressure [Pa] Pr Pr<strong>and</strong>tl number [-] R specific gas constant [J/K-mol] R f reflection coefficient [-] q heat flux [W/m 2 ] ˙q rate <strong>of</strong> heat release (per unit mass) [J/kg] Q measure <strong>of</strong> identification quality [%] ˙Q rate <strong>of</strong> heat release (per unit area) [J/s-m 2 ] ˙Q V heat production (per unit volume) [J/s-m 3 ] s entropy [J/K] s signal [-] s st mass stoichiometric ratio [-] s L laminar flame speed [m/s] xi
Page 1: Technische Universität München In
Page 4 and 5: und ihre Geduld besonders für die
Page 7 and 8: Contents 1 Introduction 1 1.1 Techn
Page 9: CONTENTS 7.2.2 Impact</stro
Page 13 and 14: Nomenclature λ air-fuel</s
Page 15 and 16: 1 Introduction 1.1 Technology backg
Page 17 and 18: 1.2 Thermo-acoustic instabilities 1
Page 19 and 20: 1.2 Thermo-acoustic instabilities d
Page 21 and 22: 1.3 Control of the
Page 23 and 24: 1.3 Control of the
Page 25 and 26: 1.4 Intention and
Page 27 and 28: 1.5 Terminology and</strong
Page 29 and 30: 1.5 Terminology and</strong
Page 31 and 32: 2 Numerical analysis of</st
Page 33 and 34: 2.1 Overview of me
Page 39 and 40: 2.2 Flame dynamics of</stro
Page 47 and 48: 2.3 Identification of</stro
Page 57 and 58: 3 Acoustics Before analyzing the ac
Page 59 and 60: 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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6.4 Identification of</stro
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6.4 Identification of</stro
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7 Acoustic analysis Once the acoust
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7.1 Setup of the a
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7.2 Acoustic network model results
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8 Summary and Conc
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The flame element of</stron
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Bibliography [1] Verband</s
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BIBLIOGRAPHY [18] L. Crocco. Theore
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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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