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

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Nomenclature s t turbulent flame speed [m/s] S c reaction source term [kg/m 2 -s] S sr Scattering matrix [-] Sc c,t turbulent Schmidt number [-] t time [s] t n sampling instant [s] T temperature [K] T f g Transfer matrix described by f <strong>and</strong> g [-] T per oscillation period [s] T c cycle time [s] △t sampling interval [s] T t simulation time [s] u velocity [m/s] u velocity vector [m/s] u absolute velocity [m/s] u i velocity component i or vector u [m/s] V volume [m 3 ] x input signal [-] X axial distance from point <strong>of</strong> <strong>fuel</strong> injection [m] y output signal (response) [-] ŷ predictor [-] Y radial distance from point <strong>of</strong> <strong>fuel</strong> injection [m] Y mass fraction [-] Z acoustic <strong>impedance</strong> [-] Z M mixture fraction [-] Greek letters α [-] ǫ prediction error [-] ǫ t turbulent dissipation [m 2 /s 3 ] γ ratio <strong>of</strong> specific heats [-] Γ auto-correlation matrix [-] xii
Nomenclature λ air-<strong>fuel</strong> ratio [-] λ t thermal conductivity [W/m-K] λ w wavelength [m] η k Kolmogorov length scale [m] ϕ regression vector [-] ϕ u velocity potential [1/s] φ equivalence ratio [-] µ t turbulent dynamic viscosity [kg/m-s] ρ density [kg/m 3 ] Σ flame surface per unit volume [m −1 ] τ stress tensor [Pa] τ c chemical time scale [s] τ k Kolmogorov time [s] τ t turbulent time scale [s] ˆθ least-square estimate [-] ω angular frequency [1/s] ω t turbulent frequency [1/s] ˙ω reaction rate [kg/m 3 -s] χ u thermal diffusivity [W/m-K] ζ pressure loss coefficient [-] Operators (.) ′ acoustic fluctuation (.) ′′ turbulent fluctuation (.) ¯ mean value (Reynolds average) (.) ˜ mass-weighted average (Favre average) xiii
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 and 10: CONTENTS 7.2.2 Impact</stro
Page 11: Nomenclature G stretch factor [-] h
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
Page 61 and 62: 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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