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

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Introduction Plenum Fuel Supply Combustion chamber Z US Air Z i Fuel Swirler u' F,i u' A,i φ' i u' fl p' Flame p' fl . Q' p',u’ Z DS Mixing section u' b Turbulence (s ) t Flame front kinematics (A) Hydrodynamic instabilities . Heat release rate (Q) Swirl number (A) Equivalence ratio (s , s , ∆H) L t Figure 1.1: Overview <strong>of</strong> the acoustic interaction <strong>of</strong> the flame the <strong>fuel</strong> injection stages i , i = 1,..., N, where N denotes the total number <strong>of</strong> <strong>fuel</strong> injectors in the system, are represented by their acoustic characteristics in form <strong>of</strong> the acoustic <strong>impedance</strong>s Z US , Z DS <strong>and</strong> Z 2 i . The downstream part <strong>of</strong> the figure presents an overview over the different impacts <strong>of</strong> the acoustics on the heat release rate. Following Ducruix et al. [27], Fleifil et al. [29] or Lawn <strong>and</strong> Polifke [65] the overall heat release rate is expressed as ∫ ˙Q = ρ u △H Σ s t dV, (1.1) where ρ u is the unburnt gas density,△H the enthalpy or heat <strong>of</strong> reaction per unit mass <strong>of</strong> the mixture, Σ the flame surface per unit volume, s t the turbulent flame speed <strong>and</strong> V the volume. The heat release rate fluctuations can be 2 The acoustic <strong>impedance</strong> Z is defined as the ratio <strong>of</strong> acoustic pressure <strong>and</strong> velocity <strong>and</strong> is a description <strong>of</strong> the local acoustic field. 4
1.2 Thermo-acoustic instabilities decomposed in the linear regime into separate contributions <strong>of</strong> fluctuating unburnt density, heat <strong>of</strong> reaction, flame area <strong>and</strong> flame speed: 3 ˙Q ′ ¯˙Q ≈ ρ′ u ¯ρ u + △H′ △ ¯H + A′ Ā + s′ t ¯s t . (1.2) Here, A denotes the total flame front area. The total heat release rate can thus be described as a superposition <strong>of</strong> the individual effects. The fluctuations <strong>of</strong> the unburnt density in Eqn. (1.2) can usually be neglected in typical leanpremixed combustion systems burning hydrocarbon <strong>fuel</strong>s at low Mach numbers. For practical premixed flames, two dominant interaction mechanisms between heat release rate <strong>and</strong> acoustic fluctuations have been identified: 1) flame front kinematics, i.e. the time-delayed adjustment <strong>of</strong> flame shape, flame surface area <strong>and</strong> flame position to a change in the velocity <strong>of</strong> the flow through the burner u ′ . These fluctuations result b in kinematic perturbations, which are convected along the flame front [11, 13, 22, 29, 65, 68, 121]. The acoustic velocity fluctuation u ′ b also influences the local turbulent flow field, especially in the shear layer within <strong>and</strong> beyond the burner, which can modulate the turbulent burning velocity <strong>and</strong> thus the <strong>fuel</strong> consumption rate [76, 90]. At large amplitudes, vortical disturbances <strong>of</strong> the flow, induced by acoustic oscillations, can manifest themselves as large-scale vortex structures. They strongly influence the mixing <strong>of</strong> fresh <strong>fuel</strong>/air mixture <strong>and</strong> hot combustion products <strong>and</strong> thereby the heat release rate. Vortices observed during combustion oscillations can also be due to hydrodynamic instabilities [94]. They have an impact on the local turbulent burning velocity <strong>and</strong> can enhance or reduce the combustion process or even lead to local quenching <strong>of</strong> the flame. 3 Acoustic fluctuations are throughout this work denoted by an apostrophe ′ , whereas mean values are represented by an overbar ¯. 5
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 and 12: Nomenclature G stretch factor [-] h
Page 13 and 14: Nomenclature λ air-fuel</s
Page 15 and 16: 1 Introduction 1.1 Technology backg
Page 17: 1.2 Thermo-acoustic instabilities 1
Page 21 and 22: 1.3 Control of the
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Page 25 and 26: 1.4 Intention and
Page 27 and 28: 1.5 Terminology and</strong
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Page 31 and 32: 2 Numerical analysis of</st
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Page 39 and 40: 2.2 Flame dynamics of</stro
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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,
Page 63 and 64: 3.2 Linear acoustic equations p ′
Page 65 and 66: 3.3 Acoustic network model p ′ (x
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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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