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

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Numerical simulation towards the burner <strong>and</strong> at the inner shear layer even into the mixing section. This undulating motion, generated at the burner exit in the outer <strong>and</strong> inner flame front, is then convected along the entire flame, leading to an increase <strong>of</strong> the overall flame surface area <strong>and</strong> heat release rate (state ”B”). Close to the downstream end <strong>of</strong> the flame the outer <strong>and</strong> the inner flame front merge, separating the remaining downstream <strong>fuel</strong> from the main combustion zone. The downstream end <strong>of</strong> the flame extinguishes, which is denoted as status ”C”. At this time the disturbance produced at the axial swirler reaches the burner exit where it results in a similar response (state ”D”, ”E”). A similar behavior (states ”A”, ”B”, ”C”) was described by Schuller et. al. [120]. In their work they investigated a laminar premixed flame <strong>and</strong> observed as well a sudden decrease <strong>of</strong> the flame surface due to the interaction <strong>of</strong> neighboring flame fronts at the tip <strong>of</strong> the flame. Flame response to equivalence ratio fluctuations at the burner exit In a second simulation, impulse forcing was applied to the <strong>fuel</strong> mass flow rate at injector ”2” without perturbation <strong>of</strong> the main flow. Unit impulse responses <strong>of</strong> the flame, obtained from impulse <strong>and</strong> DRBS broadb<strong>and</strong> excitation, respectively, are compared in Fig. 6.24. The basic trend matches again. However, the amplitude <strong>of</strong> the impulse response is only 60% <strong>of</strong> the UIR computed from broadb<strong>and</strong> forcing with SI. This is due to the small impact <strong>of</strong> the <strong>fuel</strong> mass flow added at injector ”2” compared to the overall mass flow. An alternating sign <strong>of</strong> the impulse UIRs for larger time delays is also clearly seen. As above the impulse response <strong>of</strong> the flame surface area <strong>and</strong> the heat release rate are investigated. As mentioned in chapter 1.2 the overall rate <strong>of</strong> heat release ˙Q <strong>of</strong> a premixed flame may be expressed as a function <strong>of</strong> the unburnt gas density ρ u , the flame surface per unit volume Σ, the (turbulent) burning velocity s t <strong>and</strong> the heat <strong>of</strong> reaction per unit mass <strong>of</strong> premixture△H. Once the richer <strong>fuel</strong>-air mixture arrives at the flame front, the heat released per unit mass <strong>of</strong> premixture ∆H <strong>and</strong> therefore the overall heat release rate ˙Q increases as shown in Fig. 6.25. As the turbulent burning velocity s t also increases, the flame propagates upstream, resulting in a reduction <strong>of</strong> total flame surface 132
6.3 Identifiction <strong>of</strong> the flame transfer functions 0.08 0.06 0.04 Amplitude 0.02 0 −0.02 −0.04 0 200 400 600 Time steps Figure 6.24: UIR φ,2 computed with DRBS (--) <strong>and</strong> impulse forcing <strong>of</strong> mass flow rate <strong>of</strong> <strong>fuel</strong> at injector ”2” (−−) 0.04 Amplitude 0.02 0 −0.02 −0.04 200 300 400 500 Time steps Figure 6.25: Response <strong>of</strong> flame surface area (--) <strong>and</strong> heat release rate (−−) to impulse forcing <strong>of</strong> mass flow rate <strong>of</strong> <strong>fuel</strong> at injector ”2” 133
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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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Page 95 and 96: 5 System Identification Flame trans
Page 97 and 98: 5.1 Model structures and</s
Page 99 and 100: 5.2 System Identification 5.2 Syste
Page 101 and 102: 5.3 Excitation signals the zero mea
Page 103 and 104: 5.4 A posteriori validation <strong
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Page 107 and 108: 5.5 Proof
Page 119 and 120: 6 Numerical simulation MISO model i
Page 121 and 122: 6.1 Practical premixed combustor co
Page 129 and 130: 6.2 Steady-state simulations <stron
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Page 133 and 134: 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
Page 155 and 156: 7.1 Setup of the a
Page 157 and 158: 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
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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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Impact of fuel supply impedance and fuel staging on gas turbine ...

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