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

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Acoustic analysis how effective it is to tune the <strong>fuel</strong> injector <strong>impedance</strong> <strong>and</strong> to choose favorable locations for the <strong>fuel</strong> injection stages. The last remaining parameter, which could be adjusted during the design process in a system with <strong>fuel</strong> <strong>staging</strong>, is the amount <strong>of</strong> <strong>fuel</strong>, which is injected at a certain <strong>fuel</strong> injection stage. Similar to the pressure loss coefficient, which determines the amplitude <strong>of</strong> the acoustic velocity fluctuation in the <strong>fuel</strong> injection tube, the mass flow split between the mean <strong>fuel</strong> mass flow at injection i ( ¯ṁ i ) <strong>and</strong> the total <strong>fuel</strong> mass flow ( ∑ N ¯ṁ i=1 F,i ) defines the strength <strong>of</strong> the impact, which was already explained in chapter 2.2: ( u ′ F,i (ω) F φ,i (ω) φ′ i (ω) ¯φ = F φ,i (ω) ū F,i − u′ A,i (ω) ) ū A,i ¯ṁ F,i ∑ N i=1 ¯ṁ F,i . Here, N denotes again the number <strong>of</strong> <strong>fuel</strong> injection stages. Thus the <strong>fuel</strong> split can be seen as a fine-tuning parameter to adjust the impact distribution between the different <strong>fuel</strong> injection stages. It should be noted that each <strong>fuel</strong> injection stage should, in general, be placed at a location <strong>and</strong> designed in a way that it has a positive influence on the acoustics <strong>of</strong> the entire combustion system. 166
8 Summary <strong>and</strong> Conclusions In the present work a numerical design method was developed to analyze the impact <strong>of</strong> <strong>fuel</strong> injector <strong>impedance</strong>, <strong>fuel</strong> injector location <strong>and</strong> <strong>fuel</strong> <strong>staging</strong> on the thermo-acoustic stability <strong>of</strong> practical premixed combustion systems. Fuel <strong>staging</strong> denotes in this context, that the <strong>fuel</strong> is injected at multiple locations into the mixing section <strong>of</strong> the combustion system. In terms <strong>of</strong> thermo-acoustic stability analysis a physical underst<strong>and</strong>ing <strong>and</strong> an accurate description <strong>of</strong> the flame dynamics is essential. In practical premixed combustion systems the flame responds to acoustic disturbances <strong>of</strong> the velocity at the flame holder <strong>and</strong> <strong>of</strong> the equivalence ratio, which are the result <strong>of</strong> acoustic velocity fluctuations <strong>of</strong> the air <strong>and</strong> <strong>fuel</strong> stream at the location <strong>of</strong> <strong>fuel</strong> injection. In such a system, a physically meaningful, consistent <strong>and</strong> unambiguous description <strong>of</strong> the overall flame dynamics can in general only be obtained if the flame response is described as a multiple-input single-output (MISO) model with two or more flame transfer functions, which relate the heat release rate <strong>of</strong> the flame to the various disturbances. In order to determine the flame transfer functions for such a model structure, a system identification method was developed, which is based on correlation analysis <strong>of</strong> time series data <strong>and</strong> the inversion <strong>of</strong> the Wiener-Hopf equation. As the identification <strong>of</strong> a MISO model is, because <strong>of</strong> partly correlated input signals, a challenging task, quality criteria were implemented to analyze how accurately an identified model reproduces the system dynamics. The method was validated successfully against test data generated with a time domain model, designed to qualitatively represent a practical premixed combustion system. To obtain the flame dynamics for the present purpose the MISO identification was applied to data generated by a transient computational fluid dynamics (CFD) simulation <strong>of</strong> a generic configuration <strong>of</strong> a practical premixed combustor with two <strong>and</strong> three <strong>fuel</strong> injection stages. The CFD 167
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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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Page 129 and 130: 6.2 Steady-state simulations <stron
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Page 153 and 154: 7 Acoustic analysis Once the acoust
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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 and 200: BIBLIOGRAPHY [130] A. Widenhorn. pr
Page 201 and 202: A.2 Estimation of
Page 203 and 204: A.3 Main flow parameters an
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