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

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Numerical simulation aCFL=(u+ c) △t △x . (6.4) It is an extension <strong>of</strong> the CFL number, which is based on the mean flow velocity. The CFL number determines the number <strong>of</strong> grid cells through which a flow disturbance is convected in one time step. In terms <strong>of</strong> computational fluid dynamics it is a condition for the algorithms for solving partial differential equations to be convergent. An explicit method becomes unstable if the CFL value exceeds one. However, a fully implicit discretization method allows CFL values over one, although the accuracy <strong>of</strong> the discrete schemes diminishes. It has been shown that for aCFL≫1 the propagation <strong>of</strong> an acoustic wave could be resolved adequately. The important criteria to minimize the numerical dispersion effects are the number <strong>of</strong> grid cells per wavelength <strong>and</strong> time steps per Figure 6.6: Streamlines around a swirler blade showing the flow separation <strong>and</strong> the resulting secondary flow 114
6.2 Steady-state simulations <strong>of</strong> the combustor configurations period. In the present simulations a minimum <strong>of</strong> 100 grid cells <strong>and</strong> 20 time steps per period was ensured for an acoustic wave with a frequency <strong>of</strong> 2000 Hz. Details about a numerical test case, in which the propagation <strong>of</strong> a plane acoustic wave in a simple duct was analyzed, can be found in H<strong>of</strong>fmann [44]. 6.2 Steady-state simulations <strong>of</strong> the combustor configurations As a starting point for the transient simulations to determine the flame transfer functions, steady-state simulations were performed. They are required to obtain the main characteristics <strong>of</strong> the two combustion configurations regarding mixing quality <strong>and</strong> axial heat release distribution. The heat release distribution is necessary to define an appropriate axial location <strong>of</strong> the flame in the acoustic network models. 1500 1000 Counts 500 0 0.5 0.6 0.7 0.8 0.9 Equivalence ratio Figure 6.7: Equivalence ratio distribution upstream <strong>of</strong> the burner mouth, case A To judge the air-<strong>fuel</strong> mixing quality the grid cell value <strong>of</strong> the equivalence ratio measured on a cut through the mixing section were exported <strong>and</strong> analyzed. The cut was placed slightly in front <strong>of</strong> the burner mouth. As each cell exhibits a 115
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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
Page 77 and 78: 3.3 Acoustic network model pressure
Page 79 and 80: 3.3 Acoustic network model The eige
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Page 83 and 84: 4 Modeling of turb
Page 85 and 86: 4.1 Theory and num
Page 87 and 88: 4.1 Theory and num
Page 89 and 90: 4.2 Theoretical and</strong
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
Page 105 and 106: 5.4 A posteriori validation <strong
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
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Page 131 and 132: 6.2 Steady-state simulations <stron
Page 133 and 134: 6.3 Identifiction of</stron
Page 149 and 150: 6.4 Identification of</stro
Page 151 and 152: 6.4 Identification of</stro
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
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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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