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

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Numerical simulation Velocity inlet (<strong>fuel</strong>+air) Measurement planes (SI) Pressure outlet Velocity inlet (<strong>fuel</strong>) Figure 6.5: Sketch <strong>of</strong> the computational domain <strong>and</strong> location <strong>of</strong> ”measurement” planes (case A) for the SI-method teristic boundary conditions (NSCBC) <strong>of</strong> Poinsot <strong>and</strong> Lele [95], which was implemented in the CFX environment by Widenhorn [130]. The inlet boundary conditions <strong>of</strong> the main air-<strong>fuel</strong> <strong>and</strong> the <strong>fuel</strong> stream(s) are overlaid by acoustic velocity excitation. As the discrete r<strong>and</strong>om binary signal with limited frequency content led to heat release fluctuations, which can not be described completely by a linear relationship <strong>and</strong> might be due to non-linearities, the unlimited signal (f max = 1/△t ) was used in the following. These unexplained deviations, which are also present at low level using the unlimited signal, are described in more detail in chapter 6.3. The excitation amplitude at the inlet Inlet, case A: Main stream Fuel stream Velocity u [m/s] 18.6 85.6 Density ρ [kg /m 3 ] 1.167 0.66 Fuel mass fraction Y CH4 [−] 0.0218 1 Inlet, case B: Main stream Fuel stream 1 Fuel stream 2 Velocity u [m/s] 18.02 61.84 93.01 Density ρ [kg /m 3 ] 1.18 0.66 0.66 Fuel mass fraction Y CH4 [−] 0.0044 1 1 Table 6.1: Inlet flow parameters. 112
6.1 Practical premixed combustor configuration boundary conditions equals 4% <strong>of</strong> the mean flow velocity in the combustion configuration with two <strong>fuel</strong> injection stages <strong>and</strong> 3% for the one with three <strong>fuel</strong> injection stages. The velocity fluctuations <strong>and</strong> the volume integrated heat release rate, which are the signals used for the identification <strong>of</strong> the flame dynamics, are recorded at the ”measurement” planes at every time step <strong>of</strong> the simulation. To suppress possible turbulent contributions <strong>and</strong> to account for density fluctuations <strong>of</strong> the <strong>fuel</strong>-air mixture, mass flow rate fluctuations were exported instead <strong>of</strong> the velocity fluctuations. The ”measurement” plane at the burner mouth was placed 5 mm upstream <strong>of</strong> the burner exit to minimize errors due to the fluctuating flame front, which is able to travel slightly inside the burner. At the point <strong>of</strong> injection the ”measurement” planes in the <strong>fuel</strong> line <strong>and</strong> in the mixing section were placed 2.5 mm upstream <strong>of</strong> the stream crossing point. The ”measurement” planes are also shown in Fig. 6.5. The size <strong>of</strong> the grid is a compromise between computational effort <strong>and</strong> a sufficient resolution <strong>of</strong> the flow structures <strong>and</strong> acoustics. Especially in the vicinity <strong>of</strong> the swirler a fine grid was necessary to realize the flow separation at the swirler blade <strong>and</strong> the secondary flow. The secondary flow further enhances the mixing quality due to the additional imposed turbulence. It develops from the point <strong>of</strong> flow separation <strong>and</strong> is due to the pressure gradient, which drives the fluid to the middle <strong>of</strong> the swirler passage. The chosen grid predicts a slightly higher strength <strong>of</strong> the passage vortex compared to a simulation case where the boundary layer is fully resolved as described in H<strong>of</strong>fmann [44]. Figure 6.6 shows the critical area <strong>of</strong> the swirler with the passage vortex, which is highlighted by stream lines. In the present work the propagation <strong>of</strong> acoustic waves up to 2000 Hz are resolved in the unsteady RANS context, reflecting the amplitude <strong>and</strong> the phase <strong>of</strong> an acoustic wave correctly. The quality <strong>of</strong> an acoustic wave traveling through the CFD domain can be judged by mainly two parameters: the grid size or length <strong>of</strong> a grid cell △x <strong>and</strong> the time step △t <strong>of</strong> the simulation. Both parameters can be combined into one parameter, the acoustic Courant- Friedrichs-Lewy (aCFL) number, which is defined as: 113
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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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Page 83 and 84: 4 Modeling of turb
Page 85 and 86: 4.1 Theory and num
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Page 95 and 96: 5 System Identification Flame trans
Page 97 and 98: 5.1 Model structures and</s
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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
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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
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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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