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

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Numerical simulation can be calculated for a single jet injected into a circular duct. J represents the impulse ratio <strong>of</strong> the <strong>fuel</strong> <strong>and</strong> main stream <strong>and</strong> is defined as: J = ρ F u 2 F ρ A u 2 . (6.3) A The subscripts F <strong>and</strong> A represent again the <strong>fuel</strong> <strong>and</strong> main stream, respectively. In configuration A, for example, the main flow velocity is equal to u A = 18.6 m/s. The density has a value <strong>of</strong> ρ A = 1.167 kg/m 3 . With the properties for the <strong>fuel</strong> stream (u F = 85.6 m/s, ρ F = 0.66 kg/m 3 ) an impulse ratio <strong>of</strong> J = 12.0 is computed for the present case. The <strong>fuel</strong> injection including stream lines <strong>and</strong> the <strong>fuel</strong> mass fraction at a downstream location are presented exemplarily for the configuration A in Fig. 6.4. The legend refers to the plane presented whereas the colors <strong>of</strong> the streamlines indicate the amplitude <strong>of</strong> the velocity. The <strong>fuel</strong> is distributed well over the radial direction, with the main part <strong>of</strong> the <strong>fuel</strong> located in the middle between the outer wall <strong>and</strong> the center body. The maximum depth according to Eqn. (6.2) would be 0.005 m, which is slightly too low. The optimum number <strong>of</strong> circumferential holes was estimated according to Holdeman et al. [45] <strong>and</strong> lies in the range between 6.1 <strong>and</strong> 10.2 for the configuration analyzed (see appendix A.2 for more details). CFD simulations with different numbers <strong>of</strong> holes showed that the configuration with eight injection holes exhibits adequate mixing characteristics. 6.1.2 Numerical setup <strong>of</strong> the combustion system To determine the flame transfer functions, a three-dimensional unsteady RANS computation <strong>of</strong> the compressible turbulent reacting flow in the combustor has been performed using the s<strong>of</strong>tware package ANSYS-CFX. According to the discussion in chapter 2.3.2, the computational domain can be reduced to the mixing section, the <strong>fuel</strong> injection holes, the axial swirler <strong>and</strong> the combustion chamber. A sketch <strong>of</strong> the computational domain including the ”measurement” planes for case A, at which the time series <strong>of</strong> the required velocity fluctuations are recorded, is shown in Fig. 6.5. To save computational time only a 90 ◦ segment is simulated using periodic boundary conditions. A second order backward Euler scheme <strong>and</strong> the high-resolution scheme were 110
6.1 Practical premixed combustor configuration Figure 6.4: Streamlines <strong>of</strong> the injected <strong>fuel</strong> <strong>and</strong> <strong>fuel</strong> mass fraction <strong>of</strong> combustion configuration, case A used in time <strong>and</strong> space discretization, respectively. More details about the numerical methods can be found in [5]. The simulations were performed with the Shear Stress Transport turbulence model <strong>and</strong> the partially burning velocity combustion model <strong>of</strong> CFX. Both models are described in chapter 4.1.2 <strong>and</strong> 4.2.2. For simplicity all walls are assumed to be adiabatic. The chosen time step is△t = 2.5×10 −5 s. The main inlet flow parameters <strong>of</strong> the two simulation cases are shown in Table 6.1. The temperature for all inlets was set to T = 298 K. The inlet turbulence intensity, which is defined as the ratio <strong>of</strong> turbulent velocity fluctuations to the mean flow velocity, has a value <strong>of</strong> 5%. CFX nonreflecting boundary conditions are used for the inlets <strong>and</strong> the outlet to prevent resonant amplification with high amplitudes in the vicinity <strong>of</strong> eigenfrequencies, which deteriorates the quality <strong>of</strong> identification results. This condition is realized using a modified algorithm on the basis <strong>of</strong> the Navier-Stokes charac- 111
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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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Page 83 and 84: 4 Modeling of turb
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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
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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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