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

More documents

Recommendations

Info

Acoustic analysis model <strong>of</strong> the configuration containing three <strong>fuel</strong> <strong>supply</strong> stages is built up in a similar way with an additional ”T-junction” <strong>and</strong> <strong>fuel</strong> injection stage as shown in appendix A.3. Closed end Legend: Boundary Condition Simple Duct Area Change T-junction Flame Axial Swirler Resonator tube Fuel plenum AC IV Fuel injection tube Closed end (loudspeaker) Plenum AC I Mixing section I Air-<strong>fuel</strong> T-junction Mixing section II Axial Swirler Mixing section III AC II Combustion chamber I Flame Combustion chamber II partly reflecting Open End Figure 7.1: Sketch <strong>of</strong> the acoustic network model <strong>of</strong> the combustion test rig with two <strong>fuel</strong> injection stages (configuration A) The <strong>fuel</strong> <strong>supply</strong> stage including the <strong>fuel</strong> injection tubes, the <strong>fuel</strong> plenum <strong>and</strong> the resonator tube are substituted by a simplified model to reduce the computational effort associated with the search routine to find the complex eigenfrequencies <strong>of</strong> the system. Because only plane waves can travel through the combustion system in the frequency range considered, all <strong>fuel</strong> injection holes face the same acoustic conditions. Therefore, they are combined into one injection slot for simplicity. In addition, the <strong>fuel</strong> plenum <strong>and</strong> the resonator tube, 140
7.1 Setup <strong>of</strong> the acoustic network model which have the same cross-section, are merged into one duct. Finally the network model <strong>of</strong> the <strong>fuel</strong> injection stage contains a ”Closed end”, a simple duct representing the ”Resonator tube” <strong>and</strong> ”Fuel plenum”, an area change (”AC IV”) between <strong>fuel</strong> plenum <strong>and</strong> the ”Fuel injection tube” (simple duct), which is connected by the ”Air-<strong>fuel</strong> T-junction” (”T-junction”) to the mixing section <strong>of</strong> the combustor. To estimate the error, which is made with the simplified model, a finite element-based acoustic model was set up using the commercial s<strong>of</strong>tware package COMSOL. The model consists <strong>of</strong> the <strong>fuel</strong> injector including the single injection tubes. An open end boundary condition (p ′ = 0) is used as the termination on the injection tube side. The opposite side, the resonator end, is realized as a rigid wall (u ′ = 0). The length <strong>of</strong> the resonator tube was set exemplarily to L R = 0.3 m. As the finite element method solves the homogeneous wave equation, mean flow effects <strong>and</strong> pressure losses are not considered. Fig. 7.2 shows the first two eigenmodes <strong>of</strong> the <strong>fuel</strong> injector. The scale <strong>of</strong> the legend is arbitrary <strong>and</strong> indicates the maximum <strong>and</strong> minimum pressure fluctuations. The first eigenmode <strong>of</strong> the finite element model exhibits nearly a λ/4 mode, whereas the second one approximates a 3λ/4 eigenmode. The overall length corresponding to the λ/4 modes can be composed <strong>of</strong> the geometrical length <strong>of</strong> the resonator <strong>and</strong> half <strong>of</strong> the circumference <strong>of</strong> the <strong>fuel</strong> plenum. The acoustic field inside the <strong>fuel</strong> plenum ring is almost constant. The acoustic characteristics <strong>of</strong> the <strong>fuel</strong> <strong>supply</strong> changes with increasing frequency as the acoustics <strong>of</strong> the <strong>fuel</strong> plenum becomes more complex. This is shown in table 7.1, in which the eigenfrequencies <strong>of</strong> the finite element-based model are compared against the simplified network model with <strong>and</strong> without the effect <strong>of</strong> mean flow <strong>and</strong> pressure losses. Here <strong>and</strong> in the following, the eigenfrequencies are normalized with the Strouhal number, where the reference speed is the mean axial velocity in the mixing section <strong>of</strong> case A. In the network model the length <strong>of</strong> the <strong>fuel</strong> <strong>supply</strong> tube was set to L R = 0.355 m. This length is slightly less than the one considered above, but results in a more accurate match in terms <strong>of</strong> the first <strong>and</strong> second eigenfrequency. The mean flow <strong>and</strong> the pressure loss have in general only a small effect on the eigenfrequencies. The deviation <strong>of</strong> the first eigenfrequency between the network <strong>and</strong> finite element model is rather low. As mentioned before, the error increases as the frequency increases. Nevertheless, in the Strouhal range up to Sr = 2 the simplified net- 141
Page 1:
Technische Universität München In
Page 4 and 5:
und ihre Geduld besonders für die
Page 7 and 8:
Contents 1 Introduction 1 1.1 Techn
Page 9 and 10:
CONTENTS 7.2.2 Impact</stro
Page 11 and 12:
Nomenclature G stretch factor [-] h
Page 13 and 14:
Nomenclature λ air-fuel</s
Page 15 and 16:
1 Introduction 1.1 Technology backg
Page 17 and 18:
1.2 Thermo-acoustic instabilities 1
Page 19 and 20:
1.2 Thermo-acoustic instabilities d
Page 21 and 22:
1.3 Control of the
Page 23 and 24:
1.3 Control of the
Page 25 and 26:
1.4 Intention and
Page 27 and 28:
1.5 Terminology and</strong
Page 29 and 30:
1.5 Terminology and</strong
Page 31 and 32:
2 Numerical analysis of</st
Page 33 and 34:
2.1 Overview of me
Page 35 and 36:
2.1 Overview of me
Page 37 and 38:
2.1 Overview of me
Page 39 and 40:
2.2 Flame dynamics of</stro
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
2.3 Identification of</stro
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
3 Acoustics Before analyzing the ac
Page 59 and 60:
3.1 Basic acoustic equations as a f
Page 61 and 62:
3.2 Linear acoustic equations Here,
Page 63 and 64:
3.2 Linear acoustic equations p ′
Page 65 and 66:
3.3 Acoustic network model p ′ (x
Page 67 and 68:
3.3 Acoustic network model matrix e
Page 69 and 70:
3.3 Acoustic network model The <str
Page 71 and 72:
3.3 Acoustic network model where A
Page 73 and 74:
3.3 Acoustic network model coming c
Page 75 and 76:
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
Page 81 and 82:
3.3 Acoustic network model tine. To
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 91 and 92:
Page 93 and 94:
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
Page 129 and 130: 6.2 Steady-state simulations <stron
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: 7 Acoustic analysis Once the acoust
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
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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?