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

More documents

Recommendations

Info

Numerical simulation 6.3.3 Analysis <strong>and</strong> interpretation <strong>of</strong> identification results The unit impulse responses <strong>and</strong> flame transfer functions identified show some remarkable results, which are analyzed in more detail in this section. The unit impulse responses exhibit an undershoot h k < 0 for a range <strong>of</strong> time lags k∆t , whereas the gain <strong>of</strong> the flame transfer functions exceeds one (|F (ω)|>1) for a range <strong>of</strong> frequencies ω. Both phenomena are strongly related to each other, which is described in the following. Furthermore a physicsbased interpretation <strong>of</strong> the impulse responses to velocity <strong>and</strong> equivalence ratio fluctuations will be developed on the basis <strong>of</strong> results obtained with impulse forcing imposed on transient CFD simulations. The flame transfer function is determined by the z-transform <strong>of</strong> the unit impulse response (see chapter 5): F (ω)= M∑ h k e −i ωk△t . (6.5) k=0 The conservation equations <strong>of</strong> mass <strong>and</strong> energy requires that the flame transfer functions F φ,i <strong>and</strong> F u have to approach unity for ω→0 (see [100]). To realize the correct low frequency limit the sum over all unit impulse response coefficients has also to approach unity: lim F (ω)= lim ω→0 ω→0 M∑ M∑ h k e −i ωk△t = h k = 1. (6.6) k=0 If all coefficients h k <strong>of</strong> a unit impulse response vector are positive, the gain <strong>of</strong> the flame transfer function decreases with increasing frequency. The reason is due to the index k in the phase factor exp(−i ωk△t ) <strong>of</strong> the z-transform, which is responsible for a phase difference between the contributions <strong>of</strong> the individual coefficients. These phase differences lead with increasing frequencies to an increasing destructive superposition <strong>of</strong> the contributions. The result is a reduction <strong>of</strong> the sum over all weighted UIR coefficients. The flame acts therefore as a low pass filter with a maximum gain <strong>of</strong> unity at zero frequency. An UIR with positive <strong>and</strong> negative values, however, can result in a gain|F (ω)|> 1 for a range <strong>of</strong> frequencies as the phase factors can, in this case, lead to 128 k=0
6.3 Identifiction <strong>of</strong> the flame transfer functions constructive superposition between the contributions <strong>of</strong> the individual coefficients. To further analyze the relevant physical mechanism <strong>of</strong> the behavior observed, simulations <strong>of</strong> the configuration with two <strong>fuel</strong> injection stages were carried out using impulse forcing. Flame response to impulse forcing <strong>of</strong> velocity at the burner exit The first transient CFD simulation with impulse forcing was performed with excitation <strong>of</strong> only the main air-<strong>fuel</strong> velocity inlet. The <strong>fuel</strong> mass flow rate at <strong>fuel</strong> injector ”2” was kept constant. The amplitude <strong>of</strong> the impulse in flow velocity was set to 10% <strong>of</strong> the mean value. As it is not possible to numerically resolve an impulse that is enforced during only one time step, a impulse duration <strong>of</strong> 20 time steps is chosen. The results obtained are normalized according to the excitation level <strong>of</strong> the CFD/SI simulation. The response <strong>of</strong> the flame should exhibit a similar behavior as the UIR u obtained with broadb<strong>and</strong> forcing. A comparison between the CFD/SI unit impulse response <strong>and</strong> the UIR determined with impulse forcing is presented in Fig. 6.20. For the first time delays both response vectors match very well. For later times, the result <strong>of</strong> the impulse forcing shows oscillations, caused by partial reflection <strong>of</strong> the impulse signal at the boundaries <strong>of</strong> the computational domain. These spurious features are not representative <strong>of</strong> the response <strong>of</strong> the flame to the impulse excitation. To explain the undershoot <strong>of</strong> the UIR, the temporal development <strong>of</strong> flame front surface area <strong>and</strong> heat release rate are tracked, which is presented in Fig. 6.21. The flame front is defined as an iso-surface <strong>of</strong> the progress variable with c = 0.5. In addition a cut through the flame in a meridional plane at several instances in time is presented in Fig. 6.22 <strong>and</strong> 6.23. The undisturbed flame front is shown in Fig. 6.21 <strong>and</strong> 6.22 <strong>and</strong> is denoted as state ”A”. When the increased mass flow reaches the burner exit, the flame is first pushed downstream resulting in a stretched flame front at the burner exit, especially in the inner shear layer. After a short time delay the flame is reacting to the disturbance with an increased flame speed <strong>and</strong> heat release rate. As a consequence, the flame moves again 129
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: 4.2 Theoretical and</strong
Page 93 and 94: 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
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 141: 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
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 ...

Create successful ePaper yourself

Delete template?

Save as template?