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

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Numerical analysis <strong>of</strong> thermo-acoustic instabilities input u ′ b <strong>and</strong> output ˙Q ′ as shown in Fig. 2.3. The flame response <strong>of</strong> a perfect premixed combustion system, in which no equivalence ratio fluctuations exist, is completely described by such a SISO system. u' b . Q' Figure 2.3: SISO system representing a perfect premixed flame A proper choice <strong>of</strong> the reference location "b" for the velocity fluctuation u ′ b is crucial to obtain a flame transfer function which is independent <strong>of</strong> the acoustic <strong>impedance</strong> at the burner. The acoustic <strong>impedance</strong> at the burner is characterized by the acoustic properties <strong>and</strong> the acoustic boundary conditions <strong>of</strong> the combustion system. As the flame dynamics is mainly controlled by the flame front kinematics, the proper reference location is the burner exit. At this location acoustic fluctuations generate vortical perturbations in the flow field (shear layer), which are transported with the speed <strong>of</strong> the flow to <strong>and</strong> through the flame, modulating the flame area <strong>and</strong> turbulent flame speed. The strength <strong>of</strong> the disturbance is directly related to the amplitude <strong>of</strong> the velocity fluctuation at this position. A velocity signal, which is taken at a different location, may be influenced in a spurious manner by the acoustics <strong>of</strong> the combustion system. If the distance between burner exit (x b ) <strong>and</strong> the reference location (x ˜b) is not much smaller than a acoustic wave length (speed <strong>of</strong> sound divided by frequency), the acoustic velocities at both locations differ in terms <strong>of</strong> amplitude <strong>and</strong> phase. If now the acoustics <strong>of</strong> the system is changed, e.g. by changing the upstream boundary condition, the amplitude <strong>and</strong> phase difference between the acoustic velocities at both locations is modified. This is clarified in Fig. 2.4, which shows the spatial amplitude <strong>of</strong> the acoustic velocity <strong>of</strong> two cases a) <strong>and</strong> b) with a different upstream boundary condition Z 1 <strong>and</strong> Z 2 . As the velocity fluctuation at x b is the driving parameter, a high velocity value at x ˜b would result in almost no heat release rate fluctuation in case a). However, the contrary is demonstrated in case b), in which a low value at x ˜b corresponds to a strong response <strong>of</strong> the flame. The modification <strong>of</strong> the system changes there- 26
2.2 Flame dynamics <strong>of</strong> a practical premixed combustion system Z 1 u' u' b ~ u' b . Q' X a) x~ b Z 2 u' b ~ u' u' b x b . Q' X x b b) x~ b Figure 2.4: <strong>Impact</strong> <strong>of</strong> the combustion system acoustics on the choice <strong>of</strong> the reference location fore also the relation – the transfer function – between the velocity fluctuation at x ˜b <strong>and</strong> the heat release rate fluctuation. A transfer function using the reference location x ˜b is thus not independent <strong>of</strong> the acoustics <strong>of</strong> the combustion system. It is therefore not a useful description <strong>of</strong> the flame dynamics. Indeed, the latter was demonstrated by Truffin <strong>and</strong> Poinsot [127]. In their work they showed that the values <strong>of</strong> phase <strong>and</strong> gain <strong>of</strong> the flame response depend significantly on the combustor outlet reflection coefficient, if a reference location far upstream is selected. Here, Truffin <strong>and</strong> Poinsot proposed, that the distance x ˜b− x b , expressed as a Helmholtz number, should not exceed 0.01 to obtain consistent results. This limit is a surprisingly strict criterion, indicating that already a distance <strong>of</strong> a few millimeter can have a noticeable effect on the results. 27
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 39: 2.2 Flame dynamics of</stro
Page 43 and 44: 2.2 Flame dynamics of</stro
Page 45 and 46: 2.2 Flame dynamics of</stro
Page 47 and 48: 2.3 Identification of</stro
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
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4.2 Theoretical and</strong
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4.2 Theoretical and</strong
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5 System Identification Flame trans
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5.1 Model structures and</s
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5.2 System Identification 5.2 Syste
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5.3 Excitation signals the zero mea
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5.4 A posteriori validation <strong
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5.4 A posteriori validation <strong
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5.5 Proof
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5.5 Proof
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5.5 Proof
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5.5 Proof
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5.5 Proof
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5.5 Proof
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6 Numerical simulation MISO model i
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6.1 Practical premixed combustor co
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6.2 Steady-state simulations <stron
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6.2 Steady-state simulations <stron
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6.3 Identifiction of</stron
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6.4 Identification of</stro
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6.4 Identification of</stro
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7 Acoustic analysis Once the acoust
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7.1 Setup of the a
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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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