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Introduction 2) equivalence ratio fluctuations (φ ′ i ): they are created by fluctuations <strong>of</strong> the air mass flow past the injector i or <strong>of</strong> the pressure at the injector i . These inhomogeneities are transported convectively to the flame, where they lead to a modification <strong>of</strong> the enthalpy <strong>of</strong> reaction per unit volume <strong>of</strong> the mixture (△H), laminar (s L ) <strong>and</strong> turbulent burning velocity (s t ), flame position <strong>and</strong> hot gas temperature (”entropy waves”) [14, 31, 53, 71, 99, 101, 107, 112]. The acoustic pressure (p ′ f l ) <strong>and</strong> velocity (u′ ) at the flame front could also f l modify the heat release rate. Their influence is rather small in practical applications like gas turbines or domestic heaters <strong>and</strong> can therefore be neglected. Other effects, like a fluctuating swirl, which changes mainly the flame area, can also play a role but are not considered explicitly in the present work. All effects mentioned lead to fluctuations in the heat release rate <strong>and</strong> thus to a fluctuating volume expansion, which result in acoustic fluctuations (p ′ , u ′ ). As shown in Fig. 1.1, the acoustic waves caused by the flame travel through the combustion system <strong>and</strong> are partly reflected at the gas turbine parts, which are located upstream <strong>and</strong> downstream <strong>of</strong> the combustion chamber. The amplitude <strong>and</strong> phase <strong>of</strong> the reflection are determined by the acoustic characteristics in terms <strong>of</strong> the <strong>impedance</strong> at the outlet <strong>of</strong> the compressor or at the inlet <strong>of</strong> the turbine. The reflected waves are causing acoustic fluctuations at the flame front, at the burner outlet <strong>and</strong> at the location <strong>of</strong> <strong>fuel</strong> injection, which give rise to a direct or time-delayed response <strong>of</strong> the flame. The acoustic pressure fluctuations in the vicinity <strong>of</strong> the flame <strong>and</strong> the fluctuating heat release rate form therefore a thermodynamic feedback cycle, which is closed by the acoustics <strong>of</strong> the combustion system. Whether the cycle excites or damps possible combustion oscillations depends on the phase shift between the two characteristics <strong>and</strong> is known as the Rayleigh criterion. According to Lord Rayleigh [105], who discovered this correlation in the 19th century, the conditions for the occurrence <strong>of</strong> instabilities are met, when heat is released at the moment <strong>of</strong> greatest compression. In other words a combustion oscillation can occur if pressure <strong>and</strong> heat release rate fluctuations are in phase, i.e. the integral <strong>of</strong> the product <strong>of</strong> pressure <strong>and</strong> heat release rate fluctuations over a oscillation period T per is 6
1.3 Control <strong>of</strong> thermo-acoustic instabilities positive: ∮ t+Tper t ∫ V cc p ′ (x, y, z, t ) ˙Q ′ (x, y, z, t )dV d t > 0. (1.3) The integration in Eqn. (1.3) is performed spatially over the combustion chamber volume V cc . A positive Rayleigh integral is a necessary, but not sufficient condition for the occurrence <strong>of</strong> combustion instabilities. The generated energy <strong>of</strong> the thermo-acoustic process has to outweigh the acoustic losses in the system <strong>and</strong> the radiation <strong>of</strong> the oscillation energy over the boundaries. To realize a low-oscillation combustion chamber three main possible approaches can be deduced from the latter consideration: • Increase <strong>of</strong> the damping characteristics <strong>of</strong> the combustion system • Reduction <strong>of</strong> the heat release rate fluctuations in the combustion chamber • Favorable modification <strong>of</strong> the phase relationship between fluctuations <strong>of</strong> pressure <strong>and</strong> heat release rate 1.3 Control <strong>of</strong> thermo-acoustic instabilities Beside the fact that many different methods were developed to suppress thermo-acoustic oscillations, the prediction <strong>of</strong> these instabilities in the early design stage is still a challenging task. Following the three approaches mentioned, the manifold strategies to reduce unwanted pressure oscillations <strong>and</strong> to control possible thermo-acoustic oscillations can be divided into active <strong>and</strong> passive control mechanism. Active feedback control involves an actuator, which modifies certain parameters <strong>of</strong> the system in response to a measured signal. In many cases the <strong>fuel</strong> mass flow is modulated to counteract the heat release rate perturbation that 7
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: 1.2 Thermo-acoustic instabilities d
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 and 40: 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
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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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3.3 Acoustic network model Z i Air
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3.3 Acoustic network model pressure
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3.3 Acoustic network model The eige
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3.3 Acoustic network model tine. To
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4 Modeling of turb
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4.1 Theory and num
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4.1 Theory and num
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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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Impact of fuel supply impedance and fuel staging on gas turbine ...

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