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

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Numerical simulation tors i = 2 for the second injector <strong>and</strong> i = 3 for the third injector 1 . As discussed in chapter 2.2.2, the nominal fluctuations <strong>of</strong> equivalence ratio at the injectors can in turn be expressed in terms <strong>of</strong> the velocity fluctuations <strong>of</strong> the <strong>fuel</strong> mass flow u ′ F,i <strong>and</strong> the main mass flow u′ A,i at the location <strong>of</strong> injection i , see Eqn. (2.10). 6.1.1 Design <strong>of</strong> the <strong>fuel</strong> injector The <strong>fuel</strong> <strong>supply</strong> nozzle is designed similar to the one described in Richards <strong>and</strong> Robey [108]. The <strong>fuel</strong> plenum is arranged as an annulus <strong>of</strong> rectangular cross section around the mixing section. In addition, a resonator tube with variable length L R is attached to the <strong>fuel</strong> plenum to change the acoustic <strong>impedance</strong> <strong>of</strong> the <strong>fuel</strong> injection system. A sketch <strong>of</strong> the <strong>fuel</strong> <strong>supply</strong> dimensions is shown in Fig. 6.3. From the <strong>fuel</strong> plenum, <strong>fuel</strong> is injected radially inward through eight holes, which are equally distributed around the circumference. The injection holes have a diameter <strong>of</strong> d j = 1.2 mm. The choice <strong>of</strong> the number <strong>of</strong> holes, the diameter <strong>of</strong> the holes <strong>and</strong> chosen <strong>fuel</strong> mass flow is a trade-<strong>of</strong>f between the acoustic characteristics <strong>and</strong> the premixing quality <strong>of</strong> the air <strong>and</strong> <strong>fuel</strong>: For the present purposes the pressure drop over the <strong>fuel</strong> injection nozzles has, on the one h<strong>and</strong>, to be small enough to ensure an acoustically coupled <strong>fuel</strong> injection system. On the other h<strong>and</strong> the impulse ratio <strong>of</strong> the <strong>fuel</strong> <strong>and</strong> main stream has to be high enough to ensure a sufficient penetration <strong>and</strong> mixing <strong>of</strong> the <strong>fuel</strong>. The pressure loss coefficients from the <strong>fuel</strong> plenum to the injection tube (ζ 1 ) <strong>and</strong> from the tube to the mixing section (ζ 2 ) were determined with a steadystate CFD simulation <strong>and</strong> are equal to 0.73 <strong>and</strong> 0.84. The coefficient is, in general, defined as (see also Eqn. (3.42)): ζ≡ 2△p ρu 2 . (6.1) In both cases the pressure loss coefficients depend on the velocity u in the injection tube. In case A, for example, the pressure loss over the <strong>fuel</strong> injection 1 As the first injector is acoustically decoupled the equivalence ratio fluctuations at injector i = 1 are zero (φ ′ 1 = 0) 108
6.1 Practical premixed combustor configuration A-A L F,3 Ø1,2 L R,3 A-A Ø16 Ø40 5 L R,2 Ø8 Ø10 55 A-A 125 L F,2 60 30 Figure 6.3: Dimensions <strong>of</strong> <strong>fuel</strong> <strong>supply</strong> <strong>and</strong> mixing section (mm) system is △p 1 = 3794 Pa or △p 1 = 0.037 p atm , where p atm denotes the st<strong>and</strong>ard atmospheric pressure. Beside the relatively low pressure loss, the mixing quality between air <strong>and</strong> <strong>fuel</strong> should be adequate. The impulse <strong>of</strong> the <strong>fuel</strong> stream in relation to the main stream should be high enough that the <strong>fuel</strong> jet penetrates to a radial position near the middle <strong>of</strong> the mixing section. Various estimations <strong>of</strong> the penetration depth exist in the literature <strong>and</strong> can be found in e.g. Lefebvre [69]. Many <strong>of</strong> these estimates are validated for liners in combustion chambers. The diameter <strong>of</strong> the liner holes is commonly an order <strong>of</strong> magnitude larger than the one used in the present work. Therefore, these relations can only be used as a first starting point. In contrast to the cases described in literature, the configuration analyzed exhibits a rather low distance between the injection <strong>and</strong> the burner center body. According to [69] a penetration depth <strong>of</strong> Y max = 1.15d j √ J (6.2) 109
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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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Page 83 and 84: 4 Modeling of turb
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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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