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4 CONTENTS 3.4.1 Preconditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4.2 Dynamic preconditioning: the embedded GMRES . . . . . . . . . . . . . 56 4 Validation of the acoustic code AVSP-f 58 4.1 Fundamental validation cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.1.1 A Monopole in free space . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.1.2 A Dipole in free space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.1.3 Three poles out of phase in free space . . . . . . . . . . . . . . . . . . . . 62 4.2 The 2D premixed laminar flame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.1 CFD computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2.2 Input data for the acoustic code . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Assessment of combustion noise in a premixed swirled combustor 72 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.2 Experimental configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 Combustion noise Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3.1 Direct Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3.2 Hybrid approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.4 Filtering a LES pressure field to find the corresponding acoustic field . . . . . . 87 5.4.1 Finding ∂u i,hyd ∂x i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.4.2 Finding the Acoustic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.5 LES vs. Hybrid Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6 Boundary conditions for low Mach number acoustic codes 95 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.2 The quasi 1D Linearized Euler Equations - SNozzle . . . . . . . . . . . . . . . . . 97 6.3 The 1D linearized Euler equations for compact systems . . . . . . . . . . . . . . 98 6.3.1 The transmitted and reflected waves . . . . . . . . . . . . . . . . . . . . . 100
CONTENTS 5 6.4 Transmitted and reflected acoustic waves in isentropic nozzles . . . . . . . . . . 103 6.4.1 Acoustic Response of Chocked and Unchocked Nozzles . . . . . . . . . . 104 6.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.5 When entropy does not remain constant through a duct . . . . . . . . . . . . . . 106 6.5.1 Analytic Solution : Building the linear system of equations . . . . . . . . 108 6.5.2 The mean flow in SNozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.6 Transmitted and Reflected Waves through an ideal Compressor: the enthalpy jump case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.6.1 Building the linear system of equations for the analytical solution . . . . 112 6.6.2 The mean flow in SNozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.6.3 Introducing π c in the momentum equation . . . . . . . . . . . . . . . . . 114 6.6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7 Computation of the Reflection Coefficient on the Inlet air circuit of an Helicopter combustor chamber 120 7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.2 Mean parameters of the Intake Duct . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.3 Acoustic Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.4 Helmholtz Solver Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A About the π ′ c = 0 assumption 135 A.1 When is π T ′ equal to zero? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 B Publications 139
Page 1: UNIVERSITE MONTPELLIER II SCIENCES
Page 5: An expert is a man who has made all
Page 8 and 9: Y gracias familia mía!!, que así
Page 11: Abstract Today, much of the current
Page 16 and 17: List of Figures 1.1 Main sources of
Page 18 and 19: 8 LIST OF FIGURES 5.19 Acoustic ene
Page 20: List of Tables 1.1 EU recommended r
Page 24 and 25: 14 Chapter 1: General Introduction
Page 30 and 31: 2 Computation of noise generated by
Page 32 and 33: 22 Chapter 2: Computation of noise
Page 52 and 53: 42 Chapter 3: Development of a nume
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54 Chapter 3: Development of a nume
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56 Chapter 3: Development of a nume
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4 Validation of the acoustic code A
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60 Chapter 4: Validation of the aco
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5 Assessment of combustion noise in
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7 Computation of the Reflection Coe
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Chapter 7: Computation of the Refle
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Bibliography [1] AGARWAL, A., MORRI
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130 BIBLIOGRAPHY [30] FRAYSSÉ, V.,
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132 BIBLIOGRAPHY [62] NICOUD, F., B
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134 BIBLIOGRAPHY [93] SENSIAU, C. S
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136 Chapter A: About the π ′ c =
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138 Chapter A: About the π ′ c =
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140 Chapter B: Publications
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