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List of Figures 1.1 Main sources of aircraft noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2 Acoustic solvers: The Euler acoustic solver is used beforehand to provide proper boundary conditions to the low Mach number acoustic solver. . . . . . . . . . . 19 3.1 A triangular element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2 A set of six triangular cells embedded in a mesh grid . . . . . . . . . . . . . . . . 44 3.3 A set of three triangular cells at the boundary of the computational domain . . 44 3.4 Typical Matrices for a non-structured 3D problem [93]. Non-zero entries are shown as dark points. Here C T is the transpose of C. The dyadic product CC T is shown to display the non-zero elements of C j . . . . . . . . . . . . . . . . . . . 46 3.5 Reduction of the linear system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.6 Hessenberg decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.7 The GMRES Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.8 The embedded GMRES Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.1 Monopoles placed at y and listener placed at x . . . . . . . . . . . . . . . . . . . 59 4.2 Outputs of AVSP-f. Monopole case . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3 Acoustic field produced by a monopole. p ′ = | ˆp| cos(arg( ˆp)) . . . . . . . . . . . 60 4.4 Analytical solution vs Numerical solution. . . . . . . . . . . . . . . . . . . . . . . 61 4.5 Outputs of AVSP-f. Dipole case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.6 Acoustic field produced by a dipole. p ′ = | ˆp| cos(arg( ˆp)) . . . . . . . . . . . . . 62 4.7 Analytical solution vs Numerical solution. . . . . . . . . . . . . . . . . . . . . . . 63 4.8 Outputs of AVSP-f. Three monopoles out of phase . . . . . . . . . . . . . . . . . 64 4.9 Acoustic field produced by three monopoles out of phase. p ′ = | ˆp| cos(arg( ˆp)) . 64 6
LIST OF FIGURES 7 4.10 Analytical solution vs Numerical solution . . . . . . . . . . . . . . . . . . . . . . 65 4.11 The 2D laminar premixed flame burner . . . . . . . . . . . . . . . . . . . . . . . 65 4.12 2D premixed laminar flame. Steady state . . . . . . . . . . . . . . . . . . . . . . . 67 4.13 2D premixed laminar flame. Four snapshorts for one cycle. u ′ /ū = 0.1 . . . . . 68 4.14 Exercise of comparison: CFD method vs. Acoustic solver . . . . . . . . . . . . . 69 4.15 2D premixed laminar flame. Comparison between LES and AVSP-f (u ′ /ū = 0.1). 70 4.16 2D premixed laminar flame. Four snapshorts for one cycle. u ′ /ū = 0.5 . . . . . 70 4.17 2D premixed laminar flame. Comparison between LES and AVSP-f (u ′ /ū = 0.5). 71 5.1 Schematic view of a tranversal section through the premixer and circular manifolds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.2 Two staged swirled premixed combustor. (Courtesy of École Centrale Paris) . . 75 5.3 Computational grid of EC2 combustor . . . . . . . . . . . . . . . . . . . . . . . . 76 5.4 Instantaneous Field of Pope’s Criterion. The black line stands for the isocontour line Q LES = 0.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.5 Velocity Profiles: ◦ Experimental PIV measurements . . . . . . . . . . . . . . . . 79 5.6 Velocity Profiles: ◦ Experimental PIV measurements . . . . . . . . . . . . . . . . 80 5.7 Heat Release and rate of change of heat release . . . . . . . . . . . . . . . . . . . 80 5.8 Sound Pressure Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.9 Exercise of comparison: Direct Approach vs. Hybrid Approach . . . . . . . . . . 82 5.10 Typical iso-surface of the instantaneous unsteady heat release rate ˙ω T . . . . . 83 5.11 Mean sound velocity ¯c over a longitudinal plane of the EC2 combustor . . . . . 83 5.12 The combustion source of noise oscillating at 377 Hz. 5 snapshots during one cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.13 Sound Pressure Levels from the direct and hybrid approaches . . . . . . . . . . 84 5.14 Sound Pressure Levels from the direct and hybrid approaches . . . . . . . . . . 84 5.15 Longitudinal pressure waves oscillating at 377 Hz . . . . . . . . . . . . . . . . . . 85 5.16 Longitudinal pressure waves oscillating at 251 Hz . . . . . . . . . . . . . . . . . . 85 5.17 Longitudinal pressure Waves oscillating at 954 Hz . . . . . . . . . . . . . . . . . 86 5.18 Longitudinal pressure Waves oscillating at 1658 Hz . . . . . . . . . . . . . . . . . 86
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 14 and 15: 4 CONTENTS 3.4.1 Preconditioning .
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
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4 Validation of the acoustic code A
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5 Assessment of combustion noise in
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7 Computation of the Reflection Coe
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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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