THESE de DOCTORAT - cerfacs
THESE de DOCTORAT - cerfacs THESE de DOCTORAT - cerfacs
8 LIST OF FIGURES 5.19 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 87 5.20 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 87 5.21 Sound Pressure Levels from the direct and hybrid approaches . . . . . . . . . . 90 5.22 Sound Pressure Levels from the direct and hybrid approaches . . . . . . . . . . 90 5.23 Longitudinal pressure Waves oscillating at 251 Hz . . . . . . . . . . . . . . . . . 91 5.24 Longitudinal pressure Waves oscillating at 377 Hz . . . . . . . . . . . . . . . . . 91 5.25 Longitudinal pressure Waves oscillating at 954 Hz . . . . . . . . . . . . . . . . . 92 5.26 Longitudinal pressure Waves oscillating at 1658 Hz . . . . . . . . . . . . . . . . . 92 5.27 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 93 5.28 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 93 6.1 A compact nozzle acting on a wave . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2 Some possible configurations under the compact assumption . . . . . . . . . . 102 6.3 Chocked and Unchocked configurations studied . . . . . . . . . . . . . . . . . . 105 6.4 Reflection and Transmission coefficients for both unchoked and choked cases . 107 6.5 1D Flame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.6 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.7 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.8 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.9 1D Flame - Entropy Jump Case. Lines correspond to analytical solutions. Symbols (△,▽,◦) represent SNozzle solutions . . . . . . . . . . . . . . . . . . . . . . 111 6.10 compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.11 Mean Flow. Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.12 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.13 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.14 Mean and Fluctuation profiles of total pressure . . . . . . . . . . . . . . . . . . . 117 6.15 Modulus of the Reflection Coefficient. Lines represent SNozzle solutions. Symbols (◦) stands for Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.16 Argument of the Reflection Coefficient. Lines represent SNozzle solutions. Symbols (◦) stands for Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 119
LIST OF FIGURES 9 7.1 Air-intake duct configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.2 Adimensional section area of the aeroengine air-intake duct . . . . . . . . . . . 122 7.3 Total Pressure and Total Temperature profiles . . . . . . . . . . . . . . . . . . . . 123 7.4 Reflection Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.5 Acoustic Admittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.6 Acoustic Mode of the Aeroengine combustor. 507.9 Hz . . . . . . . . . . . . . . . 125 7.7 Admittance vs. Reflection Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.8 Eigen Frequency vs. Reflection Coefficient (Helmholtz solver results) . . . . . . 127 A.1 Velocity triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
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8 LIST OF FIGURES<br />
5.19 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 87<br />
5.20 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 87<br />
5.21 Sound Pressure Levels from the direct and hybrid approaches . . . . . . . . . . 90<br />
5.22 Sound Pressure Levels from the direct and hybrid approaches . . . . . . . . . . 90<br />
5.23 Longitudinal pressure Waves oscillating at 251 Hz . . . . . . . . . . . . . . . . . 91<br />
5.24 Longitudinal pressure Waves oscillating at 377 Hz . . . . . . . . . . . . . . . . . 91<br />
5.25 Longitudinal pressure Waves oscillating at 954 Hz . . . . . . . . . . . . . . . . . 92<br />
5.26 Longitudinal pressure Waves oscillating at 1658 Hz . . . . . . . . . . . . . . . . . 92<br />
5.27 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 93<br />
5.28 Acoustic energy. Direct and hybrid approaches . . . . . . . . . . . . . . . . . . . 93<br />
6.1 A compact nozzle acting on a wave . . . . . . . . . . . . . . . . . . . . . . . . . . 101<br />
6.2 Some possible configurations un<strong>de</strong>r the compact assumption . . . . . . . . . . 102<br />
6.3 Chocked and Unchocked configurations studied . . . . . . . . . . . . . . . . . . 105<br />
6.4 Reflection and Transmission coefficients for both unchoked and choked cases . 107<br />
6.5 1D Flame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108<br />
6.6 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109<br />
6.7 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110<br />
6.8 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110<br />
6.9 1D Flame - Entropy Jump Case. Lines correspond to analytical solutions. Symbols<br />
(△,▽,◦) represent SNozzle solutions . . . . . . . . . . . . . . . . . . . . . . 111<br />
6.10 compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112<br />
6.11 Mean Flow. Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115<br />
6.12 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115<br />
6.13 Typical Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116<br />
6.14 Mean and Fluctuation profiles of total pressure . . . . . . . . . . . . . . . . . . . 117<br />
6.15 Modulus of the Reflection Coefficient. Lines represent SNozzle solutions. Symbols<br />
(◦) stands for Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 118<br />
6.16 Argument of the Reflection Coefficient. Lines represent SNozzle solutions. Symbols<br />
(◦) stands for Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 119
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