 | Lahiri C. Acoustic performance of bias flow liners in gas turbine combustors: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Antriebstechnik, Berlin. - Köln: DLR, 2014. - xix, 343 p.: ill. - (Forschungsbericht; 2014-39). - Bibliogr.: p.297-343. - ISSN 1434-8454
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1 introduction ................................................. 1
1.1 Motivation .............................................. 7
1.2 Outline ................................................. 8
2 bias flow liners ............................................ 11
2.1 Combustor Liner ........................................ 11
2.1.1 Parameter Overview .............................. 15
2.2 Geometry Parameters .................................... 16
2.2.1 Orifice Geometry ................................ 17
2.2.2 Perforation Geometry ............................ 20
2.2.3 Cavity Geometry ................................. 24
2.3 Thermodynamic Parameters ............................... 26
2.3.1 Temperature ..................................... 26
2.3.2 Pressure ........................................ 27
2.4 Acoustic Parameters .................................... 27
2.4.1 Frequency ....................................... 27
2.4.2 Amplitude / Sound Pressure Level ................ 28
2.5 Flow Parameters ........................................ 32
2.5.1 Grazing Plow .................................... 32
2.5.2 Bias Plow ....................................... 33
3 Literature on bias flow liners .............................. 43
3.1 Bias Flow as a Concept of Impedance Control ............ 43
3.2 Sound Absorption due to Vorticity Shedding ............. 45
3.3 Recent Developments .................................... 49
3.4 Chronological Overview ................................. 52
4 modeling of bias flow liners ................................ 57
4.1 Rayleigh Conductivity .................................. 57
4.2 Acoustic Impedance ..................................... 59
4.2.1 Impedance Modeling of Perforations .............. 61
4.2.2 Grazing Plow Impedance .......................... 67
4.2.3 Bias Plow Impedance ............................. 67
4.3 Howe Rayleigh Conductivity Model ....................... 68
4.4 Jing Model (Modified Howe Model) ....................... 71
4.5 Luong Model (Simplified Howe Model) .................... 73
4.6 Bauer Impedance Model .................................. 73
4.7 Bette Impedance Model .................................. 75
4.8 Bellucci Impedance Model ............................... 76
4.9 Application to a Cylindrical Geometry .................. 79
4.9.1 Transfer Matrix Method .......................... 80
4.9.2 Eldredge & Dowling Method ....................... 85
4.10 Some Comparisons ....................................... 89
4.10.1 Impedance Models ................................ 89
4.10.2 Transfer Matrix Method vs. Eldredge & Dowling
Method .......................................... 93
4.10.3 Howe vs. Luong .................................. 95
5 duct acoustics .............................................. 97
5.1 Acoustic Wave Equation ................................. 97
5.2 Three-Dimensional Waves ............................... 101
5.2.1 Cut-On Frequency ............................... 104
5.2.2 Evanescent Modes ............................... 105
5.2.3 Resonances in an Annular Cavity ................ 108
5.3 Plane Waves ........................................... 109
5.4 Attenuation of Sound .................................. 111
5.4.1 Losses at the Wall ............................. 114
5.4.2 Losses due to Turbulent Flow ................... 126
5.4.3 Losses Within the Fluid ........................ 130
6 experimental method & analysis ............................. 139
6.1 Spectral Analysis ..................................... 140
6.1.1 Welch Method ................................... 140
6.1.2 Rejection of Flow Noise ........................ 143
6.2 Plane Wave Decomposition .............................. 144
6.3 Reflection and Transmission Coefficients .............. 151
6.4 Dissipation Coefficient ............................... 154
6.4.1 Average Dissipation Coefficient ................ 155
6.4.2 Dissipation Error .............................. 156
6.4.3 Compared to the Absorption Coefficient ......... 156
6.5 Duct Acoustic Test Rig ................................ 159
6.5.1 Setup & Instrumentation ........................ 159
6.5.2 Microphone Calibration ......................... 162
6.5.3 End-Reflections ................................ 165
6.5.4 Influence of Evanescent Modes .................. 165
6.5.5 Accuracy ....................................... 170
6.6 Hot Acoustic Test Rig ................................. 171
6.6.1 Setup & Instrumentation ........................ 172
6.6.2 Air Supply ..................................... 177
6.6.3 Microphone Probes .............................. 183
6.6.4 Estimation of the Humidity ..................... 189
6.6.5 Attenuation at Elevated Pressure and
Temperature .................................... 190
6.6.6 Accuracy ....................................... 193
7 parameter study ............................................ 195
7.1 Sound Pressure Level .................................. 195
7.2 Bias Flow ............................................. 204
7.3 Grazing Flow .......................................... 213
7.4 Simultaneous Grazing & Bias Flow ...................... 219
7.5 Porosity .............................................. 222
7.6 Wall Thickness ........................................ 228
7.7 Orifice Cross-Section Shape ........................... 231
7.8 Orifice Edge Geometry ................................. 236
7.9 Orifice Angle ......................................... 241
7.10 Double-Skin Configuration ............................. 247
7.11 Cavity Volume ......................................... 249
7.12 Partitioned Cavity .................................... 253
7.13 Perforation Placement ................................. 255
7.14 Perforation Pattern ................................... 260
7.15 Temperature ........................................... 264
7.16 Pressure .............................................. 269
7.17 Strouhal Number ....................................... 271
8 concluding remarks ......................................... 275
A properties of air .......................................... 283
A.1 Equations of Ideal Gas Properties ..................... 283
A.2 Ideal Gas vs. Real Gas ................................ 284
A.3 Tables of Real Gas Properties ......................... 285
В some mathematics ........................................... 293
B.1 Rayleigh Conductivity and Impedance ................... 293
B.2 Conversion of Transfer Matrix into Scattering Matrix .. 294
Bibliography .................................................. 297
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