1 Introduction ................................................. 1
1.1 State of the art and literature review .................. 2
1.2 Motivation for this work ............................... 14
1.3 Outline and methodology of the thesis .................. 17
2 Theory ...................................................... 19
2.1 Governing equations for fluid motion ................... 19
2.2 The transport equations for entropy, vorticity and
acoustic fluctuations .................................. 20
2.2.1 Constant mean flow .............................. 21
2.2.2 Non-constant or swirling mean flow .............. 22
2.3 Acoustic analogies ..................................... 23
2.3.1 Powell .......................................... 24
2.3.2 Möhring ......................................... 25
2.3.3 Howe ............................................ 25
2.4 Discussion on the source term .......................... 26
2.4.1 Vorticity Equation .............................. 26
2.4.2 Vorticity change trough acceleration ............ 27
2.5 ID-Theory of Marble and Candel ......................... 28
3 Setup and instrumentation ................................... 29
Vorticity Wave Generator test rig ........................... 29
3.1 Setup and test rig configurations ...................... 30
3.1.1 Setup ........................................... 30
3.1.2 Designation of the test rig configurations ...... 33
3.2 Vorticity Wave Generator modules ....................... 35
3.2.1 Vorticity Wave Generator Module 1 ............... 35
Description of the module components ............ 36
Vortex module ................................... 36
Injector nozzle ................................. 36
3.2.2 Vorticity Wave Generator Module 2 ............... 37
Description of the module components ............ 37
Vortex module ................................... 37
Inlet chambers .................................. 38
3.2.3 Vorticity Wave Generator Module 3 ............... 39
Description of the module components ............ 42
Hollow shaft .................................... 42
Vortex generator ................................ 42
Bearing ......................................... 42
Electrical drive ................................ 42
Timing belt drive ............................... 43
Photo interrupter ............................... 43
3.3 Vortex generation principles ........................... 43
3.3.1 Application of Vorticity Wave Generator
Module 1: Generation of flow field
perturbations through changes between swirl
free and swirling tube flows .................... 44
3.3.2 Application of Vorticity Wave Generator
Module 2: Generation of swirling flows with
imposed fluctuations ............................ 45
3.3.3 Application of Vorticity Wave Generator
Module 3: Generation of rigid-body-like
vortices with imposed fluctuations .............. 48
3.4 Test rig components except VWG-Modules ................. 49
3.4.1 Hot-wire Module ................................. 49
3.4.2 Nozzle and diffuser ............................. 51
3.5 Mass flow supply and control ........................... 53
3.5.1 Main mass flow supply ........................... 53
3.5.2 Circumferential mass flow supply ................ 54
3.5.3 Temporary injected mass flow via the valve ...... 54
Fast-switching valve ............................ 54
Valve inlet pressure and added mass flow rate ... 55
Power supply of the valve ....................... 55
Valve circuit and trigger signal ................ 55
3.6 Instrumentation: Measurement equipment ................. 56
3.6.1 Microphones ..................................... 56
3.6.2 X-wire probes ................................... 56
3.7 Vorticity Wave Generator test rig control .............. 57
3.8 Data acquisition devices and measured quantities ....... 58
3.8.1 Data acquisition with Agilent data
acquisition/switch unit ......................... 58
Determination of the nozzle Mach number ......... 58
Determination of the current consumption and
profile of the valve ............................ 59
3.8.2 Data acquisition with OROS OR-36 analyzer ....... 59
3.9 Measurement principle Hot-wire Anemometry .............. 59
3.9.1 Calibration procedure ........................... 60
3.9.2 Basics on the velocity determination with
X-wire probes ................................... 62
4 Data acquisition and post processing ........................ 63
4.1 Data acquisition and measurement grid .................. 63
4.2 Post processing ........................................ 65
4.2.1 Velocity vector orientation in the X-wire
probe-shaft and test rig coordinate system ...... 66
4.3 Recording time and measurement accuracy ................ 66
5 Measurement results ......................................... 69
5.1 Sound generation of accelerated flow field
perturbations induced in a tube flow ................... 69
5.1.1 Velocity field .................................. 69
Illustration of the flow field perturbation ..... 69
Temporal velocity changes due to air-injection
into a swirl free tube flow ..................... 73
Comparison of the undisturbed and disturbed
flow field ...................................... 73
5.1.2 Vorticity field ................................. 76
Illustration of the streamwise vorticity ........ 76
Time signals of the streamwise vorticity ........ 78
5.1.3 Velocity field for low and high mass flow rate
injection ....................................... 79
5.1.4 Acoustics ....................................... 81
Microphone signals .............................. 81
Influence of the X-probe position on the
acoustics ....................................... 82
5.1.5 Identification and separation of direct and
indirect noise .................................. 83
Vorticity and vortex sound decay due to the
distance variation between VWG-Module 1 and
nozzle .......................................... 85
5.1.6 Vortex sound dependency on the injected mass
flow rate in case of a choked nozzle ............ 89
5.1.7 Vortex sound dependency on the upstream
vorticity fluctuation amplitude in case of
a choked nozzle ................................. 90
Comparison between the time signals of the
streamwise maximum negative vorticity and the
pressure signals ................................ 90
Vortex sound dependency on the upstream of the
choked nozzle induced vorticity fluctuation ..... 91
5.1.8 Conclusion of the measurements with the VWG1-
Module .......................................... 94
5.2 Sound generation of accelerated flow field
perturbations induced in swirling flows ................ 95
5.2.1 Velocity field .................................. 95
Illustration of the flow field perturbation ..... 95
Temporal velocity changes due to the air-
injection into a swirling tube flow ............. 99
5.2.2 Flow field comparison: Swirling tube flow with
induced fluctuations and perturbation of
a tube flow ..................................... 99
5.2.3 Acoustics ...................................... 102
5.2.4 Identification and separation of direct and
indirect noise in a swirling tube flow ......... 104
5.2.5 Vortex sound generation in swirl free and
swirling tube flows ............................ 106
5.2.6 Modification of the number of inlet ports
used for the temporary air-injection and its
influence on the vortex sound amplitude ........ 106
5.2.7 Vortex sound generation in swirling tube
flows of various swirl intensities ............. 109
5.2.8 Conclusion of the measurements with the VWG2-
Module ......................................... 110
5.3 Sound generation of accelerated rigid-body-like
vortex fluctuations ................................... 111
5.3.1 Operating test of the VWG-Module 3 ............. 1ll
5.3.2 Velocity alteration due to rapid speed
changes ........................................ 114
5.3.3 Alteration within the acoustic pressure
signals due to rapid speed changes ............. 116
5.3.4 Comparison of the velocity and the acoustic
signal to identify the sound source origin ..... 117
5.3.5 Conclusion of the measurements with the VWG3-
Module ......................................... 118
6 Broadband noise due to accelerated vorticity ............... 121
6.1 Flow noise up- and downstream of nozzle and diffuser .. 121
6.1.1 Mass flow rate influence on the downstream
power spectra .................................. 121
6.1.2 Power spectra and coherence of the microphone
signals up- and downstream of nozzle and
diffuser ....................................... 124
6.1.3 Propagation speed and direction of the waves ... 129
6.1.4 Conclusion of the gained knowledge from the
comparison of the nozzle and diffuser
configuration .................................. 131
6.2 Effect of a nozzle on the generated vortex sound ...... 132
6.2.1 Theory on the effect of a duct contraction on
the turbulence and its application to the
test rig configuration VWG1-s flow field
quantities ..................................... 133
6.2.2 Measured flow field characteristics upstream
of the nozzle .................................. 136
6.2.3 Measured sound field characteristics
downstream of the nozzle ....................... 139
6.2.4 Nozzle Mach number dependent change of the
measured velocity and pressure fluctuations .... 141
6.2.5 Approximated velocity fluctuations and
turbulence level in dependence of the nozzle
Mach number .................................... 143
6.2.6 Relation between the longitudinal and lateral
velocity difference and the downstream
measured pressure .............................. 144
6.2.7 Influence of the generated vortex sound on
the total emitted indirect sound ............... 146
7 Conclusion and outlook ..................................... 147
A Appendices ................................................. 149
A.l Appendix: Theory ...................................... 151
A.1.1 Transport equations for entropy, vorticity
and acoustic waves in a non-uniform,
one-dimensional flow ........................... 151
A.1.2 Swirl number ................................... 151
A.1.3 Equations of the ID-theory of Marble and
Candel ......................................... 152
A.2 Appendix: Set up and instrumentation .................. 153
A.2.1 Test rig configurations with VWG-Module 1 ...... 153
A.2.2 Test rig configurations with VWG-Module 2 ...... 155
A.2.3 Test rig configurations with VWG-Module 3 ...... 157
A.2.4 Test rig drawing with mounted VWG-Module 1 ..... 159
A.2.5 Test rig drawing with mounted VWG-Module 2 ..... 160
A.2.6 Test rig drawing with mounted VWG-Module 3 ..... 161
A.3 Appendix: Data acquisition and post processing ........ 163
A.3.1 X-wire probe alignment and velocity
orientation .................................... 163
A.3.2 Equations for the velocity vector conversion
from X-wire probe shaft coordinates to test
rig coordinates ................................ 164
A.4 Appendix: Measurement results VWG-Module 1 ............ 165
A.4.1 VWGls: Lateral velocities (vectors,magnitude) .. 167
A.4.2 VWGls: Axial velocity (magnitude) .............. 171
A.4.3 VWGls: Streamwise vorticity .................... 175
A.4.4 VWG1-HW0,-HW1,-HW2: Lateral velocities
(vectors, mag.) ................................ 179
A.4.5 VWG1-HW0,-HW1,-HW2: Axial velocity
(magnitude) .................................... 181
|
