A New Experimental Approach to Study Helicopter
Blade-Vortex Interaction Noise
by
Sudarshan N. Koushik
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2007
Advisory Commmittee:
Professor Fredric H. Schmitz, Chair/Advisor
Professor James Baeder
Professor Inderjit Chopra
Professor Christopher Cadou
Professor Amr Baz
ABSTRACT
Title of dissertation: A New Experimental Approach to Study Helicopter
Blade-Vortex Interaction Noise
Sudarshan N. Koushik, Doctor of Philosophy, 2007
Dissertation directed by: Professor Fredric H. Schmitz
Department of Aerospace Engineering
A unique and novel experimental approach has been developed to study the aerodynamics and
acoustics of the helicopter Blade-Vortex Interaction in a controlled hover environment. This is
achieved by having a non-lifting single-bladed rotor with a rigid hub interact with a carefully con-
trolled gust disturbance that replicates the essential characteristics of the vortex velocity. This ex-
perimental approach termed the Blade-Controlled Disturbance-Interaction or the BCDI, decouples
the rotor parameters from the charactersitics of the incident disturbance velocity, thus providing an
ideal setup for studying the blade?s aerodynamics and acoustic response in detail. Moreover, the
angle of interaction between the disturbance field and the rotor blade can be controlled by orienting
the gust, providing the ability to study both parallel and oblique interactions. The noise data was
recorded at thirty different microphone locations.
A series of experiments at various rotor tip Mach numbers and interaction angles, replicat-
ing many of the conditions of helicopter BVI, were performed. The results show that the the
directionality of the BVI noise is strongly determined by the interaction angle. A small change
in interaction angle results in the radiation of noise over a larger azimuthal area compared to the
parallel interaction. Moreover, as the interaction becomes more oblique, the peak noise elevation
angle approaches closer to the rotor plane.
A linear unsteady lifting-line aerodynamic theory (corrected for chord-wise non-compactness
)was used to estimate the blade aerodynamics during the interaction and hence the radiated noise.
Although the theory under-predicted the noise levels for most of the cases, and did not replicate
exactly the general pulse shape, the general directionality trends were predicted reasonably well.
The theory was used to separate the contribution to the acoustics, from different spanwise blade
sections, providing significant insights into the phasing mechanism of BVI noise.
c? Copyright by
Sudarshan N. Koushik
2007
DEDICATION
To My Parents and Kripa and Priya. Your love and support has made this possible.
ii
Acknowledgements
I am grateful to a lot of people for without their support and help this thesis would not have
come to fruition.
First and foremost, I would like to thank my advisor, Prof. Fredric Schmitz, for accepting to
work with me, for keeping his faith in me throughout and for providing guidance ? both academic
as well as practical. Even though he was not always physically present owing to his health, he
was always available over the phone irrespective of where in the country he was to provide the
guidance, and practical and moral support through the various stages of this thesis. I have learnt
an immense lot from him during the past few years.
Special thanks are due to my parents for teaching and strengthening my fundamentals through
my younger years, and inculcating in me the thirst for research. It was by their encouragement and
guidance that I started on my thesis in the first place, and their and my sisters? love and faith which
saw me through the thesis. Thanks also to my friends Shaju and Gunjan for understanding what I
was going through during my ?down times? and bringing out of it every time, by encouraging me
iii
and helping me put things in perspective.
I also owe thanks to my friends and fellow graduate students at the Rotorcraft center at the
University of Maryland, for the various discussions on my research. Many of them helped me at
various times during the setting of the experiment with their time and labor, without which the
thesis would not have been what it is ? Ben Sim, Manikandan, Shreyas, Shaju, Arun, Anand,
Vinit, Beerinder, Jaina, Karthik, Eric Greenwood, Rick Sickenberger, Cal Sargent, Gaurav, Andy
Drysdale . . . and the list goes on. Thanks also go to my friends outside of school, Shaju, Rahul,
Rajagopal, Srikant, Anuj, Gunjan, Marylin, Ashok, and many others, who made the past few years
enjoyable, for those times when a little change from academics proved to be incalculably enriching
both for academics as well as the larger perspective of life.
iv
Table of Contents
List of Tables ix
List of Figures x
List of Symbols xviii
1 Introduction 1
1.1 Sources of Helicopter Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Blade-Vortex Interaction Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 BVI Noise: Challenges and Prior Art . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.1 Unsteady Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.2 Aeroacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3.3 Experimental Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4 Objectives of Current Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
v
2 Approach 36
2.1 Experimental BVI Simulation ? The BCDI Experiment . . . . . . . . . . . . . . 36
2.2 The Assembled Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3 Experimental Design and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1 The Gust Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.2 Comparison of Gust to Vortex Induced Velocity Profile . . . . . . . . . . . 52
2.3.3 Rotor Test Stand and Operation . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.4 Acoustic Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3.5 Microphone Measurement System . . . . . . . . . . . . . . . . . . . . . . 62
2.3.6 Data Acquisition and Reduction Technique . . . . . . . . . . . . . . . . . 62
2.4 Experimental Cases Studied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.4.1 Case 1 ? Parallel BCDI . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.4.2 Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 Experimental Results 70
3.1 Data Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.1.1 Background Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.1.2 Acoustic Pulse Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1.3 Repeatability of Acoustic Data . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Noise radiation due to nozzle presence . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.1 Case 1 ? Parallel BCDI . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.2 Case 2 ? 3.3? Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . 78
vi
3.2.3 Case 3 ? 8.8? Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.4 Case 4 ?15.3? Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3 BCDI Acoustic Data ? Parallel BCDI . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.1 Acoustic Time Histories . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.2 Frequency Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.3 Effect of tip Mach number . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4 Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.1 Case 2 ? 3.3? Oblique Interaction . . . . . . . . . . . . . . . . . . . . . . 94
3.4.2 Case 3 ? 8.8? Oblique Interaction . . . . . . . . . . . . . . . . . . . . . . 102
3.4.3 Case 4 ? 15.3? Oblique Interaction . . . . . . . . . . . . . . . . . . . . . 103
3.5 Effect of Interaction Angle on Noise Levels . . . . . . . . . . . . . . . . . . . . . 111
3.6 Effect of tip Mach number on Case 4 (15.3?) Oblique BCDI . . . . . . . . . . . . 112
4 Theoretical Comparison 118
4.1 Theoretical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.1.1 Linear Unsteady Indicial Aerodynamics . . . . . . . . . . . . . . . . . . . 119
4.1.2 The Acoustics Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2 Comparison with Experiment ? Parallel Interaction . . . . . . . . . . . . . . . . 125
4.3 Oblique Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3.1 Case 2 ? 3.3? Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3.2 Case 3 ? 8.8? Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . 139
4.3.3 Case 4 ? 15.3? Oblique BCDI . . . . . . . . . . . . . . . . . . . . . . . . 146
vii
4.4 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5 Summary and Conclusions 153
5.1 The BCDI Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.2 BCDI Experimental Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.3 Indicial Aerodynamics and Acoustic Predictions . . . . . . . . . . . . . . . . . . . 156
5.4 Recommendations for Further Research . . . . . . . . . . . . . . . . . . . . . . . 157
A Gust Generator Fabrication and Operational Details 160
B Rotor Test Stand Dynamics 168
C Effect of Nozzle Interference on the Acoustic Time Histories 170
D Comparison Between Compact and Non-Compact Acoustic Formulations 175
E Comparison of Frequency Spectrum Between Theory and Experiment 180
F Scaling of the Acoustics Data 185
F.1 Choice of Scaling Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
References 191
viii
List of Tables
2.1 Some key characteristics of the rotor . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Tip Mach numbers tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1 Coefficients of the Indicial gust function, ?g . . . . . . . . . . . . . . . . . . . . . 120
ix
List of Figures
1.1 Source of helicopter noise [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Frequency spectrum of radiated noise from a typical hovering helicopter [5] . . . . 6
1.3 Preferred radiation directions of some noise sources [13] . . . . . . . . . . . . . . 9
1.4 A 4-bladed rotor undergoing BVI . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Top view of helicopter in BVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Side view of helicopter BVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.7 Two-dimensional schematic of the BVI . . . . . . . . . . . . . . . . . . . . . . . 13
1.8 Locus of possible blade-vortex interactions for two-bladed rotor for two different
advance ratios (? = 0.1 and ? = 0.164) . . . . . . . . . . . . . . . . . . . . . . . . 15
1.9 Trace Mach number of BVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.10 Directivity patterns obtained from wave tracing and MT R approach (? = 0.164,MT =
0.664) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.11 In-flight acoustic measurement technique [8] . . . . . . . . . . . . . . . . . . . . . 28
1.12 A schematic of the BVI experiment by Leverton . . . . . . . . . . . . . . . . . . . 31
1.13 A schematic of the wind tunnel experimental setup used by Kitaplioglu et al [84] . 33
x
2.1 Helicopter BVI geometry for a two-bladed rotor . . . . . . . . . . . . . . . . . . . 38
2.2 Two-dimensional schematic of the BVI . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Typical vortex induced velocity profile and its gradient . . . . . . . . . . . . . . . 39
2.4 Sectional lift coefficient induced by a vortex on the airfoil . . . . . . . . . . . . . . 40
2.5 Schematic of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.6 Trace Mach Number of BVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7 Layout of the different components inside the acoustic chamber . . . . . . . . . . 45
2.8 Schematic of the final assembled experimental setup . . . . . . . . . . . . . . . . 46
2.9 Photograph of a portion of the experimental setup inside the chamber . . . . . . . 47
2.10 Schematic of experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.11 Schematic showing different sections of the ?Gust Generator? . . . . . . . . . . . 49
2.12 Schematic of the final nozzle design . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.13 Variation of velocity distribution across the span of the nozzle . . . . . . . . . . . 53
2.14 Variation of velocity distribution with height above the nozzle . . . . . . . . . . . 54
2.15 Comparison of measured gust and vortex induced velocity . . . . . . . . . . . . . 56
2.16 Schematic of the setup showing the relative positions of the gust and the rotor blade
during interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.17 Reflection characteristics of chamber prior to treatment . . . . . . . . . . . . . . . 60
2.18 Reflection characteristics of chamber after acoustic treatment . . . . . . . . . . . . 61
2.19 Top view of microphone measurement locations . . . . . . . . . . . . . . . . . . . 63
2.20 Side view of microphone measurement locations . . . . . . . . . . . . . . . . . . 64
xi
2.21 Comparison of the parallel interaction in the experiment with a real BVI . . . . . . 67
2.22 Schematic of the oblique interaction angles and corresponding trace Mach number
profiles (MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1 Power spectrum of the gust flow noise . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2 Ratio of main acoustic pulse to the first reflected pulse . . . . . . . . . . . . . . . 72
3.3 Revolution-to-Revolution fidelity of the rotor setup . . . . . . . . . . . . . . . . . 74
3.4 SPL trends of noise radiation due to the nozzle ? parallel BCDI . . . . . . . . . . 75
3.5 SPL trends with gust strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6 Acoustic time history comparison with and without the gust, showing the effect of
the nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.7 SPL trends of noise radiation due to the nozzle ? Case 2 . . . . . . . . . . . . . . 79
3.8 Acoustic time history comparison with and without the gust, for Case 2 at ? =
120.9? (MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.9 SPL trends of noise radiation due to the nozzle ? Case 3 . . . . . . . . . . . . . . 81
3.10 Acoustic time history comparison with and without the gust, for Case 3 at ? =
120.9? (MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.11 SPL trends of noise radiation due to the nozzle ? Case 4 . . . . . . . . . . . . . . 83
3.12 Acoustic time history comparison with and without the gust, for Case 4 at ? =
120.9? (MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.13 Top view of acoustic wavefronts radiating from the parallel interaction . . . . . . . 85
3.14 Unaveraged data for two revolutions for the parallel interaction at ? = 120.9? . . . 86
xii
3.15 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (MT = 0.702 ? Parallel Interaction) . . . . . . 90
3.16 Directionality trends at 0.702MT for the Parallel Interaction . . . . . . . . . . . . . 92
3.17 Frequency spectrum of noise at various microphones ? Sound pressure in dB vs.
Single-blade rotor harmonics (MT = 0.702 ? Parallel Interaction) . . . . . . . . . 93
3.18 Variation of peak-to-peak noise level with tip Mach number ? Parallel BCDI . . . 95
3.19 Variation of peak-to-peak level with increase in tip Mach number for the parallel
BCDI at ? = 107? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.20 Top view of acoustic wavefronts for Case 2 oblique BCDI . . . . . . . . . . . . . 97
3.21 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) ? Case 2 (3.3? Oblique Interaction MT = 0.702) 98
3.22 Frequency spectrum of noise at various microphones ? Sound pressure in dB vs.
Single-blade rotor harmonics ? Case 2 (3.3? Oblique Interaction MT = 0.702) . . 99
3.23 Directionality trends for Case 2 (3.3? Oblique Interaction) at MT = 0.702 . . . . . 101
3.24 Top view of acoustic of the wavefronts for Case 3 oblique BCDI . . . . . . . . . . 103
3.25 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) ? Case 3 (8.8? Oblique Interaction MT = 0.702)104
3.26 Frequency spectrum of noise at various microphones ? Sound pressure in dB vs.
Single-blade rotor harmonics ? Case 3 (8.8? Oblique Interaction MT = 0.702) . . 105
3.27 Directionality trends for Case 3 (MT = 0.702) . . . . . . . . . . . . . . . . . . . . 106
3.28 Top view of acoustic of the wavefronts for Case 4 oblique BCDI . . . . . . . . . . 107
xiii
3.29 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) ? Case 4 (15.3? Oblique Interaction MT = 0.702)109
3.30 Frequency spectrum of noise at various microphones ? Sound pressure in dB vs.
Single-blade rotor harmonics ? Case 4 (15.3? Oblique Interaction MT = 0.702) . . 110
3.31 Directionality trends for Case 4 (MT = 0.702) . . . . . . . . . . . . . . . . . . . . 111
3.32 Variation of peak-to-peak noise levels with interaction angle (MT = 0.702) . . . . . 113
3.33 Variation of trace Mach number as function of tip Mach number ? Case 4 oblique
BCDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.34 Acoustic directivity variation with tip Mach number ? Case 4 (15.3? Oblique BCDI)116
3.34 (Cont?d) Acoustic directivity variation with tip Mach number ? Case 4 (15.3?
Oblique BCDI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1 Weissinger-L lifting line model for the rotor blade . . . . . . . . . . . . . . . . . . 121
4.2 Comparison between compact and non-compact chord approaches ? Parallel In-
teraction at MT = 0.702 (? = 107? & ? = 53.75?) . . . . . . . . . . . . . . . . . . 124
4.3 Difference in peak-to-peak sound pressure between compact and non-compact ap-
proaches ? Case 1 parallel BCDI at MT = 0.702 . . . . . . . . . . . . . . . . . . 126
4.4 Difference in sound pressure between compact and non-compact approaches ?
Case 4 (15.3? Oblique BCDI) at MT = 0.702 . . . . . . . . . . . . . . . . . . . . 127
4.5 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (MT = 0.702 ? Parallel Interaction) . . . . . . 129
xiv
4.6 Comparison of the directionality trends between theory and experiment for the
parallel interaction (MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.7 Spanwise acoustic phasing effect for the parallel interaction (MT = 0.702) . . . . . 133
4.8 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) ? Case 2 (3.3? Oblique BCDI; MT = 0.702) . 135
4.9 Comparison of the directionality trends between theory and experiment ? Case 2
(3.3? Oblique BCDI; MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.10 Spanwise acoustic phasing effect ? Case 2 (3.3? Oblique BCDI) at MT = 0.702 . 137
4.11 Trace Mach number along the radiation direction for Case 2 (3.3? Oblique BCDI) . 139
4.12 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (Case 3 ? 8.8? Oblique BCDI) at MT = 0.702 . 141
4.13 Comparison of the directionality trends between theory and experiment ? Case 3
(8.8? Oblique BCDI) at MT = 0.702 . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.14 Spanwise acoustic phasing effect ? Case 3 (8.8? Oblique BCDI; MT = 0.702) . . 144
4.15 Trace Mach number along the radiation direction for Case 3 (8.8? Oblique BCDI) . 145
4.16 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) ? Case 4 (15.3? Oblique BCDI; MT = 0.702) . 147
4.17 Comparison of the directionality trends between theory and experiment ? Case 4
(15.3? Oblique BCDI; MT = 0.702) . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.18 Spanwise acoustic phasing effect ? Case 4 (15.3? Oblique BCDI; MT = 0.702) . . 149
4.19 Trace Mach number along the radiation direction for Case 4 (15.3? Oblique BCDI) 151
xv
A.1 Schematic of early nozzle design . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
A.2 Velocity profile obtained from the first nozzle design . . . . . . . . . . . . . . . . 163
A.3 RMS variation of velocities across nozzle width . . . . . . . . . . . . . . . . . . . 165
A.4 Frequency distribution of turbulence at various locations . . . . . . . . . . . . . . 167
B.1 Resonant frequencies associated with the RTS . . . . . . . . . . . . . . . . . . . . 169
C.1 Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Parallel In-
teraction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
C.2 Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Case 2) . . . . 172
C.3 Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Case 3) . . . . 173
C.4 Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Case 4) . . . . 174
D.1 Comparison between Compact and Non-compact chord formulations (MT = 0.702
? Parallel Interaction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
D.2 Comparison between Compact and Non-compact chord formulations (MT = 0.702
? Case 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
D.3 Comparison between Compact and Non-compact chord formulations (MT = 0.702
? Case 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
D.4 Comparison between Compact and Non-compact chord formulations (MT = 0.702
? Case 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
E.1 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (MT = 0.702 ? Parallel Interaction) . . . . . . 181
xvi
E.2 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (MT = 0.702 ? Case 2) . . . . . . . . . . . . 182
E.3 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (MT = 0.702 ? Case 3) . . . . . . . . . . . . 183
E.4 Acoustic time histories at the various microphones in terms of Acoustic Pressure
(in Pa) vs. Rotor Azimuth (in Deg) (MT = 0.702 ? Case 4) . . . . . . . . . . . . 184
F.1 Directionality trends for parallel BCDI when scaled about 0.8R (MT = 0.702) . . . 187
F.2 Directionality trends for parallel BCDI when scaled about the hub (MT = 0.702) . 187
F.3 Directionality trends for the 3.3? oblique BCDI when scaled about 0.8R (MT = 0.702)188
F.4 Directionality trends for the 3.3? oblique BCDI when scaled about the hub(MT =
0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
F.5 Directionality trends for the 8.8? oblique BCDI when scaled about 0.8R (MT = 0.702)189
F.6 Directionality trends for the 8.8? oblique BCDI when scaled about the hub (MT =
0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
F.7 Directionality trends for the 15.3? oblique BCDI when scaled about 0.8R (MT =
0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
F.8 Directionality trends for the 15.3? oblique BCDI when scaled about the hub (MT =
0.702) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
xvii
List of Symbols
(?) Derivative with respect to source time
?T PP Rotor tip path plane angle
? Glauert?s factor,=radicalbig1?M2?
?CP Differential pressure on the airfoil
? Vortex circulation, m2/s
? Interaction angle
? Advance Ratio of the helicopter
? Rotor angular velocity, rad/s
? Azimuth location with respect to rotor hub, deg
?g Indicial response function
?b Azimuthal location of the blade tip, rad
?w Azimuthal location of a vortex, rad
?0 Density of quiescent medium, kg/m3
? Rotor Solidity
? Elevation above rotor plane, deg
xviii
a Local speed of sound, m/s
a0 Speed of sound in the medium, m/s
Cl Lift coefficient
Ct Thrust coefficient
G1,G2,g1,g2 Indicial coefficients
L Length of nozzle, m
l Sectional blade load
lr Component of sectional load along observer direction
Mr Mach number along direction of observer
MT Tip Mach number
MT R Trace Mach number (in the rotor plane)
Nb Number of blades
n j Local surface normal
p Observed acoustic pressure
pL Acoustic pressure due to loading term
Pi j Surface pressure
R Blade radius, m
r Blade radial station
rc Distance from center of vortex, non-dimensionalized by c
robs Distance between observer and source,m/s
s Reduced chord
xix
Ti j Lighthill?s stress tensor
Um Mean horizontal velocity
um Horizontal component of gust velocity, m/s
V Velocity, m/s
V? Tangential velocity induced by a vortex, m/s
vn Velocity component normal to surface, m/s
vz Vertical component of velocity, m/s
VT R Trace Velocity
wg Vertical component of gust velocity, m/s
Wm Mean vertical velocity
wm Vertical component of gust velocity, m/s
xc Horizontal distance from vortex center, non-dimensionalized by c
xi,x j Space coordinates
xtip,ytip Coordinates of the tip vortex
zc Vertical distance from vortex center, non-dimensionalized by c
xx
Chapter 1
Introduction
Mankind has had a fascination for flying vehicles for centuries, and helicopter flight was among
the first forms of flight envisioned by man. The ancient Chinese played with a hand-spun top that
rose upwards when revolved rapidly and as early as 1490 Leonardo da Vinci made drawings of a
machine that resembles the modern helicopter. One of the main reasons for the keen interest in
rotary winged flight is also one of its biggest advantages compared to fixed wing, namely vertical
take-off and landing. This ability combined with the capability to hover almost motionless has
made the rotorcraft indispensable to the military and in certain civilian applications. Although,
people were experimenting with various rotarcraft design even before the Wright-Flyer, it was not
until 1939 that the first practical helicopter flew. Even to this day, rotorcraft advancement has
lagged behind their fixed wing counterparts.
Despite various innovations, the present day helicopters are noisy and suffer from aerome-
chanical and vibration issues. The noise and vibrations cause passenger discomfort and increase
annoyance levels around communities as well as reduce military effectiveness of helicopters in
1
enemy territories. Over the last few decades, considerable effort has gone into mitigating rotor-
craft noise and making it a smoother ride. However, these efforts have only had limited success.
This is because the fundamental principles governing rotorcraft are very complex, and the essential
technical aspects and physics governing the aerodynamics are not completely understood. Another
significant issue with rotor noise is the fact, that it is inherent to any lifting rotor system.
In a fixed wing aircraft most of the noise is due to the engine, with some additional noise
coming from the airframe and control surfaces. In general, an increase in thrust causes an increase
in engine noise, while increasing the velocity and performing maneuvers results in increase in noise
radiation from the airframe and the control surfaces. Since the engine and the control surfaces are,
for the most part functionally unrelated, changes can be made to reduce noise on a component by
component basis, without significantly affecting the low-noise design of other components or the
overall performance. Moreover, improving the efficiency of the engine (in small to moderate sized
aircraft such as the 737), through increase in by-pass ratios, has also resulted in the reduction of
noise. In the case of the rotorcraft, the main source of noise is the helicopter main and tail rotors
which perform the functions of providing lift and thrust, as well as controlling and maneuvering the
aircraft. The various components in the helicopter are much more tightly coupled than in the case
of the fixed wing aircraft. Thus the decoupling of the noise problem from the ?overall efficiency?
of the helicopter is next to impossible, and any effort to reduce helicopter noise has to be made
with a particular eye towards not affecting the performance adversely.
The distinctive nature of helicopter noise calls attention to it even when the radiated noise
levels are somewhat low by community standards [1]. The characteristic impulsive ?Wop-Wop-
2
Wop? sound from the main rotor, the propeller like noise from the tail rotor or the whine of the
Fenestron cause an awareness to nearby rotorcraft operation and increases annoyance. Excessive
noise levels near community heliports are among the main impediments to increasing civilian use
of helicopters. Noise reduction is also important from a militaristic standpoint. Stealth in a military
offensive is desirable when the element of surprise can be used to a tactical advantage. Helicopter
noise reduction, though traditionally not a design driver has been gaining prominence off late.
Performance metrics have almost always superseded acoustic considerations of annoyance and
stealth in traditional rotorcraft design, but acoustics is becoming an increasingly important design
and operational criteria for operators and manufacturers [2, 3].
Many efforts have been directed at understanding helicopter noise sources and in developing
techniques to reduce external noise. One of the more persistent sources, which has evaded sig-
nificant abatement is what is termed ?Blade-Vortex Interaction? or BVI noise. Unlike in fixed
wing aircraft or even propellers, where the trailed tip vortices from the wing or propeller tip are
convected behind when the aircraft moves forward, the trailed tip vortices from the tip of the he-
licopter?s main rotor blades are convected below the main rotor. Most operating conditions of the
helicopter result in these tip vortices coming close to the main rotor, resulting in an interaction
between the vortex and the oncoming rotor blade. The tip vortex induces a sharp change in the
effective angle-of-attack observed by the interacting blade leading to a sudden change in pressure
on the blade surface. This rapid pressure change radiates out from the rotor in the form of an
impulsive noise referred to as BVI.
This thesis provides a novel, carefully controlled experimental approach to study the helicopter
3
BVI problem in order to develop deeper insights into the physics of noise radiations of the rotor
blade as it moves through a vortex, and to help develop techniques and/or specially tailored blades
to help reduce BVI noise. In this chapter an overview of the various sources of helicopter noise,
along with the accompanying physics is presented. This is followed by a discussion on the noise
reduction techniques deployed by previous researchers with a particular emphasis on Blade-Vortex
Interaction Noise.
1.1 Sources of Helicopter Noise
Noise is primarily the propagation of pressure fluctuations in a medium like air. Changes in
pressure on the aerodynamic surface, associated with lift or drag radiates as noise to an observer
moving with respect to the surface. The helicopter main rotor, the tail rotor and the engine along
with the rest of the body contribute to the noise. The helicopter main rotor is the primary source
by virtue of the complex aerodynamic phenomena. Even during normal flight conditions, the
helicopter rotor undergoes various unsteady aerodynamic phenomena (Fig. 1.1). These, including
dynamic stall, interaction between the main rotor and the wake system, transonic flow resulting in
shocks on the blade surface, and the complex interaction between the main rotor wake and the tail
rotor. Many of these phenomena lead to vibration and noise radiation.
Fig. 1.2 shows the typical frequency spectrum of the noise radiated by a hovering helicopter [5].
The lower frequencies (0-100Hz) are dominated by the main rotor harmonics of revolution. The
mid-frequencies (60-200) are dominated by the tail rotor harmonics. At higher frequencies the
noise is more broad-band (less tonal) and the main contributions are possibly due to the interac-
4
Figure 1.1: Source of helicopter noise [4]
5
Figure 1.2: Frequency spectrum of radiated noise from a typical hovering helicopter [5]
tion of the rotor with the turbulence, and due to the gearbox and engine. In general, the relative
importance of each of these sources depends on the specific rotor design.
When the helicopter moves into forward flight, the unsteady aerodynamic blade loads, includ-
ing BVI contribute to the lower and mid-frequency spectrum. Other unsteady phenomena such as
dynamic stall and interaction of the tail rotor with the wake of the main rotor might also generate
broadband noise. The important noise sources on a helicopter in forward flight, each possess dis-
tinct characteristics and have preferred propagation directions. The noise sources can broadly be
classified into the following:
6
? Main rotor noise
? Main rotor thickness noise ? The thickness noise is a result of the displacement of
the fluid around the blade as it passes through the medium and is present in both hover
and forward flight. The noise sources on the rotor blade can be represented by a series
of sources and sinks (monopoles) [6] and results in noise radiation mostly in the plane
of the rotor (Fig. 1.3).
? Main rotor harmonic noise ? This is a result of the steady and unsteady loading
on the main rotor and is strongly influenced by the constantly changing loads of a
helicopter rotor in forward flight. This source of noise is usually modelled as a series
of dipoles distributed over the blade. The loading noise due to the steady and unsteady
lift radiates mostly below the rotor plane (Fig. 1.3), while the noise due to steady and
unsteady drag radiates more in the plane of the rotor.
? Main rotor High Speed Impulsive (HSI) Noise ? This source of noise occurs mostly
in high speed forward flight and is an extreme case of ?thickness noise? discussed
above. This very intense pulse is strongly influenced by the transonic effects on the
blade surface. At very high transonic tip Mach numbers, the shock formed on the blade
surface, can extend past the rotor blade tip and can propagate into the far-field. This
phenomenon known as ?delocalization? [6, 7] of the shock results in a particularly im-
pulsive sound referred to as High-Speed Impulsive (HSI) Noise. This source of noise
typically observed in older ?Huey Helicopters?, can be mitigated to some extent by
operating the helicopter at low advancing tip Mach numbers. Since the ?delocalized?
7
shock wave tends to radiate in-plane, this sound source is mostly focused in and slightly
below the plane of the rotor and is particularly important for military detection. In the
recent past, several flight tests [8] and pioneering experiments conducted in wind tun-
nels and hover chambers [6, 7, 9] have been conducted to characterize and understand
this particular source. Some of the solutions including lower rotor tip speeds and/or
innovative blade designs, like the BERP tip [10] have been incorporated in modern
helicopters. Moreover, theoretical predictions of HSI noise signature using ?state-of-
the-art? codes has reached a reasonably good level of accuracy [11].
? Main rotor Blade-Vortex Interaction (BVI) Noise ? It is the typical ?popping? or
?slapping? sound heard most often when the observer is in front and to the advancing-
blade side of the helicopter, or to the rear and retreating-blade side of the helicopter.
This particular phenomenon has been a topic of extensive research for the past decades [12].
As discussed earlier, this impulsive noise mostly occurs when the wake of the main ro-
tor passes near the rotor tip path plane. The primary radiation direction is to front and
below the rotor (Fig. 1.3).
? Tail rotor harmonic noise ? Occurs due to the steady & unsteady airloads on the tail rotor.
It is similar in nature to the rotor harmonic noise, but of a higher frequency as the RPM of
the tail rotor is a higher than that of the main rotor as can be seen from Fig. 1.2.
? Other noise sources ? The gearbox of the transmission system, engine and airframe also
contribute to some broadband noise. These sources are however, significantly lower in mag-
nitude than the main rotor noise sources, as can be seen from Fig. 1.2.
8
Figure 1.3: Preferred radiation directions of some noise sources [13]
1.2 Blade-Vortex Interaction Noise
Blade-Vortex Interaction noise mainly occurs during low speed descending flight, low speed
turning descents and during some maneuvering flights [14]. These conditions are conducive to the
rotor blade passing close to a vortex that is trailed from previous blades (Fig 1.4). The induced
velocity of each tip vortex essentially induces a sharp change in effective angle of attack observed
by the interacting blade, leading to a sharp change in surface pressure. This rapid pressure change
radiates out in the form of the impulsive noise known as Blade-Vortex Interaction or BVI noise.
BVI noise is known to be highly directional and quite sensitive to flight conditions. The fact
that most of the acoustic energy is concentrated in the frequency range from 75Hz to 1500Hz (5
rotor harmonics to 100 rotor harmonics) makes it quite annoying as the human ear is very sensitive
to sound at the higher end of the frequency range. The noise generation itself is a complex aeroa-
coustic phenomenon and depends on a variety of factors encompassing rotor design, operational
9
Figure 1.4: A 4-bladed rotor undergoing BVI
conditions and even atmospheric conditions. The nature and strength of the effective BVI noise
sources, the associated propagation mechanisms and the geometry of the interaction determine the
BVI noise radiation to the far-field.
Fig. 1.5 shows the geometry of two-bladed rotor undergoing BVI as seen from the top view.
As is apparent from the figure, each blade intersects the vortices trailed from the blade tips at
earlier times. Even for a two-bladed rotor, several interactions are possible and are dependant
on the trajectory of the tip vortex. The strength of the tip vortex and its trajectory, in turn, are
dependant on various rotor parameters including rotor tip Mach number and advance ratio. Under
most flight conditions such as hover or steady level flight, the tip vortices are mostly below the
plane of the rotor as seen in Fig. 1.6(a) and the interaction between the blade and vortices do not
lead to significant noise radiation. However, certain flight conditions such as low speed descent,
10
Figure 1.5: Top view of helicopter in BVI
lead to the tip vortices passing close to rotor plane (Fig. 1.6(b)). The closer the tip vortices are to
the rotor plane, the stronger and more impulsive is the noise radiated.
Certain interactions, for example BVI #3 in Fig. 1.5, are such that the interacting tip vortex
filament with the blade is nearly parallel to the rotor blade. The resulting interaction can then
be idealized as a series of two-dimensional interactions between the blade section and a two-
dimensional vortex. A two-dimensional section of the rotor blade airfoil undergoing BVI is shown
as a schematic in Fig. 1.7 along with the typical vortex induced velocity. The velocity induced by
11
(a) Helicopter in steady level flight
(b) Helicopter in low speed descent
Figure 1.6: Side view of helicopter BVI
12
Figure 1.7: Two-dimensional schematic of the BVI
an idealized vortex on the blade is given by the Biot-Savart law:
V? = ?2pir (1.1)
where V? is the tangential velocity induced by the vortex, ? is the vortex strength and r is the radial
distance from the vortex center. The blade surface pressure and hence the lift is most affected by
the vertical component of the induced velocity and is given by
Vz = ?2pi xcr2
c ?(z2c +x2c)
(1.2)
where Vz is the vertical component of the velocity induced at the quarter chord location of an airfoil
which is separated vertically by a distance zc and horizontally by a distance xc from the vortex.
The unsteadiness of the induced surface pressures, and hence the strength of the radiated noise
depends quite strongly on the vertical ?miss-distance (zc)? between the blade and the vortex, the
strength (?) and core radius (rc) of the vortex.
A relatively simple analysis can be performed to estimate the tip-vortex trajectory for a rotor
in steady forward flight. Assuming that the tip vortex convects along with the rotor downwash
13
and is undistorted in the rotor tip path plane, the tip vortex coordinates can be obtained using the
following equations [15]:
xtip
R = cos(?b ??w)+??w
ytip
R = sin(?b ??w) (1.3)
where xtip and ytip are the coordinates of the tip vortex filament, R is the blade radius, ?b and ?w
are the azimuthal angles of the blade and the tip vortex filament under consideration, respectively
and ? is the advance ratio of the helicopter. This basic equation although possibly over-simplified,
captures the essential parameters affecting the BVI. Moreover, this set of equations also helps
predict the locations of important BVIs. The locus of possible BVIs for an Nb-bladed rotor, in
a rotor fixed reference frame, can then be determined by solving the following two equations,
simultaneously:
r cos
parenleftbigg
?b ? 2pi(i?1)N
b
parenrightbigg
= cos(?b ??w)+??w
r sin
parenleftbigg
?b ? 2pi(i?1)N
b
parenrightbigg
= sin(?b ??w) (1.4)
Fig. 1.8 shows the locus of possible BVIs for a two bladed helicopter at two different advance
ratios of 0.1 and 0.164 obtained from the rigid wake (Eqn. 1.4), in the rotor fixed reference frame.
It should be noted that a rigid wake model is not entirely accurate as the rotor downwash and in-
teraction between the individual shed vortices causes the wake to modify even during steady flight
conditions. Nevertheless, the trajectory described by the rigid wake model provides an important
understanding of the interaction geometry and in identifying the important interactions for BVI
noise radiation.
14
Figure 1.8: Locus of possible blade-vortex interactions for two-bladed rotor for two different ad-
vance ratios (? = 0.1 and ? = 0.164)
If one were to consider the instantaneous interaction point between the tip vortex and the blade
as the noise source, then the trajectory of the source in the undisturbed medium is obtained from
the tip vortex trajectory depicted in Fig. 1.8. Confining this trajectory to lie in a plane parallel to
the rotor disk causes the aerodynamic loading and the resulting acoustics of the BVI to be predom-
inantly dependant on the basic top-view geometry of the BVI process. The controlling parameters
are the advance ratio (?) and the hover tip Mach number (MT ) of the rotor [16]. From these two
parameters, a third parameter called the trace Mach number [17] can be obtained (Eqn. 1.5). The
trace Mach number (MT R) is the speed (VT R in Fig. 1.9) of the locus of the interaction geometry,
with respect to the undisturbed medium, non-dimensionalized by the speed of sound.
MT R = ?r(?+sin?b)a
0 sin?
(1.5)
Both the three-dimensional interaction geometry and the trace Mach number determine the
15
Vc
?
V? +?Rsin(?)
? ?
VT R
BVI Trajectory
Figure 1.9: Trace Mach number of BVI
phasing of the acoustic events and hence the directionality of the BVI noise radiation [18, 19, 20,
21, 22]. When viewed in a medium fixed frame of reference, the BVI trajectory can be treated as a
single acoustic source (of varying strength) moving along the epi-cycloidal tip vortex trajectory at a
non-dimensionalized speed given by the trace Mach number. At each instant in time, this acoustic
source triggers an acoustic disturbance (BVI wavelet) that propagates away from the blade surface
at the speed of sound. If the trace Mach number at points along the trajectory becomes large, a
series of these acoustic disturbances can group together with the undesirable effect of strong noise
focusing and amplification. The noise focusing is directly related to the trace Mach number.
For a parallel BVI, the interaction angle ?, in Fig. 1.9 is zero resulting in a trace Mach number
of infinity (from Eqn. 1.5). Physically, this is because all the acoustic sources along the BVI tra-
jectory are triggered simultaneously. The wavefront resulting from the summing of these acoustic
waves propagates almost perpendicular to the initial interaction. A schematic of the wavefront
for a helicopter undergoing near-parallel (slightly curved) BVI is shown in Fig. 1.10(a) and the
corresponding trace Mach number profile in Fig. 1.10(b). This interaction ? corresponding to
16
BVI #3 in Fig. 1.5 ? has an infinite trace Mach number for most of the interaction, resulting in
a simultaneous summing of the BVI wavelets. Such interactions are typically the strongest, with
most of the acoustic energy focused in front and to the advancing side of the rotor.
Oblique BVIs tend to be of a lesser magnitude due to summing of the waves from the acoustic
source as the blade sweeps the tip vortex trajectory. For the oblique BVI, the trace Mach number
being finite, results in non-simultaneous summing of the acoustic waves. This results in an en-
tirely different azimuthal directionality of noise radiation. A schematic of a helicopter undergoing
oblique BVI (corresponding to BVI #2 in Fig. 1.5) is shown in Fig. 1.10(c). This interaction has
a decelerating trace Mach number profile as shown in Fig. 1.10(d). Most of the acoustic energy in
this case is directed towards the front of the rotor.
From the discussion so far, it is apparent that the helicopter BVI is a strong function of the
helicopter wake.
Significant research effort has been directed at reducing BVI noise in the past decades. Various
blade and/or rotor design modifications including active and passive approaches, X-Force control
and flight path management have been attempted with success. However, they require significant
modifications to the helicopter airframe. A significant portion of the problem has been the lack of
understanding of the real cause and effect. For instance, changes in blade planform affects the tip
vortex characteristics which in turn modifies the unsteady induced loads. However, the change in
blade planform also affects the trace Mach number profile of the interaction as the blade sweeps
over the tip vortex, thus affecting the phasing and hence directionality of the acoustic energy. Given
that the tip vortex trajectory is far more complex than is represented by Eqn. 1.3 the real effect of
17
(a) Parallel BVI (BVI #3) (b) trace Mach number profile for near-
parallel BVI
(c) Oblique BVI (BVI #1) (d) trace Mach number of the oblique
BVI
Figure 1.10: Directivity patterns obtained from wave tracing and MT R approach (? = 0.164,MT =
0.664) 18
the blade design change is hard to predict and control. Similar coupled effects occur with almost
all rotor parameter changes making BVI noise reduction a real challenge.
1.3 BVI Noise: Challenges and Prior Art
Accurate prediction of helicopter BVI noise is a difficult challenge that has yet to be accom-
plished. BVI noise prediction requires good estimates of the rotor trim state and very accurate
estimates of the vortex strength, trajectory and vortex structure, blade aerodynamics and aeroelas-
ticity.
In predicting rotorcraft noise on the ground, therefore, there are typically two challenges in-
volved:
? Estimate the blade loads and blade surface pressure distribution at a given operating condi-
tion. This requires a very detailed knowledge of the wake dynamics, especially the vortex
locations and the evolution characteristics to sufficiently high degree of resolution. More-
over, the turbulence and near shed-wake dynamics also contribute to some of the acoustics.
The complexity of the wake and unsteadiness of the whole system makes this a very chal-
lenging task.
? Once the aerodynamic environment is known, experimentally or computationally, Eqn. 1.6
or other suitable equations can be applied to calculate the noise radiated to the ground. Even
at this stage, the non-linearities involved at high transonic tip Mach numbers, make accurate
noise prediction complicated
19
A brief review of previous work undertaken by researchers in understanding these challenges is
provided below.
1.3.1 Unsteady Aerodynamics
Beginning with Theodersen?s [23] analysis of two-dimensional oscillating airfoils, various the-
ories have been put forward for understanding unsteady aerodynamics, including heaving and
pitching airfoils [24, 25] and airfoils moving through gusts [26]. Wagner first proposed the in-
dicial approach, whereby the empirically estimated the airfoil response to a step change in angle of
attack is integrated using the Duhamel integral to obtain the airfoil response to arbitrary unsteady
angle of attack changes. This approach has been extended by various researchers to other airfoil
motions including pitching and heaving. Beddoes [27] and, later Leishman [28] extended the ap-
proach for the motion of an airfoil through a gust. Leishman obtained the airfoil response to a
sharp-edged gust using an two-dimensional unsteady Reynolds Averaged Navier-Stokes (RANS)
CFD solution, which was then used to estimate the airfoil loads for an arbitrary gust. Such tech-
niques when tailored for specific Mach number regimes can account for compressibility effects to
some extent, and have been used with a reasonable degree of accuracy to predict BVI noise [29].
However, all the above theories being based on potential flow are truly valid only for sufficiently
low Mach numbers and relatively small changes in aerodynamic character.
While the above approaches mostly concern airfoil-gust interactions and are essentially two-
dimensional in nature, Widnall and Chu [30] and later Martinez and Widnall [31] attempted the
development of a theoretical model for the interaction of an infinite wing with an oblique gust.
20
While this approach helped solidify the trace Mach number concept proposed by Widnall [17],
comparison with experiment [32, 33] was not satisfactory due to the assumptions of low reduced
frequency and moderate tip Mach numbers.
BVI induced loads are of very high frequency in nature and can cause acceleration of the flow
to transonic Mach numbers. Since BVI far-field acoustics is more a function of the rate of change
of loads than the level of the loads itself, the radiated noise predicted using these aerodynamic
models tend to be wrong. Moreover, they very quickly lose validity at higher Mach numbers.
These potential theories, nevertheless have been used in three dimensional calculations for
various helicopter manuevers. Vortex based models have been used to represent the wake behind
the helicopter, and the induced blade loads. Prescribed wake methods [34, 35], where the wake
structure is modelled a priori or is obtained from empirical estimates, and free wake methods [36,
37], where the wake structures evolves as a part of the solution have been developed. These
techniques, although successful to some extent in predicting the wake dynamics, precise location
of BVIs require extremely high level of resolution of the wake, thus increasing the computational
time by orders of magnitudes.
With the advent of cheaper and faster computers, full-fledged solutions of the Navier-Stokes
equation for the flow field surrounding the rotor has become possible. Datta et al [38] present
a detailed review of the development of CFD based approaches used by researches in the last
decade. The main advantage of this approach is the accurate description of the flow field around
the rotor blade. With sufficient resolution in grids and using the right discretization, the formation
of vorticity on the surface of the rotor blades, its convection into the trailing vortex sheet, and
21
rollup into one or more vortex structures can be calculated accurately. However, they require
very fine grid resolution in order to prevent numerical dissipation of the vortex structures. Some
hybrid formulations which use the Lagrangian free-vortex approach (or prescribed wake in some
cases) approach for the far-field wake and solve the flow equations in the near field have been
used to work around this problem [39]. Computationally more intensive techniques such as direct
wake capturing scheme [40, 41] and vorticity confinement techniques [42] have also been applied
to the problem. These computational techniques are under active development and might prove
very useful for the simulation of the rotor wake aerodynamics problem. However, they are still
in the infancy and lot more research is needed before they can be used in full fledged rotorcraft
comprehensive codes.
1.3.2 Aeroacoustics
Acoustic pressure in the far-field is simply the aerodynamic perturbation pressure that radiates
a net energy from the source. Thus in theory, one expects that a solution to the full Navier-Stokes
equations over the entire flow field (including the observer), would provide the desired solution.
However, this approach for practical problems is beyond any currently available computing capac-
ity and will be so in the foreseeable future [43]. However, once the aerodynamic field around a
rotor blade has been estimated, the application of the appropriate acoustic propagation equation
can yield the acoustic pressure at the observer location [44].
Some of the earliest acoustics research with regards to rotating systems was focused on the pro-
peller. By the late 1930s it was known that for rotating blades, both loading and the blade thickness
22
could generate noise by different mechanisms. The first estimate of harmonic loading noise due
to the steady loading on the blade was obtained by Gutin [45]. This early theory though based on
simple aerodynamic estimates of the loading brought out the extremely directional nature of the
loading noise and its dipole nature. Demming [46] and Ernsthausen [47] worked independently
on the problem of thickness noise in propellers. These loading and thickness noise estimates were
derived for propellers that were simply rotating in one place. Garrick and Watkins [48] extended
Gutin?s results to the propeller in forward flight in the early fifties.
By the 1960s the noise of helicopters became an important issue. It was realized that unsteady
blade loading in addition to steady loading was a significant contributor to the discrete and broad-
band noise of the helicopter rotors. However, the acoustic theories developed earlier for propellers
were only applicable to helicopters in hover or axial climb, because they did not account for the
unsteady blade loading during the helicopter?s forward flight. Some of the first noise prediction
theories applied specifically to helicopter rotors were developed by Lowson [49] and Wright [50]
Lighthill?s [51, 52] paper where he recast the Navier-Stokes equation as a wave equation propa-
gating pressure was among the first to mathematically model pure aerodynamic sources (other than
monopoles and dipoles). This approach termed the ?acoustic analogy?, was originally derived for
jet noise and is not directly applicable to the rotor noise problem.
Working on similar lines as the Lighthill?s analogy, and using generalized functions, the Navier-
Stokes equation was recast into a non-homogeneous wave equation, which can be applied to any
arbitrary surface by Ffowcs-Williams and Hawkings [53]. This equation, now called the ?Ffowcs-
Williams and Hawkings Equation? is more general than other rotorcraft acoustic modelling and has
23
been used extensively for the rotor noise problem. The classic derivation assumes an impermeable
surface and the solution is derived using the Green?s function over free unbounded space. The
acoustic pressure can be expressed in tensor notation:
p(x,t) =? ??x
i
ZZ bracketleftbigg P
i jn j
r|1?Mr|
bracketrightbigg
dS
bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright
Loading (dipole) term
+ ??t
ZZ bracketleftbigg ?
0vn
r|1?Mr|
bracketrightbigg
dS
bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright
Thickness (monopole) term
(1.6)
+ ?
2
?xi?x j
ZZZ bracketleftbigg T
i j
r|1?Mr|
bracketrightbigg
dV
bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright
Quadrupole term
where, p represents the acoustic pressure at the observer, r is the distance between the acoustic
source and the observer, Mr is the Mach number of the source along the direction of the observer,
Pi j and Ti j are the local pressure and stress tensors respectively and n j represents the local normal
to the surface containing the acoustic sources. Finally, the terms within the square brackets are
evaluated at the right retarded time (time of acoustic emission from the source).
The acoustic pressure, p, in the far-field is given as the sum of three terms: the loading term,
the thickness term and the quadrupole term. The ?loading? term, also a surface integral, accounts
for the steady and unsteady aerodynamic forces of lift and drag on the surface. This term is dipole
in nature and radiates in a double-dumbbell shaped pattern perpendicular to the rotor plane for
noise due to lift and parallel to the rotor plane for noise due to drag. The ?thickness? term, a
surface integral, accounts for the displacement of the medium due to the thickness of the surface.
It is a monopole term and in the case of the helicopter, results in radiation mostly in the plane of
the rotor. The third term, a volume integral, is simply termed as a quadrupole and accounts for all
24
other sources including non-linearities at transonic Mach numbers, turbulence and aerodynamic
stresses produced in the flow-field. This term can be extremely complicated to compute and most
initial researchers either dropped this term all together or developed formulations which reduced
the complexity of the computation involved.
The Ffowcs-Williams Hawkings equation (Eqn. 1.6) itself has been the subject of significant
research in the past two decades and recast into more useful forms. Notable among them are
Farassat?s formulations [54, 55] which are used in many comprehensive rotorcraft codes including
WOPWOP [56].
While the ?dipole? (loading) term and ?monopole? (thickness) term relate directly to far-field
radiated noise due to airloads on the rotor blade, the ?quadrupole? term encompasses the entire
flow-field, including the aerodynamics of the rotor wake along with turbulent fluctuations and
other non-linearities all the way out to the observer. The quadrupole term is really a manifestation
of choosing a linear solution formulation of the rotor acoustic problem. This term also accounts
for non-linearities due to local variations in speed of sound induced by compressibility. Unfortu-
nately, this term is extremely complicated to calculate accurately and truly requires a full-blown
CFD estimation of the important flow-field variables. The effect of the non-linearities is usually
very small far away from the rotor blade and are neglected, and most formulations only try to cap-
ture the quadrupole term near the blade. Although this term does play an important role in BVI
noise generation, particularly at higher tip Mach numbers [57], it is neglected in most preliminary
calculations.
Farassat and Myers [58, 59] developed the Kirchoff surface formulation to eliminate the need
25
to estimate the quadrupole source term. The Kirchoff surface encloses the blade and the near
field wake so that the primary contribution of the quadrupole term is contained within the surface.
CFD methods are then used to compute the flow inside this surface [44], and to estimate the flow
velocities and pressure, and their spatial and temporal derivatives. These values are then input
into the acoustic propagation formulations to compute the far-field noise. Lyrintzis et al [43]
provide a good review of approaches and methods of implementation of the Kirchoff surface to
rotor problems. The Kirchoff surface can either surround the entire rotor and be fixed with respect
to the flow-field of interest, or it can encompass a single blade and rotate in the medium. Although
both these methods and the conventional method of dropping the effect of the quadrupole term
provide very similar results for low speed problems, in the transonic flow regime the non-rotating
Kirchoff surface is seen to give better results.
The impermeable Kirchoff [60] surface formulation is valid only in the region where the linear
wave propagation governs the flow. In regions close to the blade, where non-linear acoustic phe-
nomena dominate, unphysical solutions have been obtained by this method [4]. Also it has been
shown that the Kirchoff surface can give unreliable results in situations with vorticity transport-
ing across the surface. This is particularly important for rotor problems. di Fransescantonio [61]
revised the Ffowcs-Williams Hawkings (Eqn. 1.6) equation using a permeable surface boundary
condition. Recently many researchers have been employing the permeable surface formulation
for the rotor noise problem as it helps better capture the noise radiation due to aerodynamic non-
linearities around the blade [62, 63].
Caradonna et al [64] presented a comparison of various computational methodologies, to ex-
26
perimental results of BVI induced blade loads and noise. Full-fledged CFD, indicial methods using
blade element theory and aeroacoustics formulation using experimental blade pressures [65] were
compared to a controlled parallel blade vortex interaction. It was observed that most theoretical
approaches predicted blade loads reasonably well, when vortex parameters and blade motion were
accurately known. However, there were discrepancies in the noise prediction. Most approaches
over-predicted the magnitude and/or the pulse-width.
1.3.3 Experimental Approaches
Flight tests have been performed for a very long time to estimate helicopter noise for research
purposes, community noise acceptance studies and certification [66]. Microphones mounted on
the ground, or on tall poles or cranes [67] are used to obtain far-field noise information. The effect
of atmospheric absorption can be accounted for and studies can be conducted for different flight
maneuvers. However, using this technique it is hard to accurately measure the noise when the noise
signature or directivity changes during a flyby. Certain flight segments such as high speed flight
preclude averaging of the data and hence pose difficulties in accurate noise measurements.
The In-Flight Rotor Acoustic Program (IRAP) at NASA Ames developed by Schmitz and
Boxwell [9, 8, 68] consists of a fixed wing aircraft flying in formation with the helicopter be-
ing tested (Fig. 1.11). The fixed wing aircraft acts as an instrumented ?flying platform? for making
acoustic measurements. This approach has two distinct advantages over ground based measure-
ment approaches. The periodic data obtained can be ensemble averaged and tied to discrete aero-
dynamic events on the helicopter rotor. Moreover, the ?flying platform? can be flown at different
27
Figure 1.11: In-flight acoustic measurement technique [8]
azimuth and elevation angles at a fixed distance from the helicopter to obtain directivity informa-
tion.
A Mohawk (OV-1C) instrumented with microphones was flown in formation with a UH-1H
helicopter (Fig.1.11), positioning the helicopter to obtain periodic noise at the microphone on the
OV-1C. This was the first successfull attempt at characterizing the full-scale impulsive noise of
this helicopter. This flight test also showed that the helicopter cabin noise measurements are not
necessarily indicative of noise radiated outside, particularly for High-Speed Impulsive (HSI) noise.
Later, an instrumented Y0-3A was used to measure noise characteristics of the AH-1S and the UH-
1H. Tests were performed at different advance ratios and moderate rates of sink. It was shown that
BVI noise radiated mostly forward and below the main rotor.
28
Experiments conducted by Boxwell et al [16] suggested that the main non-dimensional param-
eters are the advance ratio (?), the thrust coefficient (CT ), rotor tip-path plane angle (?T PP), and
hover tip Mach number (MT ). The study also showed that when these parameters are matched,
full-scale flight BVI acoustics are comparable to experimental wind-tunnel BVIs for low to mod-
erate advance ratios. These non-dimensional parameters affect the radiated noise, primarily by
altering the vortex characteristics and wake structure. The change in thrust coefficient and tip path
plane angle affects the miss-distance and strength of the vortex thus affecting the induced pressure
on the blade surface. The hover tip Mach number and the advance ratio affect the basic vortex
characteristics as well the trajectory of the tip vortices, changing the interaction geometry.
Several wind tunnel tests have further explored the effect of these parameters on BVI noise.
Burley and Martin [69] present detailed time histories of BVI noise associated with a model BO-
105 helicopter in the DNW wind tunnel on a ground plane under the scaled rotor. It was implicitly
assumed that the model rotor acoustics were similar to the full-scale BO-105. The researchers
extensively covered the effect of tip path plane angle and advance ratio and concluded that BVI
noise peaks in a narrow range of tip-path plane angles and that this range reduces as the advance
ratio decreases.
The Higher Harmonics Control Aeroacoustic Rotor Test (HART) [70, 71, 72] program at the
DNW wind tunnel, tested an instrumented BO-105 rotor for various operating conditions with
and without applying Higher-Harmonic control (HHC). The wake geometry (including the vor-
tex strength and structure) was also measured using Particle Imaging Velocimetry (PIV) and Laser
Doppler Velocimetry (LDV). Several computational approaches have used these results for validat-
29
ing the acoustics and near wake aerodynamic predictions [73, 74, 75]. These experiments however,
in simulating a full BVI problem had the same rotor-wake coupling issue discussed earlier. The
wake geometry and blade motions were reported to have a very important effect on the acoustics
predictions.
The in-flight measurement approach was used once again by Yamauchi [76] to study the
acoustic characteristics of the S-76 and perform comparisons with full-scale wind tunnel tests.
Comparisons at low advance ratios between the time histories of wind tunnel and flight tests were
reasonable. However, at higher advance ratios (? > 0.25) the wind tunnel measurements showed
much higher blade-to-blade and revolution-to-revolution variability, and slightly different pulse
shapes compared to flight data, possibly due to wind tunnel turbulence. It was observed that peak
BVI noise radiation increased with increasing tip-path plane angle until it reached a maximum
value for a given advance ratio. Further increases in the tip-path plane angle resulted in a reduction
in peak BVI noise.
Sim and Schmitz [77] conducted a series of flight test experiments to establish the relation
between the azimuthal directivity of BVI and flight conditions such as rate-of-sink and forward
speed. A microphone instrumented boom was mounted on the helicopter while flying it at various
flight conditions. This set of experiments provides a particularly useful dataset as it allowed to keep
the microphones at precisely known location with respect to the main rotor during flight. Efforts
are also underway to instrument the helicopter with tip path plane measurement system to quantify
its role as a fundamental parameter for BVI noise radiation.
30
Figure 1.12: A schematic of the BVI experiment by Leverton
Experimental Simulations of BVI Noise
Among the first experimental studies of the BVI noise was performed by Leverton [78, 79]. He
used a series of jets impinging on a rotating blade while measuring the radiated noise (Fig. 1.12).
Although this experiment had several limitations, it was successful in establishing the general
origin of BVI noise as occurring due to a vortex interaction.
McCormick and Surendraiah [80] were the first to conduct controlled experiments with a sta-
tionary vortex. A semi-span wing mounted in a wind tunnel was used to generate a tip vortex,
which when convected downstream underwent a parallel interaction with a two-bladed rotor. The
31
rotor itself was non-lifting so that it did not generate any noticeable tip vortices. The strength of
the vortex and the miss distance could be controlled by changing the angle of attack and by mov-
ing the wing-tip relative to the rotor system. An independantly generated vortex provided known
parameters for the blade-vortex interaction and significantly reduced the complexity, enabling a
paramteric study of unsteady loads and acoustics. However, the upstream vortex strength was not
strong enough to be representative of full-scale BVI.
Several experiments have since been performed to study the Blade-Vortex interaction [81, 82,
83]. One particularly important experiment was a parallel Blade-Vortex Interaction conducted
by Kitaplioglu et al [84, 85]. A vortex shed from a fixed-wing tip interacted with a scaled OLS
blade further downstream in the 80?120 ft wind tunnel (Fig. 1.13). Blade surface pressures at
various spanwise locations were recorded simultaneously with far-field as well as near-field noise.
This experiment has since been the validation point for almost all BVI simulation methodologies
developed. However, the vortex size was about 15% of the rotor chord which is on the larger
side of typically encountered vortices during BVI. Thus it contained a lower frequency content
than is typical. Although the setup had the capability to move the rotor with respect to the vortex
trajectory it was not performed and no oblique BVI interaction cases were studied to determine the
noise radiation characteristics of the rotor.
1.4 Objectives of Current Research
Although significant amount of research has gone into studying the BVI noise problem in the
recent past, quiet rotor designs are hard to come by in the real world. Accurately predicting the
32
Figure 1.13: A schematic of the wind tunnel experimental setup used by Kitaplioglu et al [84]
airloads and the resulting rotor noise has been a challenging problem owing to the complex wake
structure behind the rotor. Past experience has shown that accurately predicting BVI noise depends
strongly on the tip vortex characteristics like vortex core size, peak swirl velocity of the vortex and
the tip vortex geometry during the interaction [71]. Another key parameter determining accurate
noise prediction is the blade aeroelastic deflection [74]. Modifications to the rotor characteristics
such as the tip Mach number, blade planform etc. result in significant changes to the tip vortex
characteristics and hence further complicate the accuracy of the prediction.
Approaches to study the simplified BVI problem in a controlled environment by decoupling the
interacting vortex from the rotor parameters and blade geometry have been useful, albeit limited in
their scope. Most previous experiments have been focused on the parallel BVI situation. Moreover,
the vortex generated in the wind-tunnel is somewhat larger compared to the typical tip vortex
undergoing BVI, resulting in lower frequency content. These experiments have mostly focused on
the peak noise direction, and have not covered azimuthal variation.
The primary objective of the present study is to simulate BVI through the interaction be-
tween the rotor blade and controlled gust which replicates the key features and governing param-
33
eters of the vortex induced velocity in a hover environment. This Blade-Controlled Disturbance-
Interaction, termed the BCDI, is the primary focus of the present study. The experimental facility
needed to achieve this objective is built from the ground up. The controlled disturbance is provided
in the form of a gust field with a velocity profile tailored to replicate that of a typical tip vortex.
The first objective therefore, is to design and fabricate a ?gust generator? that outputs a disturbance
field that replicates the impulsiveness and the induced velocity profile of a typical tip vortex. The
gust field needs to be well-characterized and have a relatively low turbulence to ensure repeatabil-
ity. The nozzle should also be orientable at any angle with respect to the rotor blade to simulate
oblique interactions and to match realistic trace Mach number.
The rotor stand built for the experiment consists of a single-bladed, non-lifting to reduce the
complexity of the problem. It has the capability to spin at full-scale tip Mach numbers in order
to accurately scale the acoustic phenomena. The large acoustic chamber present at the University
of Maryland is used for the experiment. A set of tests were conducted to check the reflection
characteristics within the chamber. The chamber was then treated with acoustic material to improve
the sound absorbing characteristics of the wall for the frequency range expected.
The ultimate objective is to study in detail the acoustics of the BCDI at different tip Mach
numbers and interaction angles and identify the radiation characteristics, including directionality
for different trace Mach numbers. This will help identify the key parameters affecting the noise ra-
diation. As mentioned earlier, in order to achieve oblique interaction angles, the nozzle of the gust
generator is orientable with respect to the blade. Furthermore, to obtain the detailed directionality
information acoustic data is recorded at several microphone locations around the chamber.
34
Another objective of the present research is to study the effect of spanwise phasing on the radi-
ated noise and directionality trends. In order to study contribution of the spanwise blade sections
a lifting line approach combined with unsteady indicial aerodynamics and Farassat?s formulation
1A for calculating the acoustics is used. This approach will be useful in helping design quieter
rotor blades.
35
Chapter 2
Approach
2.1 Experimental BVI Simulation ? The BCDI Experiment
This chapter explains in detail the fundamental ideas behind the experimental approach used in
this study along with the experimental setup and the associated theoretical modeling to understand
the fundamental physics behind the BVI acoustics.
As described in the previous chapter, predicting BVI noise involves two steps:
1. Estimating the unsteady aerodynamic loads on the blade due to the tip vortex interaction and
2. Estimating the radiated acoustics resulting from the changes in blade aerodynamic loads.
The first step of the approach enumerated above is extremely complicated owing to the tightly
coupled nature of the helicopter blade aerodynamics to the wake structure.
The approach detailed in this dissertation is to study the BVI problem by decoupling the vortex
characteristics from the rotor characteristics. This simplifies the problem significantly and allows
36
studying the blade response to a fixed velocity field that simulates a vortex of known character-
istics. This in turn, allows the comparison of the acoustic response of the rotor blade to changes
in blade planform and other features. In the present experiment the tip vortex is simulated by an
independently controlled velocity field which is not dependent on the characteristics of the rotor
being tested. This controlled velocity field is tailored so as to match the essential tip vortex char-
acteristics responsible for BVI. A crucial hypothesis this approach is based on is that the unsteady
blade aerodynamic response to the controlled velocity field is similar in character to the response
during an interaction with a real tip vortex. This simulated BVI experiment is thus referred to in
the dissertation as the Blade Controlled-Disturbance Interaction or BCDI.
Fig 2.1 shows the top and side view of a two bladed helicopter rotor exhibiting blade-vortex
interaction. The top view (Fig. 2.1(a)) clearly suggests that the rotor blade passes near multiple
vortices during one revolution and that each interaction is strongly dependant on the angle the blade
makes with the interaction vortex. This interaction angle, combined with the tip Mach number
of the blade and the advance ratio determines the three-dimensional geometry of the interaction,
and hence plays a crucial role in the BVI noise generation process [22, 86]. The side view of
the schematic (Fig. 2.1(b)) shows the vertical distance between the vortex and the rotor blade ?
usually referred to as the miss distance. The miss distance determines the velocity field induced by
the vortex on the rotor blade section, and hence the unsteady aerodynamics during the interaction.
In experimentally simulating a blade-vortex interaction it is important to faithfully replicate the
both the induced velocity field as well as the overall three-dimensional geometry of the interaction.
If one were to consider a near parallel interaction, the BVI aerodynamics is mostly two-
37
(a) Top View of a Helicopter In BVI
(b) Side View of a Helicopter in BVI
Figure 2.1: Helicopter BVI geometry for a two-bladed rotor
38
Figure 2.2: Two-dimensional schematic of the BVI
Figure 2.3: Typical vortex induced velocity profile and its gradient
dimensional (Fig. 2.2) inboard from tip of the blade. A sketch of the two-dimensional chord-wise
cross-section of a typical vortex induced velocity profile at the quarter chord location along with
the gradient of the velocity profile with time is shown in Fig. 2.3. A rapid change in induced ve-
locity occurs as the blade passes near the vortex and results in sharp changes in blade aerodynamic
loads (Fig. 2.4). This sharp change induces a reactionary changing pressure on the fluid as per the
loading term of the Ffowcs-Williams and Hawking?s equation (Eqn. 1.6 on pg. 24). A part of this
changing pressure propagates outwards as a radiated impulsive pressure pulse.
39
-0.1
-0.08
-0.06
-0.04
-0.02
 0
 0.02
 0.04
 0.06
 0.08
 0.1
 0  10  20  30  40  50  60  70  80
Sectional Lift Co-efficient (C
l)
Rotor Azimuth (Deg)
Figure 2.4: Sectional lift coefficient induced by a vortex on the airfoil
40
Since BVI noise is primarily a result of the unsteady lift ? which is caused by the vertical
component of the vortex induced velocity ? only the component perpendicular to the rotor plane
has been simulated at this time in the BCDI experiment. The important characteristics required
to replicate the impulsiveness of the problem are: (i) the magnitude of the peak induced velocity
and (ii) the gradient of the induced velocity. In the present BCDI approach, a controlled vertical
velocity field is provided in the form of a gust located at a fixed azimuthal position with respect to
the rotor (Fig. 2.5(a)).
The nozzle of the gust generator is designed so that the key vortex velocity characteristics,
viz. the vertical velocity gradient (which defines the impulsiveness of the problem) and the peak
velocity, are replicated. Unfortunately, in this simulation approach it is not possible to replicate the
negative portion of the vortex induced velocity. However, the fundamental nature of the problem
remains unchanged as the impulsiveness can still be sufficiently replicated. The three-dimensional
geometry of the interaction is matched by orienting the gust at different angles with respect to the
blade. The gust when oriented parallel to the blade replicates a parallel Blade-Vortex Interaction,
while an oblique interaction with a straight line vortex is replicated by orienting the gust at an angle
with the blade. However, it should be noted that in a real BVI, the tip vortex filament undergoing
the interaction with the blade is curved (Fig. 2.1(a)) and not straight. This can be achieved by using
a curved nozzle and is left for future work (Fig. 2.5(b)).
Apart from the vortex vertical velocity characteristics and geometry, it is also important to
match the rotor characteristics to scale the phenomenon faithfully. In real BVI conditions the
helicopter is almost always in forward flight and most often in mild descent. As discussed earlier, in
41
(a) The BCDI approach
Curved Nozzle
(to match BVI)
Straight Nozzle
TOP VIEW
(b) Straight and curved interaction with different nozzle
shapes
Figure 2.5: Schematic of the experiment
42
Vc
?
V? +?Rsin(?)
? ?
VT R
BVI Trajectory
Figure 2.6: Trace Mach Number of BVI
order to carefully control the interaction parameters, the present experiment is conducted in hover.
Thus it is difficult to precisely match the spanwise variation in velocity during the interaction.
However, for problems that depend on wave collection processes, it is very important to match
the tip Mach number of the blade. Therefore, the tip Mach number of the hovering rotor in the
experiment has to be matched to the advancing tip Mach number of the rotor in forward flight
undergoing BVI. An important point to remember is that the interaction geometry resulting from
the epi-cycloid like pattern laid out by the tip vortices in space, is a result of the forward speed
combined with the hover tip Mach number of the rotor. When the rotor blade sweeps over the tip
vortex (Fig. 2.6), it can be considered as a series of two-dimensional interactions, each of which
radiate noise in the medium. The rate at which these ?sectional acoustic sources? sum in the
medium is critical to the resulting phasing and hence the strength and directionality of the radiated
noise. The velocity of these ?sectional sources? non-dimensionalized with respect to the speed
of sound is termed the trace Mach number. The trace Mach number is given by the following
43
equation:
MT R = ?r(?+sin?b)a
0 sin?
(2.1)
While the acoustic phasing along the rotor plane is determined by the trace Mach number profile,
the actual three-dimensionality of aerodynamics is determined by the interaction geometry.
2.2 The Assembled Experimental Setup
Fig. 2.7 shows the layout of the experiment along with the additional acoustic treatment (
melamine wedges) and microphone positions inside the chamber. The rotor stand is positioned to
one side of the chamber in order to maximize the distance from the rotor hub to the microphone
locations. The fan-blower of the Gust Generator is placed outside the chamber to reduce extraneous
noise sources inside the chamber. The nozzle of the Gust Generator is placed vertically below the
rotor stand as seen in Fig. 2.8.
2.3 Experimental Design and Calibration
The experimental setup consists of many components (see Fig. 2.9), each of which was devel-
oped and tested, including the ?Gust Generator?, the Rotor Test Stand, and the Acoustic Chamber
alongwith their respective instrumentation. The following sections describe in detail the various
components of the setup.
A schematic of the hardware necessary to perform this experimental BVI simulation is shown in
Fig. 2.10. The hovering rotor stand along with the gust generator is placed in an acoustic chamber.
44
Figure 2.7: Layout of the different components inside the acoustic chamber
45
Figure 2.8: Schematic of the final assembled experimental setup
46
Figure 2.9: Photograph of a portion of the experimental setup inside the chamber
47
Figure 2.10: Schematic of experimental setup
While the acoustic chamber was already available at the beginning the program, the other critical
components have been developed and tested in-house as a part of this experiment.
2.3.1 The Gust Generator
The ?Gust Generator? shown in Fig. 2.11 is a critical part of the BCDI setup. It is basically
an open jet wind-tunnel with a specially designed nozzle so that the obtained velocity profile at
the blade-passage section mimics a vortex induced profile. The gust generator consists of various
sections, each performing a certain function in obtaining a specially tailored low turbulence jet at
48
Figure 2.11: Schematic showing different sections of the ?Gust Generator?
49
the blade passage location. An important requirement was the ability to orient the nozzle at any
angle with respect to the interacting blade to simulate oblique interactions. This is achieved with
the help of the turn-table sections which share a circular cross-section. The details of the key parts
of the ?Gust Generator? are given in Appendix A.
The most important section of the gust generator is the nozzle, which has been designed based
on the concept of free jet mixing. As mentioned previously, the nozzle simulates the vertical veloc-
ity field of the vortex by attempting to replicate the asymmetry of the vertical velocity component.
To provide vertical flow-field asymmetry, the curved wall was built shorter than the flat wall, as
shown in Fig. 2.12. This results in greater mixing on the curved wall, thus smoothing out the
flow and resulting in a reduction of the velocity gradient on the curved side. For a free jet, the
jet width is proportional to 1/l, where l is the mixing length. As the mixing width on the curved
side is greater than that on the flat wall of the nozzle, the flow diffuses and spreads out to a greater
extant on the curved side than on the flat side, resulting in an asymmetric flow profile as seen in
Fig. 2.13(a). Since the main feature of the flow is the sharp rising edge, the classical technique of
boundary layer suction was employed to control the velocity gradient on the flat side. Slots were
made on the flat side (Fig. 2.12) to provide boundary layer suction, further increasing the gradient
of the velocity on the flat wall side.
Mean Flow Characteristics
A set of measurements were performed at three positions along the length of the nozzle,
viz. y = 0.25L, y = 0.5L and y = 0.75L to ensure the uniformity of the flow across the nozzle
50
Mixing Zone
Slo
ts
to
rem
ov
ea
ir
Nozzle Outlet
Flow Entering Nozzle
R2
R1
Figure 2.12: Schematic of the final nozzle design
51
length. Fig. 2.13 shows the mean vertical and chordwise velocity components (wm and um, resp.)
measured at each location. A second set of measurements were performed at different heights
above the nozzle at the mid-point locations (y = 0.5L), viz z = 0.625inches, 0.875inches and
1.275inches (Fig. 2.14). These data were taken with a calibrated two-component hotwire probe.
The main character of the flow-field necessary for replicating BVI is clearly shown. The span-wise
variation in velocity is seen to be almost negligible. As the height of blade passage location above
the nozzle increases, the flow starts diverging on the flat side of the nozzle, decreasing the slope of
the rising edge of the velocity profile. This suggests that an optimal height exists for simulating a
chosen BVI.
The various other sections constituting the gust generator along with detailed turbulence mea-
surements of the flow are described in Appendix A
2.3.2 Comparison of Gust to Vortex Induced Velocity Profile
To complete the comparison, it is useful to know the type of BVI and the equivalent vortex
characteristics being simulated by the present B-CD-I experiment. For the present nozzle, the
event that is chosen to set the strength of the vertical velocity field is a parallel BVI.
The following analysis can be used to establish some of the equivalent vortex characteristics
that are simulated. Using Biot-Savart Law, we know that for a parallel BVI, the induced velocity
on the blade is given as,
w = ?Rpi Ct? zhz2
h +r2c
?
?
?? xzh
1+
parenleftBig
x
zh
parenrightBig2
?
?? (2.2)
52
(a) Vertical velocity component(Wm)
(b) Chord-wise velocity component(Um)
Figure 2.13: Variation of velocity distribution across the span of the nozzle
53
(a) Vertical velocity component (Wm)
(b) Chord-wise velocity component(Um)
Figure 2.14: Variation of velocity distribution with height above the nozzle
54
Differentiating Eqn. 2.2 and equating to zero, we get xp, the point where w peaks as,
xp = zh (2.3)
This gives,
wp = ?Rpi Ct? zhz2
h +r2c
(2.4)
Since we are trying to achieve equivalence between the interaction in the hover experiment
and the real BVI events, we can idealize the velocity obtained with the nozzle at the blade pas-
sage location to be represented by Eqn.2.2. For the gust generator case, the peak velocity from
Fig. 2.13(a) is 155.4ft/s, and occurs at xp = 0.0572 (non-dimensionalized w.r.t the blade chord).
This is equivalent to a miss distance of 7% and the core radius of 5% of the blade chord signifying a
strong BVI. It is possible to modify these equivalent vortex parameters by changing the gust peak
velocity and by adjusting the height of blade passage above the nozzle. Fig. 2.15 compares the
measured gust vertical velocity with the induced velocity due to such a vortex. It is observed that
the peak and gradient of the vortex induced velocity and the gust match closely. However, the tail
of the gust falls off more rapidly than the vortex induced velocity. The impulsive noise from the
BVI primarily results from the rising edge of the velocity profile. Since this is closely replicated in
the gust velocity field, it is assured that the main acoustic peak will be captured in the experiment.
However, the steeper falling edge in the gust velocity field will result in a change in the character
of the acoustic pulse.
55
?0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.40
20
40
60
80
100
120
140
160
Nozzle Width (inches)
Vertical Velocity (ft/s)
 
 
Measured Velocity Profile
Vortex Induced Profile
Figure 2.15: Comparison of measured gust and vortex induced velocity
56
2.3.3 Rotor Test Stand and Operation
The rotor (shown in Fig. 2.9) is a rigid single-bladed counter-weighted 1:7 scale, untwisted,
model UH-1H blade with the ability to spin to high RPMs. Having a single blade greatly reduces
the chances of rotor-to-rotor aerodynamic interference, providing a cleaner experimental setup.
Further, the blade is run at a small pitch angle (2?), resulting in a very small thrust in order to
prevent the blade?s wake from staying in the rotor plane. The blade is positioned to pass 1.62 inches
above the outlet of the nozzle, close enough to maintain the simulated vortex characteristic, but far
enough to minimize the interference effects of the nozzle. The whole setup is oriented so that
the tip of the blade passes well within the gust field and hence is free of the three-dimensionality
associated with the outer edge of the nozzle (Fig. 2.16). The inboard half of the blade, contributes
little to the acoustic field as the Mach number is very small. Moreover, if the nozzle extended
inboard, these blade sections could experience a high angle of attack resulting in stall. In order to
avoid such complications, the inner edge of the nozzle is located at the 48% spanwise section of
the blade.
The rotor stand is also instrumented with thermocouples on the bearings and accelerometers.
The signals from these sensors are sampled 10 times every second and are constantly monitored to
ensure the safety of the system. A magnet attached to the shaft of the rotor stand triggers a hall-
switch once every revolution. There is also a 10bit quadrature encoder that provides 1024 pulses
every revolution. Since this signal perfectly phase-locked to the shaft it is used to estimate the blade
location accurately at any given time instant. Accelerometer recordings when striking the rotor test
stand with an impact hammer were used to establish safe operating conditions. In particular, it was
57
Figure 2.16: Schematic of the setup showing the relative positions of the gust and the rotor blade
during interaction
found that the operating close to 2500RPM resulted in some vibrations in the rotor, and hence was
avoided for the experiment (see Appendix B). A summary of the rotor operational characteristics
is presented in table 2.1.
2.3.4 Acoustic Chamber
The acoustic chamber is an octagonal chamber that is 20ft?20ft wide and 30ft tall. The walls
of the chamber consist of 8inches of fiber glass sandwiched between two metal plates. The metal
plate on the inside of the chamber is porous. This construction is mainly designed to prevent
external noise from contaminating the acoustic environment, but also has limited acoustic treatment
(the fiber glass) to minimize wall reflections within the chamber. The relatively small size of the
chamber implies that it is not ideal for testing low-frequency noise sources. The thickness of the
58
1:7 scale untwisted UH-1H single-bladed rotor
Blade airfoil NACA 0009
Airfoil chord 3 inches
Blade radius 38.75 inches
Blade pitch angle -2?
Max. rotor RPM 2640 RPM
Max. tip Mach number 0.77
Table 2.1: Some key characteristics of the rotor
fiber-glass filled chamber walls result in a cutoff frequency of about 500Hz. While this frequency is
acceptable for the BVI experiment, it was also found that the walls were not sufficiently absorptive
and tended to reflect significant amount of the impulsive noise.
A test was designed to estimate the amount of sound reflected by a high frequency noise pulse
with the aim of improving the chamber characteristics. A speaker was placed close to the expected
interaction location and an impulsive signal generated by a function generator was fed to it through
an amplifier. The fed signal was chosen to match the frequency range expected from simulating
the BVI experiment ? 200Hz to 2000Hz.
Fig. 2.17 shows a representative example of the direct and the reflected acoustic pulses mea-
sured at one microphone location. The acoustic pressure measured at the microphone has been
normalized by the maximum observed pressure, since we are only interested in relative magni-
tudes. The first reflection off the wall behind the microphone shows only a 33% (?2.5dB) re-
duction in peak-to-peak value. For a good acoustic experiment we require at least a factor of
59
0 1 2 3 4 5?1.5
?1
?0.5
0
0.5
1
Time (msec)
Normalized Acoustic Pressure
 
 
Before Treatment
Main Pulse
First Reflection
Second 
Reflection
Figure 2.17: Reflection characteristics of chamber prior to treatment
three (?9.5dB) between the main signal and any reflected signals or background noise. In order
to improve the absorption characteristic of the chamber various sound absorbing materials were
tested on the chamber wall to decide on the ideal treatment option. Fiber glass panels of different
thickness varying from two inches to six inches and two different types of foam with and without
wedge shapes were tested Finally, the six inch deep melamine foam wedges were chosen because
they had the best absorption characteristic providing a ratio 5 (?14dB) between the main pulse and
the reflected pulse (Fig. 2.18). It was decided not use deeper wedges as it would overly reduce the
measurement space available in the chamber.
60
0 1 2 3 4 5?1.5
?1
?0.5
0
0.5
1
Time (msec)
Normalized Acoustic Pressure
 
 
After Treatment
Main Pulse
First Reflection
Second 
Reflection
Figure 2.18: Reflection characteristics of chamber after acoustic treatment
61
2.3.5 Microphone Measurement System
The chamber is instrumented with a vertical microphone array consisting of four 0.5 inch B&K
microphones placed at various elevation angles. The microphones are mounted on a traverse that
can be moved to different azimuthal locations, with respect to the rotor hub, allowing the measure-
ment of the directional nature of the acoustic field. Figs. 2.19 and 2.20 shows the top and front
view of different microphone locations used to obtain data during the course of the experiment. It
is known that for a parallel interaction the peak azimuthal directivity of the noise is about a per-
pendicular line drawn from the 75% span section of the rotor blade at the interaction. This is close
to 104? azimuth microphone location. The other microphones were placed about 10??15? apart
from each other one either side of the peak azimuth location. The microphones vary from 2.8R to
3.5R in distance from the hub and can be considered to be in acoustic far-field for the experiment.
It should, however, be noted that this distance is not ideal, but acceptable because the BCDI events
occur only over half the blade span.
2.3.6 Data Acquisition and Reduction Technique
The data for the four microphones were obtained simultaneously using a 16 bit data acquisition
system sampled at 50kHz and triggered by a 1/rev hall sensor mounted on the rotor stand. The 1024
pulses per revolution signal from the encoder mounted on the rotor shaft is also simultaneously
recorded. As mentioned earlier this can be used to provide the azimuthal location of the blade at
any instant of time to 0.35? accuracy.
For each microphone data is recorded for close to 100 rotor revolutions after an initial start up
62
Figure 2.19: Top view of microphone measurement locations
63
Figure 2.20: Side view of microphone measurement locations
64
Rotor RPM 1950 2108 2260 2410 2640
tip Mach Number 0.569 0.614 0.659 0.702 0.768
Table 2.2: Tip Mach numbers tested
period to let the flow transients die down. However, because power fluctuations and the accuracy
of the motor controller, the rotor RPM is not always constant over this time period. The fluctuation
in RPM is ?2 RPM about the nominal value. In order to perform the averaging the 1024 pulse
per revolution signal is used to add the acoustic time history corresponding to the correct blade
location. This is very accurate since the encoder is fixed to shaft and records the variations in RPM
faithfully. The microphone data corresponding to time samples in between two successive pulses
are obtained by interpolation. The correct acoustic time histories are then summed over 80 such
revolutions and averaged.
2.4 Experimental Cases Studied
A controlled experiment such as this one, offers the possibility of wide variation in parameters.
A total of five rotor tip Mach numbers (Table 2.2) were studied. At each of these tip Mach numbers
four different interaction geometries (discussed below as Cases 1-4) were studied.
2.4.1 Case 1 ? Parallel BCDI
The first set of experiments performed were for the parallel interaction (Fig. 2.21(a)). Although
perfect parallel Blade-Vortex interactions do not occur in a helicopter because of the curvature of
65
the tip vortex trajectory, near parallel interactions (Fig. 2.21(b)), where the trace Mach number is
well above supersonic (Fig. 2.21(c)) over most of the blade span do occur and have very similar
acoustic radiation characteristics to the parallel interaction.
The parallel BCDI performed in the acoustic chamber using the straight nozzle has an infinite
trace Mach number through the entire blade span. Thus, it is more impulsive than the near-parallel
(slightly curved) BVI. The testing with a slight curved nozzle to match the right trace Mach number
profile for the near-parallel BVI is left for a future effort.
2.4.2 Oblique BCDI
Most of the previous experiments on BVI in conducted in wind tunnels [64] have focused pri-
marily on parallel BVIs. The experiment described in this dissertation takes the understanding of
BVIs a step further with the ability to study oblique interactions. As mentioned earlier, the inter-
actions are conducted with a straight nozzle. The oblique interactions in the current experimental
setup are obtained simply by orienting the nozzle at the required angle with respect to the blade.
This is achieved with the help of the two sections of the gust generator that share a circular cross-
section (see Fig. 2.11) so that the top three sections including the nozzle can be rotated without
affecting the flow through the nozzle.
A set of three oblique interactions have been studied and are presented here. All the interac-
tions start at the tip of the blade and sweep in-board as shown in the schematics. The result of
this orientation is a decelerating trace Mach number profile, similar to the oblique interaction in
Figs. 1.10(c) & 1.10(d) in Chapter 1. The trace Mach number variation determines the speed of
66
?
(a) Schematic of the parallel in-
teraction in the experiment
?
(b) Schematic of a near-parallel
BVI in the real helicopter
(c) trace Mach number profile for near-
parallel BVI
Figure 2.21: Comparison of the parallel interaction in the experiment with a real BVI
67
Mtr
Case 2 ? 3.3? at blade tip
?
(a)
0 0.2 0.4 0.6 0.8 10
2
4
6
8
10
12
14
Rotor Span (r/R)
trace Mach number (M
tr)
(b)
Case 3 ? 8.8? at blade tip
?
(c)
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Rotor Span (r/R)
trace Mach number (M
tr)
(d)
Case 4 ? 15.3? at blade tip
?
(e)
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Rotor Span (r/R)
trace Mach number (M
tr)
(f)
Figure 2.22: Schematic of the oblique interaction angles and corresponding trace Mach number
profiles (MT = 0.702)
68
the acoustic sources in the medium, and hence the phasing of the waves from these sources. This
affects the radiation patterns in the plane of the rotor. For the real helicopter BVI, the trace Mach
number profiles contain within them information about the advance ratio of the helicopter (?) and
the tip Mach number of the rotor. While the experiment is performed in hover, the trace Mach
number profiles obtained by orienting the nozzle match similar conditions as in helicopter forward
flight case.
69
Chapter 3
Experimental Results
The previous chapter discussed the experimental setup in detail. The number of possible pa-
rameter variations in this experiment is quite extensive. For the present dissertation, the parameter
variations has been restricted to values that are closer to those that occur in real helicopter BVI
situations. As discussed earlier, in the real BVI case, the trajectory of the interaction follows an
epicycloid-like geometry, the nozzle in this experiment that is used to simulate the vortex induced
velocity is not curved. However, the interaction between the rotor blade and straight gust captures
most of the relevant physics with regards to the aerodynamics as well as the acoustics. This chapter
covers the experimental results obtained during the study, beginning with parallel interaction and
later discussing the oblique interaction angles.
70
0 100 200 300 400 500 600 700 800 900 100020
30
40
50
60
70
80
90
100
110
120
Frequency (Hz)
SPL (dB)
 
 
Gust
Typical BCDI event
Fan/Motor Rotational 
Harmonics
Figure 3.1: Power spectrum of the gust flow noise
3.1 Data Quality
3.1.1 Background Noise
Fig. 3.1 shows the acoustic power spectrum of the noise due to the gust flow from the nozzle
inside the chamber at the microphone azimuth and elevation of 129? and 53.75?, respectively. The
fan/motor powering the gust is spinning at close to 1210 revolutions per minute, resulting in a few
harmonics associated with this frequency. Prominent are the first (20.22Hz), second (40.44Hz) and
the eleventh (222.42Hz) harmonic, the last one being present because the fan has eleven blades.
The total noise generated is less than 80dB. This is more than 20dB less than the noise of a typical
BCDI pulse shown in the figure.
71
40 60 80 100 120 140 160 1805
10
15
20
25
30
35
40
Mic Azimuth (Deg)
Signal?to?Noise Ration (dB)
 
 
53.75o
41.4o
27.6o
Figure 3.2: Ratio of main acoustic pulse to the first reflected pulse
3.1.2 Acoustic Pulse Reflection
Once the entire setup was assembled inside, the chamber was re-evaluated to check for unac-
ceptable reflections at every microphone location used for the experiment using the method out-
lined in section 2.3.4. Figure 3.2 shows the ratio of peak-to-peak amplitudes of the direct acoustic
pulse and the first reflection for each microphone. Except for the extreme azimuthal locations of the
microphones (? > 140?) the ratio of the direct acoustic pulse to the first reflected pulse is greater
than 15dB. Even at the highest azimuthal location the ratio is more than 10dB for the topmost mi-
crophone and the data at that location is therefore, quite reliable. Moreover, since the experiment
72
is run with a single-bladed rotor, the acoustic pulse reflected off the wall does not overlap with the
acoustic pulse corresponding to the interaction event.
3.1.3 Repeatability of Acoustic Data
Fig. 3.3 shows the revolution-to-revolution variation in the measured noise for the parallel
interaction case at the topmost (53.75? elevation) microphone placed at 104? azimuth at 0.612 MT .
The figure shows instantaneous data from 80 revolutions plotted on top of each other along with
the ensemble averaged data. The total variation in magnitude of noise from revolution to revolution
is less than 5%. Moreover, azimuthal variation of the event is less than 0.2? corresponding to the
time interval between successive samples recorded by the data acquisition system.
3.2 Noise radiation due to nozzle presence
The presence of the nozzle very close to blade (1.62 inches below) results in some radiation of
impulsive noise even without the gust turned on, as the blade passes over it. This noise radiation
is most likely because of the fluid that is dragged along by the blade having to accelerate over the
nozzle wall.
3.2.1 Case 1 ? Parallel BCDI
Figure 3.4 shows the SPL trends for radiated noise, with the rotor running over the nozzle
? without the gust turned on ? for all the 30 microphone locations for the parallel BCDI. The
peak noise is about 108dB. As can also be seen from the figure the radiation reduces when the
73
155 160 165 170 175
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Un?Averaged
Averaged
Figure 3.3: Revolution-to-Revolution fidelity of the rotor setup
74
40608010012014016018090
95
100
105
110
115
120
Rotor Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
53.75
41.43
27.62
Rotor Direction
Figure 3.4: SPL trends of noise radiation due to the nozzle ? parallel BCDI
microphone elevation angle increases, unlike the BVI situation where the noise increases as the
microphone elevation increases. Moreover, there is not much azimuthal variation in the noise. The
azimuthal variation is only about 7dB for the lower microphone elevation, while for the topmost
microphone it is less than 5dB.
Figure 3.5 shows the variation of sound pressure level at the 107? azimuth microphones as a
function of the peak gust velocity as the gust strength is increased. At the first non-zero gust veloc-
ity ( 80ft/s) shown in the graph, the sound pressure levels are almost equal for the three elevations.
At the highest gust strength (corresponding to a peak gust velocity of 160ft/s), the difference be-
75
0 20 40 60 80 100 120 140 160106
108
110
112
114
116
118
Peak Gust Velocity (ft/s)
Acoustic Pressure (SPL)
 
 
53.75o
41.43o
27.62o
Figure 3.5: SPL trends with gust strength
tween the gust-on and the gust-off (0ft/s) case is about 12dB for the topmost microphone and 8dB
for the lowest. Moreover, the velocity profile at the highest peak velocity case matches closely
with the original design point discussed previously in Sec. 2.3.2.
Figure 3.6 shows the time history recorded at the three microphones at the 107? azimuth. The
figure shows the acoustic pressure time histories for the three microphone elevations with and
without the simulated vortex velocity profile. The noise recorded at the microphones without the
gust turned on, is impulsive and occurs over the same azimuthal range as the main BCDI event,
confirming that it is due to the proximity of the nozzle. Moreover, the pulse radiated by the nozzle
interaction is of opposite sign compared to the BCDI event. However, the noise radiation from the
blade due to the nozzle presence alone is significantly lower than total noise radiated when the gust
76
30 40 50 60 70 80?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(a) Microphone elevation = 53.75?
10 20 30 40 50 60
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(b) Microphone elevation = 41.43?
340 350 360 370 380 390
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(c) Microphone elevation = 27.62?
Figure 3.6: Acoustic time history comparison with and without the gust, showing the effect of the
nozzle
77
is turned on. In order to remove the effect of the nozzle from the acoustic data, the noise from the
nozzle alone (without any flow) is subtracted from the total noise radiated. This not only removes
the effect of the nozzle on the acoustics, but also eliminates the thickness noise and steady loading
noise from the blade as it is of equal magnitude in both the situations. All further results presented
are with the effect of the nozzle subtracted from the data and with the peak gust velocity at 160ft/s.
3.2.2 Case 2 ? 3.3? Oblique BCDI
Fig. 3.7 shows the noise levels due to the nozzle interference at all the microphone locations.
The microphones at the lower elevation record more noise than at the higher elevation angles for
most of the microphone azimuths. The radiation from the nozzle is opposite in sign to the total
noise radiation, as can be seen from Fig. 3.8. However, the noise radiated due to the interference
effect from the nozzle is significantly lower than the total noise radiated at all the microphone
locations.
3.2.3 Case 3 ? 8.8? Oblique BCDI
Fig. 3.9 shows the noise levels due to the nozzle interference at all the microphone locations.
The microphones at the lower elevation record more noise than at the higher elevation angles for
most of the microphone azimuths. The radiation from the nozzle is opposite in sign to the total
noise radiation, as can be seen from Fig. 3.10. However, the noise radiated due to the interference
effect from the nozzle is significantly lower than the total noise radiated at all the microphone loca-
tions. Moreover, the noise levels for this interaction angle are lower than the previous interactions.
78
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.7: SPL trends of noise radiation due to the nozzle ? Case 2
79
405 410 415 420 425 430 435 440 445 450
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(a) Microphone elevation = 53.75?
370 375 380 385 390 395 400 405 410 415
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(b) Microphone elevation = 41.43?
350 355 360 365 370 375 380 385 390 395
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(c) Microphone elevation = 27.62?
Figure 3.8: Acoustic time history comparison with and without the gust, for Case 2 at ? = 120.9?
(MT = 0.702) 80
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.9: SPL trends of noise radiation due to the nozzle ? Case 3
3.2.4 Case 4 ?15.3? Oblique BCDI
Fig. 3.11 shows the noise levels due to the nozzle interference at all the microphone locations.
The microphones at the lower elevation record more noise than at the higher elevation angles for
most of the microphone azimuths. The radiation from the nozzle is opposite in sign to the total
noise radiation, as can be seen from Fig. 3.12. However, the noise radiated due to the interference
effect from the nozzle is significantly lower than the total noise radiated at all the microphone
81
405 410 415 420 425 430 435 440 445 450
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(a) Microphone elevation = 53.75?
370 375 380 385 390 395 400 405 410 415
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(b) Microphone elevation = 41.43?
350 355 360 365 370 375 380 385 390 395
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(c) Microphone elevation = 27.62?
Figure 3.10: Acoustic time history comparison with and without the gust, for Case 3 at ? = 120.9?
(MT = 0.702) 82
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.11: SPL trends of noise radiation due to the nozzle ? Case 4
locations. The noise levels for this interaction angle are significantly lower than the previous
interactions, and there is a greater difference between the total radiation with the gust on and the
interference due to the nozzle.
For complete acoustic time histories of the effect of the nozzle at other azimuthal angles, please
see Appendix C.
83
400 405 410 415 420 425 430 435 440 445
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(a) Microphone elevation = 53.75?
365 370 375 380 385 390 395 400 405 410
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(b) Microphone elevation = 41.43?
345 350 355 360 365 370 375 380 385 390
?140
?120
?100
?80
?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
Total Noise Radiation
Interference from Nozzle
Radiation from Gust
(c) Microphone elevation = 27.62?
Figure 3.12: Acoustic time history comparison with and without the gust, for Case 4 at ? = 120.9?
(MT = 0.702) 84
Figure 3.13: Top view of acoustic wavefronts radiating from the parallel interaction
3.3 BCDI Acoustic Data ? Parallel BCDI
As mentioned earlier, the parallel interaction has a trace Mach number of infinity. This results
in the span-wise acoustic sources being triggered simultaneously (Fig. 3.13), and arrive in-phase at
the far-field observer position assumed to be perpendicular to mid-span of the interaction, leading
to significant noise radiation. Typically, this case results in maximum noise radiation from the
helicopter. These near-parallel interactions occur close to 60? azimuth on the advancing side of
the rotor (for a two-bladed helicopter) and tend to radiate most of noise to the starboard side of the
helicopter, around a perpendicular line drawn from the 80% blade span location at the time of the
interaction. This corresponds to a microphone azimuthal angle of 107? in the BCDI experiment.
Fig. 3.14 shows the unaveraged data for two revolutions of the rotor at the microphones at
? = 120.9? for the parallel interaction at 0.702 tip Mach number. It should be noted that the data
in these figures have not been scaled with different microphone locations. Thus the amount of
85
100 200 300 400 500 600 700 800 900?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
(a) Microphone elevation = 53.75?
100 200 300 400 500 600 700 800 900?60
?40
?20
0
20
40
60
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
(b) Microphone elevation = 41.43?
100 200 300 400 500 600 700 800 900?40
?30
?20
?10
0
10
20
30
40
50
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
(c) Microphone elevation = 27.62?
Figure 3.14: Unaveraged data for two revolutions for the parallel interaction at ? = 120.9?
86
spherical spreading of the acoustic waves from the source to the microphone is different for each
of the microphones. Firstly, it is obvious that there are quite a few reflections recorded by the
microphones. However, they are significantly lesser in magnitude than the main pulse due to the
interaction. Secondly, it also seen that the pulses are slightly different from revolution to revolution.
This is mostly, of the turbulence levels in the gust and to a lesser extent due to recirculation setup
in the room.
In order to study the directionality characteristics, it would be ideal to position microphones at
a fixed distance from the acoustic source, and distribute the microphones on the surface of a sphere.
However, this is not possible within the constraints of the chamber, and so the spherical spreading
of the noise from the interaction is different for different microphones. In order to compare the
noise across microphones, this effect needs to be normalized. It was decided to normalize the
all the microphone pressure data to a distance of 3R from the hub of the rotor. This would be
equivalent to distributing the microphones on a sphere with radius 3R and centered at the rotor
hub. Ideally, this sphere should be centered about the acoustic source. However, in the case of
the experiment, there is no single point of origin for the noise. While for the parallel interaction
most of the acoustic activity occurs close to the 80% blade span, when comparing the acoustics
across different interaction angles there is no particular fixed point in space to choose as the center
of the sphere. Thus, in order to be able to compare the results across the various parameters, it
was decided to normalize the microphone pressure data at a fixed distance about the rotor hub.
Moreover, changing the center of scaling to the 80% blade span section during at the interaction,
does not result in significant changes to the relative noise levels and the directionality for different
87
interaction angles. For some results and discussion with regards to this, please refer to Appendix F.
The distance of 3R was chosen because it is in between the range of microphone distances used in
the experiment. The acoustic pressure data are normalized using a far-field solution to an acoustic
point source and are divided by the distance of the microphone from the rotor hub. All the data
presented here onwards is for microphones whose distances have been normalized to a distance of
3R from the rotor hub.
The infinite trace Mach number along the blade span essentially means that all the acoustic
sources along that the blade span are triggered simultaneously, and are perfectly in phase when
they radiate from the rotor blade. However, the directional characteristics of this interaction is de-
cided by the arrival times of these acoustic pulses at different observer locations. The microphone
location where the important pulses add in phase records the maximum noise. This peak noise
azimuthal location is close to a perpendicular line drawn from the 80% blade span location at the
time of the interaction. For the parallel interaction, elevation angle does not affect the phasing of
the acoustic signals. The variation of noise across the elevation above the rotor plane is determined
by the dipole nature of the acoustic sources and hence are expected to increase up to a certain
microphone elevation (? 60?) and reduce thereafter. In the present experimental setup, the highest
microphone is at 53.75?? close to the 60? angle.
3.3.1 Acoustic Time Histories
Fig. 3.15 shows the acoustic time histories for the parallel interaction at most of the micro-
phones, after subtracting the effect of the nozzle from the time histories. The plots are truncated in
88
time to show only the acoustics of the interaction event. It is observed from these plots, that there
are two strong peaks ? a negative peak followed by a positive one. The first negative peak is a
result of the velocity gradient in the gust velocity field, while the positive peak is caused by the
negative velocity gradient of the gust field. The asymmetry in the gust (higher positive velocity
gradient compared to the negative velocity gradient) results in a higher negative peak in the acous-
tics. This is most easily observable at the 107? azimuth microphones, where most of the span-wise
acoustic disturbances arrive almost in-phase resulting in a distinct pulse, and hence high frequency
noise.
At the microphones at lower azimuthal angles (? < 107?), the acoustic disturbances from the
tip of the blade arrive earlier than from further inboard of the blade. The first pulse arriving from
towards the blade tip results in the initial negative gradient in the acoustics. The following pulses
from further in board of the blade, arrive a little later in time, resulting in a broadening of the
positive peak in the acoustics. At even lower microphone azimuths, the span-wise acoustic pulses
become more out of phase and result in almost no positive peak.
For microphones at azimuth larger than 107?, the opposite is true. The acoustic pulses from the
in board blade locations arrive earlier than from the tip of the blade. This results in out-of-phase
summation in the negative peak of the acoustic pulse and hence a lowering of the magnitude of the
negative peak relative to the positive peak. As the microphone azimuth is increased (? > 133.7?),
particularly at the lower microphone elevations, the typical shape of pulse is almost completely
lost.
Figure 3.16 shows the variation in sound pressure level with azimuth and elevation for a tip
89
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100
Expt.
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Rotor azimuth (Deg)
P a
Figure 3.15: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(MT = 0.702 ? Parallel Interaction)
90
Mach number of 0.702. The peak noise levels occurs at the ? = 107? microphone location. This
is to be expected ? as explained earlier ? as this microphone location is perpendicular to blade
around the 80% blade span location when the interaction occurs. As expected the SPL values
increase with increasing microphone elevation due to the dipole nature of the loading during the
interaction. The radiated noise has a sharp peak in the azimuthal direction close to 107? and
falls quite rapidly on either side. The asymmetry about the peak noise azimuth observed can
be attributed to the choice of the rotor hub as the center of normalizing the spherical spreading.
Most of the acoustic energy is concentrated close to the blade tip. Since the microphones at higher
azimuthal angle are farther away from the interaction, they end up being scaled to a greater distance
than the microphones closer to the interaction. An appropriate choice of the scaling center (?80%
blade span at the interaction) would reduce this asymmetry for the parallel interaction, however,
as explained earlier, this would make it difficult to compare the results across different interaction
angles.
3.3.2 Frequency Spectrum
Fig. 3.17 shows the frequency spectrum of the noise recorded at most of the microphone loca-
tions. The microphones recording high amplitudes (> 60dB) at frequencies as high as 200 rotor
harmonics are at ? = 107?. This corresponds to the strong narrow time history of the pulse (see
Fig. 3.15). As the microphones are moved to azimuths away from the peak noise location, the time
histories exhibit wider waveforms and correspondingly lower magnitude at these high frequencies.
91
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.16: Directionality trends at 0.702MT for the Parallel Interaction
92
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Expt.
Rotor Harmonics
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
P a
Figure 3.17: Frequency spectrum of noise at various microphones ? Sound pressure in dB vs. Single-blade rotor harmonics
(MT = 0.702 ? Parallel Interaction)
93
3.3.3 Effect of tip Mach number
Fig. 3.18 shows the variation of the peak-to-peak noise observed at the various microphones as
a function of the rotor tip Mach number. Clearly, as the tip Mach number increases, the noise level
also goes up. It is also observed that the noise levels increase almost monotonically with increase
in tip Mach number. While this increase occurs for the microphones close to the peak microphone
locations, this is not true for all microphone azimuths. In particular for the lowest microphones
positions at ? = 61.6? and ? = 148?. This is probably due to reflections from the gust generator
affecting the former microphone, while reflections off of the rotor stand itself affecting the latter.
For the peak noise microphone location at the 107? azimuthal location, Fig. 3.19 shows the peak-
to-peak variation with rotor tip Mach number. As can be seen, the noise level increases almost
linearly up to a tip Mach number of about 0.65. At the higher tip Mach numbers the noise level
increases slower than the linear increase rate, particularly for the lower microphone location.
3.4 Oblique BCDI
3.4.1 Case 2 ? 3.3? Oblique Interaction
The first interaction angle (starting with 3.3? at the blade tip) studied is shown in Fig. 2.22(a).
The interaction starts out at the tip of the blade at a small 3.3? angle and sweeps inboard. This near-
parallel interaction has a completely supersonic trace Mach number profile(Fig. 2.22(b)). This im-
plies that the noise sources are triggered very rapidly creating the in-plane acoustic wave pattern
shown in Fig. 3.20. In effect the BCDI summation process can be viewed as a decelerating super-
94
51.8 61.6 75.5 91.4 107  120.9133.7148  162.2176.7115
120
125
130
135
140
145  
Microphone Azimuth (Deg)
 
Peak?to?peak Pressure (dB)
MT=0.569
MT=0.614
MT=0.658
MT=0.702
MT=0.768
Rotor Direction
(a) Microphone elevation = 53.75?
51.8 61.6 75.5 91.4 107  120.9133.7148  162.2176.7115
120
125
130
135
140
145  
Microphone Azimuth (Deg)
 
Peak?to?peak Pressure (dB)
MT=0.569
MT=0.614
MT=0.658
MT=0.702
MT=0.768
Rotor Direction
(b) Microphone elevation = 41.43?
51.8 61.6 75.5 91.4 107  120.9133.7148  162.2176.7115
120
125
130
135
140
145  
Microphone Azimuth (Deg)
 
Peak?to?peak Pressure (dB)
MT=0.569
MT=0.614
MT=0.658
MT=0.702
MT=0.768
Rotor Direction
(c) Microphone elevation = 27.62?
Figure 3.18: Variation of peak-to-peak noise level with tip Mach number ? Parallel BCDI
95
0.55 0.6 0.65 0.7 0.75 0.8135
136
137
138
139
140
141
142
143
Rotor tip Mach number
Acoustic Pressure (Peak?to?Peak dB)
 
 
53.7o
41.4o
27.6o
Figure 3.19: Variation of peak-to-peak level with increase in tip Mach number for the parallel
BCDI at ? = 107?
96
Figure 3.20: Top view of acoustic wavefronts for Case 2 oblique BCDI
sonic unit acoustic source. The envelope of this wave pattern shows the grouping of the waves that
contribute to the peak levels of radiated noise in the rotor plane.
Fig. 3.21 shows the time history of the noise at most of the microphone locations for the 3.3?
oblique angle at a tip Mach number equal to 0.702. It is interesting to note that while the pulse
shapes close to the peak noise azimuth (? = 120.9? to ? = 91.4?) are similar to that during the
parallel interaction, the pulse shapes at higher microphone azimuth angles are also still preserved,
unlike for the parallel interaction case (Fig. 3.15). At higher microphone azimuths the phasing of
the spanwise sources results in less destructive interference of the sources originating at the most
inboard location as well the tip of the blade, leading to a strong and well-defined pulse shape with
higher noise levels.
The small change in interaction angle results in a significant change in the phasing relation
between the spanwise acoustic sources, and hence the resulting radiation pattern. This can be seen
97
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?100
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335 340 345 350 355?200
?100
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325 330 335 340 345?200
?100
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?100
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?100
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55 60 65 70?200
?100
0
100
Expt.
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Rotor azimuth (Deg)
P a
Figure 3.21: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
? Case 2 (3.3? Oblique Interaction MT = 0.702)
98
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0 200 400
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0 200 400
60
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100
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure 3.22: Frequency spectrum of noise at various microphones ? Sound pressure in dB vs. Single-blade rotor harmonics ?
Case 2 (3.3? Oblique Interaction MT = 0.702)
99
in the sketch of the wavefronts radiation from the blade for the parallel (Fig. 3.13) and the 3.3?
oblique interaction (Fig. 3.20). The in-phase summing of the spanwise acoustic sources for this
small oblique interaction angle, results in a higher frequency content at the 120.9? microphone az-
imuthal location (Fig. 3.22) and slightly lower frequencies at the microphones at 107?, compared to
the parallel interaction. The frequency content of the measured noise at the microphones at higher
azimuths, particularly for the topmost microphone, is higher compared to the parallel interaction.
Fig. 3.23 shows the peak noise levels observed at the various microphone locations for the
tip Mach number of 0.702. As before the pressure values have been scaled using 1/R law to
a distance of 3R from the rotor hub. The small change in interaction angle results in quite a
different directionality profile when compared to the parallel interaction (Fig 3.16). While the
parallel interaction had a sharp peak in the azimuthal direction, the small oblique interaction has a
much shallower peak, falling off more slowly with changes in azimuth, particularly towards higher
azimuth angles. The peak noise level has also shifted to a higher microphone azimuth for the top
most microphone, compared to the parallel interaction.
100
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.23: Directionality trends for Case 2 (3.3? Oblique Interaction) at MT = 0.702
101
3.4.2 Case 3 ? 8.8? Oblique Interaction
Fig. 2.22(c) shows an in-plane schematic of the second oblique interaction angle which starts
out at 8.8? at the tip of the blade and proceeds inboard. The corresponding trace Mach number
shown in Fig. 2.22(d) is supersonic throughout the entire interaction, just as in Case 2. The corre-
sponding sketch of the radiating wavefront in the rotor plane is shown if Fig. 3.24. This suggests
that the azimuthal phasing of the spanwise sources would be similar to the previous case discussed.
However, the trace Mach number for the Case 3 oblique BCDI is much lower than the previous
case. Thus, for the topmost microphone location, the component of the trace Mach number will
become subsonic. When the trace Mach number becomes 1, the acoustic sources are triggered
at the speed of sound, and hence the waves emanating from these sources would all collect in
the medium and radiate outwards to the microphone (similar to a sonic boom). However, for the
particular interaction angle under consideration, the trace Mach number is low enough for the
component above the rotor plane to become subsonic only at around the 50% blade span location,
which does not have a significant contribution to the acoustics (due to the very low Mach number
at the blade section).
Fig. 3.25 and Fig. 3.26 show the time histories and the frequency spectrum at the microphones.
As expected the trends are similar to Case 2 oblique BCDI, as the trace Mach number profiles are
similar. Just as in the previous case, at azimuths greater 107? there is a lesser extent of destructive
interference compared to the parallel interaction resulting in higher noise levels. The frequency
content (Fig. 3.26) at the microphones at ? = 120.9? is higher than the parallel interaction case ?
similar to Case 2.
102
Figure 3.24: Top view of acoustic of the wavefronts for Case 3 oblique BCDI
The peak noise levels in decibels for this interaction angle for a tip Mach number of 0.702 are
shown in Fig. 3.27. The asymmetry in the azimuthal direction is much more prominent for this
interaction than was for the two previous interactions discussed. The reason for this, once again,
is the phasing of the spanwise sources radiating from the blade at the time of the interaction. It is
interesting to note that at although the peak noise level (? = 120.9?) has reduced from the parallel
interaction case, the noise levels at higher azimuth have in fact increased compared to the parallel
interaction.
3.4.3 Case 4 ? 15.3? Oblique Interaction
The third oblique interaction angle (Fig. 2.22(e)) starts out at an angle of 15.33? at the tip and
proceeds inboard as the blade rotates. For the case of the blade spinning with a tip Mach number
equal to 0.702, the in-plane trace Mach number is supersonic for the outboard blade sections,
103
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Expt.
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Rotor azimuth (Deg)
P a
Figure 3.25: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
? Case 3 (8.8? Oblique Interaction MT = 0.702)
10
4
0 200 400
60
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0 200 400
60
80
100
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure 3.26: Frequency spectrum of noise at various microphones ? Sound pressure in dB vs. Single-blade rotor harmonics ?
Case 3 (8.8? Oblique Interaction MT = 0.702)
10
5
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.27: Directionality trends for Case 3 (MT = 0.702)
106
Figure 3.28: Top view of acoustic of the wavefronts for Case 4 oblique BCDI
but crosses 1 and becomes subsonic close to the 60% blade span location. This implies that the
waves emanating from the triggered spanwise sources, collect close to the 60% blade span location
(Fig. 3.28). These waves then propagate in the medium resulting in increase in the noise level.
However, the fact that for the 0.702 tip Mach number, this process occurs at 60% blade span ?
where the contribution to the acoustics is relatively low ? means that the final effect of this process
is relatively small.
The acoustic waveform for the interaction consists of negative peak followed by a positive peak
(Fig. 3.29). The negative peak is a result of the sharper edge of the gust velocity profile and hence
has a higher frequency content compared to the positive side of the waveform, which is a result
of the more gradual velocity gradient. Because of the wider waveform shape on the positive side
of the pulse (because of the lower frequency content), there is a greater possibility of constructive
interference. Thus, even if the waves from the spanwise sources are slightly out of phase, there is
107
a greater possibility of these waves summing up on the positive side of the waveform. This effect
is seen at the 107? azimuth (Fig. 3.29). The positive peak for the microphone at 27.6? is slightly
higher compared to the topmost microphone, and this results in the slightly higher peak noise
levels observed from Fig. 3.31. This is also more clearly visible at the 120.9? azimuth location
where the lowest microphone once again has a higher positive peak compared to the topmost. The
microphone at 41.43? however, has higher negative peak compared to the other two microphones
because of fortuitous constructive interference at that location.
It can be seen from Fig. 3.30 at 120.9.? azimuth location, the microphone at 41.4? has a greater
energy at the higher frequencies compared to the other two microphones at that azimuth. Also
the frequency content is significantly higher for the microphones at the higher azimuth angles
compared all the previous cases discussed this far.
Fig. 3.31 shows the variation in peak noise level expressed as decibels. Two things stand
out when compared to the results of the previous interactions. Firstly, the azimuthal asymmetry is
significantly higher than all the previous cases. Secondly, for some microphone azimuths, the lower
microphones actually, record a greater noise level. This is purely because of the simultaneous and
in-phase addition of the waves from a greater region of the blade span at the lower microphones
than at the higher ones.
For the microphones at 120.9? azimuth the acoustic waves from the last 10% of the blade span
arrive simultaneously at the microphone that is 41.4? location resulting in higher noise levels. At
the other elevations the acoustic waves from the blade tip arrive somewhat out of phase, resulting
in higher noise levels at the second microphone at the 120.9?.
108
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Expt.
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Rotor azimuth (Deg)
P a
Figure 3.29: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
? Case 4 (15.3? Oblique Interaction MT = 0.702)
10
9
0 200 400
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0 200 400
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0 200 400
60
80
100
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure 3.30: Frequency spectrum of noise at various microphones ? Sound pressure in dB vs. Single-blade rotor harmonics ?
Case 4 (15.3? Oblique Interaction MT = 0.702)
11
0
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 3.31: Directionality trends for Case 4 (MT = 0.702)
A similar situation occurs at 107? azimuth resulting in the lowest (27.6?) elevation microphone
having a higher noise level compared to the topmost microphone (53.7?).
3.5 Effect of Interaction Angle on Noise Levels
Previous researchers have studied the acoustics and the aerodynamics of the parallel interaction
in controlled environments of the wind tunnel. For the first time, in this experiment a comparison
between various interaction angles can be performed.
As before the tip Mach number of 0.702 is used for this comparison. Fig. 3.32 shows the vari-
111
ation with interaction angle for all the microphone locations. Clearly, for a given elevation above
the rotor plane, the parallel interaction has the maximum peak noise level across the azimuthal
angles. However, the parallel interaction has a sharp peak at the 107? azimuth and then falls off
rapidly on either side for all elevations.
The oblique interactions have a lower peak noise level at a given elevation, but the azimuthal
variation is shallower and the noise levels tend to fall of less rapidly, particularly along the direction
of the trace Mach number. With the oblique interaction starting out at 15.3? at the blade tip (Case
4), the peak noise levels roll off very slowly at higher microphone azimuths. In fact, the noise levels
are higher for higher interaction angles at microphone azimuth locations greater than about 120?.
The acoustic energy is therefore, spread out over much wider azimuthal area (towards the direction
of the acoustic trace velocity). Moreover, as noted earlier, as the interaction angle increases, the
noise levels at the lower elevations can increase above that at the higher elevations (Fig. 3.31).
3.6 Effect of tip Mach number on Case 4 (15.3?) Oblique BCDI
The acoustics directivity is a strong function of the tip Mach number for the parallel interaction.
As discussed earlier, the noise level increases with increase in tip Mach number. It did not result
in any significant change in the directionality patterns, either along the azimuthal or elevation
directions. The noise level trends in the elevation direction were directly related to the dipole
nature of the spanwise acoustics sources. The 53.7? elevation microphone always had the highest
noise level, followed by the 41.4? and the 27.6? elevations microphones, at any given azimuthal
location. The noise levels were affected because increase in the impulsiveness of the event as the
112
406080100120140160180105
110
115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
Case 1 ?? Parallel
Case 2 ?? 3.3o Oblique
 Case 3 ?? 8.8o Oblique
 Case 4 ?? 15.3o Oblique
Rotor Direction
(a) Microphone elevation = 53.75?
406080100120140160180105
110
115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
Rotor Direction
(b) Microphone elevation = 41.43?
406080100120140160180105
110
115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
Rotor Direction
(c) Microphone elevation = 27.60?
Figure 3.32: Variation of peak-to-peak noise levels with interaction angle (MT = 0.702)
113
tip Mach number was increased. The oblique interaction, however, is different. Changing the
tip Mach number when keeping the interaction angle constant, changes the trace Mach number
and hence phasing. This results in differences in directionality trends both along the azimuth and
elevation.
Fig. 3.33 shows the trace Mach number for the five tip Mach numbers studied. As the tip Mach
number decreases, the percentage of the blade near the sonic region of the trace Mach number
also increases. More importantly, the trace Mach number crosses the sonic point closer to the tip
of the blade as the tip Mach number is reduced. Thus, the relative contribution of the acoustic
sources in phase increases closer to the rotor plane with the reduction in tip Mach number for a
given interaction angle.
Fig. 3.34 shows the directionality trends for four of the tip Mach numbers ? 0.614, 0.658,
0.702 and 0.768, respectively. It can be seen that for tip Mach numbers of 0.614 (Fig. 3.34(a)) and
0.658 (Fig. 3.34(b)), the noise levels at the 41.4? elevation microphone are greater than at other
elevations over much larger azimuthal range compared to both the MT = 0.702 (Fig. 3.34(c)) and
MT = 0.768 (Fig. 3.34(d)). Moreover, the noise levels at the 27.6? elevation microphone and the
53.7? microphone are close to each other over a wider azimuthal range. Once again, as explained
earlier, this is due to the phasing of the spanwise acoustic sources.
114
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
Blade Span (r/R)
trace Mach number M
TR
 
 M
T=0.568
MT=0.614
MT=0.658
MT=0.702
MT=0.768
Figure 3.33: Variation of trace Mach number as function of tip Mach number ? Case 4 oblique
BCDI
115
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
(a) MT = 0.614
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB SPL)
 
 
53.7?
41.4?
27.6?
Rotor Direction
(b) MT = 0.658
Figure 3.34: Acoustic directivity variation with tip Mach number ? Case 4 (15.3? Oblique BCDI)
116
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
(c) MT = 0.702
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
(d) MT = 0.768
Figure 3.34: (Cont?d) Acoustic directivity variation with tip Mach number ? Case 4 (15.3?
Oblique BCDI)
117
Chapter 4
Theoretical Comparison
4.1 Theoretical Approach
The experimental results presented in Chapter 3 show that the acoustics is a very strong func-
tion of the phasing of the spanwise sources distributed on the blade during the time of the interac-
tion. Using the data recorded from the microphones alone, it is not always possible to understand
clearly the contributions of the blade span-sections to acoustic time histories. Understanding the
phasing of these blade spanwise acoustic sources, could have implications to quiet blade designs
? both passive and active techniques ? by modifying the relative phasing of the sources to re-
duce noise radiation in certain directions. A thorough investigation of the radiation characteristics
during BVI requires a comprehensive and detailed understanding of the unsteady surface pressure
distribution on the rotor blade. This requires a comprehensive three-dimensional CFD analysis of
the experiment, followed by a solution to the Ffowcs-Williams and Hawking?s equation (Eqn. 1.6)
using the off-surface formulation, and is beyond the scope of this dissertation. However, simpler
118
approaches such as the indicial method has been used in the past to understand BVI aerodynamics
and acoustics. It has been shown [28, 29] to predict with reasonable accuracy the magnitude and
pulse shape of the acoustic pressure for the parallel interaction. This approach is used here to study
the acoustics as it is easier to implement as well as being much faster than a CFD simulation.
4.1.1 Linear Unsteady Indicial Aerodynamics
A simpler approach, geared primarily towards understanding the phasing effects of the acous-
tics, can be implemented using a simpler unsteady aerodynamics approach which provides inte-
grated sectional loads on the blade rather than a full surface pressure history. One such approach
is the unsteady indicial approach developed used initially by Beddoes [27], and later extended by
Leishman [28, 29] for studying helicopter BVI noise. The unsteady indicial theory involves es-
timating the two-dimensional airfoil response to a step change in induced velocity on the airfoil.
This indicial function can then used to calculate the blade loads for an arbitrary induced velocity
using the Duhamel?s integral.
The indicial function used on the present study is one derived by Leishman [29] and is of the
form:
?g(s) = 1?G1e?g1t +G2e?g2t (4.1)
where G1, G2, g1 and g2 are the indicial coefficients, and ?g(s) is the indicial response as a func-
tion airfoil semi-chord, s. By choosing the indicial coefficients judicially, compressibility effects
at moderately high Mach numbers can be accounted for. The indicial coefficients used in this
study (Table 4.1) are those derived by Leishman [29] by comparing the step response of the airfoil
119
using two-dimensional CFD analysis of the Kitapliouglu and Caradonna [84] wind tunnel BVI
experiment. The Duhamel?s integral for the change in lift coefficient is solved using a recursive
G1 g1 G2 g2
0.67 0.1753 0.33 1.637
Table 4.1: Coefficients of the Indicial gust function, ?g
algorithm [15]:
Z1(s) = Z1(s??s)e?g1?2?s +G1 [wg(s)?wg(s??s)] (4.2)
Z2(s) = Z2(s??s)e?g2?2?s +G1 [wg ?wg(s??s)] (4.3)
?Cl(t) = 2pi? 1V [wg(s)?Z1(s)?Z2(s)] (4.4)
where, ? is the Glauert factor given as
? =
radicalBig
1?M2? (4.5)
To capture the effect of the spanwise distribution of lift, the outer 50% of the blade is divided
into 50 spanwise lifting elements. The three-dimensionality due to the tip vortex is accounted for
by employing the Weissinger-L approach [87], a schematic of which is shown if Fig. 4.1. The
Weissinger-L model is a vortex method with one horseshoe vortex for each blade section. The
vortex is placed at the quarter chord location and the induced velocity is evaluated at the three-
quarter chord location of the airfoil. This approach accounts for the three-dimensional effect of the
tip vortex. The induced velocity on the blade used for the aerodynamic calculations is the measured
vertical velocity field at the blade passage location, presented earlier in section 2.3.2 (Fig. 2.13(a)).
120
Figure 4.1: Weissinger-L lifting line model for the rotor blade
4.1.2 The Acoustics Formulation
As discussed later in Chapter 3 the process of subtracting the effect of the nozzle also removes
the thickness noise from the the resulting acoustics. Thus for comparison, only the acoustic contri-
bution from the blade loading needs to be calculated. The sectional lift coefficient can be directly
used to estimate the radiated noise using the loading noise terms of Farassat?s formulation 1A [55].
This formulation of the Ffowcs-Williams and Hawking?s equation is dependant on the force ex-
erted by the body on the surrounding medium (which is equal and opposite to the lift force on the
airfoil), and is dependant only on the source time (equal to rotor angular velocity in rad/s divided
by the rotor azimuth in radians). The acoustic pressure at the observer location is calculated by
repeated evaluation of the integrands in Eqn. 4.6 at the correct retarded time [55] over the blade
surface for each spanwise blade element and summed up to arrive at the acoustic pressure at the
121
required observer time.
4pipL(vectorx,t) = 1a
Z bracketleftbigg ?l
i ?ri
robs(1?Mr)2
bracketrightbigg
ret
dS+
Z bracketleftbigg l
r ?liMi
r2obs(1?Mr)2
bracketrightbigg
ret
dS
+ 1a
Z bracketleftbiggl
r(robs ?Mi ?ri +aMr ?aM2)
r2obs(1?Mr)3
bracketrightbigg
ret
dS (4.6)
where l is the sectional load on the blade, and the dots on li and Mi denote the derivative with
respect to source time. The integrands are bracketed within [...]ret to reinforce the fact that the
terms are to evaluated at the correct retarded times. The first term in the equation varies as 1/robs
with the observer distance from the source, and decays more slowly compared to the other two
terms, which decay as 1/r2obs. The first term is therefore, referred to as the far-field term, while the
last two terms are referred to as the near-field term and do not have a significant contribution far
away from the source, although the actual computational results includes all the terms.
When evaluating the surface integral in Eqn. 4.6, if the blade is discretized only along the
spanwise direction, the acoustic representation is said to be ?non-compact? (distributed) in span,
and ?compact? (acting at a point) in chord. A more detailed acoustic representation is to dis-
tribute the acoustic sources in the chord-wise direction, as well as in the spanwise direction. This
acoustic modeling of the problem is said to be ?non-compact? in both the spanwise and chord-
wise directions. Strictly speaking, the unsteady aerodynamics and the acoustics of the problem
should be consistent at all levels. This requires that the unsteady aerodynamic solutions be fully
three-dimensional and ?non-compact? when non-compact solutions to the acoustic problem are
employed. However, this approach has not been studied in this thesis because of the added com-
plexity involved. Nevertheless, some of the important effects of acoustic compactness can be
explored by assuming a chordwise pressure distribution over the blade surface. Various pressure
122
distributions including triangular distribution [88], two-point chordwise distribution and the an-
alytical flat plate pressure distribution in incompressible flow [28] have been used by previous
researchers. In this dissertation, the sectional lift coefficient obtained from the indicial model was
converted to a chordwise differential pressure distribution on the mean chord using a flat plate
model, and is given by:
?CP = 2Clpi
radicalbigg
1?x
x (4.7)
where x is the chordwise station non-dimensionalized with respect to the local airfoil chord.
Distributing the acoustic sources over the chord result in a non-zero time interval between the
arrival of the acoustic waves at the microphone from the successive chord-wise sources. For the
case of the parallel interaction, this results in a wider waveform of lesser magnitude compared to
the compact chord acoustics, as can be seen in Fig. 4.2. The non-compact chord predictions are
much closer to the measured data, both in magnitude and pulse width. However, the non-compact
formulation does not have the same effect at all microphone locations. Microphones near the peak
impulsive noise azimuth angle and those located nearer to the plane of rotation see the largest
reduction. Microphones located away from the peak level directivity see much lower reductions in
pulse amplitude.
A microphone at ? = 107? and in the plane of the rotor would see the chordwise section
?straight on? resulting in a finite time interval between the arrival of the chord-wise pulses. While
a microphone at the same azimuth but out of the rotor plane would see the blade such that the
chord-wise sources are almost equidistant from the microphone resulting in an almost simultane-
ous arrival of the pulses. Thus, this case would result in a lesser difference between the compact
123
170 175 180 185 190 195 200 205
?200
?150
?100
?50
0
50
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 Compact Chord
Non?Compact Chord
Expt.
Figure 4.2: Comparison between compact and non-compact chord approaches ? Parallel Interac-
tion at MT = 0.702 (? = 107? & ? = 53.75?)
124
and non-compact chord predictions compared to the microphone nearer to the rotor plane. A sim-
ilar argument can be applied for variation in the azimuth location of the microphone. This result
is presented in Fig. 4.3 as a plot of the difference in sound pressure level between the compact and
non-compact approaches versus microphone azimuth angle for the three elevations. At the peak
noise azimuth, the difference could be as much as 5dB at lower elevation levels. The difference
between the compact and the non-compact chord approach reduces slightly as the interaction be-
comes more oblique, but the difference remains as high as 5dB for the lowest microphone even for
the Case 4 BCDI (Fig. 4.4). At higher microphone elevations, the spanwise phasing becomes more
important for the oblique interaction and the difference between the compact chord approach and
non-compact chord approach reduced significantly. See Appendix D for time history comparisons
between the compact and non-compact chord formulations.
4.2 Comparison with Experiment ? Parallel Interaction
Fig. 4.5 shows the time history comparisons at some of the microphone azimuths at the three
different elevation angles. For some cases, in particular for microphones at ? = 107? and ? =
120.9?, the time histories from the theoretical predictions do not overlap with the experimental
observations precisely. This is possibly a result of inaccuracies in the measurement of the micro-
phone coordinates with respect to the rotor during the interaction. There is an error of up to 3?
of rotor azimuth in the time histories. For the case under consideration in Fig. 4.5, the rotor is
spinning at a frequency of 40Hz. This translates to an error of 2.5% in the distance from the mi-
crophone to the rotor hub. Although great care was taken to accurately, position the microphone,
125
4060801001201401601800
1
2
3
4
5
6
7
Microphone Azimuth (Deg)
Compact chord dB ? Non?compact chord dB
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 4.3: Difference in peak-to-peak sound pressure between compact and non-compact ap-
proaches ? Case 1 parallel BCDI at MT = 0.702
126
60801001201401601800
1
2
3
4
5
6
Microphone Azimuth (Deg)
Compact chord dB ? Non?compact chord dB
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure 4.4: Difference in sound pressure between compact and non-compact approaches ? Case
4 (15.3? Oblique BCDI) at MT = 0.702
127
the fact that the microphone array needed to be moved frequently, resulted in some inaccuracies
in the positions. However, as can be seen, these errors are still within acceptable range to make
reasonable comparison between the theory and the experiment.
As discussed earlier, the pulse shapes obtained in the experiment, have a strong negative peak
followed by a positive peak. The positive peak is most prominent close to the peak noise azimuth
of 107? and is smaller in magnitude for other microphone azimuths. The theory tends to predict the
negative peak very closely for all the microphone locations. However, the positive peak is under
predicted for all the cases. It should be noted that the width of the gust is about half the blade
chord, implying that there is a point of time during the interaction when the chord stations ahead
of the quarter chord point experience no gust field, while stations behind the quarter chord location
experience a strong upwash from the gust. The unsteady indicial model, being a compact chord
aerodynamic approach cannot account for such steep gradients along the chordwise direction. The
indicial approach nevertheless, captures the negative pulse of the acoustic history as this event is
dominated by the leading edge of the airfoil.
Fig. 4.6 shows the directionality trends computed using the linear indicial theory approach for
the parallel interaction for the tip Mach number of 0.702. Firstly, for the parallel interaction case,
the general azimuthal directionality at the three elevations are captured reasonably well by the
non-compact chord theoretical approach. The peak noise occurs at the same azimuth (? = 107?)
location for all the elevations as in the experimental case. The azimuthal directivity has a sharper
peak at ? = 107? and rolls off more rapidly compared to the experimental results.
The theoretical results, however, under predict the noise. For microphone positions that are at
128
5 10 15 20 25?200
?100
0
100
45 50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
45 50 55 60 65?200
?100
0
100
10 20 30?200
?100
0
100
345 350 355 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
0 10 20?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340 345?200
?100
0
100
350 360 370?200
?100
0
100
30 40 50?200
?100
0
100
0 5 10 15?200
?100
0
100
350 360 370?200
?100
0
100
15 20 25 30 35?200
?100
0
100
45 50 55 60?200
?100
0
100
50 60 70?200
?100
0
100
Expt.
Theory
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure 4.5: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(MT = 0.702 ? Parallel Interaction)
12
9
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7? ?? Expt.
53.7? ?? Theory
41.4? ?? Expt.
41.4? ?? Theory
27.6? ?? Expt.
27.6? ?? Theory
Rotor Direction
Figure 4.6: Comparison of the directionality trends between theory and experiment for the parallel
interaction (MT = 0.702)
130
lower azimuth angles compared to the peak noise azimuth, i.e. ? ? 107?, the theory under predicts
by less than 3dB. However, for microphone azimuths above 107?, the difference increases and can
be as high as 6dB in some cases. This difference between the theory and experiment is mostly
because the theory does not predict the second positive peak in the acoustic time history.
One of the main advantages of using a simple theoretical formulation is the ability to study the
spanwise phasing and its effect on the radiation pattern of the acoustic energy. Fig. 4.7 shows the
spanwise contribution for blade elements at 5% spanwise distance from the each other (every fifth
element start on the rotor blade). As can be seen in all the figures, the contribution from the blade
element at 95% span station is slightly smaller than the contribution from the 90% span station.
This is due to three-dimensional effect of the tip vortex modelled by the Weissinger-L approach.
Apart from the contribution from the element near the blade tip, all the other contributions scale
directly with the local sectional Mach number. As can be seen, the blade sectional element at 50%
span contributes a significantly lesser amount to the over all noise levels, due to the lower sectional
Mach number. The acoustics of inner 50% of the blade span is not computed as the contribution is
very small. Moreover, in the experiment, the inner 50% of the blade does not experience the gust
interaction.
Figs. 4.7(a)-4.7(c) correspond to the microphone just to one side of the peak noise azimuth. It
can be seen that the acoustic waves from the blade tip arrive at this microphone azimuth location
earlier than from further inboard of the blade. At the peak noise azimuth location (? = 107?) shown
in figs. 4.7(d)-4.7(f), all the waves from the spanwise sources arrive simultaneously, resulting in
the sharp acoustic time history seen in Fig. 4.5. This microphone location corresponds to the
131
wavefront of the acoustic wavelets sketched in Fig. 3.13. The arrival of these pulse is the same at
all the three microphone elevations because the trace Mach number is infinity for this case. The
simultaneous in-phase summing of the pulse at this location results in strong and sharp acoustic
pulse.
At microphone azimuth locations greater than 107? (Figs 4.7(g)-4.7(l)), the acoustic waves
from the inboard blade section arrive earlier than from the tip of the blade. This results in the over-
lapping of the positive acoustic peak from the spanwise sections further inboard with the negative
peaks of the waves from the sections closer to the tip of the blade. This results in some destructive
interference leading to the reduction in noise. A similar situation occurs for the microphones at
? = 133.7?. The difference in the interference of the spanwise acoustic waves, before and after the
peak noise azimuth explains to some extent the asymmetry (the sharper fall off noise for ? > 107?)
observed in Fig. 4.6.
4.3 Oblique Interactions
4.3.1 Case 2 ? 3.3? Oblique BCDI
A comparison of the time histories in Fig. 4.8 shows that negative peak of the acoustic pulses is
reasonably well captured at most location, except at the lowest microphone location for ? > 120?.
However, just as in the parallel interaction case, the positive peak of the acoustic pulse is notably
under-predicted by the theory, and results in the smaller decibel value shown in Fig. 4.9. Moreover,
the predicted pulses at the peak noise azimuth is sharper compared to the experiment. This can also
132
?10 ?5 0 5?5
?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(a) ? = 91.4?,? = 27.6
10 15 20 25?5
?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(b) ? = 91.4?,? = 41.4
45 50 55 60?5
?4
?3
?2
?1
0
1
2
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(c) ? = 91.4?,? = 53.7
5 10 15 20?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(d) ? = 107.0?,? = 27.6
20 25 30 35?5
?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(e) ? = 107.0?,? = 41.4
50 55 60 65?5
?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(f) ? = 107.0?,? = 53.7
20 25 30 35?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(g) ? = 120.9?,? = 27.6
25 30 35 40?5
?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(h) ? = 120.9?,? = 41.4
45 50 55 60?5
?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(i) ? = 120.9?,? = 53.7
0 5 10 15?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(j) ? = 133.7?,? = 27.6
15 20 25 30?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(k) ? = 133.7?,? = 41.4
50 55 60 65?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(l) ? = 133.7?,? = 53.7
Figure 4.7: Spanwise acoustic phasing effect for the parallel interaction (MT = 0.702)
133
be seen from the larger amplitudes of high frequencies in the frequency spectrum plots in Fig. E.2.
Fig. 4.9 shows a comparison of the noise levels expressed in decibels between theory and ex-
periment for Case 2 oblique BCDI at MT = 0.702. The peak azimuth location is captured for
the lower two microphone elevations, but the peak azimuth locations is different for the highest
microphone elevation. Once again, similar to the parallel interaction case, the theoretical predic-
tions are closer to the experimental results for microphone azimuths less than 107?. At the higher
microphone azimuths, the difference between the experiment and theory is now about 10dB.
Fig. 4.10 shows the spanwise acoustic contributions to some of the microphones for the Case
2 oblique interaction. For the microphones at 91.4? azimuth, the acoustic waves from the blade
tip arrive earlier than from the inboard blade sections. This slight difference in phasing leads to a
certain amount of destructive interference between the positive peaks of the spanwise waves from
the tip and the negative peaks of the inboard sections, resulting in an almost complete removal of
the positive peak in the final acoustic pulse (see Fig. 4.8). At the peak noise azimuth locations
the spanwise acoustic waves no longer arrive perfectly in-phase, unlike in the parallel interaction
case. For the lowest microphone, most of the waves from near the blade tip arrive almost simul-
taneously, but are slightly out of phase with the waves from further inboard. As the microphone
elevation increases, the outboard waves too arrive somewhat out of phase resulting in some de-
structive interference. However, due to their dipole nature, the spanwise acoustic sources tend to
radiate more acoustic energy out of plane. Nevertheless, this is difference is insufficient to dif-
ferentiate between the final acoustic levels at the 53.7? and the 41.4? elevation microphones at
134
5 10 15 20 25?200
?100
0
100
45 50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
?5 0 5 10?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
345 350 355 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
0 5 10 15?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340 345?200
?100
0
100
350 355 360 365?200
?100
0
100
30 35 40 45?200
?100
0
100
0 10 20?200
?100
0
100
?5 0 5 10?200
?100
0
100
20 30 40?200
?100
0
100
45 50 55 60?200
?100
0
100
55 60 65 70?200
?100
0
100
Expt.
Theory
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure 4.8: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
? Case 2 (3.3? Oblique BCDI; MT = 0.702)
13
5
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 53.7? ?? Expt.
53.7? ?? Theory
41.4? ?? Expt.
41.4? ?? Theory
27.6? ?? Expt.
27.6? ?? Theory
Rotor Direction
Figure 4.9: Comparison of the directionality trends between theory and experiment ? Case 2 (3.3?
Oblique BCDI; MT = 0.702)
136
?15 ?10 ?5 0?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(a) ? = 91.4?,? = 27.6
5 10 15 20?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(b) ? = 91.4?,? = 41.4
40 45 50 55?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(c) ? = 91.4?,? = 53.7
10 15 20 25?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(d) ? = 107.0?,? = 27.6
20 25 30 35?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(e) ? = 107.0?,? = 41.4
50 55 60 65?4
?3
?2
?1
0
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(f) ? = 107.0?,? = 53.7
20 25 30 35?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(g) ? = 120.9?,? = 27.6
25 30 35 40?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(h) ? = 120.9?,? = 41.4
45 50 55 60?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(i) ? = 120.9?,? = 53.7
0 5 10 15?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(j) ? = 133.7?,? = 27.6
15 20 25 30?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(k) ? = 133.7?,? = 41.4
50 55 60 65?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(l) ? = 133.7?,? = 53.7
Figure 4.10: Spanwise acoustic phasing effect ? Case 2 (3.3? Oblique BCDI) at MT = 0.702
137
? = 107?. The two microphones record almost the same noise levels (Fig. 4.9) due to the slight
difference in phasing of the waves alone.
At the ? = 120.9? microphone azimuth, the acoustic waves from the inboard blade sections
arrive earlier than from near the blade tip for the lower two microphones. However, for the highest
microphone (Fig. 4.10(i)), some of the waves from the inboard blade sections arrive almost simul-
taneously, followed a little later by the waves from closer to the blade tip. This in-phase arrival of
the waves results very slight change in the final noise level (Fig. 4.9) between highest microphone
at ? = 120.9? and ? = 107? azimuth, in the theoretical predictions. Even a slight change in either
the microphone or the interaction location could lead to a stronger in-phase summing of the waves,
resulting in higher noise levels.
As for the parallel interaction case, for the microphone azimuth of 133.7?, the waves from the
inboard section arrive earlier than from the blade tip, resulting in a destructive interference of the
positive side of the acoustic time history.
The summation of the acoustic waves from the spanwise blade sections is a function of the
interaction geometry as well as the location of the microphones. While the trace Mach number
profile (see Chapter 2) determines the summation of the waves in the rotor plane, the component
of the trace Mach number in the direction along each microphone is representative of the spanwise
summation process discussed above (Fig. 4.10). Figure 4.11 shows the trace Mach number profile
along the radiation direction for four azimuthal microphone locations. The trace Mach numbers
remain supersonic over a large portion of the blade for microphone azimuth greater than 120.9?
suggesting that the acoustic waves from the outboard section arrive later than the from the inboard
138
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(a) ? = 107?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(b) ? = 120.9?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(c) ? = 133.7?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(d) ? = 148?
Figure 4.11: Trace Mach number along the radiation direction for Case 2 (3.3? Oblique BCDI)
sections. For microphones at 107? azimuth, the trace Mach number (Fig. 4.11(a)) becomes equal
to 1 close to the blade tip, implying that waves from this portion of the blade arrive in-phase at the
microphone azimuth leading to increase in noise levels.
4.3.2 Case 3 ? 8.8? Oblique BCDI
Fig. 4.12 shows the acoustic time histories comparisons for the theory and experiment for the
8.8? oblique interaction at MT = 0.702. The theoretical results under predict the acoustics signif-
139
icantly at many the microphone locations, particularly for microphones at ? > 107?. Part of this
is probably due to the increasing three-dimensional effect on the aerodynamics as the interaction
angle increases. Moreover, while in the experimental results, the magnitude of the positive peak
increases relative to the negative peak, the theory misses the positive peak altogether. This results
in some significant underprediction in the peak-to-peak noise levels as shown in Fig. 4.13. Never-
theless, the relative noise levels at the different microphone locations are similar for the theoretical
and experimental cases. The peak noise azimuth is the same, and the azimuthal asymmetry are
similar in both cases.
For Case 3 BCDI event, the peak noise azimuth is at 120?. As before, for the microphone
azimuths ? < 120.9?, the acoustic waves from near the blade tip sections arrive earlier than from
the inboard section. However, unlike the previous cases, at the ? = 120.9? azimuth locations,
there is a significant amount of destructive interference between the spanwise waves at all the
three elevations. At the lowest elevation microphone (Fig. 4.14(d)), the acoustic wave from the
close to the 70% blade span section arrives first followed simultaneously, by acoustic waves from
the sections on either side of the blade. At 41.4? (Fig. 4.14(e)) elevation, the most of the waves
from the outboard blade section arrive in-phase resulting in a constructive interference. At the
highest microphone locations at ? = 120.9?, the outboard waves arrive earlier than from the further
inboard of the blade. While, the trace Mach number describes to some extent the spanwise phasing
along the azimuthal direction, clearly, spanwise phasing plays a significant role in determining the
noise trends along the elevation as well. Similar trends occur for the other azimuth microphone
locations shown in Fig. 4.14. The difference in the phasing of the spanwise waves at the different
140
5 10 15 20 25?200
?100
0
100
45 50 55 60 65?200
?100
0
100
10 20 30?200
?100
0
100
?5 0 5 10?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
345 350 355 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
0 5 10 15?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340 345?200
?100
0
100
350 355 360 365?200
?100
0
100
25 30 35 40 45?200
?100
0
100
0 10 20?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
20 30 40?200
?100
0
100
40 50 60?200
?100
0
100
55 60 65 70?200
?100
0
100
Expt.
Theory
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure 4.12: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(Case 3 ? 8.8? Oblique BCDI) at MT = 0.702
14
1
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7? ?? Expt.
53.7? ?? Theory
41.4? ?? Expt.
41.4? ?? Theory
27.6? ?? Expt.
27.6? ?? Theory
Rotor Direction
Figure 4.13: Comparison of the directionality trends between theory and experiment ? Case 3
(8.8? Oblique BCDI) at MT = 0.702
142
microphone azimuth, clearly determines the azimuthal variation.
The trace Mach number profiles along the microphone directions are shown in Fig. 4.15. The
trace Mach number profile at the 107? azimuth location (Fig. 4.15(a)) is subsonic for the micro-
phones at the higher elevations. For the two highest microphones it becomes to equal to one for the
outboard blade sections at the 120.9? azimuth suggesting that the peak noise levels would occur at
this azimuth (Fig. 4.13). For the microphone at 27.6? elevation, the trace Mach number becomes
equal to 1 close to the blade tip at the 107? microphone azimuth. At the 120.9? azimuth, the trace
Mach number becomes 1 at the outboard sections for the lower microphone elevation and has a
higher subsonic value over the rest of the blade when compared to the 107? location. This results in
a greater number of the spanwise sources being in-phase at the 120.9? azimuth compared to 107?
azimuth for the lower elevation microphone (Figs. 4.14(c) & 4.14(f)). This results in the noise
levels at these two locations being very close to each other as can be seen in Fig. 4.13.
143
15 20 25 30?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(a) ? = 107.0?,? = 27.6
25 30 35 40?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(b) ? = 107.0?,? = 41.4
55 60 65 70?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(c) ? = 107.0?,? = 53.7
20 25 30 35?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(d) ? = 120.9?,? = 27.6
25 30 35 40?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(e) ? = 120.9?,? = 41.4
45 50 55 60?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(f) ? = 120.9?,? = 53.7
0 5 10 15?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(g) ? = 133.7?,? = 27.6
15 20 25 30?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(h) ? = 133.7?,? = 41.4
50 55 60 65?2.5
?2
?1.5
?1
?0.5
0
0.5
1
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(i) ? = 133.7?,? = 53.7
5 10 15 20?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(j) ? = 148.0?,? = 27.6
25 30 35 40?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(k) ? = 148.0?,? = 41.4
55 60 65 70?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(l) ? = 148.0?,? = 53.7
Figure 4.14: Spanwise acoustic phasing effect ? Case 3 (8.8? Oblique BCDI; MT = 0.702)144
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(a) ? = 107?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(b) ? = 120.9?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(c) ? = 133.7?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(d) ? = 148?
Figure 4.15: Trace Mach number along the radiation direction for Case 3 (8.8? Oblique BCDI)
145
4.3.3 Case 4 ? 15.3? Oblique BCDI
Figs. 4.16 and 4.17 show the comparison between the experiment and theory for the Case 4
BCDI event (15.3? at the blade tip) at a tip Mach number of 0.702. Once again, the theory under
predicts significantly ? 8dB-12dB depending on the microphone location. The general trends
of the radiation directionality, both along the azimuth as well as the elevation are picked up by
the theory for most of the microphone locations. The peak noise levels occur at slightly different
azimuth locations for the lower two microphones as predicted by the theory. Nevertheless, the
theory does manage to pick up the effect of the 41.4? elevation microphone recording a higher
noise level at the 120.9? microphone azimuth.
Fig. 4.18 shows the phasing of spanwise acoustic waves at some microphone locations. Clearly,
the maximum in-phase arrival of the spanwise waves at the microphone has moved to higher mi-
crophone azimuth angles. However, unlike the previous cases, there is no single location where
all the waves arrive in-phase. Most waves from the outboard span locations arrive close to each
other at 120.9? microphone azimuth. At this azimuth location, there is higher in-phase summation
of the waves at the lowest elevation. However, the spanwise waves themselves at this low eleva-
tion are lower in magnitude compared to the radiation at higher elevations. The summing of the
waves at the 41.4? microphone elevation for this azimuth location results in a higher noise level
than the highest microphone. The fact that this trend is carried over to the next microphone az-
imuth (? = 133.7?) in the experiment, but not in the theoretical predictions, could be attributed to
the lower predicted positive peaks. A higher magnitude positive peak from the spanwise sources,
could results in significant increase in the noise levels.
146
5 10 15 20?200
?100
0
100
45 50 55 60 65?200
?100
0
100
10 20 30?200
?100
0
100
350 360 370?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
340 350 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340?200
?100
0
100
345 350 355 360 365?200
?100
0
100
25 30 35 40 45?200
?100
0
100
0 10 20?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
20 30 40?200
?100
0
100
40 50 60?200
?100
0
100
55 60 65 70?200
?100
0
100
Expt.
Theory
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure 4.16: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
? Case 4 (15.3? Oblique BCDI; MT = 0.702)
14
7
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7? ?? Theory
41.4? ?? Expt.
41.4? ?? Theory
27.6? ?? Expt.
27.6? ?? Theory
Rotor Direction
Figure 4.17: Comparison of the directionality trends between theory and experiment ? Case 4
(15.3? Oblique BCDI; MT = 0.702)
148
15 20 25 30?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(a) ? = 107.0?,? = 27.6
25 30 35 40?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(b) ? = 107.0?,? = 41.4
55 60 65 70?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(c) ? = 107.0?,? = 53.7
25 30 35 40?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(d) ? = 120.9?,? = 27.6
30 35 40 45?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(e) ? = 120.9?,? = 41.4
50 55 60 65?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(f) ? = 120.9?,? = 53.7
0 5 10 15?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(g) ? = 133.7?,? = 27.6
20 25 30 35?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(h) ? = 133.7?,? = 41.4
50 55 60 65?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(i) ? = 133.7?,? = 53.7
5 10 15 20?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(j) ? = 148.0?,? = 27.6
25 30 35 40?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(k) ? = 148.0?,? = 41.4
55 60 65 70?2.5
?2
?1.5
?1
?0.5
0
0.5
Rotor Azimuth (Deg)
Acoustic Pressure (Pa)
 
 
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
(l) ? = 148.0?,? = 53.7
Figure 4.18: Spanwise acoustic phasing effect ? Case 4 (15.3? Oblique BCDI; MT = 0.702)149
Figure 4.19 shows the trace Mach number profiles along the radiation direction for the 15.2?
oblique BCDI. Note that for the 107? azimuth location the profiles almost entirely subsonic, sug-
gesting that this is not the peak noise azimuth any longer. At the 120.9? azimuth, the trace Mach
number remains subsonic for the highest microphone (at 53.7? elevation), but crosses 1 close to the
blade tip for the lower elevations. This helps explain why the peak noise elevation moves closer
to the rotor plane at this azimuth (as seen in Fig. 4.17). Moreover, the trace Mach number profiles
are very similar for the microphone azimuths greater than 120?, resulting in similar phasing of the
spanwise sources at these microphone locations (Fig. 4.18). This also helps explain the reason for
the distribution of acoustic energy over a larger azimuthal region for this oblique interaction.
4.4 Summary of Results
Indicial aerodynamics, combined with a non-compact chord rotor acoustic formulation predicts
the acoustic pulse shape reasonably well for the parallel and near-parallel interaction angles. The
negative peak of the pulse is well predicted, however, the positive peak is not captured sufficiently.
Moreover, it is seen that using a non-compact chordwise aerodynamic approach is essential to cap-
ture the noise levels adequately, particularly for the peak noise microphone locations. The acoustic
predictions become more divergent from the experiment as the obliqueness of the interaction in-
creases, and under-predict the noise levels. Nevertheless, the relative negative peak noise levels
and the trends at the different microphone locations are captured reasonably well. In particular, the
general trend of the broadening of azimuthal directivity towards the direction of the trace Mach
number with increasing BVI obliqueness is captured to some degree. Moreover, it is seen that the
150
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(a) ? = 107?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(b) ? = 120.9?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(c) ? = 133.7?
0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
r/R
Trace Mach number
 
 
53.7o
41.4o
27.6o
(d) ? = 148?
Figure 4.19: Trace Mach number along the radiation direction for Case 4 (15.3? Oblique BCDI)
151
phasing of the spanwise acoustic waves plays an important role in the spatial distribution of the
acoustic energy and could result in the peak noise elevation levels moving closer to the plane of
the rotor as the interaction angle increases. This resulting distribution of the acoustic energy can
be explained in terms of the trace Mach number profiles in the radiation direction.
152
Chapter 5
Summary and Conclusions
This chapter discusses the conclusions that been arrived at from the experimental investigations
and measurements discussed in the previous chapters. The main purpose of the present work was to
better understand the physics of the blade-vortex interaction and their effect on noise radiation char-
acteristics. The present fundamental work decouples the interacting vortex parameters from the
blade parameters, by replicating the vortex parameters in a controlled manner. In essence, the BVI
problem is transformed into an experimental simulation called the Blade-Controlled Disturbance-
Interaction (BCDI) that captures the major features of the BVI event but allows independent eval-
uation of the important governing parameters.
A unique and novel experimental facility has been developed from the ground up in order to
study the BVI acoustics in a controlled manner. This experiment now facilitates a true comparison
of the blade response ? both aerodynamic and acoustic response ? when blade planform is
modified or rotor parameters are changed. Previous experiments which similarly decoupled the
vortex parameters from the rotor parameters focused primarily on the parallel interaction, despite
153
the fact that real helicopter BVIs are never truly parallel. For the first time in the present work,
oblique BVIs at different interaction angles have been studied. This experimental facility offers
the ability to study in detail the effect of passive and active blade design changes on BVI noise.
5.1 The BCDI Facility
A unique experimental facility has been developed, calibrated and used to understand the fun-
damental mechanism involved in the helicopter BVI noise generation. The BCDI experiment con-
sists of a single-bladed hovering rotor that is capable of operating at high tip Mach numbers passing
through a controlled two-dimensional gust field. The rotor tip Mach numbers that are capable of
being tested cover the full operational range of modern helicopters.
The gust field that the rotor passes through has been designed to simulate the vertical veloc-
ity field induced by a vortex filament, the strength and orientation of which are close to a typical
vortex filament during a BVI event. A special ?gust generator? has been designed, built and cali-
brated to generate this controlled disturbance. Detailed measurement of the gust field using hotwire
anemometry has shown that the gust field is predominantly two-dimensional in nature, with a neg-
ligible velocity in the blade?s chordwise direction and capable of simulating the BVI. A residual
acoustic response of the rotor blade due to the close passage of the rotor blade to the nozzle lip was
identified as an additional source of acoustic radiation and a possible limitation of this approach.
A superposition technique was developed that effectively removes this source of error from the
BCDI acoustic time histories.
The BCDI testing space has been acoustically treated to lessen the reflection of the BCDI
154
acoustic pulses from the surrounding walls and apparatus, being recorded by the microphones. A
suite of microphones has been positioned in this acoustically treated testing chamber to measure
the acoustic directivity, including time histories and power spectrum of the radiated noise.
The successful development of this facility brings a new research tool to the helicopter acoustic
community to help understand the basic mechanisms involved in BVI noise. The facility can also
be used for applied research to study the effect of different blade design changes, such as planform
or even some active control techniques on the BVI noise radiation.
5.2 BCDI Experimental Findings
Some basic mechanisms of the BVI have been explored using the BCDI facility. The BCDI
experimental acoustic results present a first quantitative simulation of the oblique BVI problem
and a method of isolating the key governing parameters. The measured acoustic pulse consists of
two distinct pulses ? a negative pulse followed by a smaller positive pulse.
The geometry of the interaction is shown to play a significant role in the acoustic waveform
and directivity of the radiated noise ? a good part of the effect being a result of the phasing of the
acoustic signals over the span of the rotor blade. Acoustic signals from the parallel BCDI emanate
from the blade in-phase, resulting in the largest overall pulse in a direction perpendicular to the
rotor span, with the levels decreasing on either side. Measured noise levels in this case, were
highest out of the plane of the rotor due to the dipole nature of the acoustic sources. Their detailed
pulse shapes did not change character with decrease in microphone elevation angles.
Noise levels for the oblique BVI are generally slightly less in peak magnitude, but spread the
155
acoustic energy over wider azimuth angles. A small non-zero interaction angle results in a more
acoustic energy being distributed to higher azimuth angles compared to the parallel interaction.
The peak noise directivity for the oblique interaction angle is primarily along the direction of the
BVI trace velocity.
For a given interaction angle, as the tip Mach number is decreased, the point where the trace
Mach number becomes one moves further outboard along the blade. This results in an increase in
the effective strength of spanwise waves that arrive at a near in-plane microphone in phase. For
very higher BVI interaction angles, the noise levels at lower microphone elevation angles increase
because this effect becomes larger at lower elevations that at higher elevation.
5.3 Indicial Aerodynamics and Acoustic Predictions
Indicial aerodynamic theory (when corrected for compressibility and three-dimensional effects)
and when combined with a Green?s function solution of the three-dimensional wave equation for
fixed sources in space, predicts the acoustic pulse shape reasonably well for parallel BVI. It is
necessary to treat the acoustic sources on the rotor blade as a non-compact source to the bring the
predicted peak noise levels more in-line with the measured data. However, this approach does not
predict the smaller positive pulse adequately.
Acoustic predictions using indicial aerodynamics become more divergent from the experimen-
tal measurements with increasing BVI obliqueness. However, the general trend of broadening di-
rectivity with increasing BVI obliqueness is captured to some degree, but theoretical calculations
substantially under-predict the noise levels.
156
Acoustic time tracing methods show that distinct events on the blade are related to the mea-
sured pulse shape and help develop a more complete understanding of the mechanism of the BVI.
This approach has shown that span-wise phasing of the acoustic waves plays a significant role in
determining the directionality both along the azimuth as well elevation direction. It is also seen
that the trace Mach number in the radiation direction plays a significant role in the spanwise phas-
ing of the acoustic sources at the corresponding observer locations, and hence also determines the
distribution of the total acoustic energy due to the interaction event.
5.4 Recommendations for Further Research
The BCDI experimental facility provides an ideal condition for testing the blade response to
known velocity disturbance field for a variety of blade parameters. The parameters used in the
present study can easily be extended to include higher tip Mach numbers and different interaction
geometries. Some of recommendations for future work in this facility as listed below:
? Most helicopter BVIs occur at higher transonic tip Mach numbers where compressibility
become important. The experimental setup developed in this work can be used to study
the BCDI at higher transonic tip Mach numbers. This will provide valuable information
regarding the effect of the aerodynamic non-linearity in BVI noise.
? Moreover, it would be interesting and very useful to study higher oblique interaction angles
at these high transonic tip Mach numbers as the trace Mach number becomes 1 closer to the
blade tip. The resulting collection of strong spanwise acoustic waves on the blade could re-
157
sult in interesting acoustic as well as aerodynamic phenomena, and might play an important
role in the final generated noise.
? As a natural extension of the work so far, it is suggested that curved interaction geometries
to closely match the real trace Mach numbers be tested. This is also important since the
spanwise acoustic phasing would be differ from the straight interaction cases and could have
an effect on the resulting acoustics.
? In order to understand the acoustics completely, it is essential to understand the detailed
aerodynamic events occurring on the blade. It is therefore, suggested to test rotor blades
instrumented with a sufficient number of pressure transducers placed at carefully chosen
locations to capture important aerodynamic events, particularly those associated with the
wave collection process on the blade at higher transonic tip Mach numbers.
? As mentioned already, one important advantage of the present approach is the ability to
objectively compare the aerodynamic and acoustic response of different blade designs to a
given velocity disturbance. Thus different passive, as well as active blade designs could be
tested in this facility.
? The Weissinger-L lifting line approach used to correct the indicial aerodynamics for three-
dimensional effects needs further research to make it applicable for oblique BVI cases. A
more complete theory that resolves the pressure distribution over the blade chord, as well as
along the span, is required for accurate oblique BVI predictions.
? A CFD approach could be used to model the experiment and be validated against the exper-
158
imental data. Either pressure measurements on the blade surface (if available), or hotwire
and pressure measurements in the near-field of the blade could be used to validate the CFD.
159
Appendix A
Gust Generator Fabrication and Operational Details
The Gust Generator consists of various sections which aid in achieving a clean flow with less
turbulence. A brief description of the sections are given here.
Fan Blower The fan-blower assembly was sized as per the procedure laid out in Pope?s Wind-
Tunnel Design and Testing [89], keeping in mind the losses due to the screens and various
sections of the gust generator and the final required peak velocity of the flow. The fan-
blower is placed outside of the chamber in order to prevent contamination of the acoustic
environment within the chamber due to the fan.
Diffuser section A long rectangular section with a small divergence angle to slow the flow. The
divergence angle is kept small to prevent flow separation along the walls. It also consists
of screens to smoothen the flow and reduce the turbulence levels. The diffuser section was
also built, keeping in mind the chamber dimensions to ensure that the fan-blower assembly
remains outside the chamber.
160
Corner Section Since the flow starts out horizontal, it needs to be turned by 900 as the final
velocity required is in the vertical directions perpendicular to the rotor plane. This section
primarily consists of vanes which were designed based on [90, 91] to achieve the required
flow rotation.
Turn-table Sections An important design criteria for the gust generator was the ability to orient
the nozzle at any angle with respect to the blade to simulate oblique BVIs. This was achieved
by fabricating two sections such that the interface between the two was circular. One section
was a transition from a square to a circular cross-section, and the other was a transition from
a circular to rectangular cross-section. The dimensions of these two sections were based on
keeping the divergence angle to a minimum to prevent flow separation along the walls. The
top section along with all the sections above it can be oriented at any angle.
Settling Chambers Two settling chambers ? one after the diffuser and one after the turn-table
sections equipped with screens reduce the turbulence levels and allow the flow to settle.
Nozzle The nozzle is the most critical section of the gust generator as it decides the velocity profile
of the ensuing gust at the nozzle outlet. The detailed design of the nozzle is discussed in the
following section.
Nozzle Design
The dimensions of the gust are chosen to match a typical BVI for Mach-scaled rotor blade
of radius 38.125in. The DNW tests [92] have shown that a typical vortex shed from a blade has
a core radius(rc) of 0.05c and vorticity (?) of 5.46 ft2/s, giving rise to a peak velocity of about
161
W W
Nozzle 1
R1
R21 2
H
Figure A.1: Schematic of early nozzle design
150?170 ft/s1. In order to minimize the three dimensional effects of the nozzle edges, the blade
would be run such that one edge of the nozzle lies outside the blade radius, while the other edge sits
within 50% of the blade radius. These criteria require that the nozzle dimensions be 24in.?1in.
Various nozzle designs were attempted before the current one was realized. In most of the
designs, the two walls of the nozzle were parallel to each other at the outlet. On the curved wall, it
was postulated that the boundary layer would be thicker as the flow has to travel a greater distance.
This reduces the velocity gradient on the curved wall, thus causing an asymmetry in the velocity
profile. Moreover, the negative static pressure gradient has the advantage of preventing boundary
layer separation and reducing turbulence in the shear layer. A schematic of the this nozzle design
is shown in Fig. A.1. However, pitot probe measurements of flow on this nozzle (Fig. A.2) showed
that the asymmetry between the flows on either wall, was not sufficient enough to generate the
required velocity profile. However, building this nozzle demonstrated that a span-wise uniform
1Based on OLS rotor [92]
162
Figure A.2: Velocity profile obtained from the first nozzle design
163
flow was achievable with the present gust generator design, and that the flow was effectively two-
dimensional.
Gust Turbulence Characteristics
The rotor blade, when passing over the gust is also affected by the turbulence present in the
gust. Since, the mean velocity profile is generated by exploiting mixing regions, there is a tendency
for the turbulence to be high when the mixing region is long. Thus it is necessary to characterize
the turbulence and study its contribution to the radiated noise, to show that the main features of
BVI noise can be replicated by the current experiment. Measurements were carried out using a TSI
1241-20 two component Hotfilm sensor probe and a TSI 1050 series anemometer. A sampling rate
of 12800Hz was used to cover a wide range of frequencies that might affect the blade response,
including possible BVI frequencies. The obtained data was averaged over 75 frames of 0.32 sec-
onds. In situ calibration was considered impractical, given the rapid change in velocity along the
nozzle width. The calibration was carried out in the Glenn L. Martin Calibration Facility Wind
Tunnel over the velocity entire velocity range that encompasses the a single gust velocity profile.
The turbulence levels, measured by w? and u? are also uniform across the nozzle length, sug-
gesting that the flow is effectively two-dimensional. The RMS values of the turbulent velocities are
shown in Fig. A.3. The trend shown is typical of mixing flows. The first peak represents the mixing
layer developed on the flat side of the nozzle, while the second corresponds to the mixing layer on
the curved side (x = 1in). Since the mixing length on this side is higher as compared to that for
x = 0, this is to be expected. Nevertheless, the RMS values are significantly lower than the mean
164
?1.5 ?1 ?0.5 0 0.5 1 1.5 2 2.50
5
10
15
20
25
u? at x=2.490000 and z=0.625000 pt?5
x(in.)
RMS velocity variation(ft/s)
wrms
urms
Figure A.3: RMS variation of velocities across nozzle width
165
velocity. The dip in the turbulence level near x = 0 is purely due to wind tunnel turbulence and has
little contribution from the mixing. The wind tunnel itself has significantly lower turbulence levels
because of the screens placed in the two settling chambers.
Fig. A.4(a) and Fig. A.4(b) show frequency domain representation of the data after a Fast
Fourier Transform at 0.625in and 1.275in above the nozzle. The bumps in the graphs between
500Hz and 1000Hz correspond to some coherence in the mixing layers. The disturbances corre-
sponding to 500Hz and 1000Hz appear at 1.275in above the nozzle as well. However, across the
nozzle width the variation in amplitude appear to be less than that at 0.625in.
While the mean and turbulence levels are only statistical quantities, the blade ?sees? something
different. When the blade moves over the gust, the instantaneous values of the velocity are quite
different from the mean values. However, one can view the turbulence fluctuations (u?) as a high
frequency signal superimposed over the mean velocity (vectoru). Now, the aerodynamic response of the
blade is such that it acts as a low pass filter, responding strongly to lower frequencies ? in the range
of the mean velocity profile ? and not so strongly to the higher frequencies ? associated with the
turbulence fluctuations. Thus, the turbulence in the gust would not result in significant effect on
the acoustics of the blade, in the frequency range associated with the BVI. However, it would be
interesting to see what the effect is on the higher frequencies, and broadband noise in general.
166
0 500
1000 1500
2000 2500?1
?0.5
0
0.5
1
?4
?3
?2
?1
0
1
Nozzle Width (in.)f (Hz)
log(u?)
(a) 0.625in above Nozzle
0 500
1000 1500
2000 2500?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
0.6
0.8
1
?4
?3
?2
?1
0
1
Nozzle Width (in.)f (Hz)
log(u?)
(b) 1.275in above Nozzle
Figure A.4: Frequency distribution of turbulence at various locations
167
Appendix B
Rotor Test Stand Dynamics
It is important to establish the smoothest operating conditions of the motor/rotor dynamical
system during the operation. Every complex dynamical system has resonance like operating con-
ditions that should be avoided. Strike tests with an impulse hammer were performed at key loca-
tions on the rotor stand while recording accelerometer data in order to identify these resonant like
fundamental frequencies of the rotor stand. The modes corresponding to these frequencies could
be excited when the rotor is spinning at the corresponding RPMs and are to be avoided or passed
through quickly. Fig. B.1 shows the natural frequencies of the stand. The impact hammer strike test
suggests that Rotor RPMs close to 1200 and 3600, (corresponding to 20Hz and 60Hz, respectively)
are to be avoided. With the shaft spinning (without the rotor blade), two more stand frequencies
show some resonance like characteristics at about 42Hz (2520RPM) and 84Hz (5040RPM). Out
of the four critical frequencies, the one closest to the operating range is the one at 42Hz, and so the
rotor was not operated close to 2520RPM for any of the experiments.
168
Figure B.1: Resonant frequencies associated with the RTS
169
Appendix C
Effect of Nozzle Interference on the Acoustic Time
Histories
As mentioned in Chapter 3, the proximity of the nozzle lip to the rotor blade results in some
noise radiation by itself. This radiation is impulsive and occurs over the same time interval as the
main BCDI event, possibly limiting the scope of the experiment. The acoustic pulse radiated from
the rotor blade due to the nozzle presence alone is significantly lower than the main BCDI pulse
and its effect is removed from the acoustic data by subtracting it from the total noise radiated.The
radiation of noise resulting from the nozzle?s proximity to the rotor blade peaks azimuthally at the
same microphone location as the BCDI event. However, it seems to be directed more in the plane
of the rotor, suggesting it is not due to impulsive lift on the blade. At this point, the reason for this
noise is speculated to be a result of the fluid dragged along the by the blade having to accelerate
over the nozzle wall. For completeness, the time histories of this acoustic event is presented here
in Figs. C.1-C.4 for all the microphones at a rotor blade tip Mach number of 0.702.
170
10 20 30
?20
0
20
50 60 70
?20
0
20
15 20 25 30 35
?20
0
20
0 5 10 15
?20
0
20
0 10 20
?20
0
20
20 30 40
?20
0
20
50 60 70
?20
0
20
150 155 160 165
?20
0
20
200 205 210 215
?20
0
20
350 360 370
?20
0
20
45 50 55 60 65
?20
0
20
5 10 15 20 25
?20
0
20
350 360 370
?20
0
20
340 350 360
?20
0
20
0 5 10 15
?20
0
20
35 40 45 50 55
?20
0
20
190 200 210
?20
0
20
10 15 20 25
?20
0
20110 120 130
?20
0
20
50 60 70
?20
0
20
155 160 165 170 175
?20
0
20
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure C.1: Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Parallel Interaction)
17
1
15 20 25 30
?20
0
20
50 60 70
?20
0
20
15 20 25 30 35
?20
0
20
?5 0 5 10 15
?20
0
20
?5 0 5 10 15
?20
0
20
15 20 25 30 35
?20
0
20
50 60 70
?20
0
20
145 150 155 160 165
?20
0
20
15 20 25 30 35
?20
0
20
350 360 370
?20
0
20
125 130 135 140
?20
0
20
5 10 15 20 25
?20
0
20
350 360 370
?20
0
20
340 350 360
?20
0
20
60 65 70 75
?20
0
20
135 140 145 150
?20
0
20
160 170 180
?20
0
20
0 10 20
?20
0
20110 120 130
?20
0
20
50 60 70
?20
0
20
155 160 165 170 175
?20
0
20
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure C.2: Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Case 2)
17
2
10 20 30
?20
0
20
160 165 170 175
?20
0
20
20 30 40
?20
0
20
?5 0 5 10 15
?20
0
20
?5 0 5 10 15
?20
0
20
15 20 25 30 35
?20
0
20
150 160 170
?20
0
20
145 150 155 160 165
?20
0
20
15 20 25 30 35
?20
0
20
350 360 370
?20
0
20
125 130 135 140
?20
0
20
15 20 25 30
?20
0
20
350 360 370
?20
0
20
340 345 350 355
?20
0
20
5 10 15 20 25
?20
0
20
130 140 150
?20
0
20
85 90 95 100 105
?20
0
20
0 5 10 15
?20
0
20110 120 130
?20
0
20
160 170 180
?20
0
20
55 60 65 70 75
?20
0
20
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure C.3: Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Case 3)
17
3
125 130 135 140 145
?20
0
20
155 160 165 170 175
?20
0
20
25 30 35 40 45
?20
0
20
5 10 15 20 25
?20
0
20
5 10 15 20
?20
0
20
100 105 110 115
?20
0
20
150 160 170
?20
0
20
145 150 155 160 165
?20
0
20
15 20 25 30 35
?20
0
20
350 355 360 365
?20
0
20
125 130 135 140 145
?20
0
20
80 90 100
?20
0
20
350 360 370
?20
0
20
50 55 60 65
?20
0
20
85 90 95 100 105
?20
0
20
205 210 215 220
?20
0
20
5 10 15 20 25
?20
0
20
?5 0 5 10 15
?20
0
20110 115 120 125
?20
0
20
160 170 180
?20
0
20
155 160 165 170
?20
0
20
Expt.
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure C.4: Acoustic time history due to nozzle alone (No gust) (MT = 0.702 ? Case 4)
17
4
Appendix D
Comparison Between Compact and Non-Compact
Acoustic Formulations
The acoustics formulation used in Chapter 4 is a non-compact formulation, which distributes
the lift over the blade chord using a steady flat-plate assumption (Eqn. 4.7). This approach pro-
vides for better prediction of negative peak of the BCDI event. As discussed earlier, for a parallel
interaction, the non-compact chord formulation results in a slightly wider pulse width and lower
magnitude at the 107? microphone azimuth. This effect is most prominent at the peak noise az-
imuth at the lower elevation. The difference between the compact and non-compact formulation
decreases for the microphones on either side as was shown in Fig. 4.3. The acoustic time his-
tory comparisons between the compact and non-compact formulations for the various microphone
locations are shown here in Figs. D.1-D.4.
175
5 10 15 20 25?200
?100
0
100
45 50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
45 50 55 60 65?200
?100
0
100
10 20 30?200
?100
0
100
345 350 355 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
0 10 20?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340 345?200
?100
0
100
350 360 370?200
?100
0
100
30 40 50?200
?100
0
100
0 5 10 15?200
?100
0
100
350 360 370?200
?100
0
100
15 20 25 30 35?200
?100
0
100
45 50 55 60?200
?100
0
100
50 60 70?200
?100
0
100
Non-Compact Chord
Expt.
Compact Chord
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure D.1: Comparison between Compact and Non-compact chord formulations (MT = 0.702 ? Parallel Interaction)
17
6
5 10 15 20 25?200
?100
0
100
45 50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
?5 0 5 10?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
345 350 355 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
0 5 10 15?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340 345?200
?100
0
100
350 355 360 365?200
?100
0
100
30 35 40 45?200
?100
0
100
0 10 20?200
?100
0
100
?5 0 5 10?200
?100
0
100
20 30 40?200
?100
0
100
45 50 55 60?200
?100
0
100
55 60 65 70?200
?100
0
100
Non-Compact Chord
Expt.
Compact Chord
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure D.2: Comparison between Compact and Non-compact chord formulations (MT = 0.702 ? Case 2)
17
7
5 10 15 20 25?200
?100
0
100
45 50 55 60 65?200
?100
0
100
10 20 30?200
?100
0
100
?5 0 5 10?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
345 350 355 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
0 5 10 15?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340 345?200
?100
0
100
350 355 360 365?200
?100
0
100
25 30 35 40 45?200
?100
0
100
0 10 20?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
20 30 40?200
?100
0
100
40 50 60?200
?100
0
100
55 60 65 70?200
?100
0
100
Non-Compact Chord
Expt.
Compact Chord
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure D.3: Comparison between Compact and Non-compact chord formulations (MT = 0.702 ? Case 3)
17
8
5 10 15 20?200
?100
0
100
45 50 55 60 65?200
?100
0
100
10 20 30?200
?100
0
100
350 360 370?200
?100
0
100
350 360 370?200
?100
0
100
10 20 30?200
?100
0
100
45 50 55 60 65?200
?100
0
100
50 55 60 65?200
?100
0
100
15 20 25 30?200
?100
0
100
340 350 360?200
?100
0
100
35 40 45 50 55?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
335 340 345 350 355?200
?100
0
100
325 330 335 340?200
?100
0
100
345 350 355 360 365?200
?100
0
100
25 30 35 40 45?200
?100
0
100
0 10 20?200
?100
0
100
?5 0 5 10 15?200
?100
0
100
20 30 40?200
?100
0
100
40 50 60?200
?100
0
100
55 60 65 70?200
?100
0
100
Non-Compact Chord
Expt.
Compact Chord
Rotor azimuth (Deg)
P aGust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
91.4? 75.5?
61.6?107.0
?
51.8?
30?
Figure D.4: Comparison between Compact and Non-compact chord formulations (MT = 0.702 ? Case 4)
17
9
Appendix E
Comparison of Frequency Spectrum Between
Theory and Experiment
Figs. E.1-E.4 show a comparison of the frequency spectrum between the theory and experi-
ment for the different interaction angles at MT = 0.702. The theory tends to under predict the
magnitude of the frequencies for the corresponding peak microphone azimuths. This corresponds
in the time history plots (Figs. 4.5, 4.8, 4.12 & 4.16) to a wider pulse width predicted by theory
at the corresponding microphones. Part of the reason could be a strong tip vortex predicted by the
Weissinger-L model based on the two-dimensional indicial results. Since the indicial aerodynam-
ics is assumes a compact chord approach (which might is not true in reality) the strength of the tip
vortex and hence the contribution to the acoustics from the blade tip might actually be higher than
that predicted by the theory.
180
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
Expt.
Theory
Rotor Harmonics
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure E.1: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(MT = 0.702 ? Parallel Interaction)
18
1
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
Expt.
Theory
Rotor Harmonics
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure E.2: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(MT = 0.702 ? Case 2)
18
2
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
Expt.
Theory
Rotor Harmonics
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure E.3: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(MT = 0.702 ? Case 3)
18
3
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
0 200 40050
60
70
80
90
100
Expt.
Theory
Rotor Harmonics
Gust Disturbance
?176.7
?
162.2?
148.0?
133?
120.9?
107.0? 91.4? 75.5? 61.6?
51.8?
30?
Figure E.4: Acoustic time histories at the various microphones in terms of Acoustic Pressure (in Pa) vs. Rotor Azimuth (in Deg)
(MT = 0.702 ? Case 4)
18
4
Appendix F
Scaling of the Acoustics Data
F.1 Choice of Scaling Origin
The experimental and theoretical results have been scaled to a distance of 3R from the hub,
for easier comparison, as has been mentioned in the thesis. As discussed earlier, the parallel
interaction peaks about a line drawn perpendicular to the blade at the 80% span location during the
interaction event. Moreover, most of the noise is radiated from the outboard region of the blade
for all the interaction angles, as the sectional Mach number is higher at those sections compared
to the inboard sections. Thus, one could also scale the results about a location that is not the hub,
but rather a point on the outboard section of the blade during the interaction, as it would be more
representative of the source of sound. For a truly far-field observer, this choice of scaling would
have a very negligible effect. However, given the size of the chamber, the microphones cannot be
considered truly far-field with respect to the spanwise sources.
Figures F.1,F.3,F.5 & F.7 show the measured peak-to-peak noise expressed in decibels when
185
scaled about the 80% blade span location during the interaction. The corresponding plots with the
measured data scaled about the hub are also shown for easy comparison (Figs. F.2,F.4,F.6 & F.8.
Although there is some difference in the noise levels, for the two choices of scaling origin, the over
all azimuthal trends do not change. Moving the origin of scaling to the 80% blade section at the
interaction, increases the distance between the microphones from the effective sound source. Thus,
the scaling results in an increase in magnitude, when compared to the values scaled with respect to
the hub.
For different interaction angles, the 80% span section of the blade undergoes the interaction
event at a different azimuth. This makes it difficult to compare the noise levels across different
interaction angles.
186
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure (dB Peak?to?peak)
 
 
53.7?
41.4?
27.6?
Figure F.1: Directionality trends for parallel BCDI when scaled about 0.8R (MT = 0.702)
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.2: Directionality trends for parallel BCDI when scaled about the hub (MT = 0.702)
187
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.3: Directionality trends for the 3.3? oblique BCDI when scaled about 0.8R (MT = 0.702)
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.4: Directionality trends for the 3.3? oblique BCDI when scaled about the hub(MT =
0.702)
188
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.5: Directionality trends for the 8.8? oblique BCDI when scaled about 0.8R (MT = 0.702)
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.6: Directionality trends for the 8.8? oblique BCDI when scaled about the hub (MT =
0.702)
189
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.7: Directionality trends for the 15.3? oblique BCDI when scaled about 0.8R (MT = 0.702)
406080100120140160180115
120
125
130
135
140
145
Microphone Azimuth (Deg)
Acoustic Pressure(dB Peak?to?Peak)
 
 
53.7?
41.4?
27.6?
Rotor Direction
Figure F.8: Directionality trends for the 15.3? oblique BCDI when scaled about the hub (MT =
0.702)
190
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